LMFDB - Embedded newform 162.3.h.a.5.16

Newspace parameters

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.h (of order $54$, degree $18$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			5.16
Character	$\chi$	$=$	162.5
Dual form			162.3.h.a.65.16

$q$-expansion

$f(q)$	$=$	$q+(0.326140 + 1.37609i) q^{2} +(2.18959 + 2.05078i) q^{3} +(-1.78727 + 0.897598i) q^{4} +(-1.03753 + 0.772415i) q^{5} +(-2.10794 + 3.68193i) q^{6} +(-4.52918 + 2.97889i) q^{7} +(-1.81808 - 2.16670i) q^{8} +(0.588642 + 8.98073i) q^{9} +O(q^{10})$	\(q+(0.326140 + 1.37609i) q^{2} +(2.18959 + 2.05078i) q^{3} +(-1.78727 + 0.897598i) q^{4} +(-1.03753 + 0.772415i) q^{5} +(-2.10794 + 3.68193i) q^{6} +(-4.52918 + 2.97889i) q^{7} +(-1.81808 - 2.16670i) q^{8} +(0.588642 + 8.98073i) q^{9} +(-1.40130 - 1.17583i) q^{10} +(-0.852172 + 7.29080i) q^{11} +(-5.75416 - 1.69990i) q^{12} +(0.717336 + 2.39607i) q^{13} +(-5.57637 - 5.26104i) q^{14} +(-3.85583 - 0.436473i) q^{15} +(2.38863 - 3.20849i) q^{16} +(12.8216 + 2.26080i) q^{17} +(-12.1663 + 3.73900i) q^{18} +(-0.163680 - 0.928274i) q^{19} +(1.16103 - 2.31180i) q^{20} +(-16.0261 - 2.76577i) q^{21} +(-10.3107 + 1.20515i) q^{22} +(23.9389 - 36.3973i) q^{23} +(0.462564 - 8.47266i) q^{24} +(-6.69023 + 22.3469i) q^{25} +(-3.06326 + 1.76858i) q^{26} +(-17.1286 + 20.8713i) q^{27} +(5.42100 - 9.38944i) q^{28} +(10.5679 - 9.97029i) q^{29} +(-0.656913 - 5.44833i) q^{30} +(-0.520156 + 8.93074i) q^{31} +(5.19421 + 2.24057i) q^{32} +(-16.8177 + 14.2163i) q^{33} +(1.07058 + 18.3811i) q^{34} +(2.39824 - 6.58910i) q^{35} +(-9.11315 - 15.5226i) q^{36} +(18.2424 - 6.63969i) q^{37} +(1.22401 - 0.527986i) q^{38} +(-3.34313 + 6.71752i) q^{39} +(3.55991 + 0.843714i) q^{40} +(2.27520 - 9.59983i) q^{41} +(-1.42079 - 22.9554i) q^{42} +(2.47852 + 5.74586i) q^{43} +(-5.02115 - 13.7955i) q^{44} +(-7.54759 - 8.86313i) q^{45} +(57.8935 + 21.0715i) q^{46} +(64.0157 - 3.72849i) q^{47} +(11.8100 - 2.12674i) q^{48} +(-7.76823 + 18.0088i) q^{49} +(-32.9334 - 1.91815i) q^{50} +(23.4377 + 31.2445i) q^{51} +(-3.43278 - 3.63853i) q^{52} +(31.0537 + 17.9289i) q^{53} +(-34.3072 - 16.7635i) q^{54} +(-4.74737 - 8.22268i) q^{55} +(14.6888 + 4.39752i) q^{56} +(1.54529 - 2.36821i) q^{57} +(17.1667 + 11.2907i) q^{58} +(-12.6486 - 108.216i) q^{59} +(7.28316 - 2.68089i) q^{60} +(55.2475 + 27.7463i) q^{61} +(-12.4592 + 2.19689i) q^{62} +(-29.4186 - 38.9218i) q^{63} +(-1.38919 + 7.87846i) q^{64} +(-2.59502 - 1.93192i) q^{65} +(-25.0478 - 18.5062i) q^{66} +(8.81515 - 9.34351i) q^{67} +(-24.9449 + 7.46801i) q^{68} +(127.059 - 30.6020i) q^{69} +(9.84938 + 1.15123i) q^{70} +(9.13600 - 10.8879i) q^{71} +(18.3884 - 17.6031i) q^{72} +(31.7996 - 26.6831i) q^{73} +(15.0864 + 22.9378i) q^{74} +(-60.4774 + 35.2105i) q^{75} +(1.12576 + 1.51215i) q^{76} +(-17.8588 - 35.5598i) q^{77} +(-10.3343 - 2.40960i) q^{78} +(-76.6120 + 18.1574i) q^{79} +5.17394i q^{80} +(-80.3070 + 10.5729i) q^{81} +13.9523 q^{82} +(-0.889177 - 3.75173i) q^{83} +(31.1254 - 9.44182i) q^{84} +(-15.0491 + 7.55795i) q^{85} +(-7.09850 + 5.28464i) q^{86} +(43.5862 - 0.158519i) q^{87} +(17.3463 - 11.4088i) q^{88} +(7.81943 + 9.31884i) q^{89} +(9.73493 - 13.2768i) q^{90} +(-10.3866 - 8.71536i) q^{91} +(-10.1150 + 86.5391i) q^{92} +(-19.4539 + 18.4880i) q^{93} +(26.0089 + 86.8756i) q^{94} +(0.886836 + 0.836687i) q^{95} +(6.77832 + 15.5581i) q^{96} +(-25.5306 + 34.2936i) q^{97} +(-27.3153 - 4.81642i) q^{98} +(-65.9783 - 3.36145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q + 72 q^{18} + 108 q^{20} + 270 q^{21} + 162 q^{23} - 54 q^{27} - 162 q^{29} - 216 q^{30} - 378 q^{33} - 486 q^{35} - 180 q^{36} - 108 q^{38} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 1728 q^{65} - 1008 q^{66} + 702 q^{67} - 216 q^{68} - 1872 q^{69} + 540 q^{70} - 1296 q^{71} - 576 q^{72} - 864 q^{74} - 900 q^{75} + 108 q^{76} - 864 q^{77} - 288 q^{78} + 108 q^{79} + 144 q^{81} + 432 q^{83} + 144 q^{84} - 540 q^{85} + 864 q^{86} + 2016 q^{87} - 216 q^{88} + 1782 q^{89} + 1440 q^{90} + 864 q^{92} + 2124 q^{93} - 756 q^{94} + 2808 q^{95} + 288 q^{96} - 918 q^{97} + 1296 q^{98} + 1800 q^{99}+O(q^{100}) $ 324 * q + 72 * q^18 + 108 * q^20 + 270 * q^21 + 162 * q^23 - 54 * q^27 - 162 * q^29 - 216 * q^30 - 378 * q^33 - 486 * q^35 - 180 * q^36 - 108 * q^38 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 1728 * q^65 - 1008 * q^66 + 702 * q^67 - 216 * q^68 - 1872 * q^69 + 540 * q^70 - 1296 * q^71 - 576 * q^72 - 864 * q^74 - 900 * q^75 + 108 * q^76 - 864 * q^77 - 288 * q^78 + 108 * q^79 + 144 * q^81 + 432 * q^83 + 144 * q^84 - 540 * q^85 + 864 * q^86 + 2016 * q^87 - 216 * q^88 + 1782 * q^89 + 1440 * q^90 + 864 * q^92 + 2124 * q^93 - 756 * q^94 + 2808 * q^95 + 288 * q^96 - 918 * q^97 + 1296 * q^98 + 1800 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{23}{54}\right)$

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 $

$2$	0.326140	+	1.37609i	0.163070	+	0.688047i
$2$	0.326140	+	1.37609i	0.163070	+	0.688047i
$3$	2.18959	+	2.05078i	0.729865	+	0.683592i
