LMFDB - Embedded newform 63.4.h.a.25.1

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	63.25
Dual form			63.4.h.a.58.1

$q$-expansion

$f(q)$	$=$	$q-5.09429 q^{2} +(5.00043 + 1.41268i) q^{3} +17.9518 q^{4} +(-3.42023 + 5.92401i) q^{5} +(-25.4737 - 7.19661i) q^{6} +(-0.241570 - 18.5187i) q^{7} -50.6973 q^{8} +(23.0087 + 14.1280i) q^{9} +O(q^{10})$	\(q-5.09429 q^{2} +(5.00043 + 1.41268i) q^{3} +17.9518 q^{4} +(-3.42023 + 5.92401i) q^{5} +(-25.4737 - 7.19661i) q^{6} +(-0.241570 - 18.5187i) q^{7} -50.6973 q^{8} +(23.0087 + 14.1280i) q^{9} +(17.4236 - 30.1786i) q^{10} +(20.5259 + 35.5519i) q^{11} +(89.7667 + 25.3602i) q^{12} +(31.8869 + 55.2298i) q^{13} +(1.23063 + 94.3396i) q^{14} +(-25.4714 + 24.7909i) q^{15} +114.653 q^{16} +(38.0175 - 65.8483i) q^{17} +(-117.213 - 71.9723i) q^{18} +(46.7854 + 81.0346i) q^{19} +(-61.3993 + 106.347i) q^{20} +(24.9530 - 92.9427i) q^{21} +(-104.565 - 181.112i) q^{22} +(-21.0641 + 36.4840i) q^{23} +(-253.509 - 71.6192i) q^{24} +(39.1040 + 67.7302i) q^{25} +(-162.441 - 281.357i) q^{26} +(95.0949 + 103.150i) q^{27} +(-4.33661 - 332.444i) q^{28} +(21.9258 - 37.9765i) q^{29} +(129.759 - 126.292i) q^{30} -200.136 q^{31} -178.495 q^{32} +(52.4149 + 206.771i) q^{33} +(-193.672 + 335.450i) q^{34} +(110.531 + 61.9071i) q^{35} +(413.047 + 253.624i) q^{36} +(-52.1566 - 90.3379i) q^{37} +(-238.338 - 412.814i) q^{38} +(81.4264 + 321.219i) q^{39} +(173.397 - 300.332i) q^{40} +(-108.674 - 188.229i) q^{41} +(-127.118 + 473.477i) q^{42} +(236.154 - 409.031i) q^{43} +(368.476 + 638.220i) q^{44} +(-162.390 + 87.9825i) q^{45} +(107.306 - 185.860i) q^{46} -17.8842 q^{47} +(573.312 + 161.967i) q^{48} +(-342.883 + 8.94711i) q^{49} +(-199.207 - 345.037i) q^{50} +(283.127 - 275.563i) q^{51} +(572.428 + 991.474i) q^{52} +(211.151 - 365.724i) q^{53} +(-484.441 - 525.477i) q^{54} -280.813 q^{55} +(12.2469 + 938.848i) q^{56} +(119.471 + 471.301i) q^{57} +(-111.696 + 193.463i) q^{58} +291.033 q^{59} +(-457.257 + 445.042i) q^{60} -154.029 q^{61} +1019.55 q^{62} +(256.074 - 429.503i) q^{63} -7.91610 q^{64} -436.243 q^{65} +(-267.016 - 1053.35i) q^{66} -838.351 q^{67} +(682.483 - 1182.10i) q^{68} +(-156.870 + 152.679i) q^{69} +(-563.078 - 315.373i) q^{70} -940.646 q^{71} +(-1166.48 - 716.254i) q^{72} +(65.8171 - 113.998i) q^{73} +(265.701 + 460.208i) q^{74} +(99.8560 + 393.922i) q^{75} +(839.881 + 1454.72i) q^{76} +(653.415 - 388.701i) q^{77} +(-414.810 - 1636.38i) q^{78} +620.364 q^{79} +(-392.138 + 679.203i) q^{80} +(329.797 + 650.134i) q^{81} +(553.616 + 958.891i) q^{82} +(102.235 - 177.076i) q^{83} +(447.952 - 1668.49i) q^{84} +(260.057 + 450.433i) q^{85} +(-1203.04 + 2083.72i) q^{86} +(163.287 - 158.925i) q^{87} +(-1040.61 - 1802.38i) q^{88} +(432.859 + 749.734i) q^{89} +(827.260 - 448.208i) q^{90} +(1015.08 - 603.846i) q^{91} +(-378.138 + 654.953i) q^{92} +(-1000.76 - 282.728i) q^{93} +91.1073 q^{94} -640.067 q^{95} +(-892.551 - 252.156i) q^{96} +(331.039 - 573.377i) q^{97} +(1746.75 - 45.5792i) q^{98} +(-30.0049 + 1107.99i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} + O(q^{10}) $	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} - 18q^{10} + 5q^{11} - 62q^{12} - 14q^{13} - 52q^{14} + 119q^{15} + 494q^{16} - 162q^{17} - 188q^{18} + 58q^{19} - 362q^{20} - 59q^{21} - 18q^{22} - 93q^{23} + 30q^{24} - 349q^{25} - 266q^{26} + 272q^{27} - 172q^{28} + 248q^{29} + 85q^{30} - 122q^{31} + 326q^{32} + 77q^{33} + 6q^{34} + 289q^{35} - 806q^{36} - 86q^{37} - 761q^{38} - 256q^{39} - 18q^{40} - 692q^{41} - 364q^{42} - 86q^{43} - 443q^{44} + 527q^{45} - 270q^{46} + 2010q^{47} - 1013q^{48} + 317q^{49} + 239q^{50} + 1209q^{51} - 335q^{52} + 258q^{53} + 577q^{54} - 870q^{55} - 1752q^{56} + 566q^{57} + 237q^{58} + 3330q^{59} + 1669q^{60} - 878q^{61} + 1812q^{62} + 2872q^{63} + 872q^{64} + 1226q^{65} + 1330q^{66} - 590q^{67} - 1374q^{68} + 1389q^{69} + 1251q^{70} + 636q^{71} - 5970q^{72} - 338q^{73} + 1119q^{74} + 2737q^{75} + 1006q^{76} + 2269q^{77} + 157q^{78} - 266q^{79} - 4817q^{80} - 505q^{81} + 6q^{82} - 1356q^{83} - 6013q^{84} + 483q^{85} - 3343q^{86} - 5755q^{87} + 369q^{88} - 2200q^{89} + 2665q^{90} + 1552q^{91} - 396q^{92} - 129q^{93} + 2382q^{94} - 6166q^{95} - 5941q^{96} - 266q^{97} + 3601q^{98} - 5395q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−5.09429			−1.80110			−0.900552	−	0.434749i	$-0.856837\pi$
$2$	−5.09429			−1.80110			−0.900552	+	0.434749i	$0.856837\pi$
$3$	5.00043	+	1.41268i	0.962334	+	0.271871i
$3$	5.00043	+	1.41268i	0.962334	+	0.271871i
$4$	17.9518			2.24397
$5$	−3.42023	+	5.92401i	−0.305915	+	0.529860i	−0.977465	−	0.211100i	$-0.932296\pi$
$5$	−3.42023	+	5.92401i	−0.305915	+	0.529860i	0.671550	+	0.740959i	$0.265629\pi$
$6$	−25.4737	−	7.19661i	−1.73326	−	0.489667i
$7$	−0.241570	−	18.5187i	−0.0130435	−	0.999915i
$7$	−0.241570	−	18.5187i	−0.0130435	−	0.999915i
$8$	−50.6973			−2.24053
$9$	23.0087	+	14.1280i	0.852173	+	0.523261i
$10$	17.4236	−	30.1786i	0.550984	−	0.954333i
$11$	20.5259	+	35.5519i	0.562617	+	0.974481i	0.997267	+	0.0738817i	$0.0235387\pi$
$11$	20.5259	+	35.5519i	0.562617	+	0.974481i	−0.434650	+	0.900599i	$0.643128\pi$
$12$	89.7667	+	25.3602i	2.15945	+	0.610071i
$13$	31.8869	+	55.2298i	0.680296	+	1.17831i	0.974891	+	0.222685i	$0.0714820\pi$
$13$	31.8869	+	55.2298i	0.680296	+	1.17831i	−0.294595	+	0.955622i	$0.595185\pi$
$14$	1.23063	+	94.3396i	0.0234928	+	1.80095i
$15$	−25.4714	+	24.7909i	−0.438445	+	0.426733i
$16$	114.653			1.79145
$17$	38.0175	−	65.8483i	0.542389	−	0.939445i	−0.456378	−	0.889786i	$-0.650853\pi$
$17$	38.0175	−	65.8483i	0.542389	−	0.939445i	0.998766	−	0.0496584i	$-0.0158133\pi$
$18$	−117.213	−	71.9723i	−1.53485	−	0.942446i
$19$	46.7854	+	81.0346i	0.564911	+	0.978454i	0.997058	+	0.0766508i	$0.0244227\pi$
$19$	46.7854	+	81.0346i	0.564911	+	0.978454i	−0.432147	+	0.901803i	$0.642244\pi$
$20$	−61.3993	+	106.347i	−0.686465	+	1.18899i
$21$	24.9530	−	92.9427i	0.259295	−	0.965798i
$22$	−104.565	−	181.112i	−1.01333	−	1.75514i
$23$	−21.0641	+	36.4840i	−0.190963	+	0.330758i	−0.945570	−	0.325419i	$-0.894495\pi$
$23$	−21.0641	+	36.4840i	−0.190963	+	0.330758i	0.754606	+	0.656178i	$0.227828\pi$
$24$	−253.509	−	71.6192i	−2.15613	−	0.609133i
$25$	39.1040	+	67.7302i	0.312832	+	0.541842i
$26$	−162.441	−	281.357i	−1.22528	−	2.12225i
$27$	95.0949	+	103.150i	0.677816	+	0.735232i
$28$	−4.33661	−	332.444i	−0.0292694	−	2.24378i
$29$	21.9258	−	37.9765i	0.140397	−	0.243175i	−0.787249	−	0.616635i	$-0.788495\pi$
$29$	21.9258	−	37.9765i	0.140397	−	0.243175i	0.927646	+	0.373460i	$0.121829\pi$
$30$	129.759	−	126.292i	0.789686	−	0.768590i
$31$	−200.136			−1.15953			−0.579765	−	0.814784i	$-0.696855\pi$
$31$	−200.136			−1.15953			−0.579765	+	0.814784i	$0.696855\pi$
$32$	−178.495			−0.986054
$33$	52.4149	+	206.771i	0.276493	+	1.09074i
$34$	−193.672	+	335.450i	−0.976898	+	1.69204i
$35$	110.531	+	61.9071i	0.533805	+	0.298977i
$36$	413.047	+	253.624i	1.91225	+	1.17418i
$37$	−52.1566	−	90.3379i	−0.231743	−	0.401391i	0.726578	−	0.687084i	$-0.241110\pi$
$37$	−52.1566	−	90.3379i	−0.231743	−	0.401391i	−0.958321	+	0.285693i	$0.907776\pi$
$38$	−238.338	−	412.814i	−1.01746	−	1.76230i
$39$	81.4264	+	321.219i	0.334325	+	1.31888i
