LMFDB - Embedded newform 63.4.s.a.47.19

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			47.19
Character	$\chi$	$=$	63.47
Dual form			63.4.s.a.59.19

$q$-expansion

$f(q)$	$=$	$q+(3.55689 - 2.05357i) q^{2} +(4.91877 + 1.67502i) q^{3} +(4.43430 - 7.68044i) q^{4} -7.61183 q^{5} +(20.9353 - 4.14318i) q^{6} +(4.76690 - 17.8963i) q^{7} -3.56749i q^{8} +(21.3886 + 16.4781i) q^{9} +O(q^{10})$	\(q+(3.55689 - 2.05357i) q^{2} +(4.91877 + 1.67502i) q^{3} +(4.43430 - 7.68044i) q^{4} -7.61183 q^{5} +(20.9353 - 4.14318i) q^{6} +(4.76690 - 17.8963i) q^{7} -3.56749i q^{8} +(21.3886 + 16.4781i) q^{9} +(-27.0744 + 15.6314i) q^{10} +7.17024i q^{11} +(34.6762 - 30.3508i) q^{12} +(-59.6417 + 34.4342i) q^{13} +(-19.7959 - 73.4442i) q^{14} +(-37.4408 - 12.7500i) q^{15} +(28.1483 + 48.7543i) q^{16} +(11.4334 + 19.8032i) q^{17} +(109.916 + 14.6877i) q^{18} +(-86.1218 - 49.7224i) q^{19} +(-33.7532 + 58.4622i) q^{20} +(53.4239 - 80.0430i) q^{21} +(14.7246 + 25.5037i) q^{22} -122.450i q^{23} +(5.97563 - 17.5477i) q^{24} -67.0601 q^{25} +(-141.426 + 244.957i) q^{26} +(77.6045 + 116.878i) q^{27} +(-116.313 - 115.969i) q^{28} +(143.427 + 82.8076i) q^{29} +(-159.356 + 31.5372i) q^{30} +(-11.9405 - 6.89384i) q^{31} +(224.957 + 129.879i) q^{32} +(-12.0103 + 35.2688i) q^{33} +(81.3346 + 46.9585i) q^{34} +(-36.2848 + 136.223i) q^{35} +(221.403 - 91.2050i) q^{36} +(126.544 - 219.181i) q^{37} -408.434 q^{38} +(-351.042 + 69.4726i) q^{39} +27.1552i q^{40} +(159.598 + 276.433i) q^{41} +(25.6490 - 394.414i) q^{42} +(156.693 - 271.399i) q^{43} +(55.0706 + 31.7950i) q^{44} +(-162.806 - 125.428i) q^{45} +(-251.459 - 435.540i) q^{46} +(-35.3934 - 61.3031i) q^{47} +(56.7906 + 286.960i) q^{48} +(-297.553 - 170.620i) q^{49} +(-238.525 + 137.713i) q^{50} +(23.0674 + 116.559i) q^{51} +610.766i q^{52} +(254.574 - 146.979i) q^{53} +(516.048 + 256.357i) q^{54} -54.5786i q^{55} +(-63.8449 - 17.0059i) q^{56} +(-340.327 - 388.829i) q^{57} +680.205 q^{58} +(230.615 - 399.437i) q^{59} +(-263.949 + 231.025i) q^{60} +(573.665 - 331.205i) q^{61} -56.6280 q^{62} +(396.854 - 304.227i) q^{63} +616.491 q^{64} +(453.983 - 262.107i) q^{65} +(29.7076 + 150.111i) q^{66} +(-359.139 + 622.047i) q^{67} +202.797 q^{68} +(205.106 - 602.302i) q^{69} +(150.683 + 559.045i) q^{70} +92.9435i q^{71} +(58.7855 - 76.3037i) q^{72} +(-882.012 + 509.230i) q^{73} -1039.47i q^{74} +(-329.853 - 112.327i) q^{75} +(-763.780 + 440.969i) q^{76} +(128.321 + 34.1798i) q^{77} +(-1105.95 + 967.996i) q^{78} +(-398.113 - 689.551i) q^{79} +(-214.260 - 371.110i) q^{80} +(185.945 + 704.887i) q^{81} +(1135.35 + 655.493i) q^{82} +(10.7079 - 18.5466i) q^{83} +(-377.868 - 765.254i) q^{84} +(-87.0290 - 150.739i) q^{85} -1287.12i q^{86} +(566.780 + 647.555i) q^{87} +25.5798 q^{88} +(-339.721 + 588.414i) q^{89} +(-836.660 - 111.800i) q^{90} +(331.937 + 1231.51i) q^{91} +(-940.467 - 542.979i) q^{92} +(-47.1852 - 53.9098i) q^{93} +(-251.780 - 145.366i) q^{94} +(655.544 + 378.479i) q^{95} +(888.963 + 1015.65i) q^{96} +(-984.068 - 568.152i) q^{97} +(-1408.74 + 4.17218i) q^{98} +(-118.152 + 153.361i) 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 $

$2$	3.55689	−	2.05357i	1.25755	−	0.726047i	0.284952	−	0.958542i	$-0.408022\pi$
$2$	3.55689	−	2.05357i	1.25755	−	0.726047i	0.972598	+	0.232495i	$0.0746889\pi$
$3$	4.91877	+	1.67502i	0.946618	+	0.322358i
$3$	4.91877	+	1.67502i	0.946618	+	0.322358i
$4$	4.43430	−	7.68044i	0.554288	−	0.960055i
$5$	−7.61183			−0.680823			−0.340411	−	0.940277i	$-0.610566\pi$
$5$	−7.61183			−0.680823			−0.340411	+	0.940277i	$0.610566\pi$
$6$	20.9353	−	4.14318i	1.42447	−	0.281908i
$7$	4.76690	−	17.8963i	0.257388	−	0.966308i
$7$	4.76690	−	17.8963i	0.257388	−	0.966308i
$8$		−	3.56749i		−	0.157662i
$9$	21.3886	+	16.4781i	0.792171	+	0.610300i
$10$	−27.0744	+	15.6314i	−0.856168	+	0.494309i
$11$			7.17024i			0.196537i	0.995160	+	0.0982686i	$0.0313304\pi$
$11$			7.17024i			0.196537i	−0.995160	+	0.0982686i	$0.968670\pi$
$12$	34.6762	−	30.3508i	0.834180	−	0.730126i
$13$	−59.6417	+	34.4342i	−1.27243	+	0.734640i	−0.975445	−	0.220241i	$-0.929316\pi$
$13$	−59.6417	+	34.4342i	−1.27243	+	0.734640i	−0.296988	+	0.954881i	$0.595982\pi$
$14$	−19.7959	−	73.4442i	−0.377906	−	1.40206i
$15$	−37.4408	−	12.7500i	−0.644479	−	0.219469i
$16$	28.1483	+	48.7543i	0.439818	+	0.761787i
$17$	11.4334	+	19.8032i	0.163118	+	0.282529i	0.935985	−	0.352039i	$-0.114512\pi$
$17$	11.4334	+	19.8032i	0.163118	+	0.282529i	−0.772867	+	0.634568i	$0.781178\pi$
$18$	109.916	+	14.6877i	1.43930	+	0.192329i
$19$	−86.1218	−	49.7224i	−1.03988	−	0.600374i	−0.120079	−	0.992764i	$-0.538315\pi$
$19$	−86.1218	−	49.7224i	−1.03988	−	0.600374i	−0.919799	+	0.392390i	$0.871648\pi$
$20$	−33.7532	+	58.4622i	−0.377372	+	0.653627i
$21$	53.4239	−	80.0430i	0.555146	−	0.831753i
$22$	14.7246	+	25.5037i	0.142695	+	0.247155i
$23$		−	122.450i		−	1.11011i	−0.831814	−	0.555055i	$-0.812697\pi$
$23$		−	122.450i		−	1.11011i	0.831814	−	0.555055i	$-0.187303\pi$
$24$	5.97563	−	17.5477i	0.0508238	−	0.149246i
$25$	−67.0601			−0.536481
$26$	−141.426	+	244.957i	−1.06677	+	1.84769i
$27$	77.6045	+	116.878i	0.553148	+	0.833083i
$28$	−116.313	−	115.969i	−0.785042	−	0.782720i
$29$	143.427	+	82.8076i	0.918404	+	0.530241i	0.883126	−	0.469136i	$-0.155435\pi$
$29$	143.427	+	82.8076i	0.918404	+	0.530241i	0.0352788	+	0.999378i	$0.488768\pi$
$30$	−159.356	+	31.5372i	−0.969809	+	0.191929i
$31$	−11.9405	−	6.89384i	−0.0691798	−	0.0399410i	0.465011	−	0.885305i	$-0.346050\pi$
$31$	−11.9405	−	6.89384i	−0.0691798	−	0.0399410i	−0.534191	+	0.845364i	$0.679384\pi$
$32$	224.957	+	129.879i	1.24273	+	0.717488i
$33$	−12.0103	+	35.2688i	−0.0633553	+	0.186046i
$34$	81.3346	+	46.9585i	0.410258	+	0.236862i
$35$	−36.2848	+	136.223i	−0.175236	+	0.657884i
$36$	221.403	−	91.2050i	1.02501	−	0.422246i
$37$	126.544	−	219.181i	0.562263	−	0.973868i	−0.435035	−	0.900413i	$-0.643264\pi$
$37$	126.544	−	219.181i	0.562263	−	0.973868i	0.997299	−	0.0734549i	$-0.0234025\pi$
$38$	−408.434			−1.74360
$39$	−351.042	+	69.4726i	−1.44133	+	0.285244i
$40$			27.1552i			0.107340i
$41$	159.598	+	276.433i	0.607929	+	1.05296i	0.991581	+	0.129486i	$0.0413328\pi$
$41$	159.598	+	276.433i	0.607929	+	1.05296i	−0.383652	+	0.923478i	$0.625334\pi$
$42$	25.6490	−	394.414i	0.0942316	−	1.44903i
$43$	156.693	−	271.399i	0.555707	−	0.962512i	−0.442141	−	0.896945i	$-0.645781\pi$
$43$	156.693	−	271.399i	0.555707	−	0.962512i	0.997848	−	0.0655670i	$-0.0208856\pi$
$44$	55.0706	+	31.7950i	0.188686	+	0.108938i
$45$	−162.806	−	125.428i	−0.539328	−	0.415506i
$46$	−251.459	−	435.540i	−0.805992	−	1.39602i
$47$	−35.3934	−	61.3031i	−0.109844	−	0.190255i	0.805863	−	0.592102i	$-0.201702\pi$
$47$	−35.3934	−	61.3031i	−0.109844	−	0.190255i	−0.915707	+	0.401847i	$0.868368\pi$
$48$	56.7906	+	286.960i	0.170771	+	0.862899i
$49$	−297.553	−	170.620i	−0.867502	−	0.497433i
$50$	−238.525	+	137.713i	−0.674651	+	0.389510i
$51$	23.0674	+	116.559i	0.0633350	+	0.320029i
$52$			610.766i			1.62881i