$3$	2.18959	+	2.05078i	0.729865	+	0.683592i
$4$	−1.78727	+	0.897598i	−0.446816	+	0.224400i
$5$	−1.03753	+	0.772415i	−0.207507	+	0.154483i	−0.695895	−	0.718143i	$-0.744992\pi$
$5$	−1.03753	+	0.772415i	−0.207507	+	0.154483i	0.488389	+	0.872626i	$0.337585\pi$
$6$	−2.10794	+	3.68193i	−0.351324	+	0.613654i
$7$	−4.52918	+	2.97889i	−0.647025	+	0.425555i	−0.830154	−	0.557534i	$-0.811748\pi$
$7$	−4.52918	+	2.97889i	−0.647025	+	0.425555i	0.183129	+	0.983089i	$0.441377\pi$
$8$	−1.81808	−	2.16670i	−0.227260	−	0.270838i
$9$	0.588642	+	8.98073i	0.0654047	+	0.997859i
$10$	−1.40130	−	1.17583i	−0.140130	−	0.117583i
$11$	−0.852172	+	7.29080i	−0.0774702	+	0.662800i	0.897586	+	0.440840i	$0.145319\pi$
$11$	−0.852172	+	7.29080i	−0.0774702	+	0.662800i	−0.975056	+	0.221960i	$0.928755\pi$
$12$	−5.75416	−	1.69990i	−0.479513	−	0.141659i
$13$	0.717336	+	2.39607i	0.0551797	+	0.184313i	0.981136	−	0.193317i	$-0.0619244\pi$
$13$	0.717336	+	2.39607i	0.0551797	+	0.184313i	−0.925957	+	0.377630i	$0.876739\pi$
$14$	−5.57637	−	5.26104i	−0.398312	−	0.375788i
$15$	−3.85583	−	0.436473i	−0.257055	−	0.0290982i
$16$	2.38863	−	3.20849i	0.149290	−	0.200531i
$17$	12.8216	+	2.26080i	0.754212	+	0.132988i	0.537519	−	0.843252i	$-0.319362\pi$
$17$	12.8216	+	2.26080i	0.754212	+	0.132988i	0.216693	+	0.976240i	$0.430473\pi$
$18$	−12.1663	+	3.73900i	−0.675908	+	0.207722i
$19$	−0.163680	−	0.928274i	−0.00861473	−	0.0488565i	0.980197	−	0.198023i	$-0.0634521\pi$
$19$	−0.163680	−	0.928274i	−0.00861473	−	0.0488565i	−0.988812	+	0.149166i	$0.952341\pi$
$20$	1.16103	−	2.31180i	0.0580515	−	0.115590i
$21$	−16.0261	−	2.76577i	−0.763147	−	0.131703i
$22$	−10.3107	+	1.20515i	−0.468670	+	0.0547797i
$23$	23.9389	−	36.3973i	1.04082	−	1.58249i	0.252137	−	0.967692i	$-0.418867\pi$
$23$	23.9389	−	36.3973i	1.04082	−	1.58249i	0.788684	−	0.614799i	$-0.210763\pi$
$24$	0.462564	−	8.47266i	0.0192735	−	0.353028i
$25$	−6.69023	+	22.3469i	−0.267609	+	0.893877i
$26$	−3.06326	+	1.76858i	−0.117818	+	0.0680222i
$27$	−17.1286	+	20.8713i	−0.634391	+	0.773012i
$28$	5.42100	−	9.38944i	0.193607	−	0.335337i
$29$	10.5679	−	9.97029i	0.364410	−	0.343803i	−0.482157	−	0.876085i	$-0.660147\pi$
$29$	10.5679	−	9.97029i	0.364410	−	0.343803i	0.846567	+	0.532281i	$0.178665\pi$
$30$	−0.656913	−	5.44833i	−0.0218971	−	0.181611i
$31$	−0.520156	+	8.93074i	−0.0167792	+	0.288088i	0.979472	+	0.201581i	$0.0646078\pi$
$31$	−0.520156	+	8.93074i	−0.0167792	+	0.288088i	−0.996251	+	0.0865078i	$0.972429\pi$
$32$	5.19421	+	2.24057i	0.162319	+	0.0700177i
$33$	−16.8177	+	14.2163i	−0.509627	+	0.430796i
$34$	1.07058	+	18.3811i	0.0314875	+	0.540620i
$35$	2.39824	−	6.58910i	0.0685210	−	0.188260i
$36$	−9.11315	−	15.5226i	−0.253143	−	0.431183i
$37$	18.2424	−	6.63969i	0.493038	−	0.179451i	−0.0835222	−	0.996506i	$-0.526617\pi$
$37$	18.2424	−	6.63969i	0.493038	−	0.179451i	0.576560	+	0.817055i	$0.304395\pi$
$38$	1.22401	−	0.527986i	0.0322108	−	0.0138944i
$39$	−3.34313	+	6.71752i	−0.0857212	+	0.172244i
$40$	3.55991	+	0.843714i	0.0889977	+	0.0210929i
$41$	2.27520	−	9.59983i	0.0554927	−	0.234142i	−0.938230	−	0.346012i	$-0.887536\pi$
$41$	2.27520	−	9.59983i	0.0554927	−	0.234142i	0.993723	+	0.111870i	$0.0356839\pi$
$42$	−1.42079	−	22.9554i	−0.0338283	−	0.546558i
$43$	2.47852	+	5.74586i	0.0576401	+	0.133625i	0.944602	−	0.328217i	$-0.106448\pi$
$43$	2.47852	+	5.74586i	0.0576401	+	0.133625i	−0.886962	+	0.461842i	$0.847189\pi$
$44$	−5.02115	−	13.7955i	−0.114117	−	0.313534i
$45$	−7.54759	−	8.86313i	−0.167724	−	0.196958i
$46$	57.8935	+	21.0715i	1.25855	+	0.458076i
$47$	64.0157	−	3.72849i	1.36204	−	0.0793296i	0.638504	−	0.769619i	$-0.279554\pi$
$47$	64.0157	−	3.72849i	1.36204	−	0.0793296i	0.723534	+	0.690289i	$0.242517\pi$
$48$	11.8100	−	2.12674i	0.246042	−	0.0443072i
$49$	−7.76823	+	18.0088i	−0.158535	+	0.367526i
$50$	−32.9334	−	1.91815i	−0.658668	−	0.0383630i
$51$	23.4377	+	31.2445i	0.459563	+	0.612636i
$52$	−3.43278	−	3.63853i	−0.0660150	−	0.0699718i
$53$	31.0537	+	17.9289i	0.585919	+	0.338280i	0.763482	−	0.645829i	$-0.223488\pi$
$53$	31.0537	+	17.9289i	0.585919	+	0.338280i	−0.177563	+	0.984109i	$0.556821\pi$
$54$	−34.3072	−	16.7635i	−0.635319	−	0.310436i
$55$	−4.74737	−	8.22268i	−0.0863157	−	0.149503i
$56$	14.6888	+	4.39752i	0.262299	+	0.0785272i
$57$	1.54529	−	2.36821i	0.0271103	−	0.0415476i
$58$	17.1667	+	11.2907i	0.295977	+	0.194667i
$59$	−12.6486	−	108.216i	−0.214383	−	1.83417i	−0.488613	−	0.872501i	$-0.662497\pi$
$59$	−12.6486	−	108.216i	−0.214383	−	1.83417i	0.274229	−	0.961664i	$-0.411577\pi$
$60$	7.28316	−	2.68089i	0.121386	−	0.0446815i
$61$	55.2475	+	27.7463i	0.905696	+	0.454858i	0.839755	−	0.542966i	$-0.182699\pi$
$61$	55.2475	+	27.7463i	0.905696	+	0.454858i	0.0659416	+	0.997823i	$0.478995\pi$
$62$	−12.4592	+	2.19689i	−0.200954	+	0.0354337i
$63$	−29.4186	−	38.9218i	−0.466963	−	0.617807i
$64$	−1.38919	+	7.87846i	−0.0217060	+	0.123101i
$65$	−2.59502	−	1.93192i	−0.0399234	−	0.0297219i
$66$	−25.0478	−	18.5062i	−0.379513	−	0.280397i