$40$	173.397	−	300.332i	0.685410	−	1.18717i
$41$	−108.674	−	188.229i	−0.413951	−	0.716984i	0.581367	−	0.813642i	$-0.302518\pi$
$41$	−108.674	−	188.229i	−0.413951	−	0.716984i	−0.995318	+	0.0966575i	$0.969185\pi$
$42$	−127.118	+	473.477i	−0.467018	+	1.73950i
$43$	236.154	−	409.031i	0.837515	−	1.45062i	−0.0544516	−	0.998516i	$-0.517341\pi$
$43$	236.154	−	409.031i	0.837515	−	1.45062i	0.891966	−	0.452102i	$-0.149326\pi$
$44$	368.476	+	638.220i	1.26250	+	2.18671i
$45$	−162.390	+	87.9825i	−0.537947	+	0.291459i
$46$	107.306	−	185.860i	0.343945	−	0.595730i
$47$	−17.8842			−0.0555038			−0.0277519	−	0.999615i	$-0.508835\pi$
$47$	−17.8842			−0.0555038			−0.0277519	+	0.999615i	$0.508835\pi$
$48$	573.312	+	161.967i	1.72397	+	0.487042i
$49$	−342.883	+	8.94711i	−0.999660	+	0.0260849i
$50$	−199.207	−	345.037i	−0.563443	−	0.975913i
$51$	283.127	−	275.563i	0.777366	−	0.756600i
$52$	572.428	+	991.474i	1.52657	+	2.64409i
$53$	211.151	−	365.724i	0.547241	−	0.947850i	−0.451221	−	0.892412i	$-0.649011\pi$
$53$	211.151	−	365.724i	0.547241	−	0.947850i	0.998462	−	0.0554374i	$-0.0176553\pi$
$54$	−484.441	−	525.477i	−1.22082	−	1.32423i
$55$	−280.813			−0.688451
$56$	12.2469	+	938.848i	0.0292244	+	2.24034i
$57$	119.471	+	471.301i	0.277620	+	1.09518i
$58$	−111.696	+	193.463i	−0.252869	+	0.437983i
$59$	291.033			0.642190			0.321095	−	0.947047i	$-0.395949\pi$
$59$	291.033			0.642190			0.321095	+	0.947047i	$0.395949\pi$
$60$	−457.257	+	445.042i	−0.983860	+	0.957578i
$61$	−154.029			−0.323302			−0.161651	−	0.986848i	$-0.551682\pi$
$61$	−154.029			−0.323302			−0.161651	+	0.986848i	$0.551682\pi$
$62$	1019.55			2.08843
$63$	256.074	−	429.503i	0.512101	−	0.858925i
$64$	−7.91610			−0.0154611
$65$	−436.243			−0.832450
$66$	−267.016	−	1053.35i	−0.497992	−	1.96453i
$67$	−838.351			−1.52867			−0.764335	−	0.644820i	$-0.776933\pi$
$67$	−838.351			−1.52867			−0.764335	+	0.644820i	$0.776933\pi$
$68$	682.483	−	1182.10i	1.21711	−	2.10809i
$69$	−156.870	+	152.679i	−0.273694	+	0.266383i
$70$	−563.078	−	315.373i	−0.961438	−	0.538489i
$71$	−940.646			−1.57231			−0.786156	−	0.618028i	$-0.787932\pi$
$71$	−940.646			−1.57231			−0.786156	+	0.618028i	$0.787932\pi$
$72$	−1166.48	−	716.254i	−1.90932	−	1.17238i
$73$	65.8171	−	113.998i	0.105525	−	0.182774i	−0.808428	−	0.588595i	$-0.799681\pi$
$73$	65.8171	−	113.998i	0.105525	−	0.182774i	0.913952	+	0.405821i	$0.133014\pi$
$74$	265.701	+	460.208i	0.417393	+	0.722947i
$75$	99.8560	+	393.922i	0.153738	+	0.606482i
$76$	839.881	+	1454.72i	1.26764	+	2.19563i
$77$	653.415	−	388.701i	0.967060	−	0.575280i
$78$	−414.810	−	1636.38i	−0.602153	−	2.37543i
$79$	620.364			0.883499			0.441749	−	0.897138i	$-0.354358\pi$
$79$	620.364			0.883499			0.441749	+	0.897138i	$0.354358\pi$
$80$	−392.138	+	679.203i	−0.548030	+	0.949215i
$81$	329.797	+	650.134i	0.452397	+	0.891817i
$82$	553.616	+	958.891i	0.745569	+	1.29136i
$83$	102.235	−	177.076i	0.135201	−	0.234176i	−0.790473	−	0.612497i	$-0.790165\pi$
$83$	102.235	−	177.076i	0.135201	−	0.234176i	0.925674	+	0.378321i	$0.123499\pi$
$84$	447.952	−	1668.49i	0.581852	−	2.16723i
$85$	260.057	+	450.433i	0.331849	+	0.574780i
$86$	−1203.04	+	2083.72i	−1.50845	+	2.61271i
$87$	163.287	−	158.925i	0.201221	−	0.195845i
$88$	−1040.61	−	1802.38i	−1.26056	−	2.18335i
$89$	432.859	+	749.734i	0.515539	+	0.892940i	0.999837	+	0.0180370i	$0.00574166\pi$
$89$	432.859	+	749.734i	0.515539	+	0.892940i	−0.484298	+	0.874903i	$0.660925\pi$
$90$	827.260	−	448.208i	0.968898	−	0.524948i
$91$	1015.08	−	603.846i	1.16933	−	0.695607i
$92$	−378.138	+	654.953i	−0.428517	+	0.742213i
$93$	−1000.76	−	282.728i	−1.11585	−	0.315242i
$94$	91.1073			0.0999680
$95$	−640.067			−0.691258
$96$	−892.551	−	252.156i	−0.948913	−	0.268079i
$97$	331.039	−	573.377i	0.346515	−	0.600182i	−0.639113	−	0.769113i	$-0.720698\pi$
$97$	331.039	−	573.377i	0.346515	−	0.600182i	0.985628	+	0.168931i	$0.0540316\pi$
$98$	1746.75	−	45.5792i	1.80049	−	0.0469815i
$99$	−30.0049	+	1107.99i	−0.0304606	+	1.12482i
$100$	701.988	+	1215.88i	0.701988	+	1.21588i
$101$	120.190	+	208.176i	0.118410	+	0.205092i	0.919138	−	0.393937i	$-0.128887\pi$
$101$	120.190	+	208.176i	0.118410	+	0.205092i	−0.800728	+	0.599028i	$0.795554\pi$
$102$	−1442.33	+	1403.80i	−1.40012	+	1.36271i
$103$	203.183	−	351.923i	0.194371	−	0.336660i	−0.752323	−	0.658794i	$-0.771067\pi$
$103$	203.183	−	351.923i	0.194371	−	0.336660i	0.946694	+	0.322134i	$0.104400\pi$
$104$	−1616.58	−	2800.00i	−1.52422	−	2.64003i
$105$	465.249	+	465.708i	0.432415	+	0.432842i
$106$	−1075.66	+	1863.10i	−0.985638	+	1.70718i
$107$	−855.526	−	1481.81i	−0.772961	−	1.33881i	−0.935933	−	0.352177i	$-0.885442\pi$
$107$	−855.526	−	1481.81i	−0.772961	−	1.33881i	0.162972	−	0.986631i	$-0.447892\pi$
$108$	1707.12	+	1851.73i	1.52100	+	1.64984i
$109$	298.924	−	517.751i	0.262676	−	0.454968i	−0.704276	−	0.709926i	$-0.748728\pi$
$109$	298.924	−	517.751i	0.262676	−	0.454968i	0.966952	+	0.254958i	$0.0820616\pi$
$110$	1430.54			1.23997
$111$	−133.187	−	525.409i	−0.113888	−	0.449276i
$112$	−27.6966	−	2123.21i	−0.0233668	−	1.79129i
$113$	374.893	+	649.334i	0.312097	+	0.540568i	0.978816	−	0.204741i	$-0.0656352\pi$
$113$	374.893	+	649.334i	0.312097	+	0.540568i	−0.666719	+	0.745309i	$0.732302\pi$
$114$	−608.620	−	2400.94i	−0.500022	−	1.97254i
$115$	−144.088	−	249.567i	−0.116837	−	0.202368i
$116$	393.607	−	681.747i	0.315047	−	0.545678i
$117$	−46.6125	+	1721.26i	−0.0368319	+	1.36009i
$118$	−1482.61			−1.15665
$119$	−1228.61	−	688.128i	−0.946439	−	0.530089i
$120$	1291.33	−	1256.83i	0.982349	−	0.956106i
$121$	−177.124	+	306.787i	−0.133076	+	0.230494i
$122$	784.669			0.582300
$123$	−277.509	−	1094.75i	−0.203432	−	0.802519i
$124$	−3592.79			−2.60195
$125$	−1390.04			−0.994630
$126$	−1304.52	+	2188.01i	−0.922346	+	1.54701i
$127$	−2519.73			−1.76055			−0.880275	−	0.474463i	$-0.842642\pi$
$127$	−2519.73			−1.76055			−0.880275	+	0.474463i	$0.842642\pi$
$128$	1468.29			1.01390
$129$	1758.70	−	1711.72i	1.20035	−	1.16828i
$130$	2222.35			1.49933
$131$	207.562	−	359.507i	0.138433	−	0.239773i	−0.788471	−	0.615073i	$-0.789127\pi$
$131$	207.562	−	359.507i	0.138433	−	0.239773i	0.926904	+	0.375299i	$0.122460\pi$
$132$	940.941	+	3711.92i	0.620442	+	2.44758i
$133$	1489.35	−	885.979i	0.971002	−	0.577625i
$134$	4270.80			2.75329
$135$	−936.310	+	210.546i	−0.596924	+	0.134229i
$136$	−1927.39	+	3338.33i	−1.21524	+	2.10485i
$137$	577.022	+	999.431i	0.359842	+	0.623264i	0.987934	−	0.154875i	$-0.0494974\pi$
$137$	577.022	+	999.431i	0.359842	+	0.623264i	−0.628093	+	0.778139i	$0.716164\pi$
$138$	799.140	−	777.792i	0.492951	−	0.479783i
$139$	644.637	+	1116.54i	0.393362	+	0.681323i	0.992891	−	0.119030i	$-0.0379785\pi$
$139$	644.637	+	1116.54i	0.393362	+	0.681323i	−0.599528	+	0.800354i	$0.704645\pi$
$140$	1984.23	+	1111.34i	1.19784	+	0.670898i
$141$	−89.4287	−	25.2647i	−0.0534132	−	0.0150898i
$142$	4791.92			2.83190
$143$	−1309.01	+	2267.28i	−0.765492	+	1.32587i
$144$	2638.00	+	1619.82i	1.52662	+	0.937393i
$145$	149.982	+	259.777i	0.0858990	+	0.148781i
$146$	−335.291	+	580.741i	−0.190061	+	0.329195i
$147$	−1727.20	−	439.645i	−0.969098	−	0.246676i
$148$	−936.305	−	1621.73i	−0.520026	−	0.900711i
$149$	−818.608	+	1417.87i	−0.450087	+	0.779574i	−0.998391	−	0.0567053i	$-0.981940\pi$