$53$	254.574	−	146.979i	0.659783	−	0.380926i	−0.132412	−	0.991195i	$-0.542272\pi$
$53$	254.574	−	146.979i	0.659783	−	0.380926i	0.792194	+	0.610269i	$0.208939\pi$
$54$	516.048	+	256.357i	1.30047	+	0.646032i
$55$		−	54.5786i		−	0.133807i
$56$	−63.8449	−	17.0059i	−0.152351	−	0.0405805i
$57$	−340.327	−	388.829i	−0.790832	−	0.903538i
$58$	680.205			1.53992
$59$	230.615	−	399.437i	0.508873	−	0.881394i	−0.491074	−	0.871118i	$-0.663396\pi$
$59$	230.615	−	399.437i	0.508873	−	0.881394i	0.999947	−	0.0102763i	$-0.00327112\pi$
$60$	−263.949	+	231.025i	−0.567929	+	0.497086i
$61$	573.665	−	331.205i	1.20410	−	0.695189i	0.242637	−	0.970117i	$-0.421987\pi$
$61$	573.665	−	331.205i	1.20410	−	0.695189i	0.961465	+	0.274928i	$0.0886541\pi$
$62$	−56.6280			−0.115996
$63$	396.854	−	304.227i	0.793633	−	0.608397i
$64$	616.491			1.20408
$65$	453.983	−	262.107i	0.866302	−	0.500159i
$66$	29.7076	+	150.111i	0.0554053	+	0.279961i
$67$	−359.139	+	622.047i	−0.654863	+	1.13426i	0.327065	+	0.945002i	$0.393940\pi$
$67$	−359.139	+	622.047i	−0.654863	+	1.13426i	−0.981928	+	0.189254i	$0.939393\pi$
$68$	202.797			0.361657
$69$	205.106	−	602.302i	0.357853	−	1.05085i
$70$	150.683	+	559.045i	0.257287	+	0.954552i
$71$			92.9435i			0.155357i	0.996978	+	0.0776787i	$0.0247508\pi$
$71$			92.9435i			0.155357i	−0.996978	+	0.0776787i	$0.975249\pi$
$72$	58.7855	−	76.3037i	0.0962214	−	0.124896i
$73$	−882.012	+	509.230i	−1.41413	+	0.816450i	−0.995774	−	0.0918323i	$-0.970728\pi$
$73$	−882.012	+	509.230i	−1.41413	+	0.816450i	−0.418358	+	0.908282i	$0.637394\pi$
$74$		−	1039.47i		−	1.63292i
$75$	−329.853	−	112.327i	−0.507842	−	0.172939i
$76$	−763.780	+	440.969i	−1.15278	+	0.665560i
$77$	128.321	+	34.1798i	0.189915	+	0.0505864i
$78$	−1105.95	+	967.996i	−1.60544	+	1.40518i
$79$	−398.113	−	689.551i	−0.566977	−	0.982033i	−0.996863	−	0.0791495i	$-0.974780\pi$
$79$	−398.113	−	689.551i	−0.566977	−	0.982033i	0.429886	−	0.902883i	$-0.358554\pi$
$80$	−214.260	−	371.110i	−0.299438	−	0.518641i
$81$	185.945	+	704.887i	0.255069	+	0.966923i
$82$	1135.35	+	655.493i	1.52900	+	0.882770i
$83$	10.7079	−	18.5466i	0.0141608	−	0.0245272i	−0.858858	−	0.512213i	$-0.828826\pi$
$83$	10.7079	−	18.5466i	0.0141608	−	0.0245272i	0.873019	+	0.487686i	$0.162159\pi$
$84$	−377.868	−	765.254i	−0.490818	−	0.994001i
$85$	−87.0290	−	150.739i	−0.111054	−	0.192352i
$86$		−	1287.12i		−	1.61388i
$87$	566.780	+	647.555i	0.698451	+	0.797991i
$88$	25.5798			0.0309865
$89$	−339.721	+	588.414i	−0.404611	+	0.700806i	−0.994276	−	0.106841i	$-0.965926\pi$
$89$	−339.721	+	588.414i	−0.404611	+	0.700806i	0.589665	+	0.807648i	$0.299260\pi$
$90$	−836.660	−	111.800i	−0.979908	−	0.130942i
$91$	331.937	+	1231.51i	0.382379	+	1.41865i
$92$	−940.467	−	542.979i	−1.06577	−	0.615320i
$93$	−47.1852	−	53.9098i	−0.0526116	−	0.0601095i
$94$	−251.780	−	145.366i	−0.276268	−	0.159503i
$95$	655.544	+	378.479i	0.707973	+	0.408748i
$96$	888.963	+	1015.65i	0.945098	+	1.07979i
$97$	−984.068	−	568.152i	−1.03007	−	0.594713i	−0.113067	−	0.993587i	$-0.536067\pi$
$97$	−984.068	−	568.152i	−1.03007	−	0.594713i	−0.917005	+	0.398875i	$0.869401\pi$
$98$	−1408.74	+	4.17218i	−1.45209	+	0.00430054i
$99$	−118.152	+	153.361i	−0.119947	+	0.155691i
$100$	−297.365	+	515.051i	−0.297365	+	0.515051i
$101$	−1542.10			−1.51926			−0.759629	−	0.650357i	$-0.774619\pi$
$101$	−1542.10			−1.51926			−0.759629	+	0.650357i	$0.774619\pi$
$102$	321.410	+	367.216i	0.312003	+	0.356468i
$103$			418.265i			0.400125i	0.979783	+	0.200062i	$0.0641145\pi$
$103$			418.265i			0.400125i	−0.979783	+	0.200062i	$0.935885\pi$
$104$	122.844	+	212.772i	0.115825	+	0.200615i
$105$	−406.654	+	609.274i	−0.377956	+	0.566276i
$106$	603.662	−	1045.57i	0.553140	−	0.958066i
$107$	1368.79	+	790.270i	1.23669	+	0.714003i	0.968416	−	0.249340i	$-0.0802138\pi$
$107$	1368.79	+	790.270i	1.23669	+	0.714003i	0.268273	+	0.963343i	$0.413547\pi$
$108$	1241.80	−	77.7626i	1.10641	−	0.0692843i
$109$	234.533	+	406.222i	0.206093	+	0.356964i	0.950480	−	0.310784i	$-0.100592\pi$
$109$	234.533	+	406.222i	0.206093	+	0.356964i	−0.744387	+	0.667748i	$0.767258\pi$
$110$	−112.081	−	194.130i	−0.0971501	−	0.168269i
$111$	989.574	−	866.137i	0.846182	−	0.740631i
$112$	1006.70	−	271.343i	0.849324	−	0.228924i
$113$	−1733.74	+	1000.97i	−1.44333	+	0.833306i	−0.998070	−	0.0620958i	$-0.980222\pi$
$113$	−1733.74	+	1000.97i	−1.44333	+	0.833306i	−0.445259	+	0.895402i	$0.646888\pi$
$114$	−2008.99	−	684.136i	−1.65052	−	0.562063i
$115$			932.066i			0.755788i
$116$	1272.00	−	734.388i	1.01812	−	0.587813i
$117$	−1843.06	−	246.283i	−1.45634	−	0.194606i
$118$		−	1894.34i		−	1.47786i
$119$	408.906	−	110.215i	0.314994	−	0.0849026i
$120$	−45.4855	+	133.570i	−0.0346020	+	0.101610i
$121$	1279.59			0.961373
$122$	1360.31	−	2356.12i	1.00948	−	1.74847i
$123$	321.998	+	1627.04i	0.236045	+	1.19273i
$124$	−105.895	+	61.1388i	−0.0766911	+	0.0442776i
$125$	1461.93			1.04607
$126$	786.813	−	1897.07i	0.556309	−	1.34130i
$127$	522.832			0.365306			0.182653	−	0.983177i	$-0.441532\pi$
$127$	522.832			0.365306			0.182653	+	0.983177i	$0.441532\pi$
$128$	393.130	−	226.974i	0.271470	−	0.156733i
$129$	1225.33	−	1072.49i	0.836316	−	0.731995i
$130$	1076.51	−	1864.57i	0.726278	−	1.25795i
$131$	2561.88			1.70864			0.854321	−	0.519746i	$-0.173973\pi$
$131$	2561.88			1.70864			0.854321	+	0.519746i	$0.173973\pi$
$132$	217.622	+	248.637i	0.143497	+	0.163947i
$133$	−1300.38	+	1304.24i	−0.847799	+	0.850313i
$134$			2950.07i			1.90184i
$135$	−590.712	−	889.658i	−0.376596	−	0.567182i
$136$	70.6479	−	40.7886i	0.0445441	−	0.0257176i
$137$		−	1.22835i		−	0.000766021i	−1.00000		0.000383011i	$-0.999878\pi$
$137$		−	1.22835i		−	0.000766021i	1.00000		0.000383011i	$-0.000121916\pi$
$138$	−507.331	−	2563.52i	−0.312948	−	1.58131i
$139$	1676.23	−	967.770i	1.02285	−	0.590541i	0.107920	−	0.994160i	$-0.465581\pi$
$139$	1676.23	−	967.770i	1.02285	−	0.590541i	0.914927	+	0.403619i	$0.132248\pi$
$140$	885.357	+	882.739i	0.534474	+	0.532893i
$141$	−71.4078	−	360.821i	−0.0426498	−	0.215508i
$142$	190.866	+	330.590i	0.112797	+	0.195370i
$143$	−246.901	−	427.645i	−0.144384	−	0.250080i
$144$	−201.325	+	1506.62i	−0.116507	+	0.871885i
$145$	−1091.74	−	630.317i	−0.625271	−	0.361000i
$146$	−2091.48	+	3622.55i	−1.18556	+	2.05345i
$147$	−1177.81	−	1337.65i	−0.660842	−	0.750525i
$148$	−1122.27	−	1943.83i	−0.623311	−	1.07961i
$149$			2427.95i			1.33494i	0.744639	+	0.667468i	$0.232622\pi$
$149$			2427.95i			1.33494i	−0.744639	+	0.667468i	$0.767378\pi$
$150$	−1403.92	+	277.842i	−0.764199	+	0.151238i
$151$	−1396.38			−0.752552			−0.376276	−	0.926508i	$-0.622796\pi$
$151$	−1396.38			−0.752552			−0.376276	+	0.926508i	$0.622796\pi$
$152$	−177.384	+	307.239i	−0.0946565	+	0.163950i
$153$	−81.7749	+	611.964i	−0.0432099	+	0.323362i
$154$	526.613	−	141.942i	0.275556	−	0.0742726i
$155$	90.8889	+	52.4747i	0.0470992	+	0.0271927i
$156$	−1023.05	+	3004.22i	−0.525059	+	1.54186i
$157$	−635.157	−	366.708i	−0.322873	−	0.186411i	0.329799	−	0.944051i	$-0.393019\pi$