$67$	8.81515	−	9.34351i	0.131569	−	0.139455i	−0.658239	−	0.752809i	$-0.728698\pi$
$67$	8.81515	−	9.34351i	0.131569	−	0.139455i	0.789808	+	0.613354i	$0.210180\pi$
$68$	−24.9449	+	7.46801i	−0.366837	+	0.109824i
$69$	127.059	−	30.6020i	1.84144	−	0.443508i
$70$	9.84938	+	1.15123i	0.140705	+	0.0164461i
$71$	9.13600	−	10.8879i	0.128676	−	0.153350i	−0.697859	−	0.716235i	$-0.745864\pi$
$71$	9.13600	−	10.8879i	0.128676	−	0.153350i	0.826536	+	0.562885i	$0.190308\pi$
$72$	18.3884	−	17.6031i	0.255394	−	0.244487i
$73$	31.7996	−	26.6831i	0.435612	−	0.365521i	−0.398453	−	0.917189i	$-0.630453\pi$
$73$	31.7996	−	26.6831i	0.435612	−	0.365521i	0.834064	+	0.551667i	$0.186008\pi$
$74$	15.0864	+	22.9378i	0.203870	+	0.309970i
$75$	−60.4774	+	35.2105i	−0.806365	+	0.469474i
$76$	1.12576	+	1.51215i	0.0148126	+	0.0198968i
$77$	−17.8588	−	35.5598i	−0.231933	−	0.461816i
$78$	−10.3343	−	2.40960i	−0.132490	−	0.0308923i
$79$	−76.6120	+	18.1574i	−0.969773	+	0.229840i	−0.684829	−	0.728704i	$-0.740123\pi$
$79$	−76.6120	+	18.1574i	−0.969773	+	0.229840i	−0.284944	+	0.958544i	$0.591975\pi$
$80$			5.17394i			0.0646742i
$81$	−80.3070	+	10.5729i	−0.991444	+	0.130529i
$82$	13.9523			0.170150
$83$	−0.889177	−	3.75173i	−0.0107130	−	0.0452016i	0.967426	−	0.253154i	$-0.0814681\pi$
$83$	−0.889177	−	3.75173i	−0.0107130	−	0.0452016i	−0.978139	+	0.207953i	$0.933320\pi$
$84$	31.1254	−	9.44182i	0.370541	−	0.112403i
$85$	−15.0491	+	7.55795i	−0.177048	+	0.0889171i
$86$	−7.09850	+	5.28464i	−0.0825407	+	0.0614493i
$87$	43.5862	−	0.158519i	0.500991	−	0.00182206i
$88$	17.3463	−	11.4088i	0.197117	−	0.129646i
$89$	7.81943	+	9.31884i	0.0878588	+	0.104706i	0.808183	−	0.588932i	$-0.200451\pi$
$89$	7.81943	+	9.31884i	0.0878588	+	0.104706i	−0.720324	+	0.693638i	$0.756007\pi$
$90$	9.73493	−	13.2768i	0.108166	−	0.147520i
$91$	−10.3866	−	8.71536i	−0.114138	−	0.0957732i
$92$	−10.1150	+	86.5391i	−0.109945	+	0.940642i
$93$	−19.4539	+	18.4880i	−0.209181	+	0.198795i
$94$	26.0089	+	86.8756i	0.276690	+	0.924209i
$95$	0.886836	+	0.836687i	0.00933512	+	0.00880723i
$96$	6.77832	+	15.5581i	0.0706075	+	0.162063i
$97$	−25.5306	+	34.2936i	−0.263202	+	0.353542i	−0.914004	−	0.405706i	$-0.867026\pi$
$97$	−25.5306	+	34.2936i	−0.263202	+	0.353542i	0.650801	+	0.759248i	$0.274433\pi$
$98$	−27.3153	−	4.81642i	−0.278727	−	0.0491472i
$99$	−65.9783	−	3.36145i	−0.666448	−	0.0339541i
$100$	−8.10135	−	45.9450i	−0.0810135	−	0.459450i
$101$	−26.4370	+	52.6404i	−0.261752	+	0.521192i	−0.985668	−	0.168697i	$-0.946044\pi$
$101$	−26.4370	+	52.6404i	−0.261752	+	0.521192i	0.723916	+	0.689889i	$0.242340\pi$
$102$	−35.3513	+	42.4426i	−0.346581	+	0.416104i
$103$	−175.813	+	20.5496i	−1.70693	+	0.199511i	−0.912847	−	0.408303i	$-0.866121\pi$
$103$	−175.813	+	20.5496i	−1.70693	+	0.199511i	−0.794080	+	0.607814i	$0.792047\pi$
$104$	3.88739	−	5.91050i	0.0373788	−	0.0568317i
$105$	18.7639	−	9.50921i	0.178704	−	0.0905639i
$106$	−14.5439	+	48.5801i	−0.137207	+	0.458303i
$107$	−176.329	+	101.804i	−1.64794	+	0.951436i	−0.670044	+	0.742321i	$0.733725\pi$
$107$	−176.329	+	101.804i	−1.64794	+	0.951436i	−0.977891	+	0.209115i	$0.932942\pi$
$108$	11.8792	−	52.6772i	0.109993	−	0.487752i
$109$	78.8570	−	136.584i	0.723459	−	1.25307i	−0.236146	−	0.971718i	$-0.575884\pi$
$109$	78.8570	−	136.584i	0.723459	−	1.25307i	0.959605	−	0.281350i	$-0.0907823\pi$
$110$	9.76687	−	9.21456i	0.0887897	−	0.0837687i
$111$	53.5599	+	22.8728i	0.482522	+	0.206062i
$112$	−1.26081	+	21.6473i	−0.0112572	+	0.193280i
$113$	−68.1553	−	29.3993i	−0.603144	−	0.260171i	0.0725362	−	0.997366i	$-0.476891\pi$
$113$	−68.1553	−	29.3993i	−0.603144	−	0.260171i	−0.675680	+	0.737195i	$0.736150\pi$
$114$	3.76286	+	1.35409i	0.0330076	+	0.0118780i
$115$	3.27643	+	56.2542i	0.0284907	+	0.489167i
$116$	−9.93831	+	27.3053i	−0.0856751	+	0.235390i
$117$	−21.0962	+	7.85263i	−0.180309	+	0.0671165i
$118$	144.790	−	52.6992i	1.22703	−	0.446603i
$119$	−64.8060	+	27.9546i	−0.544588	+	0.234912i
$120$	6.06449	+	9.14796i	0.0505374	+	0.0762330i
$121$	65.3089	+	15.4785i	0.539743	+	0.127921i
$122$	−20.1631	+	85.0749i	−0.165271	+	0.697335i
$123$	24.6689	−	16.3538i	0.200560	−	0.132958i
$124$	−7.08656	−	16.4285i	−0.0571497	−	0.132488i
$125$	−21.3797	−	58.7403i	−0.171038	−	0.469922i
$126$	43.9655	−	53.1768i	0.348932	−	0.422038i
$127$	−209.023	−	76.0783i	−1.64585	−	0.599042i	−0.657806	−	0.753187i	$-0.728515\pi$
$127$	−209.023	−	76.0783i	−1.64585	−	0.599042i	−0.988048	+	0.154146i	$0.950738\pi$
$128$	−11.2946	+	0.657834i	−0.0882388	+	0.00513933i
$129$	−6.35651	+	17.6640i	−0.0492753	+	0.136930i
$130$	1.81216	−	4.20107i	0.0139397	−	0.0323159i
$131$	25.8415	+	1.50509i	0.197263	+	0.0114893i	0.156492	−	0.987679i	$-0.449981\pi$
$131$	25.8415	+	1.50509i	0.197263	+	0.0114893i	0.0407712	+	0.999169i	$0.487019\pi$
$132$	17.2972	−	40.5038i	0.131039	−	0.306847i
$133$	3.50656	+	3.71673i	0.0263651	+	0.0279454i
$134$	15.7325	+	9.08317i	0.117407	+	0.0677848i
$135$	1.65014	−	34.8851i	0.0122233	−	0.258408i
$136$	−18.4122	−	31.8909i	−0.135384	−	0.234492i