$149$	−818.608	+	1417.87i	−0.450087	+	0.779574i	0.548304	+	0.836279i	$0.315274\pi$
$150$	−508.696	−	2006.75i	−0.276899	−	1.09234i
$151$	−190.403	−	329.788i	−0.102615	−	0.177734i	0.810147	−	0.586227i	$-0.199387\pi$
$151$	−190.403	−	329.788i	−0.102615	−	0.177734i	−0.912761	+	0.408494i	$0.866054\pi$
$152$	−2371.89	−	4108.24i	−1.26570	−	2.19225i
$153$	1805.04	−	977.968i	0.953783	−	0.516759i
$154$	−3328.69	+	1980.15i	−1.74177	+	1.03614i
$155$	684.510	−	1185.61i	0.354717	−	0.614388i
$156$	1461.75	+	5766.46i	0.750216	+	2.95953i
$157$	1591.68			0.809108			0.404554	−	0.914514i	$-0.367427\pi$
$157$	1591.68			0.809108			0.404554	+	0.914514i	$0.367427\pi$
$158$	−3160.31			−1.59127
$159$	1572.50	−	1530.49i	0.784321	−	0.763369i
$160$	610.493	−	1057.41i	0.301648	−	0.522470i
$161$	680.724	+	381.265i	0.333221	+	0.186633i
$162$	−1680.08	−	3311.97i	−0.814814	−	1.60625i
$163$	−460.445	−	797.514i	−0.221257	−	0.383228i	0.733933	−	0.679222i	$-0.237683\pi$
$163$	−460.445	−	797.514i	−0.221257	−	0.383228i	−0.955190	+	0.295994i	$0.904349\pi$
$164$	−1950.89	−	3379.04i	−0.928895	−	1.60889i
$165$	−1404.19	−	396.699i	−0.662520	−	0.187170i
$166$	−520.813	+	902.075i	−0.243512	+	0.421775i
$167$	−1489.89	−	2580.57i	−0.690367	−	1.19575i	−0.971718	−	0.236146i	$-0.924116\pi$
$167$	−1489.89	−	2580.57i	−0.690367	−	1.19575i	0.281350	−	0.959605i	$-0.409218\pi$
$168$	−1265.05	+	4711.95i	−0.580958	+	2.16390i
$169$	−935.053	+	1619.56i	−0.425605	+	0.737169i
$170$	−1324.81	−	2294.64i	−0.597695	−	1.03524i
$171$	−68.3912	+	2525.48i	−0.0305848	+	1.12941i
$172$	4239.39	−	7342.83i	1.87936	−	3.25515i
$173$	1706.64			0.750021			0.375010	−	0.927021i	$-0.377639\pi$
$173$	1706.64			0.750021			0.375010	+	0.927021i	$0.377639\pi$
$174$	−831.832	+	809.610i	−0.362419	+	0.352738i
$175$	1244.83	−	740.517i	0.537715	−	0.319873i
$176$	2353.34	+	4076.11i	1.00790	+	1.74573i
$177$	1455.29	+	411.136i	0.618002	+	0.174593i
$178$	−2205.11	−	3819.36i	−0.928539	−	1.60828i
$179$	−1526.74	+	2644.39i	−0.637507	+	1.10419i	0.348471	+	0.937320i	$0.386701\pi$
$179$	−1526.74	+	2644.39i	−0.637507	+	1.10419i	−0.985978	+	0.166875i	$0.946632\pi$
$180$	−2915.18	+	1579.44i	−1.20714	+	0.654027i
$181$	418.264			0.171764			0.0858821	−	0.996305i	$-0.472629\pi$
$181$	418.264			0.171764			0.0858821	+	0.996305i	$0.472629\pi$
$182$	−5171.11	+	3076.17i	−2.10609	+	1.25286i
$183$	−770.212	−	217.594i	−0.311124	−	0.0878962i
$184$	1067.89	−	1849.64i	0.427859	−	0.741073i
$185$	713.551			0.283575
$186$	5098.18	+	1440.30i	2.00977	+	0.567783i
$187$	3121.37			1.22063
$188$	−321.053			−0.124549
$189$	1887.23	−	1785.95i	0.726328	−	0.687348i
$190$	3260.69			1.24503
$191$	−2086.06			−0.790272			−0.395136	−	0.918623i	$-0.629303\pi$
$191$	−2086.06			−0.790272			−0.395136	+	0.918623i	$0.629303\pi$
$192$	−39.5839	−	11.1829i	−0.0148788	−	0.00420343i
$193$	−1268.95			−0.473268			−0.236634	−	0.971599i	$-0.576044\pi$
$193$	−1268.95			−0.473268			−0.236634	+	0.971599i	$0.576044\pi$
$194$	−1686.41	+	2920.95i	−0.624109	+	1.08099i
$195$	−2181.40	−	616.272i	−0.801095	−	0.226319i
$196$	−6155.37	+	160.617i	−2.24321	+	0.0585338i
$197$	−789.856			−0.285660			−0.142830	−	0.989747i	$-0.545620\pi$
$197$	−789.856			−0.285660			−0.142830	+	0.989747i	$0.545620\pi$
$198$	152.854	−	5644.43i	0.0548628	−	2.02592i
$199$	2735.94	−	4738.78i	0.974600	−	1.68806i	0.293349	−	0.956005i	$-0.405230\pi$
$199$	2735.94	−	4738.78i	0.974600	−	1.68806i	0.681250	−	0.732051i	$-0.261437\pi$
$200$	−1982.47	−	3433.74i	−0.700909	−	1.21401i
$201$	−4192.12	−	1184.32i	−1.47109	−	0.415600i
$202$	−612.284	−	1060.51i	−0.213268	−	0.369391i
$203$	−708.572	−	396.862i	−0.244985	−	0.137213i
$204$	5082.63	−	4946.86i	1.74439	−	1.69779i
$205$	1486.76			0.506535
$206$	−1035.07	+	1792.80i	−0.350082	+	0.606360i
$207$	−1000.10	+	541.855i	−0.335807	+	0.181940i
$208$	3655.92	+	6332.24i	1.21871	+	2.11087i
$209$	−1920.62	+	3326.62i	−0.635656	+	1.10099i
$210$	−2370.11	−	2372.45i	−0.778825	−	0.779593i
$211$	−835.844	−	1447.72i	−0.272710	−	0.472348i	0.696844	−	0.717222i	$-0.254587\pi$
$211$	−835.844	−	1447.72i	−0.272710	−	0.472348i	−0.969555	+	0.244874i	$0.921253\pi$
$212$	3790.54	−	6565.40i	1.22800	−	2.12695i
$213$	−4703.64	−	1328.83i	−1.51309	−	0.427465i
$214$	4358.30	+	7548.79i	1.39218	+	2.41133i
$215$	1615.40	+	2797.96i	0.512416	+	0.887531i
$216$	−4821.06	−	5229.44i	−1.51866	−	1.64731i
$217$	48.3467	+	3706.25i	0.0151244	+	1.15943i
$218$	−1522.80	+	2637.57i	−0.473107	+	0.819445i
$219$	490.157	−	477.063i	0.151241	−	0.147201i
$220$	−5041.10			−1.54487
$221$	4849.05			1.47594
$222$	678.493	+	2676.59i	0.205124	+	0.809193i
$223$	1354.96	−	2346.87i	0.406884	−	0.704743i	−0.587655	−	0.809112i	$-0.699949\pi$
$223$	1354.96	−	2346.87i	0.406884	−	0.704743i	0.994539	+	0.104368i	$0.0332821\pi$
$224$	43.1190	+	3305.49i	0.0128616	+	0.985970i
$225$	−57.1626	+	2110.84i	−0.0169371	+	0.625435i
$226$	−1909.81	−	3307.90i	−0.562119	−	0.973619i
$227$	148.473	+	257.163i	0.0434120	+	0.0751918i	0.886915	−	0.461933i	$-0.152844\pi$
$227$	148.473	+	257.163i	0.0434120	+	0.0751918i	−0.843503	+	0.537125i	$0.819511\pi$
$228$	2144.72	+	8460.70i	0.622972	+	2.45756i
$229$	−1510.16	+	2615.67i	−0.435781	+	0.754796i	−0.997359	−	0.0726285i	$-0.976861\pi$
$229$	−1510.16	+	2615.67i	−0.435781	+	0.754796i	0.561578	+	0.827424i	$0.310195\pi$
$230$	734.025	+	1271.37i	0.210436	+	0.364485i
$231$	3816.47	−	1020.60i	1.08704	−	0.290696i
$232$	−1111.58	+	1925.31i	−0.314563	+	0.544839i
$233$	−150.838	−	261.259i	−0.0424108	−	0.0734577i	0.844041	−	0.536279i	$-0.180170\pi$
$233$	−150.838	−	261.259i	−0.0424108	−	0.0734577i	−0.886452	+	0.462821i	$0.846837\pi$
$234$	237.458	−	8768.62i	0.0663381	−	2.44967i
$235$	61.1681	−	105.946i	0.0169794	−	0.0294092i
$236$	5224.56			1.44106
$237$	3102.09	+	876.377i	0.850221	+	0.240197i
$238$	6258.88	+	3505.52i	1.70464	+	0.954745i
$239$	−1040.51	−	1802.22i	−0.281611	−	0.487765i	0.690171	−	0.723647i	$-0.257535\pi$
$239$	−1040.51	−	1802.22i	−0.281611	−	0.487765i	−0.971782	+	0.235882i	$0.924202\pi$
$240$	−2920.36	+	2842.34i	−0.785451	+	0.764469i
$241$	1734.56	+	3004.35i	0.463622	+	0.803016i	0.999138	−	0.0415084i	$-0.0132163\pi$
$241$	1734.56	+	3004.35i	0.463622	+	0.803016i	−0.535516	+	0.844525i	$0.679883\pi$
$242$	902.319	−	1562.86i	0.239683	−	0.415143i
$243$	730.697	+	3716.85i	0.192898	+	0.981219i
$244$	−2765.10			−0.725481
$245$	1119.74	−	2061.85i	0.291989	−	0.537659i
$246$	1413.71	+	5576.95i	0.366402	+	1.44542i
$247$	−2983.68	+	5167.89i	−0.768613	+	1.33128i
$248$	10146.3			2.59796
$249$	761.369	−	741.030i	0.193774	−	0.188598i
$250$	7081.25			1.79143
$251$	5185.82			1.30409			0.652044	−	0.758181i	$-0.273912\pi$
$251$	5185.82			1.30409			0.652044	+	0.758181i	$0.273912\pi$
$252$	4596.99	−	7710.35i	1.14914	−	1.92741i
$253$	−1729.43			−0.429757
$254$	12836.2			3.17093
$255$	664.082	+	2619.74i	0.163084	+	0.643350i
$256$	−7416.54			−1.81068
$257$	−86.5398	+	149.891i	−0.0210047	+	0.0363812i	−0.876337	−	0.481699i	$-0.840020\pi$
$257$	−86.5398	+	149.891i	−0.0210047	+	0.0363812i	0.855332	+	0.518080i	$0.173353\pi$
$258$	−8959.34	+	8720.00i	−2.16195	+	2.10420i
$259$	−1660.34	+	987.695i	−0.398334	+	0.236959i
$260$	−7831.34			−1.86800
$261$	1041.02	−	564.021i	0.246886	−	0.133763i