$157$	−635.157	−	366.708i	−0.322873	−	0.186411i	−0.652672	+	0.757640i	$0.726352\pi$
$158$	−2832.08	−	1635.10i	−1.42600	−	0.823304i
$159$	1498.38	−	296.536i	0.747356	−	0.147905i
$160$	−1712.34	−	988.618i	−0.846075	−	0.488482i
$161$	−2191.39	−	583.705i	−1.07271	−	0.285729i
$162$	2108.92	+	2125.35i	1.02279	+	1.03076i
$163$	−1504.67	+	2606.16i	−0.723036	+	1.25233i	0.236742	+	0.971573i	$0.423920\pi$
$163$	−1504.67	+	2606.16i	−0.723036	+	1.25233i	−0.959777	+	0.280762i	$0.909413\pi$
$164$	2830.83			1.34787
$165$	91.4204	−	268.460i	0.0431337	−	0.126664i
$166$		−	87.9577i		−	0.0411256i
$167$	40.1692	+	69.5751i	0.0186131	+	0.0322388i	0.875182	−	0.483794i	$-0.160742\pi$
$167$	40.1692	+	69.5751i	0.0186131	+	0.0322388i	−0.856569	+	0.516033i	$0.827408\pi$
$168$	−285.553	−	190.590i	−0.131136	−	0.0875256i
$169$	1272.92	−	2204.77i	0.579392	−	1.00354i
$170$	−619.105	−	357.440i	−0.279313	−	0.161261i
$171$	−1022.69	−	2482.62i	−0.457353	−	1.11024i
$172$	−1389.64	−	2406.94i	−0.616043	−	1.06702i
$173$	−1373.36	−	2378.73i	−0.603553	−	1.04538i	−0.992278	−	0.124031i	$-0.960418\pi$
$173$	−1373.36	−	2378.73i	−0.603553	−	1.04538i	0.388725	−	0.921354i	$-0.372916\pi$
$174$	3345.77	+	1139.36i	1.45772	+	0.496405i
$175$	−319.669	+	1200.13i	−0.138084	+	0.518406i
$176$	−349.580	+	201.830i	−0.149719	+	0.0864405i
$177$	1803.41	−	1578.45i	0.765833	−	0.670304i
$178$			2790.56i			1.17507i
$179$	−2491.90	+	1438.70i	−1.04052	+	0.600745i	−0.919981	−	0.391964i	$-0.871796\pi$
$179$	−2491.90	+	1438.70i	−1.04052	+	0.600745i	−0.120540	+	0.992708i	$0.538463\pi$
$180$	−1685.28	+	694.237i	−0.697851	+	0.287474i
$181$			320.544i			0.131634i	0.997832	+	0.0658172i	$0.0209654\pi$
$181$			320.544i			0.131634i	−0.997832	+	0.0658172i	$0.979035\pi$
$182$	3709.65	+	3698.68i	1.51087	+	1.50640i
$183$	3376.50	−	668.223i	1.36392	−	0.269926i
$184$	−436.839			−0.175023
$185$	−963.232	+	1668.37i	−0.382801	+	0.663031i
$186$	−278.540	−	94.8531i	−0.109804	−	0.0373923i
$187$	−141.994	+	81.9801i	−0.0555273	+	0.0320587i
$188$	−627.780			−0.243540
$189$	2461.62	−	831.684i	0.947389	−	0.320085i
$190$	3108.93			1.18708
$191$	818.447	−	472.531i	0.310056	−	0.179011i	−0.336895	−	0.941542i	$-0.609377\pi$
$191$	818.447	−	472.531i	0.310056	−	0.179011i	0.646952	+	0.762531i	$0.276044\pi$
$192$	3032.38	+	1032.63i	1.13981	+	0.388146i
$193$	−393.384	+	681.362i	−0.146717	+	0.254122i	−0.930012	−	0.367528i	$-0.880204\pi$
$193$	−393.384	+	681.362i	−0.146717	+	0.254122i	0.783295	+	0.621650i	$0.213537\pi$
$194$	−4666.96			−1.72716
$195$	2672.07	−	528.813i	0.981287	−	0.194201i
$196$	−2629.87	+	1528.76i	−0.958409	+	0.557129i
$197$		−	5047.70i		−	1.82555i	−0.408462	−	0.912775i	$-0.633935\pi$
$197$		−	5047.70i		−	1.82555i	0.408462	−	0.912775i	$-0.366065\pi$
$198$	−105.314	+	788.123i	−0.0377999	+	0.282876i
$199$	1052.30	−	607.546i	0.374852	−	0.216421i	−0.300724	−	0.953711i	$-0.597228\pi$
$199$	1052.30	−	607.546i	0.374852	−	0.216421i	0.675576	+	0.737290i	$0.263895\pi$
$200$			239.236i			0.0845829i
$201$	−2808.46	+	2458.14i	−0.985541	+	0.862606i
$202$	−5485.09	+	3166.82i	−1.91054	+	1.10305i
$203$	2165.65	−	2172.07i	0.748763	−	0.750984i
$204$	997.510	+	339.689i	0.342351	+	0.116583i
$205$	−1214.84	−	2104.16i	−0.413892	−	0.716882i
$206$	858.937	+	1487.72i	0.290509	+	0.503177i
$207$	2017.74	−	2619.03i	0.677500	−	0.879396i
$208$	−3357.63	−	1938.53i	−1.11928	−	0.646215i
$209$	356.522	−	617.514i	0.117996	−	0.204375i
$210$	−195.236	+	3002.21i	−0.0641550	+	0.986534i
$211$	312.466	+	541.206i	0.101948	+	0.176579i	0.912487	−	0.409105i	$-0.134159\pi$
$211$	312.466	+	541.206i	0.101948	+	0.176579i	−0.810539	+	0.585684i	$0.800826\pi$
$212$		−	2606.99i		−	0.844570i
$213$	−155.682	+	457.168i	−0.0500807	+	0.147064i
$214$	6491.50			2.07360
$215$	−1192.72	+	2065.85i	−0.378338	+	0.655300i
$216$	416.963	−	276.854i	0.131346	−	0.0872107i
$217$	−180.293	+	180.828i	−0.0564014	+	0.0565687i
$218$	1668.41	+	963.259i	0.518345	+	0.299267i
$219$	−5191.38	+	1027.40i	−1.60183	+	0.317009i
$220$	−419.188	−	242.018i	−0.128462	−	0.0741676i
$221$	−1363.81	−	787.399i	−0.415113	−	0.239666i
$222$	1741.13	−	5112.91i	0.526384	−	1.54575i
$223$	2295.49	+	1325.30i	0.689316	+	0.397977i	0.803356	−	0.595499i	$-0.203046\pi$
$223$	2295.49	+	1325.30i	0.689316	+	0.397977i	−0.114040	+	0.993476i	$0.536379\pi$
$224$	3396.70	−	3406.78i	1.01318	−	1.01618i
$225$	−1434.32	−	1105.02i	−0.424984	−	0.327414i
$226$	−4111.14	+	7120.70i	−1.21004	+	2.09585i
$227$	817.772			0.239108			0.119554	−	0.992828i	$-0.461854\pi$
$227$	817.772			0.239108			0.119554	+	0.992828i	$0.461854\pi$
$228$	−4495.49	+	889.676i	−1.30579	+	0.258422i
$229$			702.979i			0.202857i	0.994843	+	0.101428i	$0.0323412\pi$
$229$			702.979i			0.202857i	−0.994843	+	0.101428i	$0.967659\pi$
$230$	1914.06	+	3315.25i	0.548737	+	0.950441i
$231$	573.928	+	383.062i	0.163470	+	0.109107i
$232$	295.416	−	511.675i	0.0835991	−	0.144798i
$233$	−3559.17	−	2054.89i	−1.00073	−	0.577769i	−0.0922626	−	0.995735i	$-0.529410\pi$
$233$	−3559.17	−	2054.89i	−1.00073	−	0.577769i	−0.908463	+	0.417966i	$0.862743\pi$
$234$	−7061.33	+	2908.86i	−1.97271	+	0.812641i
$235$	269.408	+	466.629i	0.0747841	+	0.129530i
$236$	−2045.23	−	3542.45i	−0.564125	−	0.977092i
$237$	−803.211	−	4058.59i	−0.220144	−	1.11238i
$238$	1228.10	−	1231.74i	0.334478	−	0.335470i
$239$	−2082.70	+	1202.45i	−0.563677	+	0.325439i	−0.754620	−	0.656162i	$-0.772179\pi$
$239$	−2082.70	+	1202.45i	−0.563677	+	0.325439i	0.190943	+	0.981601i	$0.438845\pi$
$240$	−432.280	−	2184.29i	−0.116265	−	0.587481i
$241$			726.363i			0.194146i	0.995277	+	0.0970729i	$0.0309480\pi$
$241$			726.363i			0.194146i	−0.995277	+	0.0970729i	$0.969052\pi$
$242$	4551.35	−	2627.72i	1.20897	−	0.698002i
$243$	−266.080	+	3778.64i	−0.0702430	+	0.997530i
$244$		−	5874.66i		−	1.54134i
$245$	2264.92	+	1298.73i	0.590615	+	0.338664i
$246$	4486.55	+	5125.95i	1.16281	+	1.32853i
$247$	6848.60			1.76423
$248$	−24.5937	+	42.5976i	−0.00629720	+	0.0109071i
$249$	83.7357	−	73.2906i	0.0213114	−	0.0186530i
$250$	5199.92	−	3002.17i	1.31549	−	0.759496i
$251$	−529.985			−0.133276			−0.0666382	−	0.997777i	$-0.521227\pi$
$251$	−529.985			−0.133276			−0.0666382	+	0.997777i	$0.521227\pi$
$252$	−576.826	−	4397.05i	−0.144193	−	1.09916i
$253$	877.994			0.218178
$254$	1859.66	−	1073.67i	0.459390	−	0.265229i
$255$	−175.585	−	887.224i	−0.0431199	−	0.217883i
$256$	−1533.75	+	2656.53i	−0.374450	+	0.648567i
$257$	1948.86			0.473021			0.236511	−	0.971629i	$-0.423996\pi$
$257$	1948.86			0.473021			0.236511	+	0.971629i	$0.423996\pi$
$258$	2155.95	−	6331.03i	0.520246	−	1.52772i
$259$	−3319.30	−	3309.48i	−0.796337	−	0.793982i
$260$		−	4649.05i		−	1.10893i
$261$	1703.19	+	4134.54i	0.403927	+	0.980543i
$262$	9112.31	−	5260.99i	2.14870	−	1.24055i
$263$		−	506.885i		−	0.118844i	−0.998233	−	0.0594218i	$-0.981074\pi$
$263$		−	506.885i		−	0.118844i	0.998233	−	0.0594218i	$-0.0189257\pi$
$264$	125.821	+	42.8467i	0.0293324	+	0.00998876i
$265$	−1937.78	+	1118.78i	−0.449195	+	0.259343i