$137$	151.265	+	45.2857i	1.10412	+	0.330553i	0.786454	−	0.617649i	$-0.211915\pi$
$137$	151.265	+	45.2857i	1.10412	+	0.330553i	0.317669	+	0.948202i	$0.397100\pi$
$138$	83.5503	+	164.865i	0.605437	+	1.19467i
$139$	−179.042	−	117.758i	−1.28807	−	0.847178i	−0.293990	−	0.955809i	$-0.594983\pi$
$139$	−179.042	−	117.758i	−1.28807	−	0.847178i	−0.994082	+	0.108630i	$0.965354\pi$
$140$	1.62808	+	13.9291i	0.0116292	+	0.0994937i
$141$	147.815	+	123.118i	1.04833	+	0.873177i
$142$	17.9623	+	9.02102i	0.126495	+	0.0635283i
$143$	−18.0806	+	3.18809i	−0.126437	+	0.0222943i
$144$	30.2207	+	19.5630i	0.209866	+	0.135854i
$145$	−3.26334	+	18.5073i	−0.0225058	+	0.127637i
$146$	47.0895	+	35.0569i	0.322531	+	0.240115i
$147$	−53.9412	+	23.5010i	−0.366947	+	0.159871i
$148$	−26.6442	+	28.2412i	−0.180029	+	0.190819i
$149$	204.513	−	61.2272i	1.37257	−	0.410921i	0.486181	−	0.873858i	$-0.338390\pi$
$149$	204.513	−	61.2272i	1.37257	−	0.410921i	0.886391	+	0.462937i	$0.153204\pi$
$150$	−68.1771	−	71.7390i	−0.454514	−	0.478260i
$151$	155.518	+	18.1774i	1.02992	+	0.120380i	0.614231	−	0.789126i	$-0.289466\pi$
$151$	155.518	+	18.1774i	1.02992	+	0.120380i	0.415689	+	0.909507i	$0.363540\pi$
$152$	−1.71371	+	2.04232i	−0.0112744	+	0.0134363i
$153$	−12.7563	+	116.478i	−0.0833742	+	0.761295i
$154$	43.1092	−	36.1729i	0.279930	−	0.234889i
$155$	−6.35856	−	9.66772i	−0.0410230	−	0.0623724i
$156$	−0.0545782	−	15.0068i	−0.000349860	−	0.0961972i
$157$	−140.081	−	188.162i	−0.892237	−	1.19848i	−0.979327	−	0.202282i	$-0.935164\pi$
$157$	−140.081	−	188.162i	−0.892237	−	1.19848i	0.0870898	−	0.996200i	$-0.472243\pi$
$158$	−49.9725	−	99.5034i	−0.316282	−	0.629769i
$159$	31.2269	+	102.941i	0.196396	+	0.647428i
$160$	−7.11982	+	1.68743i	−0.0444989	+	0.0105464i
$161$			236.161i			1.46684i
$162$	−40.7406	−	107.062i	−0.251485	−	0.660875i
$163$	−163.051			−1.00031			−0.500156	−	0.865935i	$-0.666724\pi$
$163$	−163.051			−1.00031			−0.500156	+	0.865935i	$0.666724\pi$
$164$	4.55040	+	19.1997i	0.0277464	+	0.117071i
$165$	6.46806	−	27.7401i	0.0392004	−	0.168122i
$166$	4.87274	−	2.44718i	0.0293538	−	0.0147420i
$167$	77.8235	−	57.9374i	0.466009	−	0.346931i	−0.338405	−	0.941001i	$-0.609887\pi$
$167$	77.8235	−	57.9374i	0.466009	−	0.346931i	0.804413	+	0.594070i	$0.202480\pi$
$168$	23.1441	+	39.7521i	0.137762	+	0.236620i
$169$	135.971	−	89.4294i	0.804561	−	0.529168i
$170$	−15.3086	−	18.2440i	−0.0900504	−	0.107318i
$171$	8.24023	−	2.01639i	0.0481885	−	0.0117917i
$172$	−9.58726	−	8.04466i	−0.0557399	−	0.0467713i
$173$	−8.91976	+	76.3134i	−0.0515593	+	0.441118i	0.942660	+	0.333753i	$0.108315\pi$
$173$	−8.91976	+	76.3134i	−0.0515593	+	0.441118i	−0.994220	+	0.107365i	$0.965759\pi$
$174$	14.4334	+	59.9270i	0.0829503	+	0.344408i
$175$	−36.2677	−	121.143i	−0.207244	−	0.692244i
$176$	21.3569	+	20.1492i	0.121346	+	0.114484i
$177$	194.231	−	262.888i	1.09735	−	1.48524i
$178$	−10.2734	+	13.7995i	−0.0577155	+	0.0775253i
$179$	−8.00503	−	1.41150i	−0.0447208	−	0.00788549i	0.151243	−	0.988497i	$-0.451672\pi$
$179$	−8.00503	−	1.41150i	−0.0447208	−	0.00788549i	−0.195964	+	0.980611i	$0.562784\pi$
$180$	21.4451	+	9.06607i	0.119139	+	0.0503670i
$181$	1.46480	+	8.30727i	0.00809279	+	0.0458965i	0.988587	−	0.150653i	$-0.0481375\pi$
$181$	1.46480	+	8.30727i	0.00809279	+	0.0458965i	−0.980494	+	0.196549i	$0.937026\pi$
$182$	8.60568	−	17.1353i	0.0472839	−	0.0941501i
$183$	64.0681	+	174.053i	0.350099	+	0.951111i
$184$	−122.385	+	14.3047i	−0.665135	+	0.0777431i
$185$	−13.7985	+	20.9796i	−0.0745865	+	0.113403i
$186$	−31.7859	−	20.7407i	−0.170892	−	0.111509i
$187$	−27.4092	+	91.5532i	−0.146573	+	0.489589i
$188$	−111.066	+	64.1242i	−0.590779	+	0.341086i
$189$	15.4050	−	145.554i	0.0815080	−	0.770127i
$190$	−0.862126	+	1.49325i	−0.00453751	+	0.00785919i
$191$	104.441	−	98.5347i	0.546810	−	0.515888i	−0.362514	−	0.931978i	$-0.618081\pi$
$191$	104.441	−	98.5347i	0.546810	−	0.515888i	0.909323	+	0.416090i	$0.136600\pi$
$192$	−19.1987	+	14.4017i	−0.0999933	+	0.0750090i
$193$	−5.76501	+	98.9815i	−0.0298705	+	0.512857i	0.949877	+	0.312623i	$0.101208\pi$
$193$	−5.76501	+	98.9815i	−0.0298705	+	0.512857i	−0.979748	+	0.200235i	$0.935830\pi$
$194$	−55.5178	−	23.9480i	−0.286174	−	0.123443i
$195$	−1.72011	−	9.55193i	−0.00882105	−	0.0489843i
$196$	−2.28076	−	39.1592i	−0.0116366	−	0.199792i
$197$	4.46552	−	12.2689i	0.0226676	−	0.0622788i	−0.927843	−	0.372972i	$-0.878339\pi$
$197$	4.46552	−	12.2689i	0.0226676	−	0.0622788i	0.950510	+	0.310693i	$0.100561\pi$
$198$	−16.8925	−	91.8886i	−0.0853156	−	0.464084i
$199$	259.167	−	94.3290i	1.30235	−	0.474015i	0.404586	−	0.914500i	$-0.367416\pi$
$199$	259.167	−	94.3290i	1.30235	−	0.474015i	0.897760	+	0.440485i	$0.145193\pi$
$200$	60.5825	−	26.1327i	0.302912	−	0.130664i
$201$	38.4630	−	2.38061i	0.191358	−	0.0118438i
$202$	−81.0602	−	19.2116i	−0.401288	−	0.0951071i
$203$	−18.1635	+	76.6378i	−0.0894753	+	0.377526i
$204$	−69.9344	−	34.8045i	−0.342816	−	0.170610i
$205$	5.05446	+	11.7175i	0.0246559	+	0.0571588i
$206$	−85.6180	−	235.234i	−0.415621	−	1.14191i