$262$	−1057.38	+	1831.44i	−0.249333	+	0.431857i
$263$	−1524.27	−	2640.12i	−0.357379	−	0.618998i	0.630143	−	0.776479i	$-0.282996\pi$
$263$	−1524.27	−	2640.12i	−0.357379	−	0.618998i	−0.987522	+	0.157481i	$0.949663\pi$
$264$	−2657.29	−	10482.8i	−0.619489	−	2.44382i
$265$	1444.37	+	2501.72i	0.334818	+	0.579922i
$266$	−7587.20	+	4513.43i	−1.74888	+	1.04036i
$267$	1105.35	+	4360.49i	0.253357	+	0.999466i
$268$	−15049.9			−3.43030
$269$	1564.23	−	2709.33i	0.354547	−	0.614093i	−0.632494	−	0.774566i	$-0.717969\pi$
$269$	1564.23	−	2709.33i	0.354547	−	0.614093i	0.987040	+	0.160473i	$0.0513019\pi$
$270$	4769.83	−	1072.58i	1.07512	−	0.241760i
$271$	−2322.28	−	4022.30i	−0.520547	−	0.901614i	−0.999715	−	0.0238903i	$-0.992395\pi$
$271$	−2322.28	−	4022.30i	−0.520547	−	0.901614i	0.479168	−	0.877723i	$-0.340939\pi$
$272$	4358.81	−	7549.68i	0.971660	−	1.68296i
$273$	5928.88	−	1585.51i	1.31440	−	0.351499i
$274$	−2939.52	−	5091.39i	−0.648112	−	1.12256i
$275$	−1605.29	+	2780.44i	−0.352010	+	0.609698i
$276$	−2816.09	+	2740.86i	−0.614162	+	0.597756i
$277$	1167.08	+	2021.44i	0.253152	+	0.438472i	0.964392	−	0.264477i	$-0.0851995\pi$
$277$	1167.08	+	2021.44i	0.253152	+	0.438472i	−0.711240	+	0.702949i	$0.751866\pi$
$278$	−3283.97	−	5688.00i	−0.708486	−	1.22713i
$279$	−4604.85	−	2827.52i	−0.988119	−	0.606736i
$280$	−5603.63	−	3138.53i	−1.19600	−	0.669867i
$281$	3471.31	−	6012.48i	0.736943	−	1.27642i	−0.216923	−	0.976189i	$-0.569602\pi$
$281$	3471.31	−	6012.48i	0.736943	−	1.27642i	0.953866	−	0.300233i	$-0.0970646\pi$
$282$	455.576	+	128.705i	0.0962026	+	0.0271784i
$283$	3887.47			0.816559			0.408280	−	0.912857i	$-0.366129\pi$
$283$	3887.47			0.816559			0.408280	+	0.912857i	$0.366129\pi$
$284$	−16886.3			−3.52823
$285$	−3200.61	−	904.211i	−0.665221	−	0.187933i
$286$	6668.50	−	11550.2i	1.37873	−	2.38803i
$287$	−3459.49	+	2057.97i	−0.711524	+	0.423268i
$288$	−4106.93	−	2521.78i	−0.840288	−	0.515963i
$289$	−434.166	−	751.997i	−0.0883708	−	0.153063i
$290$	−764.053	−	1323.38i	−0.154713	−	0.267971i
$291$	2465.34	−	2399.48i	0.496635	−	0.483368i
$292$	1181.53	−	2046.48i	0.236795	−	0.410141i
$293$	2927.47	+	5070.52i	0.583701	+	1.01100i	0.995036	+	0.0995159i	$0.0317294\pi$
$293$	2927.47	+	5070.52i	0.583701	+	1.01100i	−0.411335	+	0.911484i	$0.634937\pi$
$294$	8798.88	+	2239.68i	1.74545	+	0.444289i
$295$	−995.399	+	1724.08i	−0.196456	+	0.340271i
$296$	2644.20	+	4579.89i	0.519227	+	0.899327i
$297$	−1715.28	+	5498.05i	−0.335119	+	1.07417i
$298$	4170.23	−	7223.05i	0.810654	−	1.40409i
$299$	−2686.67			−0.519646
$300$	1792.59	+	7071.60i	0.344985	+	1.36093i
$301$	−7631.76	−	4274.45i	−1.46142	−	0.818522i
$302$	969.969	+	1680.04i	0.184819	+	0.320117i
$303$	306.918	+	1210.76i	0.0581913	+	0.229559i
$304$	5364.06	+	9290.83i	1.01201	+	1.75285i
$305$	526.815	−	912.471i	0.0989028	−	0.171305i
$306$	−9195.40	+	4982.06i	−1.71786	+	0.930736i
$307$	366.420			0.0681196			0.0340598	−	0.999420i	$-0.489156\pi$
$307$	366.420			0.0681196			0.0340598	+	0.999420i	$0.489156\pi$
$308$	11730.0	−	6977.87i	2.17006	−	1.29091i
$309$	1513.16	−	1472.74i	0.278578	−	0.271136i
$310$	−3487.09	+	6039.82i	−0.638882	+	1.10658i
$311$	9582.94			1.74726			0.873632	−	0.486588i	$-0.161759\pi$
$311$	9582.94			1.74726			0.873632	+	0.486588i	$0.161759\pi$
$312$	−4128.10	−	16284.9i	−0.749063	−	2.95498i
$313$	−8689.96			−1.56928			−0.784641	−	0.619950i	$-0.787153\pi$
$313$	−8689.96			−1.56928			−0.784641	+	0.619950i	$0.787153\pi$
$314$	−8108.49			−1.45729
$315$	1668.55	+	2985.99i	0.298451	+	0.534100i
$316$	11136.6			1.98255
$317$	−5546.72			−0.982759			−0.491380	−	0.870945i	$-0.663507\pi$
$317$	−5546.72			−0.982759			−0.491380	+	0.870945i	$0.663507\pi$
$318$	−8010.75	+	7796.76i	−1.41264	+	1.37491i
$319$	1800.18			0.315959
$320$	27.0749	−	46.8951i	0.00472979	−	0.00819224i
$321$	−2184.67	−	8618.30i	−0.379864	−	1.49853i
$322$	−3467.81	−	1942.28i	−0.600166	−	0.336145i
$323$	7114.66			1.22560
$324$	5920.45	+	11671.1i	1.01517	+	2.00121i
$325$	−2493.82	+	4319.42i	−0.425637	+	0.737225i
$326$	2345.64	+	4062.77i	0.398506	+	0.690233i
$327$	2226.16	−	2166.69i	0.376474	−	0.366417i
$328$	5509.47	+	9542.68i	0.927468	+	1.60642i
$329$	4.32028	+	331.192i	0.000723966	+	0.0554991i
$330$	7153.33	+	2020.90i	1.19327	+	0.337112i
$331$	−2346.22			−0.389606			−0.194803	−	0.980842i	$-0.562407\pi$
$331$	−2346.22			−0.389606			−0.194803	+	0.980842i	$0.562407\pi$
$332$	1835.30	−	3178.83i	0.303388	−	0.525484i
$333$	76.2429	−	2815.43i	0.0125468	−	0.463316i
$334$	7589.95	+	13146.2i	1.24342	+	2.15367i
$335$	2867.35	−	4966.40i	0.467643	−	0.809981i
$336$	2860.93	−	10656.1i	0.464513	−	1.73018i
$337$	−2875.53	−	4980.56i	−0.464807	−	0.805070i	0.534386	−	0.845241i	$-0.320543\pi$
$337$	−2875.53	−	4980.56i	−0.464807	−	0.805070i	−0.999193	+	0.0401712i	$0.987210\pi$
$338$	4763.43	−	8250.51i	0.766558	−	1.32772i
$339$	957.326	+	3776.55i	0.153377	+	0.605057i
$340$	4668.50	+	8086.08i	0.744661	+	1.28979i
$341$	−4107.96	−	7115.19i	−0.652371	−	1.12994i
$342$	348.405	−	12865.6i	0.0550864	−	2.03418i
$343$	248.519	+	6347.59i	0.0391218	+	0.999234i
$344$	−11972.4	+	20736.8i	−1.87647	+	3.25015i
$345$	−367.942	−	1451.50i	−0.0574184	−	0.226510i
$346$	−8694.13			−1.35086
$347$	−1706.97			−0.264078			−0.132039	−	0.991245i	$-0.542152\pi$
$347$	−1706.97			−0.264078			−0.132039	+	0.991245i	$0.542152\pi$
$348$	2931.30	−	2852.99i	0.451534	−	0.439472i
$349$	1098.11	−	1901.98i	0.168425	−	0.291720i	−0.769441	−	0.638717i	$-0.779465\pi$
$349$	1098.11	−	1901.98i	0.168425	−	0.291720i	0.937866	+	0.346997i	$0.112799\pi$
$350$	−6341.51	+	3772.41i	−0.968480	+	0.576125i
$351$	−2664.68	+	8541.21i	−0.405214	+	1.29885i
$352$	−3663.76	−	6345.82i	−0.554771	−	0.960891i
$353$	5323.30	+	9220.23i	0.802637	+	1.39021i	0.917875	+	0.396870i	$0.129904\pi$
$353$	5323.30	+	9220.23i	0.802637	+	1.39021i	−0.115238	+	0.993338i	$0.536763\pi$
$354$	−7413.67	−	2094.45i	−1.11308	−	0.314460i
$355$	3217.23	−	5572.40i	0.480993	−	0.833105i
$356$	7770.60	+	13459.1i	1.15686	+	2.00373i
$357$	−5171.47	−	5176.57i	−0.766675	−	0.767431i
$358$	7777.65	−	13471.3i	1.14822	−	1.98877i
$359$	−1648.66	−	2855.56i	−0.242375	−	0.419806i	0.719015	−	0.694994i	$-0.244593\pi$
$359$	−1648.66	−	2855.56i	−0.242375	−	0.419806i	−0.961390	+	0.275188i	$0.911260\pi$
$360$	8232.72	−	4460.48i	1.20528	−	0.653022i
$361$	−948.242	+	1642.40i	−0.138248	+	0.239452i
$362$	−2130.76			−0.309365
$363$	−1319.09	+	1283.85i	−0.190728	+	0.185633i
$364$	18222.5	−	10840.1i	2.62395	−	1.56092i
$365$	450.219	+	779.802i	0.0645631	+	0.111827i
$366$	3923.69	+	1108.49i	0.560367	+	0.158310i
$367$	−842.370	−	1459.03i	−0.119813	−	0.207522i	0.799880	−	0.600159i	$-0.204896\pi$
$367$	−842.370	−	1459.03i	−0.119813	−	0.207522i	−0.919693	+	0.392637i	$0.871563\pi$
$368$	−2415.05	+	4182.99i	−0.342101	+	0.592536i
$369$	158.860	−	5866.23i	0.0224117	−	0.827599i
$370$	−3635.03			−0.510747
$371$	−6823.73	−	3821.89i	−0.954907	−	0.534831i
$372$	−17965.5	−	5075.47i	−2.50395	−	0.707395i
$373$	−2420.49	+	4192.41i	−0.336000	+	0.581969i	−0.983676	−	0.179946i	$-0.942408\pi$
$373$	−2420.49	+	4192.41i	−0.336000	+	0.581969i	0.647676	+	0.761916i	$0.275741\pi$
$374$	−15901.2			−2.19848
$375$	−6950.79	−	1963.68i	−0.957166	−	0.270411i