$266$	−1946.96	+	7309.45i	−0.448782	+	1.68485i
$267$	−2656.62	+	2325.23i	−0.608922	+	0.532966i
$268$	3185.06	+	5516.69i	0.725965	+	1.25741i
$269$	3851.69	+	6671.33i	0.873018	+	1.51211i	0.858859	+	0.512213i	$0.171174\pi$
$269$	3851.69	+	6671.33i	0.873018	+	1.51211i	0.0141598	+	0.999900i	$0.495493\pi$
$270$	−3928.07	−	1951.34i	−0.885388	−	0.439833i
$271$	−4585.66	−	2647.53i	−1.02789	−	0.593455i	−0.111513	−	0.993763i	$-0.535570\pi$
$271$	−4585.66	−	2647.53i	−1.02789	−	0.593455i	−0.916380	+	0.400308i	$0.868903\pi$
$272$	−643.662	+	1114.85i	−0.143484	+	0.248522i
$273$	−430.081	+	6613.51i	−0.0953469	+	1.46618i
$274$	−2.52250	−	4.36910i	−0.000556167	−	0.000963310i
$275$		−	480.837i		−	0.105438i
$276$	−3716.44	−	4246.09i	−0.810520	−	0.926032i
$277$	4216.97			0.914705			0.457353	−	0.889285i	$-0.348798\pi$
$277$	4216.97			0.914705			0.457353	+	0.889285i	$0.348798\pi$
$278$	3974.77	−	6884.50i	0.857521	−	1.48527i
$279$	−141.793	−	344.206i	−0.0304263	−	0.0738605i
$280$	485.976	+	129.446i	0.103724	+	0.0276281i
$281$	−7104.37	−	4101.71i	−1.50823	−	0.870774i	−0.999954	−	0.00957745i	$-0.996951\pi$
$281$	−7104.37	−	4101.71i	−1.50823	−	0.870774i	−0.508271	−	0.861197i	$-0.669715\pi$
$282$	−994.960	−	1136.76i	−0.210103	−	0.240046i
$283$	1358.81	+	784.511i	0.285417	+	0.164786i	0.635873	−	0.771794i	$-0.280640\pi$
$283$	1358.81	+	784.511i	0.285417	+	0.164786i	−0.350456	+	0.936579i	$0.613973\pi$
$284$	713.847	+	412.140i	0.149152	+	0.0861127i
$285$	2590.51	+	2959.70i	0.538416	+	0.615149i
$286$	−1756.40	−	1014.06i	−0.363140	−	0.209659i
$287$	5707.90	−	1538.49i	1.17396	−	0.316426i
$288$	2671.36	+	6484.80i	0.546568	+	1.32681i
$289$	2195.06	−	3801.95i	0.446785	−	0.773854i
$290$	−5177.61			−1.04841
$291$	−3888.74	−	4442.95i	−0.783374	−	0.895018i
$292$			9032.32i			1.81019i
$293$	227.022	+	393.213i	0.0452653	+	0.0784019i	0.887770	−	0.460287i	$-0.152253\pi$
$293$	227.022	+	393.213i	0.0452653	+	0.0784019i	−0.842505	+	0.538688i	$0.818920\pi$
$294$	−6936.27	−	2339.15i	−1.37596	−	0.464021i
$295$	−1755.40	+	3040.45i	−0.346452	+	0.600073i
$296$	−781.927	−	451.446i	−0.153542	−	0.0886478i
$297$	−838.046	+	556.443i	−0.163732	+	0.108714i
$298$	4985.97	+	8635.94i	0.969226	+	1.67875i
$299$	4216.45	+	7303.11i	0.815531	+	1.41254i
$300$	−2325.39	+	2035.32i	−0.447522	+	0.391698i
$301$	−4110.10	−	4097.95i	−0.787051	−	0.784723i
$302$	−4966.75	+	2867.56i	−0.946372	+	0.546388i
$303$	−7585.25	−	2583.06i	−1.43816	−	0.489745i
$304$		−	5598.41i		−	1.05622i
$305$	−4366.64	+	2521.08i	−0.819780	+	0.473300i
$306$	965.846	+	2344.62i	0.180437	+	0.438016i
$307$		−	74.2025i		−	0.0137947i	−0.999976	−	0.00689733i	$-0.997804\pi$
$307$		−	74.2025i		−	0.0137947i	0.999976	−	0.00689733i	$-0.00219550\pi$
$308$	831.528	−	833.995i	0.153834	−	0.154290i
$309$	−700.603	+	2057.35i	−0.128983	+	0.378765i
$310$	431.042			0.0789728
$311$	3212.96	−	5565.00i	0.585820	−	1.01467i	−0.408953	−	0.912556i	$-0.634106\pi$
$311$	3212.96	−	5565.00i	0.585820	−	1.01467i	0.994773	−	0.102114i	$-0.0325608\pi$
$312$	247.843	+	1252.34i	0.0449723	+	0.227243i
$313$	6681.09	−	3857.33i	1.20651	−	0.696578i	0.244514	−	0.969646i	$-0.421372\pi$
$313$	6681.09	−	3857.33i	1.20651	−	0.696578i	0.961995	+	0.273067i	$0.0880382\pi$
$314$	−3012.24			−0.541372
$315$	−3020.78	+	2315.72i	−0.540323	+	0.414210i
$316$	−7061.41			−1.25707
$317$	−265.053	+	153.028i	−0.0469617	+	0.0271133i	−0.523297	−	0.852150i	$-0.675298\pi$
$317$	−265.053	+	153.028i	−0.0469617	+	0.0271133i	0.476335	+	0.879264i	$0.341965\pi$
$318$	4720.63	−	4131.79i	0.832452	−	0.728613i
$319$	−593.751	+	1028.41i	−0.104212	+	0.180501i
$320$	−4692.62			−0.819767
$321$	5409.03	+	6179.90i	0.940507	+	1.07454i
$322$	−8993.22	+	2424.01i	−1.55644	+	0.419517i
$323$		−	2273.98i		−	0.391727i
$324$	6238.38	+	1697.54i	1.06968	+	0.291074i
$325$	3999.58	−	2309.16i	0.682636	−	0.394120i
$326$			12359.8i			2.09983i
$327$	473.181	+	2390.96i	0.0800213	+	0.404344i
$328$	986.172	−	569.367i	0.166013	−	0.0958476i
$329$	−1265.81	+	341.184i	−0.212117	+	0.0571734i
$330$	−226.129	−	1142.62i	−0.0377212	−	0.190603i
$331$	2049.56	+	3549.94i	0.340344	+	0.589493i	0.984497	−	0.175404i	$-0.0561231\pi$
$331$	2049.56	+	3549.94i	0.340344	+	0.589493i	−0.644152	+	0.764897i	$0.722790\pi$
$332$	−94.9642	−	164.483i	−0.0156983	−	0.0271903i
$333$	6318.29	−	2602.77i	1.03976	−	0.428321i
$334$	285.755	+	164.981i	0.0468138	+	0.0270280i
$335$	2733.70	−	4734.91i	0.445845	−	0.772227i
$336$	5406.24	+	351.571i	0.877781	+	0.0570827i
$337$	−3390.68	−	5872.83i	−0.548078	−	0.949298i	−0.998406	−	0.0564355i	$-0.982026\pi$
$337$	−3390.68	−	5872.83i	−0.548078	−	0.949298i	0.450329	−	0.892863i	$-0.351307\pi$
$338$		−	10456.2i		−	1.68266i
$339$	−10204.5	+	2019.51i	−1.63490	+	0.323554i
$340$	−1543.65			−0.246224
$341$	49.4305	−	85.6161i	0.00784989	−	0.0135964i
$342$	−8735.83	−	6730.21i	−1.38123	−	1.06412i
$343$	−4471.86	+	4511.77i	−0.703959	+	0.710241i
$344$	−968.216	−	559.000i	−0.151752	−	0.0876141i
$345$	−1561.23	+	4584.62i	−0.243634	+	0.715442i
$346$	−9769.78	−	5640.59i	−1.51800	−	0.876416i
$347$	−8450.67	−	4878.99i	−1.30736	−	0.754807i	−0.325709	−	0.945470i	$-0.605603\pi$
$347$	−8450.67	−	4878.99i	−1.30736	−	0.754807i	−0.981656	+	0.190663i	$0.938936\pi$
$348$	7486.78	−	1481.66i	1.15326	−	0.228234i
$349$	−2576.08	−	1487.30i	−0.395113	−	0.228119i	0.289260	−	0.957251i	$-0.406591\pi$
$349$	−2576.08	−	1487.30i	−0.395113	−	0.228119i	−0.684373	+	0.729132i	$0.739924\pi$
$350$	1327.52	+	4925.18i	0.202739	+	0.752176i
$351$	−8653.07	−	4298.58i	−1.31586	−	0.653679i
$352$	−931.265	+	1613.00i	−0.141013	+	0.244242i
$353$	9788.58			1.47590			0.737951	−	0.674854i	$-0.235793\pi$
$353$	9788.58			1.47590			0.737951	+	0.674854i	$0.235793\pi$
$354$	3173.05	−	9317.81i	0.476401	−	1.39897i
$355$		−	707.470i		−	0.105771i
$356$	3012.85	+	5218.41i	0.448542	+	0.776897i
$357$	2195.93	+	142.803i	0.325548	+	0.0211706i
$358$	−5908.94	+	10234.6i	−0.872338	+	1.51093i
$359$	−3444.96	−	1988.95i	−0.506456	−	0.292403i	0.224919	−	0.974377i	$-0.427788\pi$
$359$	−3444.96	−	1988.95i	−0.506456	−	0.292403i	−0.731376	+	0.681975i	$0.761121\pi$
$360$	−447.465	+	580.811i	−0.0655097	+	0.0850317i
$361$	1515.14	+	2624.30i	0.220898	+	0.382606i
$362$	658.259	+	1140.14i	0.0955727	+	0.165537i
$363$	6294.00	+	2143.34i	0.910053	+	0.309906i
$364$	10930.4	+	2911.46i	1.57393	+	0.419236i
$365$	6713.72	−	3876.17i	0.962773	−	0.555858i
$366$	10637.6	−	9310.68i	1.51922	−	1.32972i
$367$			3534.28i			0.502692i	0.967897	+	0.251346i	$0.0808732\pi$
$367$			3534.28i			0.502692i	−0.967897	+	0.251346i	$0.919127\pi$
$368$	5969.95	−	3446.75i	0.845667	−	0.488246i
$369$	−1141.49	+	8542.39i	−0.161040	+	1.20515i
$370$			7912.26i			1.11173i
$371$	−1416.84	−	5256.56i	−0.198271	−	0.735599i
$372$	−623.284	+	123.350i	−0.0868704	+	0.0171920i
$373$	4725.85			0.656019			0.328010	−	0.944674i	$-0.393622\pi$
$373$	4725.85			0.656019			0.328010	+	0.944674i	$0.393622\pi$
$374$	−336.704	+	583.189i	−0.0465523	+	0.0806309i