$207$	340.966	+	193.564i	1.64718	+	0.935090i
$208$	9.40123	+	3.42177i	0.0451982	+	0.0164508i
$209$	6.90734	−	0.402307i	0.0330495	−	0.00192491i
$210$	19.2052	+	22.7196i	0.0914535	+	0.108188i
$211$	72.1799	−	167.332i	0.342085	−	0.793042i	−0.657143	−	0.753766i	$-0.728235\pi$
$211$	72.1799	−	167.332i	0.342085	−	0.793042i	0.999228	−	0.0392764i	$-0.0125053\pi$
$212$	−71.5941	−	4.16988i	−0.337708	−	0.0196693i
$213$	42.3327	−	5.10411i	0.198745	−	0.0239630i
$214$	−197.599	−	209.443i	−0.923361	−	0.978706i
$215$	−7.00974	−	4.04708i	−0.0326035	−	0.0188236i
$216$	76.3630	−	0.833204i	0.353532	−	0.00385743i
$217$	−24.2478	−	41.9984i	−0.111741	−	0.193541i
$218$	213.671	+	63.9690i	0.980144	+	0.293436i
$219$	124.349	+	6.78884i	0.567805	+	0.0309993i
$220$	15.8655	+	10.4349i	0.0721157	+	0.0474313i
$221$	3.78038	+	32.3432i	0.0171058	+	0.146349i
$222$	−14.0071	+	81.1632i	−0.0630950	+	0.365600i
$223$	189.389	+	95.1145i	0.849276	+	0.426523i	0.819531	−	0.573035i	$-0.194234\pi$
$223$	189.389	+	95.1145i	0.849276	+	0.426523i	0.0297454	+	0.999558i	$0.490530\pi$
$224$	−30.1999	+	5.32506i	−0.134821	+	0.0237726i
$225$	−204.630	−	46.9288i	−0.909466	−	0.208572i
$226$	18.2280	−	103.376i	0.0806550	−	0.457417i
$227$	−229.895	−	171.150i	−1.01275	−	0.753966i	−0.0432541	−	0.999064i	$-0.513772\pi$
$227$	−229.895	−	171.150i	−1.01275	−	0.753966i	−0.969498	+	0.245098i	$0.921180\pi$
$228$	−0.636137	+	5.61968i	−0.00279008	+	0.0246477i
$229$	192.109	−	203.623i	0.838902	−	0.889184i	−0.156231	−	0.987720i	$-0.549935\pi$
$229$	192.109	−	203.623i	0.838902	−	0.889184i	0.995133	+	0.0985362i	$0.0314160\pi$
$230$	−76.3424	+	22.8554i	−0.331923	+	0.0993714i
$231$	33.8217	−	114.486i	0.146414	−	0.495611i
$232$	−40.8159	−	4.77069i	−0.175931	−	0.0205633i
$233$	−143.960	+	171.565i	−0.617853	+	0.736329i	−0.980700	−	0.195520i	$-0.937360\pi$
$233$	−143.960	+	171.565i	−0.617853	+	0.736329i	0.362847	+	0.931849i	$0.381805\pi$
$234$	−17.6863	−	26.4693i	−0.0755824	−	0.113117i
$235$	−63.5385	+	53.3152i	−0.270377	+	0.226873i
$236$	119.741	+	182.057i	0.507376	+	0.771427i
$237$	−204.986	−	117.357i	−0.864920	−	0.495176i
$238$	−59.6039	−	80.0620i	−0.250437	−	0.336395i
$239$	−100.415	−	199.943i	−0.420147	−	0.836581i	−0.999765	−	0.0216927i	$-0.993094\pi$
$239$	−100.415	−	199.943i	−0.420147	−	0.836581i	0.579618	−	0.814888i	$-0.303202\pi$
$240$	−10.6106	+	11.3288i	−0.0442108	+	0.0472034i
$241$	−1.64012	+	0.388714i	−0.00680546	+	0.00161292i	−0.234017	−	0.972232i	$-0.575187\pi$
$241$	−1.64012	+	0.388714i	−0.00680546	+	0.00161292i	0.227212	+	0.973845i	$0.427039\pi$
$242$			94.9193i			0.392228i
$243$	−197.522	−	141.541i	−0.812849	−	0.582474i
$244$	−123.647			−0.506750
$245$	−5.85045	−	24.6850i	−0.0238794	−	0.100755i
$246$	30.5499	+	28.6130i	0.124186	+	0.116313i
$247$	2.10680	−	1.05807i	0.00852954	−	0.00428370i
$248$	20.2959	−	15.1098i	0.0818384	−	0.0609264i
$249$	5.74702	−	10.0383i	0.0230804	−	0.0403143i
$250$	73.8593	−	48.5780i	0.295437	−	0.194312i
$251$	192.234	+	229.095i	0.765872	+	0.912730i	0.998204	−	0.0599061i	$-0.0190801\pi$
$251$	192.234	+	229.095i	0.765872	+	0.912730i	−0.232332	+	0.972636i	$0.574636\pi$
$252$	87.5151	+	43.1575i	0.347282	+	0.171260i
$253$	244.965	+	205.550i	0.968242	+	0.812452i
$254$	36.5199	−	312.448i	0.143779	−	1.23011i
$255$	−48.4511	−	14.3135i	−0.190004	−	0.0561314i
$256$	−4.58885	−	15.3278i	−0.0179252	−	0.0598743i
$257$	190.036	+	179.290i	0.739439	+	0.697625i	0.960700	−	0.277590i	$-0.0895355\pi$
$257$	190.036	+	179.290i	0.739439	+	0.697625i	−0.221260	+	0.975215i	$0.571017\pi$
$258$	−26.3804	−	2.98622i	−0.102250	−	0.0115745i
$259$	−62.8442	+	84.4144i	−0.242642	+	0.325924i
$260$	6.37208	+	1.12357i	0.0245080	+	0.00432142i
$261$	95.7612	+	89.0385i	0.366901	+	0.341144i
$262$	6.35679	+	36.0511i	0.0242626	+	0.137600i
$263$	21.0528	−	41.9196i	0.0800488	−	0.159390i	−0.850048	−	0.526706i	$-0.823427\pi$
$263$	21.0528	−	41.9196i	0.0800488	−	0.159390i	0.930096	+	0.367316i	$0.119723\pi$
$264$	61.3783	+	10.5926i	0.232494	+	0.0401236i
$265$	−46.0678	+	5.38455i	−0.173841	+	0.0203191i
$266$	−3.97094	+	6.03753i	−0.0149284	+	0.0226975i
$267$	−1.98946	+	36.4404i	−0.00745115	+	0.136481i
$268$	−7.36829	+	24.6118i	−0.0274936	+	0.0918350i
$269$	−289.708	+	167.263i	−1.07698	+	0.621796i	−0.930081	−	0.367356i	$-0.880263\pi$
$269$	−289.708	+	167.263i	−1.07698	+	0.621796i	−0.146901	+	0.989151i	$0.546930\pi$
$270$	48.5433	−	9.10667i	0.179790	−	0.0337284i
$271$	−261.408	+	452.772i	−0.964605	+	1.67075i	−0.253933	+	0.967222i	$0.581724\pi$
$271$	−261.408	+	452.772i	−0.964605	+	1.67075i	−0.710672	+	0.703523i	$0.751609\pi$
$272$	37.8799	−	35.7378i	0.139264	−	0.131389i
$273$	−4.86911	−	40.3836i	−0.0178356	−	0.147925i
$274$	−12.9838	+	222.924i	−0.0473863	+	0.813591i
$275$	−157.226	−	67.8205i	−0.571730	−	0.246620i
$276$	−199.620	+	168.742i	−0.723261	+	0.611384i
$277$	22.6438	+	388.779i	0.0817465	+	1.40353i	0.750904	+	0.660412i	$0.229618\pi$
$277$	22.6438	+	388.779i	0.0817465	+	1.40353i	−0.669157	+	0.743121i	$0.733345\pi$