$376$	906.681			0.124358
$377$	2796.58			0.382046
$378$	−9614.12	+	9098.15i	−1.30819	+	1.23798i
$379$	−4006.74			−0.543040			−0.271520	−	0.962433i	$-0.587526\pi$
$379$	−4006.74			−0.543040			−0.271520	+	0.962433i	$0.587526\pi$
$380$	−11490.4			−1.55116
$381$	−12599.7	−	3559.58i	−1.69424	−	0.478642i
$382$	10627.0			1.42336
$383$	1330.57	−	2304.61i	0.177516	−	0.307467i	−0.763513	−	0.645793i	$-0.776527\pi$
$383$	1330.57	−	2304.61i	0.177516	−	0.307467i	0.941029	+	0.338325i	$0.109860\pi$
$384$	7342.06	+	2074.22i	0.975711	+	0.275650i
$385$	67.8359	+	5200.29i	0.00897984	+	0.688393i
$386$	6464.38			0.852405
$387$	11212.4	−	6074.86i	1.47276	−	0.797939i
$388$	5942.75	−	10293.1i	0.777571	−	1.34679i
$389$	−3412.56	−	5910.73i	−0.444791	−	0.770401i	0.553247	−	0.833018i	$-0.313389\pi$
$389$	−3412.56	−	5910.73i	−0.444791	−	0.770401i	−0.998038	+	0.0626168i	$0.980055\pi$
$390$	11112.7	+	3139.47i	1.44285	+	0.407623i
$391$	1601.61	+	2774.06i	0.207153	+	0.358799i
$392$	17383.3	−	453.595i	2.23976	−	0.0584438i
$393$	1545.77	−	1504.47i	0.198406	−	0.193106i
$394$	4023.76			0.514502
$395$	−2121.79	+	3675.05i	−0.270275	+	0.468131i
$396$	−538.641	+	19890.4i	−0.0683529	+	2.52407i
$397$	−1988.98	−	3445.01i	−0.251446	−	0.435516i	0.712478	−	0.701694i	$-0.247573\pi$
$397$	−1988.98	−	3445.01i	−0.251446	−	0.435516i	−0.963924	+	0.266178i	$0.914239\pi$
$398$	−13937.6	+	24140.7i	−1.75535	+	3.04036i
$399$	8699.02	−	2326.30i	1.09147	−	0.291881i
$400$	4483.38	+	7765.44i	0.560422	+	0.970680i
$401$	3992.33	−	6914.91i	0.497175	−	0.861133i	−0.502819	−	0.864391i	$-0.667704\pi$
$401$	3992.33	−	6914.91i	0.497175	−	0.861133i	0.999995	+	0.00325874i	$0.00103729\pi$
$402$	21355.9	+	6033.28i	2.64959	+	0.748539i
$403$	−6381.71	−	11053.4i	−0.788823	−	1.36628i
$404$	2157.63	+	3737.13i	0.265708	+	0.460220i
$405$	−4979.39	−	269.886i	−0.610933	−	0.0331129i
$406$	3609.67	+	2021.73i	0.441244	+	0.247135i
$407$	2141.12	−	3708.53i	0.260765	−	0.451659i
$408$	−14353.8	+	13970.3i	−1.74171	+	1.69518i
$409$	3070.90			0.371262			0.185631	−	0.982620i	$-0.440567\pi$
$409$	3070.90			0.371262			0.185631	+	0.982620i	$0.440567\pi$
$410$	−7573.97			−0.912322
$411$	1473.48	+	5812.74i	0.176841	+	0.697618i
$412$	3647.50	−	6317.65i	0.436163	−	0.755457i
$413$	−70.3047	−	5389.54i	−0.00837644	−	0.642136i
$414$	5094.82	−	2760.37i	0.604822	−	0.327692i
$415$	699.333	+	1211.28i	0.0827202	+	0.143276i
$416$	−5691.65	−	9858.23i	−0.670808	−	1.16187i
$417$	1646.14	+	6493.87i	0.193314	+	0.762604i
$418$	9784.21	−	16946.7i	1.14488	−	1.98300i
$419$	−1945.50	−	3369.70i	−0.226835	−	0.392889i	0.730034	−	0.683411i	$-0.239504\pi$
$419$	−1945.50	−	3369.70i	−0.226835	−	0.392889i	−0.956868	+	0.290522i	$0.906171\pi$
$420$	8352.05	+	8360.29i	0.970329	+	0.971286i
$421$	−2847.38	+	4931.81i	−0.329627	+	0.570930i	−0.982438	−	0.186591i	$-0.940256\pi$
$421$	−2847.38	+	4931.81i	−0.329627	+	0.570930i	0.652811	+	0.757521i	$0.273590\pi$
$422$	4258.03	+	7375.13i	0.491180	+	0.850748i
$423$	−411.491	−	252.668i	−0.0472988	−	0.0290429i
$424$	−10704.8	+	18541.2i	−1.22611	+	2.12368i
$425$	5946.56			0.678707
$426$	23961.7	+	6769.46i	2.72523	+	0.769909i
$427$	37.2088	+	2852.42i	0.00421700	+	0.323274i
$428$	−15358.2	−	26601.2i	−1.73450	−	3.00425i
$429$	−9748.59	+	9488.16i	−1.09712	+	1.06782i
$430$	−8229.33	−	14253.6i	−0.922915	−	1.59854i
$431$	−4029.23	+	6978.82i	−0.450304	+	0.779949i	−0.998405	−	0.0564630i	$-0.982018\pi$
$431$	−4029.23	+	6978.82i	−0.450304	+	0.779949i	0.548101	+	0.836412i	$0.315351\pi$
$432$	10902.9	+	11826.4i	1.21427	+	1.31713i
$433$	504.156			0.0559542			0.0279771	−	0.999609i	$-0.491093\pi$
$433$	504.156			0.0559542			0.0279771	+	0.999609i	$0.491093\pi$
$434$	−246.292	−	18880.7i	−0.0272406	−	2.08825i
$435$	382.995	+	1510.87i	0.0422142	+	0.166531i
$436$	5366.21	−	9294.56i	0.589438	−	1.02094i
$437$	−3941.96			−0.431509
$438$	−2497.00	+	2430.30i	−0.272401	+	0.265124i
$439$	−7426.91			−0.807442			−0.403721	−	0.914882i	$-0.632283\pi$
$439$	−7426.91			−0.807442			−0.403721	+	0.914882i	$0.632283\pi$
$440$	14236.5			1.54249
$441$	−8015.69	−	4638.41i	−0.865532	−	0.500854i
$442$	−24702.5			−2.65832
$443$	−15301.9			−1.64112			−0.820559	−	0.571562i	$-0.806338\pi$
$443$	−15301.9			−1.64112			−0.820559	+	0.571562i	$0.806338\pi$
$444$	−2390.95	−	9432.04i	−0.255561	−	1.00816i
$445$	−5921.91			−0.630844
$446$	−6902.58	+	11955.6i	−0.732840	+	1.26932i
$447$	−6096.39	+	5933.54i	−0.645077	+	0.627845i
$448$	1.91229	+	146.596i	0.000201668	+	0.0154598i
$449$	8469.43			0.890194			0.445097	−	0.895482i	$-0.353169\pi$
$449$	8469.43			0.890194			0.445097	+	0.895482i	$0.353169\pi$
$450$	291.203	−	10753.3i	0.0305054	−	1.12647i
$451$	4461.25	−	7727.11i	0.465792	−	0.806775i
$452$	6730.00	+	11656.7i	0.700338	+	1.21302i
$453$	−486.213	−	1918.06i	−0.0504289	−	0.198937i
$454$	−756.367	−	1310.07i	−0.0781895	−	0.135428i
$455$	105.383	+	8078.64i	0.0108581	+	0.832379i
$456$	−6056.86	−	23893.7i	−0.622014	−	2.45378i
$457$	14922.8			1.52749			0.763743	−	0.645520i	$-0.223359\pi$
$457$	14922.8			1.52749			0.763743	+	0.645520i	$0.223359\pi$
$458$	7693.17	−	13325.0i	0.784887	−	1.35946i
$459$	10407.5	−	2340.32i	1.05835	−	0.237989i
$460$	−2586.64	−	4480.18i	−0.262179	−	0.454108i
$461$	6078.32	−	10528.0i	0.614091	−	1.06364i	−0.376453	−	0.926436i	$-0.622856\pi$
$461$	6078.32	−	10528.0i	0.614091	−	1.06364i	0.990543	−	0.137200i	$-0.0438104\pi$
$462$	−19442.2	+	5199.25i	−1.95786	+	0.523574i
$463$	7641.92	+	13236.2i	0.767063	+	1.32859i	0.939149	+	0.343510i	$0.111616\pi$
$463$	7641.92	+	13236.2i	0.767063	+	1.32859i	−0.172086	+	0.985082i	$0.555051\pi$
$464$	2513.84	−	4354.11i	0.251514	−	0.435634i
$465$	5097.73	−	4961.55i	0.508390	−	0.494809i
$466$	768.412	+	1330.93i	0.0763863	+	0.132305i
$467$	9121.63	+	15799.1i	0.903852	+	1.56552i	0.822451	+	0.568836i	$0.192606\pi$
$467$	9121.63	+	15799.1i	0.903852	+	1.56552i	0.0814004	+	0.996681i	$0.474061\pi$
$468$	−836.779	+	30899.8i	−0.0826498	+	3.05201i
$469$	202.520	+	15525.2i	0.0199393	+	1.52854i
$470$	−311.608	+	539.721i	−0.0305817	+	0.0529691i
$471$	7959.10	+	2248.54i	0.778632	+	0.219973i
$472$	−14754.6			−1.43884
$473$	19389.1			1.88480
$474$	−15802.9	−	4464.52i	−1.53134	−	0.432620i
$475$	−3658.99	+	6337.56i	−0.353445	+	0.612184i
$476$	−22055.7	−	12353.1i	−2.12379	−	1.18951i
$477$	10025.3	−	5431.67i	0.962316	−	0.521382i
$478$	5300.67	+	9181.02i	0.507211	+	0.878515i
$479$	1516.21	+	2626.15i	0.144629	+	0.250505i	0.929235	−	0.369491i	$-0.120468\pi$
$479$	1516.21	+	2626.15i	0.144629	+	0.250505i	−0.784605	+	0.619995i	$0.787134\pi$
$480$	4546.51	−	4425.05i	0.432331	−	0.420782i
$481$	3326.23	−	5761.20i	0.315308	−	0.546129i
$482$	−8836.35	−	15305.0i	−0.835031	−	1.44632i
$483$	2865.31	+	2868.14i	0.269930	+	0.270196i
$484$	−3179.69	+	5507.38i	−0.298618	+	0.517222i
$485$	2264.46	+	3922.16i	0.212008	+	0.367209i
$486$	−3722.38	−	18934.7i	−0.347429	−	1.76728i
$487$	2783.79	−	4821.67i	0.259026	−	0.448646i	−0.706955	−	0.707258i	$-0.749932\pi$
$487$	2783.79	−	4821.67i	0.259026	−	0.448646i	0.965981	+	0.258612i	$0.0832652\pi$
$488$	7808.86			0.724366
$489$	−1175.79	−	4638.38i	−0.108734	−	0.428946i
$490$	−5704.27	+	10503.6i	−0.525903	+	0.968380i