$375$	7190.89	+	2448.76i	0.990229	+	0.337209i
$376$	−218.698	+	126.266i	−0.0299960	+	0.0173182i
$377$	−11405.6			−1.55815
$378$	7047.78	−	8013.32i	0.958992	−	1.09037i
$379$	5183.61			0.702545			0.351272	−	0.936273i	$-0.385749\pi$
$379$	5183.61			0.702545			0.351272	+	0.936273i	$0.385749\pi$
$380$	5813.76	−	3356.58i	0.784841	−	0.453128i
$381$	2571.69	+	875.755i	0.345805	+	0.117759i
$382$	1940.75	−	3361.48i	0.259941	−	0.450231i
$383$	6894.41			0.919811			0.459906	−	0.887968i	$-0.347883\pi$
$383$	6894.41			0.919811			0.459906	+	0.887968i	$0.347883\pi$
$384$	2313.90	−	457.931i	0.307502	−	0.0608559i
$385$	−976.754	−	260.171i	−0.129299	−	0.0344404i
$386$			3231.37i			0.426094i
$387$	7823.58	−	3222.86i	1.02764	−	0.423326i
$388$	−8727.32	+	5038.72i	−1.14191	+	0.659284i
$389$		−	2814.17i		−	0.366797i	−0.983039	−	0.183398i	$-0.941290\pi$
$389$		−	2814.17i		−	0.366797i	0.983039	−	0.183398i	$-0.0587098\pi$
$390$	8418.30	−	7368.22i	1.09302	−	0.956677i
$391$	2424.90	−	1400.02i	0.313638	−	0.181079i
$392$	−608.684	+	1061.52i	−0.0784265	+	0.136773i
$393$	12601.3	+	4291.20i	1.61743	+	0.550795i
$394$	−10365.8	−	17954.1i	−1.32544	−	2.29572i
$395$	3030.36	+	5248.75i	0.386011	+	0.668590i
$396$	653.962	+	1587.51i	0.0829869	+	0.201453i
$397$	−5248.35	−	3030.14i	−0.663494	−	0.383068i	0.130113	−	0.991499i	$-0.458466\pi$
$397$	−5248.35	−	3030.14i	−0.663494	−	0.383068i	−0.793607	+	0.608431i	$0.791799\pi$
$398$	2495.28	−	4321.95i	0.314264	−	0.544320i
$399$	−8580.90	+	4237.08i	−1.07665	+	0.531627i
$400$	−1887.63	−	3269.47i	−0.235954	−	0.408684i
$401$			12064.2i			1.50239i	0.660080	+	0.751196i	$0.270523\pi$
$401$			12064.2i			1.50239i	−0.660080	+	0.751196i	$0.729477\pi$
$402$	−4941.43	+	14510.7i	−0.613075	+	1.80032i
$403$	949.535			0.117369
$404$	−6838.15	+	11844.0i	−0.842106	+	1.45857i
$405$	−1415.38	−	5365.48i	−0.173656	−	0.658303i
$406$	3242.47	−	12173.1i	0.396357	−	1.48804i
$407$	1571.58	+	907.352i	0.191401	+	0.110506i
$408$	415.822	−	82.2929i	0.0504566	−	0.00998555i
$409$	292.292	+	168.755i	0.0353372	+	0.0204019i	0.517565	−	0.855644i	$-0.326839\pi$
$409$	292.292	+	168.755i	0.0353372	+	0.0204019i	−0.482227	+	0.876046i	$0.660172\pi$
$410$	−8642.07	−	4989.50i	−1.04098	−	0.601010i
$411$	2.05751	−	6.04196i	0.000246933	−	0.000725129i
$412$	3212.46	+	1854.71i	0.384142	+	0.221784i
$413$	−6049.11	−	6031.23i	−0.720720	−	0.718589i
$414$	1798.51	−	13459.2i	0.213507	−	1.59778i
$415$	−81.5067	+	141.174i	−0.00964098	+	0.0166987i
$416$	−17889.1			−2.10838
$417$	9866.01	−	1952.52i	1.15861	−	0.229294i
$418$		−	2928.57i		−	0.342682i
$419$	4094.25	+	7091.45i	0.477368	+	0.826826i	0.999664	−	0.0259386i	$-0.00825744\pi$
$419$	4094.25	+	7091.45i	0.477368	+	0.826826i	−0.522295	+	0.852765i	$0.674924\pi$
$420$	2876.26	+	5824.98i	0.334160	+	0.676738i
$421$	958.165	−	1659.59i	0.110922	−	0.192122i	−0.805220	−	0.592976i	$-0.797953\pi$
$421$	958.165	−	1659.59i	0.110922	−	0.192122i	0.916142	+	0.400853i	$0.131286\pi$
$422$	2222.81	+	1283.34i	0.256409	+	0.148038i
$423$	253.143	−	1894.40i	0.0290975	−	0.217752i
$424$	−524.345	−	908.193i	−0.0600577	−	0.104023i
$425$	−766.724	−	1328.01i	−0.0875096	−	0.151571i
$426$	385.082	+	1945.80i	0.0437964	+	0.221301i
$427$	−3192.74	−	11845.3i	−0.361844	−	1.34247i
$428$	12139.2	−	7008.59i	1.37096	−	0.791526i
$429$	−498.135	−	2517.05i	−0.0560610	−	0.283274i
$430$			9797.31i			1.09876i
$431$	−8604.78	+	4967.97i	−0.961665	+	0.555218i	−0.896685	−	0.442669i	$-0.854032\pi$
$431$	−8604.78	+	4967.97i	−0.961665	+	0.555218i	−0.0649800	+	0.997887i	$0.520698\pi$
$432$	−3513.89	+	7073.48i	−0.391347	+	0.787785i
$433$		−	4551.00i		−	0.505098i	−0.967584	−	0.252549i	$-0.918731\pi$
$433$		−	4551.00i		−	0.505098i	0.967584	−	0.252549i	$-0.0812688\pi$
$434$	−269.940	+	1013.43i	−0.0298561	+	0.112088i
$435$	−4314.23	−	4929.08i	−0.475521	−	0.543290i
$436$	4159.96			0.456940
$437$	−6088.49	+	10545.6i	−0.666481	+	1.15438i
$438$	−16355.3	+	14315.2i	−1.78422	+	1.56166i
$439$	−6424.18	+	3709.00i	−0.698427	+	0.403237i	−0.806761	−	0.590878i	$-0.798782\pi$
$439$	−6424.18	+	3709.00i	−0.698427	+	0.403237i	0.108335	+	0.994114i	$0.465448\pi$
$440$	−194.709			−0.0210963
$441$	−3552.77	−	8552.42i	−0.383627	−	0.923488i
$442$	−6467.91			−0.696035
$443$	−5479.67	+	3163.69i	−0.587691	+	0.339303i	−0.764184	−	0.644999i	$-0.776858\pi$
$443$	−5479.67	+	3163.69i	−0.587691	+	0.339303i	0.176493	+	0.984302i	$0.443525\pi$
$444$	−2264.24	−	11441.1i	−0.242018	−	1.22290i
$445$	2585.90	−	4478.91i	0.275468	−	0.477125i
$446$	10886.4			1.15580
$447$	−4066.87	+	11942.5i	−0.430327	+	1.26367i
$448$	2938.75	−	11032.9i	0.309917	−	1.16352i
$449$			14396.4i			1.51316i	0.653904	+	0.756578i	$0.273130\pi$
$449$			14396.4i			1.51316i	−0.653904	+	0.756578i	$0.726870\pi$
$450$	−7370.96	−	984.960i	−0.772157	−	0.103181i
$451$	−1982.09	+	1144.36i	−0.206946	+	0.119481i
$452$			17754.5i			1.84757i
$453$	−6868.45	−	2338.96i	−0.712380	−	0.242591i
$454$	2908.72	−	1679.35i	0.300690	−	0.173603i
$455$	−2526.65	−	9374.03i	−0.260332	−	0.965849i
$456$	−1387.15	+	1214.11i	−0.142454	+	0.124685i
$457$	−2573.61	−	4457.63i	−0.263432	−	0.456278i	0.703719	−	0.710478i	$-0.251521\pi$
$457$	−2573.61	−	4457.63i	−0.263432	−	0.456278i	−0.967152	+	0.254200i	$0.918188\pi$
$458$	1443.62	+	2500.42i	0.147283	+	0.255102i
$459$	−1427.28	+	2873.13i	−0.145141	+	0.292171i
$460$	7158.68	+	4133.06i	0.725598	+	0.418924i
$461$	446.618	−	773.565i	0.0451217	−	0.0781530i	−0.842583	−	0.538567i	$-0.818966\pi$
$461$	446.618	−	773.565i	0.0451217	−	0.0781530i	0.887704	+	0.460414i	$0.152299\pi$
$462$	2828.04	+	183.909i	0.284789	+	0.0185200i
$463$	5520.47	+	9561.73i	0.554121	+	0.959765i	0.997971	+	0.0636644i	$0.0202787\pi$
$463$	5520.47	+	9561.73i	0.554121	+	0.959765i	−0.443851	+	0.896101i	$0.646388\pi$
$464$			9323.59i			0.932838i
$465$	359.165	+	410.352i	0.0358191	+	0.0409239i
$466$	−16879.4			−1.67795
$467$	4900.18	−	8487.36i	0.485553	−	0.841003i	−0.514309	−	0.857605i	$-0.671952\pi$
$467$	4900.18	−	8487.36i	0.485553	−	0.841003i	0.999862	+	0.0166023i	$0.00528493\pi$
$468$	−10064.3	+	13063.4i	−0.994061	+	1.29029i
$469$	9420.34	+	9392.49i	0.927486	+	0.924744i
$470$	1916.51	+	1106.50i	0.188089	+	0.108593i
$471$	−2509.95	−	2867.66i	−0.245546	−	0.280541i
$472$	−1424.99	−	822.718i	−0.138963	−	0.0802302i
$473$	1946.00	+	1123.52i	0.189169	+	0.109217i
$474$	−11191.5	−	12786.5i	−1.08448	−	1.23904i
$475$	5775.33	+	3334.39i	0.557875	+	0.322089i
$476$	966.711	−	3629.30i	0.0930864	−	0.349472i
$477$	7866.92	+	1051.23i	0.755139	+	0.100907i
$478$	−4938.63	+	8553.95i	−0.472568	+	0.818512i
$479$	138.670			0.0132275			0.00661377	−	0.999978i	$-0.497895\pi$
$479$	138.670			0.0132275			0.00661377	+	0.999978i	$0.497895\pi$
$480$	−6766.63	−	7730.98i	−0.643444	−	0.735145i
$481$			17429.8i			1.65224i
$482$	1491.64	+	2583.59i	0.140959	+	0.244148i
$483$	−9801.24	−	6541.74i	−0.923337	−	0.616273i
$484$	5674.08	−	9827.80i	0.532878	−	0.922971i
$485$	7490.56	+	4324.68i	0.701296	+	0.404894i