$278$	103.653	−	284.784i	0.372852	−	1.02440i
$279$	−80.5107	+	0.585628i	−0.288569	+	0.00209902i
$280$	−18.6368	+	6.78324i	−0.0665600	+	0.0242258i
$281$	−294.210	+	126.910i	−1.04701	+	0.451636i	−0.848905	−	0.528545i	$-0.822738\pi$
$281$	−294.210	+	126.910i	−1.04701	+	0.451636i	−0.198105	+	0.980181i	$0.563479\pi$
$282$	−121.214	+	243.561i	−0.429835	+	0.863690i
$283$	332.732	+	78.8590i	1.17573	+	0.278654i	0.771637	−	0.636063i	$-0.219438\pi$
$283$	332.732	+	78.8590i	1.17573	+	0.278654i	0.404095	+	0.914717i	$0.367586\pi$
$284$	−6.55553	+	27.6600i	−0.0230829	+	0.0973943i
$285$	0.225955	+	3.65071i	0.000792823	+	0.0128095i
$286$	−10.2839	−	23.8408i	−0.0359577	−	0.0833593i
$287$	18.2920	+	50.2569i	0.0637353	+	0.175111i
$288$	−17.0644	+	47.9667i	−0.0592513	+	0.166551i
$289$	−112.289	−	40.8698i	−0.388542	−	0.141418i
$290$	−26.5321	+	1.54532i	−0.0914900	+	0.00532869i
$291$	−126.230	+	22.7315i	−0.433781	+	0.0781150i
$292$	−32.8837	+	76.2330i	−0.112615	+	0.261072i
$293$	−59.9780	−	3.49332i	−0.204703	−	0.0119226i	−0.0445131	−	0.999009i	$-0.514174\pi$
$293$	−59.9780	−	3.49332i	−0.204703	−	0.0119226i	−0.160190	+	0.987086i	$0.551211\pi$
$294$	−49.9320	−	66.5635i	−0.169837	−	0.226407i
$295$	96.7108	+	102.507i	0.327833	+	0.347483i
$296$	−47.5523	−	27.4543i	−0.160650	−	0.0927511i
$297$	−137.572	−	142.667i	−0.463206	−	0.480360i
$298$	150.954	+	261.461i	0.506558	+	0.877385i
$299$	104.383	+	31.2501i	0.349106	+	0.104515i
$300$	76.4843	−	117.215i	0.254948	−	0.390717i
$301$	−28.3419	−	18.6408i	−0.0941593	−	0.0619295i
$302$	25.7068	+	219.936i	0.0851218	+	0.728263i
$303$	−165.840	+	61.0447i	−0.547326	+	0.201468i
$304$	−3.36933	−	1.69214i	−0.0110833	−	0.00556626i
$305$	−78.7528	+	13.8862i	−0.258206	+	0.0455287i
$306$	−164.445	+	20.4344i	−0.537403	+	0.0667791i
$307$	−66.8265	+	378.992i	−0.217676	+	1.23450i	0.658526	+	0.752558i	$0.271180\pi$
$307$	−66.8265	+	378.992i	−0.217676	+	1.23450i	−0.876202	+	0.481944i	$0.839931\pi$
$308$	63.8369	+	47.5248i	0.207263	+	0.154301i
$309$	−427.103	−	315.558i	−1.38221	−	1.02122i
$310$	11.2299	−	11.9030i	0.0362255	−	0.0383968i
$311$	334.313	−	100.087i	1.07496	−	0.321823i	0.300071	−	0.953917i	$-0.402990\pi$
$311$	334.313	−	100.087i	1.07496	−	0.321823i	0.774891	+	0.632094i	$0.217805\pi$
$312$	20.6329	−	4.96941i	0.0661311	−	0.0159276i
$313$	514.217	+	60.1033i	1.64287	+	0.192023i	0.886696	−	0.462352i	$-0.152994\pi$
$313$	514.217	+	60.1033i	1.64287	+	0.192023i	0.756169	+	0.654376i	$0.227069\pi$
$314$	213.242	−	254.132i	0.679115	−	0.809338i
$315$	60.5866	+	17.6593i	0.192339	+	0.0560612i
$316$	120.628	−	101.219i	0.381734	−	0.320313i
$317$	−109.089	−	165.862i	−0.344131	−	0.523225i	0.621407	−	0.783488i	$-0.286561\pi$
$317$	−109.089	−	165.862i	−0.344131	−	0.523225i	−0.965538	+	0.260262i	$0.916191\pi$
$318$	−131.472	+	76.5444i	−0.413434	+	0.240706i
$319$	63.6857	+	85.5448i	0.199642	+	0.268165i
$320$	−4.64412	−	9.24720i	−0.0145129	−	0.0288975i
$321$	−594.865	−	138.703i	−1.85316	−	0.432096i
$322$	−324.980	+	77.0216i	−1.00925	+	0.239197i
$323$		−	12.2720i		−	0.0379939i
$324$	134.040	−	90.9800i	0.413703	−	0.280802i
$325$	−58.3439			−0.179520
$326$	−53.1775	−	224.373i	−0.163121	−	0.688262i
$327$	452.769	−	137.346i	1.38461	−	0.420019i
$328$	−24.9365	+	12.5236i	−0.0760258	+	0.0381816i
$329$	−278.832	+	207.583i	−0.847513	+	0.630950i
$330$	40.2825	−	0.146504i	0.122068	−	0.000443950i
$331$	−150.683	+	99.1055i	−0.455234	+	0.299412i	−0.756340	−	0.654178i	$-0.773015\pi$
$331$	−150.683	+	99.1055i	−0.455234	+	0.299412i	0.301106	+	0.953591i	$0.402644\pi$
$332$	4.95674	+	5.90722i	0.0149299	+	0.0177928i
$333$	70.3675	+	159.922i	0.211314	+	0.480245i
$334$	105.109	+	88.1966i	0.314697	+	0.264062i
$335$	−1.92894	+	16.5032i	−0.00575804	+	0.0492631i
$336$	−47.1544	+	44.8132i	−0.140341	+	0.133373i
$337$	90.2197	+	301.355i	0.267714	+	0.894227i	0.981107	+	0.193464i	$0.0619721\pi$
$337$	90.2197	+	301.355i	0.267714	+	0.894227i	−0.713393	+	0.700764i	$0.752843\pi$
$338$	167.409	+	157.942i	0.495292	+	0.467284i
$339$	−88.9410	−	204.144i	−0.262363	−	0.602194i
$340$	20.1128	−	27.0161i	0.0591552	−	0.0794592i
$341$	−64.6690	−	11.4029i	−0.189645	−	0.0334395i
$342$	5.46220	+	10.6817i	0.0159714	+	0.0312330i
$343$	−64.5884	−	366.299i	−0.188304	−	1.06793i
$344$	7.94342	−	15.8166i	0.0230913	−	0.0459786i
$345$	−108.191	+	129.893i	−0.313596	+	0.376501i
$346$	−107.923	+	12.6144i	−0.311917	+	0.0364579i
$347$	307.096	−	466.918i	0.885004	−	1.34558i	−0.0528674	−	0.998602i	$-0.516836\pi$
$347$	307.096	−	466.918i	0.885004	−	1.34558i	0.937872	−	0.346982i	$-0.112794\pi$
$348$	−77.7579	+	39.4062i	−0.223442	+	0.113236i
$349$	23.2667	−	77.7161i	0.0666667	−	0.222682i	−0.918164	−	0.396201i	$-0.870328\pi$
$349$	23.2667	−	77.7161i	0.0666667	−	0.222682i	0.984831	+	0.173518i	$0.0555136\pi$
$350$	154.875	−	89.4172i	0.442501	−	0.255478i
$351$	−62.2961	−	26.0695i	−0.177482	−	0.0742721i
$352$	−20.7619	+	35.9606i	−0.0589826	+	0.102161i
$353$	264.817	−	249.842i	0.750191	−	0.707769i	−0.212861	−	0.977082i	$-0.568278\pi$