$491$	2266.08	+	3924.96i	0.208283	+	0.360756i	0.951174	−	0.308656i	$-0.0998793\pi$
$491$	2266.08	+	3924.96i	0.208283	+	0.360756i	−0.742891	+	0.669412i	$0.766546\pi$
$492$	−4981.79	−	19652.6i	−0.456497	−	1.80083i
$493$	−1667.13	−	2887.55i	−0.152299	−	0.263790i
$494$	15199.8	−	26326.7i	1.38435	−	2.39777i
$495$	−6461.13	−	3967.34i	−0.586679	−	0.360239i
$496$	−22946.1			−2.07723
$497$	227.232	+	17419.5i	0.0205085	+	1.57218i
$498$	−3878.64	+	3775.02i	−0.349008	+	0.339684i
$499$	10318.7	−	17872.5i	0.925707	−	1.60337i	0.135287	−	0.990806i	$-0.456804\pi$
$499$	10318.7	−	17872.5i	0.925707	−	1.60337i	0.790420	−	0.612566i	$-0.209862\pi$
$500$	−24953.7			−2.23192
$501$	−3804.59	−	15008.7i	−0.339274	−	1.33840i
$502$	−26418.1			−2.34880
$503$	−8789.60			−0.779143			−0.389572	−	0.920996i	$-0.627377\pi$
$503$	−8789.60			−0.779143			−0.389572	+	0.920996i	$0.627377\pi$
$504$	−12982.3	+	21774.7i	−1.14738	+	1.92445i
$505$	−1644.31			−0.144893
$506$	8810.23			0.774037
$507$	−6963.59	+	6777.57i	−0.609988	+	0.593693i
$508$	−45233.7			−3.95063
$509$	2909.23	−	5038.93i	0.253338	−	0.438795i	−0.711104	−	0.703086i	$-0.751805\pi$
$509$	2909.23	−	5038.93i	0.253338	−	0.438795i	0.964443	+	0.264291i	$0.0851381\pi$
$510$	−3383.03	−	13345.7i	−0.293731	−	1.15874i
$511$	−2127.00	−	1191.31i	−0.184135	−	0.103132i
$512$	26035.7			2.24732
$513$	−3909.69	+	12531.9i	−0.336485	+	1.07855i
$514$	440.859	−	763.590i	0.0378316	−	0.0655263i
$515$	1389.86	+	2407.32i	0.118922	+	0.205979i
$516$	31571.9	−	30728.4i	2.69355	−	2.62160i
$517$	−367.089	−	635.816i	−0.0312274	−	0.0540874i
$518$	8458.25	−	5031.60i	0.717441	−	0.426788i
$519$	8533.95	+	2410.94i	0.721770	+	0.203909i
$520$	22116.3			1.86513
$521$	−11685.2	+	20239.4i	−0.982609	+	1.70193i	−0.330493	+	0.943808i	$0.607215\pi$
$521$	−11685.2	+	20239.4i	−0.982609	+	1.70193i	−0.652115	+	0.758120i	$0.726118\pi$
$522$	−5303.24	+	2873.29i	−0.444668	+	0.240920i
$523$	2340.45	+	4053.77i	0.195680	+	0.338927i	0.947123	−	0.320870i	$-0.103975\pi$
$523$	2340.45	+	4053.77i	0.195680	+	0.338927i	−0.751443	+	0.659798i	$0.770642\pi$
$524$	3726.11	−	6453.80i	0.310641	−	0.538045i
$525$	7270.79	−	1944.36i	0.604425	−	0.161636i
$526$	7765.08	+	13449.5i	0.643676	+	1.11488i
$527$	−7608.66	+	13178.6i	−0.628915	+	1.08931i
$528$	6009.50	+	23706.9i	0.495322	+	1.95399i
$529$	5196.11	+	8999.93i	0.427066	+	0.739700i
$530$	−7358.03	−	12744.5i	−0.603043	−	1.04450i
$531$	6696.27	+	4111.72i	0.547257	+	0.336033i
$532$	26736.6	−	15904.9i	2.17890	−	1.29618i
$533$	6930.55	−	12004.1i	0.563218	−	0.975523i
$534$	−5630.97	−	22213.6i	−0.456322	−	1.80014i
$535$	11704.4			0.945841
$536$	42502.2			3.42503
$537$	−11370.0	+	11066.3i	−0.913692	+	0.889284i
$538$	−7968.66	+	13802.1i	−0.638575	+	1.10604i
$539$	−7356.07	−	12006.5i	−0.587845	−	0.959474i
$540$	−16808.4	+	3779.68i	−1.33948	+	0.301206i
$541$	347.398	+	601.711i	0.0276078	+	0.0478181i	0.879499	−	0.475900i	$-0.157878\pi$
$541$	347.398	+	601.711i	0.0276078	+	0.0478181i	−0.851891	+	0.523718i	$0.824544\pi$
$542$	11830.3	+	20490.8i	0.937559	+	1.62390i
$543$	2091.50	+	590.874i	0.165295	+	0.0466977i
$544$	−6785.93	+	11753.6i	−0.534824	+	0.926343i
$545$	2044.78	+	3541.65i	0.160713	+	0.278363i
$546$	−30203.4	+	8077.03i	−2.36738	+	0.633086i
$547$	−1795.35	+	3109.64i	−0.140336	+	0.243069i	−0.927623	−	0.373518i	$-0.878152\pi$
$547$	−1795.35	+	3109.64i	−0.140336	+	0.243069i	0.787287	+	0.616586i	$0.211485\pi$
$548$	10358.6	+	17941.6i	0.807475	+	1.39859i
$549$	−3544.00	−	2176.13i	−0.275509	−	0.169171i
$550$	8177.81	−	14164.4i	0.634006	−	1.09813i
$551$	4103.22			0.317247
$552$	7952.87	−	7740.42i	0.613219	−	0.596837i
$553$	−149.861	−	11488.3i	−0.0115240	−	0.883424i
$554$	−5945.44	−	10297.8i	−0.455952	−	0.789733i
$555$	3568.06	+	1008.02i	0.272893	+	0.0770956i
$556$	11572.4	+	20044.0i	0.882695	+	1.52887i
$557$	−7640.68	+	13234.1i	−0.581232	+	1.00672i	0.414102	+	0.910231i	$0.364096\pi$
$557$	−7640.68	+	13234.1i	−0.581232	+	1.00672i	−0.995334	+	0.0964925i	$0.969238\pi$
$558$	23458.5	+	14404.2i	1.77971	+	1.09279i
$559$	30120.9			2.27903
$560$	12672.7	+	7097.81i	0.956283	+	0.535602i
$561$	15608.2	+	4409.50i	1.17465	+	0.331853i
$562$	−17683.9	+	30629.3i	−1.32731	+	2.29897i
$563$	−20682.9			−1.54828			−0.774138	−	0.633016i	$-0.781817\pi$
$563$	−20682.9			−1.54828			−0.774138	+	0.633016i	$0.781817\pi$
$564$	−1605.41	−	453.546i	−0.119858	−	0.0338612i
$565$	−5128.88			−0.381900
$566$	−19803.9			−1.47071
$567$	11960.0	−	6264.47i	0.885840	−	0.463991i
$568$	47688.2			3.52281
$569$	−10608.9			−0.781635			−0.390817	−	0.920468i	$-0.627808\pi$
$569$	−10608.9			−0.781635			−0.390817	+	0.920468i	$0.627808\pi$
$570$	16304.9	+	4606.31i	1.19813	+	0.338486i
$571$	11148.1			0.817045			0.408523	−	0.912748i	$-0.366044\pi$
$571$	11148.1			0.817045			0.408523	+	0.912748i	$0.366044\pi$
$572$	−23499.2	+	40701.8i	−1.71774	+	2.97522i
$573$	−10431.2	−	2946.94i	−0.760506	−	0.214852i
$574$	17623.7	−	10483.9i	1.28153	−	0.762349i
$575$	−3294.76			−0.238958
$576$	−182.139	−	111.839i	−0.0131756	−	0.00809020i
$577$	−5630.45	+	9752.22i	−0.406237	+	0.703623i	−0.994465	−	0.105073i	$-0.966492\pi$
$577$	−5630.45	+	9752.22i	−0.406237	+	0.703623i	0.588228	+	0.808695i	$0.299826\pi$
$578$	2211.77	+	3830.89i	0.159165	+	0.275682i
$579$	−6345.28	−	1792.62i	−0.455442	−	0.128668i
$580$	2692.45	+	4663.46i	0.192755	+	0.333862i
$581$	−3303.91	−	1850.48i	−0.235919	−	0.132135i
$582$	−12559.2	+	12223.7i	−0.894491	+	0.870596i
$583$	17336.2			1.23155
$584$	−3336.75	+	5779.42i	−0.236431	+	0.409510i
$585$	−10037.4	−	6163.25i	−0.709391	−	0.435588i
$586$	−14913.4	−	25830.7i	−1.05131	−	1.82092i
$587$	−2580.61	+	4469.74i	−0.181453	+	0.314286i	−0.942376	−	0.334557i	$-0.891413\pi$
$587$	−2580.61	+	4469.74i	−0.181453	+	0.314286i	0.760922	+	0.648843i	$0.224747\pi$
$588$	−31006.4	−	7892.42i	−2.17463	−	0.553534i
$589$	−9363.42	−	16217.9i	−0.655030	−	1.13455i
$590$	5070.85	−	8782.97i	0.353837	−	0.612863i
$591$	−3949.62	−	1115.81i	−0.274900	−	0.0776624i
$592$	−5979.89	−	10357.5i	−0.415155	−	0.719070i
$593$	−8750.90	−	15157.0i	−0.605998	−	1.04962i	−0.991893	−	0.127076i	$-0.959441\pi$
$593$	−8750.90	−	15157.0i	−0.605998	−	1.04962i	0.385895	−	0.922543i	$-0.373893\pi$
$594$	8738.11	−	28008.7i	0.603584	−	1.93470i
$595$	8278.60	−	4924.73i	0.570402	−	0.339318i
$596$	−14695.5	+	25453.3i	−1.00998	+	1.74934i
$597$	20375.2	−	19830.9i	1.39682	−	1.35951i
$598$	13686.7			0.935937
$599$	−16803.2			−1.14618			−0.573089	−	0.819493i	$-0.694255\pi$
$599$	−16803.2			−1.14618			−0.573089	+	0.819493i	$0.694255\pi$
$600$	−5062.43	−	19970.8i	−0.344455	−	1.35884i
$601$	−6448.81	+	11169.7i	−0.437692	+	0.758104i	−0.997511	−	0.0705106i	$-0.977537\pi$
$601$	−6448.81	+	11169.7i	−0.437692	+	0.758104i	0.559819	+	0.828615i	$0.310870\pi$
$602$	38878.4	+	21775.3i	2.63217	+	1.47424i
$603$	−19289.3	−	11844.3i	−1.30269	−	0.799892i
$604$	−3418.08	−	5920.29i	−0.230264	−	0.398829i
$605$	−1211.61	−	2098.57i	−0.0814196	−	0.141023i
$606$	−1563.53	−	6167.96i	−0.104808	−	0.413459i
$607$	−8904.81	+	15423.6i	−0.595445	+	1.03134i	0.398039	+	0.917368i	$0.369691\pi$
$607$	−8904.81	+	15423.6i	−0.595445	+	1.03134i	−0.993484	+	0.113972i	$0.963643\pi$
$608$	−8350.95	−	14464.3i	−0.557032	−	0.964808i
$609$	−2982.53	−	2985.47i	−0.198453	−	0.198649i