$486$	6813.28	+	13986.6i	0.635919	+	1.30544i
$487$	−9148.40	−	15845.5i	−0.851239	−	1.47439i	−0.880091	−	0.474806i	$-0.842518\pi$
$487$	−9148.40	−	15845.5i	−0.851239	−	1.47439i	0.0288514	−	0.999584i	$-0.490815\pi$
$488$	−1181.57	−	2046.55i	−0.109605	−	0.189842i
$489$	−11766.5	+	10298.8i	−1.08814	+	0.952406i
$490$	10723.1	−	31.7579i	0.988614	−	0.00292791i
$491$	5097.03	−	2942.77i	0.468484	−	0.270479i	−0.247121	−	0.968985i	$-0.579484\pi$
$491$	5097.03	−	2942.77i	0.468484	−	0.270479i	0.715605	+	0.698505i	$0.246151\pi$
$492$	13924.2	+	4741.70i	1.27592	+	0.434497i
$493$			3787.09i			0.345967i
$494$	24359.7	−	14064.1i	2.21861	−	1.28092i
$495$	899.352	−	1167.36i	0.0816623	−	0.105998i
$496$		−	776.201i		−	0.0702670i
$497$	1663.34	+	443.053i	0.150123	+	0.0399872i
$498$	147.331	−	432.644i	0.0132572	−	0.0389302i
$499$	534.725			0.0479711			0.0239856	−	0.999712i	$-0.492364\pi$
$499$	534.725			0.0479711			0.0239856	+	0.999712i	$0.492364\pi$
$500$	6482.63	−	11228.3i	0.579824	−	1.00429i
$501$	81.0433	+	409.508i	0.00722704	+	0.0365179i
$502$	−1885.10	+	1088.36i	−0.167602	+	0.0967649i
$503$	−10504.5			−0.931155			−0.465578	−	0.885007i	$-0.654153\pi$
$503$	−10504.5			−0.931155			−0.465578	+	0.885007i	$0.654153\pi$
$504$	−1085.33	−	1415.77i	−0.0959213	−	0.125126i
$505$	11738.2			1.03434
$506$	3122.93	−	1803.02i	0.274369	−	0.158407i
$507$	9954.25	−	8712.57i	0.871960	−	0.763193i
$508$	2318.40	−	4015.58i	0.202485	−	0.350714i
$509$	2817.87			0.245383			0.122691	−	0.992445i	$-0.460847\pi$
$509$	2817.87			0.245383			0.122691	+	0.992445i	$0.460847\pi$
$510$	−2446.51	−	2795.18i	−0.212419	−	0.242692i
$511$	4908.85	+	18212.2i	0.424961	+	1.57663i
$512$			16230.2i			1.40094i
$513$	−871.962	−	13924.5i	−0.0750449	−	1.19840i
$514$	6931.87	−	4002.12i	0.594848	−	0.343435i
$515$		−	3183.76i		−	0.272414i
$516$	−2803.68	−	14166.8i	−0.239196	−	1.20864i
$517$	439.558	−	253.779i	0.0373921	−	0.0215884i
$518$	−18602.6	−	4955.05i	−1.57790	−	0.420294i
$519$	−2770.82	−	14000.8i	−0.234346	−	1.18414i
$520$	−935.065	−	1619.58i	−0.0788564	−	0.136583i
$521$	−5520.76	−	9562.24i	−0.464240	−	0.804087i	0.534927	−	0.844898i	$-0.320339\pi$
$521$	−5520.76	−	9562.24i	−0.464240	−	0.804087i	−0.999167	+	0.0408113i	$0.987006\pi$
$522$	14548.6	+	11208.5i	1.21988	+	0.939812i
$523$	−4094.57	−	2364.00i	−0.342338	−	0.197649i	0.318967	−	0.947766i	$-0.396664\pi$
$523$	−4094.57	−	2364.00i	−0.342338	−	0.197649i	−0.661306	+	0.750117i	$0.729997\pi$
$524$	11360.1	−	19676.3i	0.947080	−	1.64039i
$525$	−3582.61	+	5367.69i	−0.297825	+	0.446219i
$526$	−1040.92	−	1802.93i	−0.0862860	−	0.149452i
$527$		−	315.280i		−	0.0260604i
$528$	−2057.58	+	407.202i	−0.169592	+	0.0335629i
$529$	−2826.93			−0.232344
$530$	−4594.97	+	7958.72i	−0.376590	+	0.652273i
$531$	11514.5	−	4743.30i	0.941029	−	0.387649i
$532$	4250.83	+	15770.9i	0.346423	+	1.28525i
$533$	−19037.5	−	10991.3i	−1.54710	−	0.893218i
$534$	−4674.25	+	13726.1i	−0.378792	+	1.11234i
$535$	−10419.0	−	6015.40i	−0.841966	−	0.486109i
$536$	2219.15	+	1281.23i	0.178830	+	0.103247i
$537$	−14666.9	+	2902.64i	−1.17863	+	0.233256i
$538$	27400.1	+	15819.5i	2.19573	+	1.26770i
$539$	1223.38	−	2133.53i	0.0977641	−	0.170496i
$540$	−9452.36	+	591.915i	−0.753268	+	0.0471703i
$541$	11254.7	−	19493.8i	0.894415	−	1.54917i	0.0598879	−	0.998205i	$-0.480926\pi$
$541$	11254.7	−	19493.8i	0.894415	−	1.54917i	0.834527	−	0.550967i	$-0.185741\pi$
$542$	−21747.6			−1.72350
$543$	−536.917	+	1576.68i	−0.0424334	+	0.124607i
$544$			5939.84i			0.468140i
$545$	−1785.22	−	3092.10i	−0.140313	−	0.243029i
$546$	12051.6	+	24406.7i	0.944614	+	1.91302i
$547$	−1219.31	+	2111.91i	−0.0953088	+	0.165080i	−0.909737	−	0.415184i	$-0.863717\pi$
$547$	−1219.31	+	2111.91i	−0.0953088	+	0.165080i	0.814429	+	0.580264i	$0.197051\pi$
$548$	−9.43426	−	5.44687i	−0.000735422	−	0.000424596i
$549$	17727.5	+	2368.88i	1.37813	+	0.184155i
$550$	−987.432	−	1710.28i	−0.0765532	−	0.132594i
$551$	−8234.79	−	14263.1i	−0.636686	−	1.10277i
$552$	−2148.71	−	731.714i	−0.165680	−	0.0564200i
$553$	−14238.2	+	3837.71i	−1.09488	+	0.295110i
$554$	14999.3	−	8659.85i	1.15029	−	0.664119i
$555$	−7532.47	+	6592.88i	−0.576100	+	0.504238i
$556$		−	17165.5i		−	1.30932i
$557$	9826.37	−	5673.25i	0.747498	−	0.431568i	−0.0772911	−	0.997009i	$-0.524627\pi$
$557$	9826.37	−	5673.25i	0.747498	−	0.431568i	0.824789	+	0.565440i	$0.191294\pi$
$558$	−1211.19	−	933.121i	−0.0918887	−	0.0707924i
$559$			21582.3i			1.63298i
$560$	−7662.84	+	2065.42i	−0.578239	+	0.155857i
$561$	−835.753	+	165.399i	−0.0628976	+	0.0124477i
$562$	−33692.6			−2.52889
$563$	8427.86	−	14597.5i	0.630891	−	1.09274i	−0.356478	−	0.934304i	$-0.616023\pi$
$563$	8427.86	−	14597.5i	0.630891	−	1.09274i	0.987370	−	0.158432i	$-0.0506440\pi$
$564$	−3087.90	−	1051.54i	−0.230539	−	0.0785071i
$565$	13196.9	−	7619.23i	0.982651	−	0.567334i
$566$	6444.19			0.478568
$567$	13501.2	+	32.4028i	0.999997	+	0.00239999i
$568$	331.576			0.0244940
$569$	−10320.6	+	5958.57i	−0.760387	+	0.439009i	−0.829435	−	0.558604i	$-0.811337\pi$
$569$	−10320.6	+	5958.57i	−0.760387	+	0.439009i	0.0690479	+	0.997613i	$0.478004\pi$
$570$	15292.1	+	5207.52i	1.12371	+	0.382665i
$571$	−10204.7	+	17675.0i	−0.747902	+	1.29540i	0.200924	+	0.979607i	$0.435606\pi$
$571$	−10204.7	+	17675.0i	−0.747902	+	1.29540i	−0.948826	+	0.315798i	$0.897728\pi$
$572$	−4379.34			−0.320121
$573$	4817.25	−	953.353i	0.351210	−	0.0695059i
$574$	17143.0	−	17193.8i	1.24657	−	1.25027i
$575$			8211.49i			0.595552i
$576$	13185.9	+	10158.6i	0.953839	+	0.734852i
$577$	−3374.84	+	1948.46i	−0.243495	+	0.140582i	−0.616782	−	0.787134i	$-0.711564\pi$
$577$	−3374.84	+	1948.46i	−0.243495	+	0.140582i	0.373287	+	0.927716i	$0.378231\pi$
$578$		−	18030.8i		−	1.29755i
$579$	−3076.26	+	2692.53i	−0.220803	+	0.193261i
$580$	−9682.23	+	5590.04i	−0.693160	+	0.400196i
$581$	−280.872	−	280.041i	−0.0200560	−	0.0199967i
$582$	−22955.7	−	7817.26i	−1.63496	−	0.556763i
$583$	1053.87	+	1825.36i	0.0748660	+	0.129672i
$584$	1816.67	+	3146.57i	0.128724	+	0.222956i
$585$	14029.1	+	1874.66i	0.991506	+	0.132492i
$586$	1614.98	+	932.410i	0.113847	+	0.0657295i
$587$	8643.77	−	14971.5i	0.607780	−	1.05271i	−0.383826	−	0.923406i	$-0.625394\pi$
$587$	8643.77	−	14971.5i	0.607780	−	1.05271i	0.991606	−	0.129300i	$-0.0412730\pi$
$588$	−15496.5	+	3114.53i	−1.08684	+	0.218437i
$589$	685.557	+	1187.42i	0.0479591	+	0.0830675i
$590$			14419.4i			1.00616i
$591$	8455.00	−	24828.5i	0.588481	−	1.72810i
$592$	14248.0			0.989173
$593$	985.742	−	1707.36i	0.0682623	−	0.118234i	−0.829874	−	0.557951i	$-0.811588\pi$
$593$	985.742	−	1707.36i	0.0682623	−	0.118234i	0.898136	+	0.439717i	$0.144921\pi$
$594$	−1838.14	+	3700.19i	−0.126969	+	0.255590i
$595$	−3112.52	+	838.939i	−0.214455	+	0.0578036i
$596$	18647.7	+	10766.3i	1.28161	+	0.739939i
$597$	6193.68	−	1225.75i	0.424607	−	0.0840314i
$598$	29994.9	+	17317.6i	2.05114	+	1.18423i
$599$	12120.3	+	6997.65i	0.826747	+	0.477323i	0.852738	−	0.522339i	$-0.174941\pi$