$353$	264.817	−	249.842i	0.750191	−	0.707769i	0.963053	+	0.269314i	$0.0867968\pi$
$354$	425.105	+	181.541i	1.20086	+	0.512829i
$355$	−1.06896	+	18.3533i	−0.00301115	+	0.0516995i
$356$	−22.3400	−	9.63652i	−0.0627527	−	0.0270689i
$357$	−199.227	−	71.6934i	−0.558060	−	0.200822i
$358$	−0.668402	−	11.4760i	−0.00186704	−	0.0320559i
$359$	218.883	−	601.377i	0.609703	−	1.67514i	−0.121171	−	0.992632i	$-0.538665\pi$
$359$	218.883	−	601.377i	0.609703	−	1.67514i	0.730874	−	0.682513i	$-0.239113\pi$
$360$	−5.48165	+	32.4672i	−0.0152268	+	0.0901867i
$361$	338.394	−	123.165i	0.937380	−	0.341178i
$362$	−10.9538	+	4.72503i	−0.0302592	+	0.0130526i
$363$	111.257	+	167.825i	0.306493	+	0.462329i
$364$	26.3864	+	6.25370i	0.0724902	+	0.0171805i
$365$	−12.3828	+	52.2471i	−0.0339255	+	0.143143i
$366$	−218.618	+	144.929i	−0.597318	+	0.395982i
$367$	−253.572	−	587.845i	−0.690931	−	1.60176i	−0.794591	−	0.607145i	$-0.792315\pi$
$367$	−253.572	−	587.845i	−0.690931	−	1.60176i	0.103660	−	0.994613i	$-0.466944\pi$
$368$	−59.5992	−	163.748i	−0.161954	−	0.444966i
$369$	87.5528	+	14.7821i	0.237270	+	0.0400599i
$370$	−33.3701	−	12.1457i	−0.0901895	−	0.0328263i
$371$	−194.056	+	11.3025i	−0.523061	+	0.0304649i
$372$	18.1745	−	50.5047i	0.0488561	−	0.135765i
$373$	−129.009	+	299.075i	−0.345867	+	0.801811i	0.653139	+	0.757238i	$0.273452\pi$
$373$	−129.009	+	299.075i	−0.345867	+	0.801811i	−0.999006	+	0.0445725i	$0.985807\pi$
$374$	−134.925	−	7.85848i	−0.360762	−	0.0210120i
$375$	73.6502	−	172.462i	0.196401	−	0.459899i
$376$	−124.464	−	131.924i	−0.331022	−	0.350862i
$377$	31.4703	+	18.1694i	0.0834755	+	0.0481946i
$378$	205.320	−	26.2722i	0.543175	−	0.0695033i
$379$	−82.7123	−	143.262i	−0.218238	−	0.378000i	0.736031	−	0.676948i	$-0.236698\pi$
$379$	−82.7123	−	143.262i	−0.218238	−	0.378000i	−0.954269	+	0.298948i	$0.903364\pi$
$380$	−2.33602	−	0.699359i	−0.00614742	−	0.00184042i
$381$	−301.657	−	595.241i	−0.791751	−	1.56231i
$382$	169.655	+	111.584i	0.444124	+	0.292105i
$383$	−5.66189	−	48.4405i	−0.0147830	−	0.126477i	0.983832	−	0.179096i	$-0.0573172\pi$
$383$	−5.66189	−	48.4405i	−0.0147830	−	0.126477i	−0.998615	+	0.0526191i	$0.983243\pi$
$384$	−26.0796	−	21.7222i	−0.0679156	−	0.0565683i
$385$	45.9961	+	23.1001i	0.119470	+	0.0600003i
$386$	−138.088	+	24.3486i	−0.357741	+	0.0630793i
$387$	−50.1431	+	25.6412i	−0.129569	+	0.0662563i
$388$	14.8481	−	84.2080i	0.0382684	−	0.217031i
$389$	−570.048	−	424.385i	−1.46542	−	1.09096i	−0.975707	−	0.219080i	$-0.929695\pi$
$389$	−570.048	−	424.385i	−1.46542	−	1.09096i	−0.489712	−	0.871884i	$-0.662898\pi$
$390$	12.5834	−	5.48229i	0.0322650	−	0.0140572i
$391$	389.222	−	412.551i	0.995452	−	1.05512i
$392$	53.1429	−	15.9099i	0.135569	−	0.0405866i
$393$	53.4957	+	56.2906i	0.136121	+	0.143233i
$394$	18.3396	+	2.14359i	0.0465471	+	0.00544057i
$395$	65.4625	−	78.0152i	0.165728	−	0.197507i
$396$	120.938	−	53.2142i	0.305399	−	0.134379i
$397$	−299.005	+	250.895i	−0.753160	+	0.631977i	−0.936337	−	0.351103i	$-0.885807\pi$
$397$	−299.005	+	250.895i	−0.753160	+	0.631977i	0.183176	+	0.983080i	$0.441362\pi$
$398$	214.330	+	325.873i	0.538518	+	0.818777i
$399$	0.0557512	+	15.3293i	0.000139727	+	0.0384193i
$400$	55.7194	+	74.8442i	0.139299	+	0.187110i
$401$	202.776	+	403.761i	0.505677	+	1.00688i	0.991164	+	0.132641i	$0.0423458\pi$
$401$	202.776	+	403.761i	0.505677	+	1.00688i	−0.485487	+	0.874244i	$0.661358\pi$
$402$	15.8203	+	52.1523i	0.0393539	+	0.129732i
$403$	−21.7718	+	5.16001i	−0.0540243	+	0.0128040i
$404$		−	117.812i		−	0.291614i
$405$	75.1546	−	73.0001i	0.185567	−	0.180247i
$406$	−111.385			−0.274346
$407$	32.8630	+	138.660i	0.0807444	+	0.340687i
$408$	25.0858	−	107.587i	0.0614847	−	0.263695i
$409$	483.034	−	242.589i	1.18101	−	0.593126i	0.253651	−	0.967296i	$-0.418368\pi$
$409$	483.034	−	242.589i	1.18101	−	0.593126i	0.927360	+	0.374169i	$0.122072\pi$
$410$	−14.4760	+	10.7770i	−0.0353073	+	0.0262853i
$411$	238.338	+	409.367i	0.579897	+	0.996028i
$412$	295.780	−	194.537i	0.717912	−	0.472178i
$413$	379.650	+	452.450i	0.919250	+	1.09552i
$414$	−155.159	+	532.329i	−0.374780	+	1.28582i
$415$	3.82044	+	3.20573i	0.00920589	+	0.00772466i
$416$	−1.64255	+	14.0529i	−0.00394845	+	0.0337811i
$417$	−150.535	−	625.017i	−0.360994	−	1.49884i
$418$	2.80637	+	9.37394i	0.00671381	+	0.0224257i
$419$	242.174	+	228.480i	0.577981	+	0.545297i	0.918745	−	0.394852i	$-0.129204\pi$
$419$	242.174	+	228.480i	0.577981	+	0.545297i	−0.340763	+	0.940149i	$0.610686\pi$
$420$	−25.0007	+	33.8380i	−0.0595254	+	0.0805665i
$421$	281.430	−	378.026i	0.668480	−	0.897924i	−0.330466	−	0.943818i	$-0.607206\pi$
$421$	281.430	−	378.026i	0.668480	−	0.897924i	0.998946	+	0.0458934i	$0.0146135\pi$
$422$	253.805	+	44.7527i	0.601434	+	0.106049i
$423$	71.1670	+	572.713i	0.168243	+	1.35393i
$424$	−17.6116	−	99.8801i	−0.0415367	−	0.235566i
$425$	−136.301	+	271.398i	−0.320709	+	0.638584i
$426$	20.8301	+	56.5891i	0.0488970	+	0.132838i
$427$	−332.879	+	38.9080i	−0.779576	+	0.0911193i
$428$	223.768	−	340.223i	0.522823	−	0.794913i