$610$	−2683.75	+	4648.39i	−0.178134	+	0.308537i
$611$	−570.272	−	987.740i	−0.0377590	−	0.0654005i
$612$	32403.7	−	17556.3i	2.14026	−	1.15959i
$613$	1507.76	−	2611.52i	0.0993439	−	0.172069i	−0.812069	−	0.583561i	$-0.801659\pi$
$613$	1507.76	−	2611.52i	0.0993439	−	0.172069i	0.911413	+	0.411492i	$0.134992\pi$
$614$	−1866.65			−0.122690
$615$	7434.43	+	2100.31i	0.487456	+	0.137712i
$616$	−33126.4	+	19706.1i	−2.16672	+	1.28893i
$617$	−9570.31	−	16576.3i	−0.624451	−	1.08158i	−0.988647	−	0.150258i	$-0.951989\pi$
$617$	−9570.31	−	16576.3i	−0.624451	−	1.08158i	0.364196	−	0.931322i	$-0.381344\pi$
$618$	−7708.46	+	7502.54i	−0.501747	+	0.488344i
$619$	−8802.90	−	15247.1i	−0.571597	−	0.990035i	−0.996402	−	0.0847501i	$-0.972991\pi$
$619$	−8802.90	−	15247.1i	−0.571597	−	0.990035i	0.424805	−	0.905285i	$-0.360343\pi$
$620$	12288.2	−	21283.7i	0.795976	−	1.37867i
$621$	−5766.42	+	1296.68i	−0.372622	+	0.0837907i
$622$	−48818.3			−3.14700
$623$	13779.5	−	8197.10i	0.886140	−	0.527142i
$624$	9335.75	+	36828.6i	0.598925	+	2.36270i
$625$	−133.758	+	231.676i	−0.00856052	+	0.0148272i
$626$	44269.2			2.82644
$627$	−14303.4	+	13921.3i	−0.911040	+	0.886703i
$628$	28573.5			1.81562
$629$	−7931.46			−0.502779
$630$	−8500.07	−	15211.5i	−0.537541	−	0.961969i
$631$	−8362.46			−0.527582			−0.263791	−	0.964580i	$-0.584973\pi$
$631$	−8362.46			−0.527582			−0.263791	+	0.964580i	$0.584973\pi$
$632$	−31450.8			−1.97950
$633$	−2134.41	−	8420.03i	−0.134021	−	0.528699i
$634$	28256.6			1.77005
$635$	8618.06	−	14926.9i	0.538578	−	0.932845i
$636$	28229.1	−	27475.0i	1.76000	−	1.71298i
$637$	−11427.6	−	18652.1i	−0.710800	−	1.16016i
$638$	−9170.65			−0.569075
$639$	−21643.0	−	13289.5i	−1.33988	−	0.822728i
$640$	−5021.87	+	8698.14i	−0.310167	+	0.537225i
$641$	13424.1	+	23251.3i	0.827178	+	1.43271i	0.900243	+	0.435388i	$0.143389\pi$
$641$	13424.1	+	23251.3i	0.827178	+	1.43271i	−0.0730647	+	0.997327i	$0.523278\pi$
$642$	11129.3	+	43904.1i	0.684175	+	2.69900i
$643$	−7757.71	−	13436.7i	−0.475792	−	0.824096i	0.523824	−	0.851827i	$-0.324505\pi$
$643$	−7757.71	−	13436.7i	−0.475792	−	0.824096i	−0.999615	+	0.0277312i	$0.991172\pi$
$644$	12220.2	+	6844.39i	0.747739	+	0.418799i
$645$	4125.09	+	16273.0i	0.251822	+	0.993412i
$646$	−36244.1			−2.20744
$647$	10083.1	−	17464.4i	0.612685	−	1.06120i	−0.378101	−	0.925765i	$-0.623423\pi$
$647$	10083.1	−	17464.4i	0.612685	−	1.06120i	0.990786	−	0.135438i	$-0.0432440\pi$
$648$	−16719.8	−	32960.1i	−1.01361	−	1.99814i
$649$	5973.70	+	10346.8i	0.361307	+	0.625802i
$650$	12704.2	−	22004.4i	0.766616	−	1.32782i
$651$	−4993.99	+	18601.1i	−0.300660	+	1.11987i
$652$	−8265.82	−	14316.8i	−0.496494	−	0.859954i
$653$	−4400.97	+	7622.70i	−0.263742	+	0.456814i	−0.967233	−	0.253890i	$-0.918290\pi$
$653$	−4400.97	+	7622.70i	−0.263742	+	0.456814i	0.703492	+	0.710704i	$0.251623\pi$
$654$	−11340.7	+	11037.8i	−0.678070	+	0.659956i
$655$	1419.82	+	2459.20i	0.0846975	+	0.146700i
$656$	−12459.7	−	21580.9i	−0.741571	−	1.28444i
$657$	3124.94	−	1693.09i	0.185564	−	0.100538i
$658$	−22.0088	−	1687.19i	−0.00130394	−	0.0999595i
$659$	−7010.77	+	12143.0i	−0.414417	+	0.717791i	−0.995367	−	0.0961482i	$-0.969348\pi$
$659$	−7010.77	+	12143.0i	−0.414417	+	0.717791i	0.580950	+	0.813939i	$0.302681\pi$
$660$	−25207.7	−	7121.46i	−1.48668	−	0.420004i
$661$	19173.7			1.12825			0.564123	−	0.825691i	$-0.309214\pi$
$661$	19173.7			1.12825			0.564123	+	0.825691i	$0.309214\pi$
$662$	11952.3			0.701721
$663$	24247.4	+	6850.16i	1.42035	+	0.401264i
$664$	−5183.03	+	8977.27i	−0.302922	+	0.524677i
$665$	154.621	+	11853.2i	0.00901645	+	0.691199i
$666$	−388.404	+	14342.6i	−0.0225981	+	0.834481i
$667$	923.691	+	1599.88i	0.0536214	+	0.0928749i
$668$	−26746.2	−	46325.9i	−1.54917	−	2.68324i
$669$	10090.8	−	9821.22i	0.583157	−	0.567579i
$670$	−14607.1	+	25300.3i	−0.842273	+	1.45886i
$671$	−3161.58	−	5476.02i	−0.181895	−	0.315051i
$672$	−4453.99	+	16589.8i	−0.255679	+	0.952329i
$673$	4962.05	−	8594.52i	0.284209	−	0.492265i	−0.688208	−	0.725514i	$-0.741602\pi$
$673$	4962.05	−	8594.52i	0.284209	−	0.492265i	0.972417	+	0.233249i	$0.0749356\pi$
$674$	14648.8	+	25372.4i	0.837166	+	1.45001i
$675$	−3267.79	+	10474.4i	−0.186337	+	0.597273i
$676$	−16785.9	+	29074.0i	−0.955046	+	1.65419i
$677$	−3151.89			−0.178932			−0.0894660	−	0.995990i	$-0.528516\pi$
$677$	−3151.89			−0.178932			−0.0894660	+	0.995990i	$0.528516\pi$
$678$	−4876.90	−	19238.9i	−0.276248	−	1.08977i
$679$	−10698.2	−	5991.90i	−0.604650	−	0.338657i
$680$	−13184.2	−	22835.7i	−0.743517	−	1.28781i
$681$	379.141	+	1495.67i	0.0213344	+	0.0841621i
$682$	20927.1	+	36246.9i	1.17499	+	2.03514i
$683$	−99.2937	+	171.982i	−0.00556276	+	0.00963499i	−0.868793	−	0.495175i	$-0.835104\pi$
$683$	−99.2937	+	171.982i	−0.00556276	+	0.00963499i	0.863231	+	0.504810i	$0.168437\pi$
$684$	−1227.74	+	45337.0i	−0.0686316	+	2.53436i
$685$	−7894.19			−0.440323
$686$	−1266.03	−	32336.4i	−0.0704623	−	1.79972i
$687$	−11246.5	+	10946.1i	−0.624574	+	0.607889i
$688$	27075.7	−	46896.4i	1.50036	−	2.59870i
$689$	26931.8			1.48914
$690$	1874.41	+	7394.34i	0.103417	+	0.407968i
$691$	21760.1			1.19796			0.598981	−	0.800763i	$-0.295572\pi$
$691$	21760.1			1.19796			0.598981	+	0.800763i	$0.295572\pi$
$692$	30637.3			1.68303
$693$	20525.8	+	287.994i	1.12512	+	0.0157864i
$694$	8695.82			0.475632
$695$	−8819.22			−0.481341
$696$	−8278.22	+	8057.07i	−0.450840	+	0.438797i
$697$	−16526.0			−0.898089
$698$	−5594.07	+	9689.22i	−0.303351	+	0.525419i
$699$	−385.179	−	1519.49i	−0.0208424	−	0.0822211i
$700$	22346.9	−	13293.6i	1.20662	−	0.717787i
$701$	1686.04			0.0908427			0.0454213	−	0.998968i	$-0.485537\pi$
$701$	1686.04			0.0908427			0.0454213	+	0.998968i	$0.485537\pi$
$702$	13574.6	−	43511.4i	0.729832	−	2.33936i
$703$	4880.33	−	8452.99i	0.261828	−	0.453500i
$704$	−162.485	−	281.432i	−0.00869870	−	0.0150666i
$705$	455.535	−	443.366i	0.0243354	−	0.0236853i
$706$	−27118.4	−	46970.5i	−1.44563	−	2.50391i
$707$	3826.10	−	2276.05i	0.203530	−	0.121075i
$708$	26125.1	+	7380.64i	1.38678	+	0.391781i
$709$	−9982.43			−0.528770			−0.264385	−	0.964417i	$-0.585169\pi$
$709$	−9982.43			−0.528770			−0.264385	+	0.964417i	$0.585169\pi$
$710$	−16389.5	+	28387.4i	−0.866319	+	1.50051i
$711$	14273.7	+	8764.52i	0.752894	+	0.462300i
$712$	−21944.8	−	38009.5i	−1.15508	−	2.00066i
$713$	4215.67	−	7301.75i	0.221428	−	0.383524i
$714$	26344.9	+	26370.9i	1.38086	+	1.38222i
$715$	−8954.27	−	15509.2i	−0.468350	−	0.811207i
$716$	−27407.7	+	47471.5i	−1.43055	+	2.47778i
$717$	−2657.05	−	10481.8i	−0.138395	−	0.545954i
$718$	8398.73	+	14547.0i	0.436543	+	0.756115i
$719$	13757.6	+	23828.8i	0.713591	+	1.23598i	0.963501	+	0.267706i	$0.0862656\pi$
$719$	13757.6	+	23828.8i	0.713591	+	1.23598i	−0.249910	+	0.968269i	$0.580401\pi$
$720$	−18618.4	+	10087.4i	−0.963703	+	0.522133i
$721$	−6566.24	−	3677.67i	−0.339167	−	0.189963i
$722$	4830.62	−	8366.88i	0.248999	−	0.431279i
$723$	4429.37	+	17473.4i	0.227842	+	0.898815i
$724$	7508.59			0.385435
$725$	3429.54			0.175683
$726$	6719.81	−	6540.30i	0.343520	−	0.334343i
$727$	−14734.5	+	25521.0i	−0.751683	+	1.30195i	0.195323	+	0.980739i	$0.437424\pi$
$727$	−14734.5	+	25521.0i	−0.751683	+	1.30195i	−0.947006	+	0.321215i	$0.895909\pi$