$599$	12120.3	+	6997.65i	0.826747	+	0.477323i	−0.0259904	+	0.999662i	$0.508274\pi$
$600$	−400.726	+	1176.75i	−0.0272660	+	0.0800676i
$601$	−17296.5	−	9986.12i	−1.17394	−	0.677774i	−0.219335	−	0.975650i	$-0.570389\pi$
$601$	−17296.5	−	9986.12i	−1.17394	−	0.677774i	−0.954605	+	0.297875i	$0.903722\pi$
$602$	−23034.6	−	6135.56i	−1.55950	−	0.415393i
$603$	−17931.6	+	7386.79i	−1.21100	+	0.498861i
$604$	−6191.95	+	10724.8i	−0.417131	+	0.722492i
$605$	−9740.00			−0.654525
$606$	−32284.4	+	6389.21i	−2.16413	+	0.428290i
$607$		−	12997.8i		−	0.869136i	−0.900639	−	0.434568i	$-0.856901\pi$
$607$		−	12997.8i		−	0.869136i	0.900639	−	0.434568i	$-0.143099\pi$
$608$	−12915.8	−	22370.8i	−0.861522	−	1.49220i
$609$	14290.6	−	7056.42i	0.950878	−	0.469525i
$610$	−10354.4	+	17934.4i	−0.687276	+	1.19040i
$611$	4221.84	+	2437.48i	0.279538	+	0.161391i
$612$	4337.53	+	3341.70i	0.286494	+	0.220719i
$613$	−3450.80	−	5976.96i	−0.227368	−	0.393812i	0.729659	−	0.683811i	$-0.239679\pi$
$613$	−3450.80	−	5976.96i	−0.227368	−	0.393812i	−0.957027	+	0.289998i	$0.906345\pi$
$614$	−152.380	−	263.930i	−0.0100156	−	0.0173475i
$615$	−2450.99	−	12384.7i	−0.160705	−	0.812034i
$616$	121.936	−	457.783i	0.00797557	−	0.0299425i
$617$	−8207.48	+	4738.59i	−0.535528	+	0.309187i	−0.743265	−	0.668998i	$-0.766724\pi$
$617$	−8207.48	+	4738.59i	−0.535528	+	0.309187i	0.207737	+	0.978185i	$0.433390\pi$
$618$	1732.95	+	8756.50i	0.112798	+	0.569964i
$619$			15581.4i			1.01174i	0.862609	+	0.505871i	$0.168829\pi$
$619$			15581.4i			1.01174i	−0.862609	+	0.505871i	$0.831171\pi$
$620$	806.058	−	465.378i	0.0522130	−	0.0301452i
$621$	14311.7	−	9502.65i	0.924814	−	0.614055i
$622$		−	26392.1i		−	1.70133i
$623$	8911.00	+	8884.65i	0.573053	+	0.571358i
$624$	−13268.3	−	15159.3i	−0.851215	−	0.972527i
$625$	−2745.44			−0.175708
$626$	15842.6	−	27440.2i	1.01150	−	1.75196i
$627$	2788.00	−	2440.23i	0.177579	−	0.155428i
$628$	−5632.96	+	3252.19i	−0.357929	+	0.206651i
$629$	5787.32			0.366861
$630$	−5989.09	+	14440.2i	−0.378748	+	0.913190i
$631$	7028.73			0.443438			0.221719	−	0.975111i	$-0.428833\pi$
$631$	7028.73			0.443438			0.221719	+	0.975111i	$0.428833\pi$
$632$	−2459.97	+	1420.26i	−0.154830	+	0.0893910i
$633$	630.415	+	3185.46i	0.0395841	+	0.200017i
$634$	−628.509	+	1088.61i	−0.0393711	+	0.0681928i
$635$	−3979.71			−0.248709
$636$	4366.76	−	12823.2i	0.272254	−	0.799485i
$637$	23621.7	−	69.9588i	1.46927	−	0.00435144i
$638$			4877.23i			0.302651i
$639$	−1531.53	+	1987.93i	−0.0948145	+	0.123069i
$640$	−2992.44	+	1727.69i	−0.184823	+	0.106707i
$641$			19240.0i			1.18555i	0.805369	+	0.592773i	$0.201967\pi$
$641$			19240.0i			1.18555i	−0.805369	+	0.592773i	$0.798033\pi$
$642$	31930.2	+	10873.4i	1.96290	+	0.668441i
$643$	2402.55	−	1387.11i	0.147352	−	0.0850737i	−0.424511	−	0.905423i	$-0.639554\pi$
$643$	2402.55	−	1387.11i	0.147352	−	0.0850737i	0.571863	+	0.820349i	$0.306221\pi$
$644$	−14200.4	+	14242.5i	−0.868905	+	0.871482i
$645$	−9327.04	+	8163.60i	−0.569383	+	0.498359i
$646$	−4669.79	−	8088.31i	−0.284412	−	0.492616i
$647$	4830.91	+	8367.38i	0.293544	+	0.508432i	0.974645	−	0.223757i	$-0.0718321\pi$
$647$	4830.91	+	8367.38i	0.293544	+	0.508432i	−0.681101	+	0.732189i	$0.738499\pi$
$648$	2514.68	−	663.358i	0.152447	−	0.0402147i
$649$	2864.06	+	1653.56i	0.173227	+	0.100012i
$650$	9484.04	−	16426.8i	0.572299	−	0.991251i
$651$	−1189.71	+	587.456i	−0.0716259	+	0.0353675i
$652$	13344.3	+	23113.0i	0.801540	+	1.38831i
$653$			11885.8i			0.712294i	0.934430	+	0.356147i	$0.115910\pi$
$653$			11885.8i			0.712294i	−0.934430	+	0.356147i	$0.884090\pi$
$654$	6593.06	+	7532.68i	0.394203	+	0.450384i
$655$	−19500.6			−1.16328
$656$	−8984.86	+	15562.2i	−0.534756	+	0.926224i
$657$	−27256.1	−	3642.16i	−1.61851	−	0.216277i
$658$	−3801.71	+	3812.99i	−0.225237	+	0.225906i
$659$	20497.2	+	11834.1i	1.21162	+	0.699529i	0.963112	−	0.269100i	$-0.0867263\pi$
$659$	20497.2	+	11834.1i	1.21162	+	0.699529i	0.248508	+	0.968630i	$0.420060\pi$
$660$	−1656.50	−	1892.58i	−0.0976959	−	0.111619i
$661$	−8316.03	−	4801.26i	−0.489344	−	0.282523i	0.234959	−	0.972005i	$-0.424505\pi$
$661$	−8316.03	−	4801.26i	−0.489344	−	0.282523i	−0.724302	+	0.689483i	$0.757838\pi$
$662$	14580.1	+	8417.83i	0.856000	+	0.494212i
$663$	−5389.38	−	6157.45i	−0.315696	−	0.360687i
$664$	−66.1650	−	38.2004i	−0.00386702	−	0.00223262i
$665$	9898.27	−	9927.63i	0.577201	−	0.578913i
$666$	17128.5	−	22232.8i	0.996569	−	1.29355i
$667$	10139.8	−	17562.6i	0.588626	−	1.01953i
$668$	712.490			0.0412681
$669$	9071.09	+	10363.9i	0.524228	+	0.598939i
$670$		−	22455.4i		−	1.29482i
$671$	2374.82	+	4113.31i	0.136630	+	0.236651i
$672$	22414.0	−	11067.6i	1.28667	−	0.635330i
$673$	−3469.40	+	6009.18i	−0.198716	+	0.344186i	−0.948112	−	0.317936i	$-0.897010\pi$
$673$	−3469.40	+	6009.18i	−0.198716	+	0.344186i	0.749397	+	0.662121i	$0.230344\pi$
$674$	−24120.6	−	13926.0i	−1.37847	−	0.795860i
$675$	−5204.16	−	7837.87i	−0.296753	−	0.446933i
$676$	−11289.1	−	19553.2i	−0.642300	−	1.11250i
$677$	4176.49	+	7233.90i	0.237098	+	0.410667i	0.959880	−	0.280410i	$-0.0904703\pi$
$677$	4176.49	+	7233.90i	0.237098	+	0.410667i	−0.722782	+	0.691076i	$0.757137\pi$
$678$	−32149.1	+	28138.8i	−1.82106	+	1.59390i
$679$	−14858.8	+	14902.8i	−0.839804	+	0.842295i
$680$	−537.759	+	310.476i	−0.0303267	+	0.0175091i
$681$	4022.43	+	1369.79i	0.226344	+	0.0770783i
$682$		−	406.036i		−	0.0227975i
$683$	8631.82	−	4983.58i	0.483583	−	0.279197i	−0.238325	−	0.971185i	$-0.576598\pi$
$683$	8631.82	−	4983.58i	0.483583	−	0.279197i	0.721908	+	0.691989i	$0.243265\pi$
$684$	−23602.5	−	3153.93i	−1.31939	−	0.176307i
$685$			9.34998i			0.000521524i
$686$	−6640.67	+	25231.1i	−0.369595	+	1.40427i
$687$	−1177.50	+	3457.79i	−0.0653924	+	0.192028i
$688$	17642.5			0.977639
$689$	−10122.2	+	17532.1i	−0.559686	+	0.969405i
$690$	3861.71	+	19513.1i	0.213062	+	1.07659i
$691$	4151.78	−	2397.03i	0.228569	−	0.131964i	−0.381343	−	0.924434i	$-0.624538\pi$
$691$	4151.78	−	2397.03i	0.228569	−	0.131964i	0.609912	+	0.792469i	$0.291205\pi$
$692$	−24359.6			−1.33817
$693$	2181.38	+	2845.54i	0.119573	+	0.155978i
$694$	−40077.4			−2.19210
$695$	−12759.2	+	7366.50i	−0.696377	+	0.402054i
$696$	2310.15	−	2021.98i	0.125813	−	0.110119i
$697$	−3649.50	+	6321.12i	−0.198328	+	0.343515i
$698$	−12217.1			−0.662499
$699$	−14064.8	−	16069.2i	−0.761056	−	0.869518i
$700$	7799.98	+	7776.92i	0.421160	+	0.419914i
$701$		−	13815.7i		−	0.744382i	−0.928156	−	0.372191i	$-0.878607\pi$
$701$		−	13815.7i		−	0.744382i	0.928156	−	0.372191i	$-0.121393\pi$
$702$	−39605.5	+	2480.13i	−2.12936	+	0.133343i
$703$	−21796.4	+	12584.2i	−1.16937	+	0.675136i
$704$			4420.39i			0.236647i
$705$	543.544	+	2746.50i	0.0290370	+	0.146722i
$706$	34816.9	−	20101.5i	1.85602	−	1.07157i
$707$	−7351.05	+	27597.9i	−0.391039	+	1.46807i
$708$	−4126.36	−	20850.3i	−0.219037	−	1.10678i
$709$	−67.3023	−	116.571i	−0.00356501	−	0.00617477i	0.864237	−	0.503084i	$-0.167801\pi$
$709$	−67.3023	−	116.571i	−0.00356501	−	0.00617477i	−0.867802	+	0.496909i	$0.834468\pi$