$728$	−51461.9	+	30613.4i	−2.61992	+	1.55853i
$729$	−1596.92	+	19618.1i	−0.0811322	+	0.996703i
$730$	−2293.55	−	3972.54i	−0.116285	−	0.201411i
$731$	−17956.0	−	31100.7i	−0.908517	−	1.57360i
$732$	−13826.7	−	3906.20i	−0.698155	−	0.197237i
$733$	−4756.36	+	8238.25i	−0.239673	+	0.415125i	−0.960620	−	0.277864i	$-0.910373\pi$
$733$	−4756.36	+	8238.25i	−0.239673	+	0.415125i	0.720948	+	0.692989i	$0.243707\pi$
$734$	4291.28	+	7432.71i	0.215796	+	0.373769i
$735$	8511.90	−	8728.29i	0.427165	−	0.438024i
$736$	3759.82	−	6512.21i	0.188300	−	0.326146i
$737$	−17207.9	−	29804.9i	−0.860055	−	1.48966i
$738$	−809.279	+	29884.3i	−0.0403658	+	1.49059i
$739$	−1612.42	+	2792.80i	−0.0802624	+	0.139019i	−0.903363	−	0.428878i	$-0.858909\pi$
$739$	−1612.42	+	2792.80i	−0.0802624	+	0.139019i	0.823100	+	0.567896i	$0.192242\pi$
$740$	12809.5			0.636334
$741$	−22220.3	+	21626.7i	−1.10160	+	1.07217i
$742$	34762.1	+	19469.8i	1.71989	+	0.963287i
$743$	−8219.64	−	14236.8i	−0.405854	−	0.702960i	0.588566	−	0.808449i	$-0.299693\pi$
$743$	−8219.64	−	14236.8i	−0.405854	−	0.702960i	−0.994420	+	0.105489i	$0.966359\pi$
$744$	50736.1	+	14333.5i	2.50010	+	0.706308i
$745$	−5599.66	−	9698.89i	−0.275377	−	0.476966i
$746$	12330.7	−	21357.3i	0.605171	−	1.04819i
$747$	4854.02	−	2629.90i	0.237750	−	0.128813i
$748$	56034.3			2.73906
$749$	−27234.6	+	16201.2i	−1.32861	+	0.790358i
$750$	35409.3	+	10003.6i	1.72395	+	0.487037i
$751$	4080.49	−	7067.62i	0.198268	−	0.343410i	−0.749699	−	0.661779i	$-0.769802\pi$
$751$	4080.49	−	7067.62i	0.198268	−	0.343410i	0.947967	+	0.318369i	$0.103135\pi$
$752$	−2050.47			−0.0994320
$753$	25931.4	+	7325.91i	1.25497	+	0.354543i
$754$	−14246.6			−0.688104
$755$	2604.89			0.125565
$756$	33879.2	−	32061.0i	1.62986	−	1.54239i
$757$	18136.9			0.870801			0.435401	−	0.900237i	$-0.356607\pi$
$757$	18136.9			0.870801			0.435401	+	0.900237i	$0.356607\pi$
$758$	20411.5			0.978072
$759$	−8647.91	−	2443.14i	−0.413570	−	0.116838i
$760$	32449.7			1.54878
$761$	−8669.64	+	15016.3i	−0.412975	+	0.715294i	−0.995214	−	0.0977241i	$-0.968844\pi$
$761$	−8669.64	+	15016.3i	−0.412975	+	0.715294i	0.582238	+	0.813018i	$0.302177\pi$
$762$	64186.8	+	18133.5i	3.05150	+	0.862084i
$763$	−9660.27	−	5410.60i	−0.458356	−	0.256719i
$764$	−37448.5			−1.77335
$765$	−380.154	+	14038.0i	−0.0179667	+	0.663455i
$766$	−6778.29	+	11740.3i	−0.319725	+	0.553780i
$767$	9280.14	+	16073.7i	0.436879	+	0.756697i
$768$	−37085.9	−	10477.2i	−1.74248	−	0.492271i
$769$	17102.1	+	29621.7i	0.801974	+	1.38906i	0.918315	+	0.395851i	$0.129550\pi$
$769$	17102.1	+	29621.7i	0.801974	+	1.38906i	−0.116341	+	0.993209i	$0.537116\pi$
$770$	−345.576	−	26491.8i	−0.0161736	−	1.23987i
$771$	−644.485	+	627.268i	−0.0301045	+	0.0293003i
$772$	−22779.9			−1.06200
$773$	14432.8	−	24998.4i	0.671556	−	1.16317i	−0.305907	−	0.952061i	$-0.598960\pi$
$773$	14432.8	−	24998.4i	0.671556	−	1.16317i

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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-5.09429 q^{2} +(5.00043 + 1.41268i) q^{3} +17.9518 q^{4} +(-3.42023 + 5.92401i) q^{5} +(-25.4737 - 7.19661i) q^{6} +(-0.241570 - 18.5187i) q^{7} -50.6973 q^{8} +(23.0087 + 14.1280i) q^{9} +O(q^{10})\)	\(q-5.09429 q^{2} +(5.00043 + 1.41268i) q^{3} +17.9518 q^{4} +(-3.42023 + 5.92401i) q^{5} +(-25.4737 - 7.19661i) q^{6} +(-0.241570 - 18.5187i) q^{7} -50.6973 q^{8} +(23.0087 + 14.1280i) q^{9} +(17.4236 - 30.1786i) q^{10} +(20.5259 + 35.5519i) q^{11} +(89.7667 + 25.3602i) q^{12} +(31.8869 + 55.2298i) q^{13} +(1.23063 + 94.3396i) q^{14} +(-25.4714 + 24.7909i) q^{15} +114.653 q^{16} +(38.0175 - 65.8483i) q^{17} +(-117.213 - 71.9723i) q^{18} +(46.7854 + 81.0346i) q^{19} +(-61.3993 + 106.347i) q^{20} +(24.9530 - 92.9427i) q^{21} +(-104.565 - 181.112i) q^{22} +(-21.0641 + 36.4840i) q^{23} +(-253.509 - 71.6192i) q^{24} +(39.1040 + 67.7302i) q^{25} +(-162.441 - 281.357i) q^{26} +(95.0949 + 103.150i) q^{27} +(-4.33661 - 332.444i) q^{28} +(21.9258 - 37.9765i) q^{29} +(129.759 - 126.292i) q^{30} -200.136 q^{31} -178.495 q^{32} +(52.4149 + 206.771i) q^{33} +(-193.672 + 335.450i) q^{34} +(110.531 + 61.9071i) q^{35} +(413.047 + 253.624i) q^{36} +(-52.1566 - 90.3379i) q^{37} +(-238.338 - 412.814i) q^{38} +(81.4264 + 321.219i) q^{39} +(173.397 - 300.332i) q^{40} +(-108.674 - 188.229i) q^{41} +(-127.118 + 473.477i) q^{42} +(236.154 - 409.031i) q^{43} +(368.476 + 638.220i) q^{44} +(-162.390 + 87.9825i) q^{45} +(107.306 - 185.860i) q^{46} -17.8842 q^{47} +(573.312 + 161.967i) q^{48} +(-342.883 + 8.94711i) q^{49} +(-199.207 - 345.037i) q^{50} +(283.127 - 275.563i) q^{51} +(572.428 + 991.474i) q^{52} +(211.151 - 365.724i) q^{53} +(-484.441 - 525.477i) q^{54} -280.813 q^{55} +(12.2469 + 938.848i) q^{56} +(119.471 + 471.301i) q^{57} +(-111.696 + 193.463i) q^{58} +291.033 q^{59} +(-457.257 + 445.042i) q^{60} -154.029 q^{61} +1019.55 q^{62} +(256.074 - 429.503i) q^{63} -7.91610 q^{64} -436.243 q^{65} +(-267.016 - 1053.35i) q^{66} -838.351 q^{67} +(682.483 - 1182.10i) q^{68} +(-156.870 + 152.679i) q^{69} +(-563.078 - 315.373i) q^{70} -940.646 q^{71} +(-1166.48 - 716.254i) q^{72} +(65.8171 - 113.998i) q^{73} +(265.701 + 460.208i) q^{74} +(99.8560 + 393.922i) q^{75} +(839.881 + 1454.72i) q^{76} +(653.415 - 388.701i) q^{77} +(-414.810 - 1636.38i) q^{78} +620.364 q^{79} +(-392.138 + 679.203i) q^{80} +(329.797 + 650.134i) q^{81} +(553.616 + 958.891i) q^{82} +(102.235 - 177.076i) q^{83} +(447.952 - 1668.49i) q^{84} +(260.057 + 450.433i) q^{85} +(-1203.04 + 2083.72i) q^{86} +(163.287 - 158.925i) q^{87} +(-1040.61 - 1802.38i) q^{88} +(432.859 + 749.734i) q^{89} +(827.260 - 448.208i) q^{90} +(1015.08 - 603.846i) q^{91} +(-378.138 + 654.953i) q^{92} +(-1000.76 - 282.728i) q^{93} +91.1073 q^{94} -640.067 q^{95} +(-892.551 - 252.156i) q^{96} +(331.039 - 573.377i) q^{97} +(1746.75 - 45.5792i) q^{98} +(-30.0049 + 1107.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} + O(q^{10}) \)	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} - 18q^{10} + 5q^{11} - 62q^{12} - 14q^{13} - 52q^{14} + 119q^{15} + 494q^{16} - 162q^{17} - 188q^{18} + 58q^{19} - 362q^{20} - 59q^{21} - 18q^{22} - 93q^{23} + 30q^{24} - 349q^{25} - 266q^{26} + 272q^{27} - 172q^{28} + 248q^{29} + 85q^{30} - 122q^{31} + 326q^{32} + 77q^{33} + 6q^{34} + 289q^{35} - 806q^{36} - 86q^{37} - 761q^{38} - 256q^{39} - 18q^{40} - 692q^{41} - 364q^{42} - 86q^{43} - 443q^{44} + 527q^{45} - 270q^{46} + 2010q^{47} - 1013q^{48} + 317q^{49} + 239q^{50} + 1209q^{51} - 335q^{52} + 258q^{53} + 577q^{54} - 870q^{55} - 1752q^{56} + 566q^{57} + 237q^{58} + 3330q^{59} + 1669q^{60} - 878q^{61} + 1812q^{62} + 2872q^{63} + 872q^{64} + 1226q^{65} + 1330q^{66} - 590q^{67} - 1374q^{68} + 1389q^{69} + 1251q^{70} + 636q^{71} - 5970q^{72} - 338q^{73} + 1119q^{74} + 2737q^{75} + 1006q^{76} + 2269q^{77} + 157q^{78} - 266q^{79} - 4817q^{80} - 505q^{81} + 6q^{82} - 1356q^{83} - 6013q^{84} + 483q^{85} - 3343q^{86} - 5755q^{87} + 369q^{88} - 2200q^{89} + 2665q^{90} + 1552q^{91} - 396q^{92} - 129q^{93} + 2382q^{94} - 6166q^{95} - 5941q^{96} - 266q^{97} + 3601q^{98} - 5395q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Properties

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