$710$	−1452.84	−	2516.39i	−0.0767945	−	0.133012i
$711$	2847.42	−	21308.7i	0.150192	−	1.12396i
$712$	2099.16	+	1211.95i	0.110491	+	0.0637919i
$713$	−844.149	+	1462.11i	−0.0443389	+	0.0767972i
$714$	8103.92	−	4001.56i	0.424764	−	0.209740i
$715$	1879.37	+	3255.16i	0.0982999	+	0.170260i
$716$			25518.5i			1.33194i
$717$	−12258.5	+	2426.00i	−0.638494	+	0.126361i
$718$	−16337.8			−0.849192
$719$	−279.689	+	484.435i	−0.0145071	+	0.0251271i	−0.873188	−	0.487384i	$-0.837951\pi$
$719$	−279.689	+	484.435i	−0.0145071	+	0.0251271i	0.858681	+	0.512511i	$0.171285\pi$
$720$	1532.45	−	11468.1i	0.0793209	−	0.593599i
$721$	7485.38	+	1993.83i	0.386644	+	0.102988i
$722$	10778.4	+	6222.89i	0.555580	+	0.320764i
$723$	−1216.67	+	3572.81i	−0.0625844	+	0.183782i
$724$	2461.92	+	1421.39i	0.126376	+	0.0729633i
$725$	−9618.23	−	5553.09i	−0.492706	−	0.284464i
$726$	26788.5	−	5301.56i	1.36944	−	0.271018i
$727$	−6529.04	−	3769.54i	−0.333079	−	0.192303i	0.324128	−	0.946013i	$-0.394929\pi$
$727$	−6529.04	−	3769.54i	−0.333079	−	0.192303i	−0.657207	+	0.753710i	$0.728262\pi$
$728$	4393.40	−	1184.18i	0.223668	−	0.0602868i
$729$	−7638.09	+	18140.6i	−0.388055	+	0.921636i
$730$	15920.0	−	27574.2i	0.807157	−	1.39804i
$731$	7166.11			0.362583
$732$	9840.19	−	28896.1i	0.496863	−	1.45906i
$733$		−	34171.1i		−	1.72188i	−0.508708	−	0.860939i	$-0.669877\pi$
$733$		−	34171.1i		−	1.72188i	0.508708	−	0.860939i	$-0.330123\pi$
$734$	7257.90	+	12571.0i	0.364978	+	0.632161i
$735$	8965.25	+	10181.9i	0.449916	+	0.510975i
$736$	15903.7	−	27545.9i	0.796490	−	1.37956i
$737$	−4460.23	−	2575.11i	−0.222923	−	0.128705i
$738$	13482.2	+	32728.4i	0.672476	+	1.63245i
$739$	−5524.56	−	9568.82i	−0.274999	−	0.476312i	0.695136	−	0.718878i	$-0.255344\pi$
$739$	−5524.56	−	9568.82i	−0.274999	−	0.476312i	−0.970135	+	0.242566i	$0.922011\pi$
$740$	8542.53	+	14796.1i	0.424364	+	0.735021i
$741$	33686.7	+	11471.6i	1.67006	+	0.568715i
$742$	−15834.3	−	15787.4i	−0.783415	−	0.781098i
$743$	−5588.14	+	3226.32i	−0.275921	+	0.159303i	−0.631575	−	0.775315i	$-0.717591\pi$
$743$	−5588.14	+	3226.32i	−0.275921	+	0.159303i	0.355655	+	0.934617i	$0.384258\pi$
$744$	−192.323	+	168.333i	−0.00947702	+	0.00829487i
$745$		−	18481.1i		−	0.908854i
$746$	16809.3	−	9704.87i	0.824977	−	0.476301i
$747$	534.640	−	220.241i	0.0261867	−	0.0107874i
$748$			1454.10i			0.0710791i
$749$	20667.8	−	20729.1i	1.00826	−	1.01125i
$750$	30605.9	−	6057.03i	1.49009	−	0.294895i
$751$	−1687.78			−0.0820081			−0.0410041	−	0.999159i	$-0.513056\pi$
$751$	−1687.78			−0.0820081			−0.0410041	+	0.999159i	$0.513056\pi$
$752$	1992.53	−	3451.16i	0.0966224	−	0.167355i
$753$	−2606.88	−	887.737i	−0.126162	−	0.0429627i
$754$	−40568.6	+	23422.3i	−1.95945	+	1.13129i
$755$	10629.0			0.512355
$756$	4527.87	−	22594.3i	0.217827	−	1.08696i
$757$	10839.9			0.520453			0.260226	−	0.965548i	$-0.416203\pi$
$757$	10839.9			0.520453			0.260226	+	0.965548i	$0.416203\pi$
$758$	18437.5	−	10644.9i	0.883485	−	0.510080i
$759$	4318.65	+	1470.66i	0.206531	+	0.0703314i
$760$	1350.22	−	2338.65i	0.0644443	−	0.111621i
$761$	9058.83			0.431514			0.215757	−	0.976447i	$-0.430778\pi$
$761$	9058.83			0.431514			0.215757	+	0.976447i	$0.430778\pi$
$762$	10945.6	−	2166.19i	0.520366	−	0.102982i
$763$	8387.86	−	2260.84i	0.397983	−	0.107271i
$764$		−	8381.38i		−	0.396895i
$765$	622.456	−	4658.16i	0.0294182	−	0.220152i
$766$	24522.6	−	14158.2i	1.15671	−	0.667826i
$767$			31764.1i			1.49535i
$768$	−11993.9	+	10497.8i	−0.563532	+	0.493238i
$769$	10991.2	−	6345.79i	0.515415	−	0.297575i	−0.219642	−	0.975581i	$-0.570489\pi$
$769$	10991.2	−	6345.79i	0.515415	−	0.297575i	0.735057	+	0.678006i	$0.237156\pi$
$770$	−4008.48	+	1080.43i	−0.187605	+	0.0505665i
$771$	9585.98	+	3264.38i	0.447770	+	0.152482i
$772$	3488.77	+	6042.73i	0.162647	+	0.281713i
$773$	10423.9	+	18054.8i	0.485023	+	0.840085i	0.999852	−	0.0172084i<

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)

\(f(q)\)	\(=\)	\(q+(3.55689 - 2.05357i) q^{2} +(4.91877 + 1.67502i) q^{3} +(4.43430 - 7.68044i) q^{4} -7.61183 q^{5} +(20.9353 - 4.14318i) q^{6} +(4.76690 - 17.8963i) q^{7} -3.56749i q^{8} +(21.3886 + 16.4781i) q^{9} +O(q^{10})\)	\(q+(3.55689 - 2.05357i) q^{2} +(4.91877 + 1.67502i) q^{3} +(4.43430 - 7.68044i) q^{4} -7.61183 q^{5} +(20.9353 - 4.14318i) q^{6} +(4.76690 - 17.8963i) q^{7} -3.56749i q^{8} +(21.3886 + 16.4781i) q^{9} +(-27.0744 + 15.6314i) q^{10} +7.17024i q^{11} +(34.6762 - 30.3508i) q^{12} +(-59.6417 + 34.4342i) q^{13} +(-19.7959 - 73.4442i) q^{14} +(-37.4408 - 12.7500i) q^{15} +(28.1483 + 48.7543i) q^{16} +(11.4334 + 19.8032i) q^{17} +(109.916 + 14.6877i) q^{18} +(-86.1218 - 49.7224i) q^{19} +(-33.7532 + 58.4622i) q^{20} +(53.4239 - 80.0430i) q^{21} +(14.7246 + 25.5037i) q^{22} -122.450i q^{23} +(5.97563 - 17.5477i) q^{24} -67.0601 q^{25} +(-141.426 + 244.957i) q^{26} +(77.6045 + 116.878i) q^{27} +(-116.313 - 115.969i) q^{28} +(143.427 + 82.8076i) q^{29} +(-159.356 + 31.5372i) q^{30} +(-11.9405 - 6.89384i) q^{31} +(224.957 + 129.879i) q^{32} +(-12.0103 + 35.2688i) q^{33} +(81.3346 + 46.9585i) q^{34} +(-36.2848 + 136.223i) q^{35} +(221.403 - 91.2050i) q^{36} +(126.544 - 219.181i) q^{37} -408.434 q^{38} +(-351.042 + 69.4726i) q^{39} +27.1552i q^{40} +(159.598 + 276.433i) q^{41} +(25.6490 - 394.414i) q^{42} +(156.693 - 271.399i) q^{43} +(55.0706 + 31.7950i) q^{44} +(-162.806 - 125.428i) q^{45} +(-251.459 - 435.540i) q^{46} +(-35.3934 - 61.3031i) q^{47} +(56.7906 + 286.960i) q^{48} +(-297.553 - 170.620i) q^{49} +(-238.525 + 137.713i) q^{50} +(23.0674 + 116.559i) q^{51} +610.766i q^{52} +(254.574 - 146.979i) q^{53} +(516.048 + 256.357i) q^{54} -54.5786i q^{55} +(-63.8449 - 17.0059i) q^{56} +(-340.327 - 388.829i) q^{57} +680.205 q^{58} +(230.615 - 399.437i) q^{59} +(-263.949 + 231.025i) q^{60} +(573.665 - 331.205i) q^{61} -56.6280 q^{62} +(396.854 - 304.227i) q^{63} +616.491 q^{64} +(453.983 - 262.107i) q^{65} +(29.7076 + 150.111i) q^{66} +(-359.139 + 622.047i) q^{67} +202.797 q^{68} +(205.106 - 602.302i) q^{69} +(150.683 + 559.045i) q^{70} +92.9435i q^{71} +(58.7855 - 76.3037i) q^{72} +(-882.012 + 509.230i) q^{73} -1039.47i q^{74} +(-329.853 - 112.327i) q^{75} +(-763.780 + 440.969i) q^{76} +(128.321 + 34.1798i) q^{77} +(-1105.95 + 967.996i) q^{78} +(-398.113 - 689.551i) q^{79} +(-214.260 - 371.110i) q^{80} +(185.945 + 704.887i) q^{81} +(1135.35 + 655.493i) q^{82} +(10.7079 - 18.5466i) q^{83} +(-377.868 - 765.254i) q^{84} +(-87.0290 - 150.739i) q^{85} -1287.12i q^{86} +(566.780 + 647.555i) q^{87} +25.5798 q^{88} +(-339.721 + 588.414i) q^{89} +(-836.660 - 111.800i) q^{90} +(331.937 + 1231.51i) q^{91} +(-940.467 - 542.979i) q^{92} +(-47.1852 - 53.9098i) q^{93} +(-251.780 - 145.366i) q^{94} +(655.544 + 378.479i) q^{95} +(888.963 + 1015.65i) q^{96} +(-984.068 - 568.152i) q^{97} +(-1408.74 + 4.17218i) q^{98} +(-118.152 + 153.361i) 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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