$429$	−46.1271	−	30.0985i	−0.107522	−	0.0701598i
$430$	3.28300	−	10.9660i	0.00763488	−	0.0255023i
$431$	486.905	−	281.115i	1.12971	−	0.652238i	0.185848	−	0.982579i	$-0.440497\pi$
$431$	486.905	−	281.115i	1.12971	−	0.652238i	0.943862	+	0.330341i	$0.107164\pi$
$432$	26.0516	+	104.811i	0.0603046	+	0.242618i
$433$	−110.676	+	191.696i	−0.255602	+	0.442715i	−0.965059	−	0.262033i	$-0.915607\pi$
$433$	−110.676	+	191.696i	−0.255602	+	0.442715i	0.709457	+	0.704749i	$0.248940\pi$
$434$	49.8855	−	47.0646i	0.114944	−	0.108444i
$435$	−45.0997	+	33.8311i	−0.103678	+	0.0777727i
$436$	−18.3405	+	314.894i	−0.0420654	+	0.722235i
$437$	−37.7050	−	16.2643i	−0.0862814	−	0.0372182i
$438$	31.2132	+	173.330i	0.0712630	+	0.395731i
$439$	34.4682	+	591.797i	0.0785153	+	1.34806i	0.775671	+	0.631137i	$0.217411\pi$
$439$	34.4682	+	591.797i	0.0785153	+	1.34806i	−0.697156	+	0.716919i	$0.745552\pi$
$440$	−9.18500	+	25.2356i	−0.0208750	+	0.0573536i
$441$	−166.305	−	59.1636i	−0.377108	−	0.134158i
$442$	−43.2744	+	15.7506i	−0.0979058	+	0.0356348i
$443$	−441.386	+	190.395i	−0.996356	+	0.429786i	−0.830894	−	0.556430i	$-0.812171\pi$
$443$	−441.386	+	190.395i	−0.996356	+	0.429786i	−0.165461	+	0.986216i	$0.552911\pi$
$444$	−116.256	+	7.19550i	−0.261839	+	0.0162061i
$445$	−15.3109	−	3.62876i	−0.0344066	−	0.00815451i
$446$	−69.1193	+	291.637i	−0.154976	+	0.653895i
$447$	573.364	+	285.348i	1.28269	+	0.638362i
$448$	−17.1772	−	39.8212i	−0.0383419	−	0.0888866i
$449$	−214.484	−	589.290i	−0.477693	−	1.31245i	−0.911447	−	0.411418i	$-0.865034\pi$
$449$	−214.484	−	589.290i	−0.477693	−	1.31245i	0.433754	−	0.901031i	$-0.357189\pi$
$450$	−2.15959	−	296.895i	−0.00479908	−	0.659767i
$451$	68.0516	+	24.7687i	0.150890	+	0.0549196i
$452$	148.200	−	8.63169i	0.327877	−	0.0190967i
$453$	303.243	+	358.733i	0.669411	+	0.791906i
$454$	160.541	−	372.176i	0.353614	−	0.819770i
$455$	17.5083	+	1.01974i	0.0384798	+	0.00224119i
$456$	−7.94067	+	0.957417i	−0.0174137	+	0.00209960i
$457$	−613.045	−	649.790i	−1.34146	−	1.42186i	−0.824517	−	0.565837i	$-0.808553\pi$
$457$	−613.045	−	649.790i	−1.34146	−	1.42186i	−0.516938	−	0.856023i	$-0.672928\pi$
$458$	342.859	+	197.950i	0.748600	+	0.432204i
$459$	−266.802	+	228.880i	−0.581267	+	0.498649i
$460$	−56.3495	−	97.6002i	−0.122499	−	0.212174i
$461$	−109.006	−	32.6341i	−0.236455	−	0.0707899i	0.166383	−	0.986061i	$-0.446791\pi$
$461$	−109.006	−	32.6341i	−0.236455	−	0.0707899i	−0.402838	+	0.915271i	$0.631976\pi$
$462$	168.574	+	9.20328i	0.364879	+	0.0199205i
$463$	442.670	+	291.148i	0.956090	+	0.628830i	0.928715	−	0.370795i	$-0.120915\pi$
$463$	442.670	+	291.148i	0.956090	+	0.628830i	0.0273752	+	0.999625i	$0.491285\pi$
$464$	−6.74678	−	57.7224i	−0.0145405	−	0.124402i
$465$	5.90366	−	34.2084i	0.0126960	−	0.0735664i
$466$	−283.040	−	142.148i	−0.607382	−	0.305039i
$467$	471.128	−	83.0725i	1.00884	−	0.177886i	0.355279	−	0.934760i	$-0.384386\pi$
$467$	471.128	−	83.0725i	1.00884	−	0.177886i	0.653560	+	0.756875i	$0.273275\pi$
$468$	30.6560	−	32.9707i	0.0655043	−	0.0704501i
$469$	−12.0921	+	68.5777i	−0.0257827	+	0.146221i
$470$	−94.0891	−	70.0467i	−0.200190	−	0.149036i
$471$	79.1565	−	699.273i	0.168060	−	1.48466i
$472$	−211.475	+	224.150i	−0.448040	+	0.474895i
$473$	−44.0041	+	13.1739i	−0.0930318	+	0.0278519i
$474$	94.6397	−	320.355i	0.199662	−	0.675853i
$475$	21.8391	+	2.55263i	0.0459771	+	0.00537395i
$476$	90.7335	−	108.132i	0.190617	−	0.227168i
$477$	−142.735	+	289.439i	−0.299234	+	0.606789i
$478$	242.391	−	203.390i	0.507093	−	0.425502i
$479$	−1.50460	−	2.28763i	−0.00314112	−	0.00477585i	0.833914	−	0.551895i	$-0.186095\pi$
$479$	−1.50460	−	2.28763i	−0.00314112	−	0.00477585i	−0.837055	+	0.547119i	$0.815725\pi$
$480$	−19.0500	−	10.9064i	−0.0396876	−	0.0227216i
$481$	28.9951	+	38.9472i	0.0602809	+	0.0809712i
$482$	−1.06981	−	2.13018i	−0.00221953	−	0.00441945i
$483$	−484.313	+	517.097i	−1.00272	+	1.07059i
$484$	−130.618	+	30.9570i	−0.269871	+	0.0639607i
$485$		−	55.3010i		−	0.114023i
$486$	130.354	−	317.971i	0.268218	−	0.654262i
$487$	−368.698			−0.757081			−0.378540	−	0.925585i	$-0.623574\pi$
$487$	−368.698			−0.757081			−0.378540	+	0.925585i	$0.623574\pi$
$488$	−40.3262	−	170.150i	−0.0826357	−	0.348668i
$489$	−357.015	−	334.381i	−0.730093	−	0.683805i
$490$	32.0608	−	16.1015i	0.0654302	−	0.0328603i
$491$	−727.451	+	541.568i	−1.48157	+	1.10299i	−0.511761	+	0.859128i	$0.671007\pi$
$491$	−727.451	+	541.568i	−1.48157	+	1.10299i	−0.969810	+	0.243861i	$0.921586\pi$
$492$	−29.4107	+	51.3713i	−0.0597778	+	0.104413i
$493$	158.038	−	103.943i	0.320564	−	0.210838i
$494$	2.14312	+	2.55407i	0.00433830	+	0.00517018i
$495$	71.0511	−	47.4750i	0.143538	−	0.0959091i
$496$	27.4118	+	23.0012i	0.0552656	+	0.0463734i
$497$	−8.94486	+	76.5282i	−0.0179977	+	0.153980i
$498$	15.6879	+	4.63456i	0.0315019	+	0.00930634i
$499$	−61.2423	−	204.564i	−0.122730	−	0.409947i	0.874439	−	0.485135i	$-0.161230\pi$
$499$	−61.2423	−	204.564i	−0.122730	−	0.409947i	−0.997169	+	0.0751878i	$0.976044\pi$
$500$	90.9364	+	85.7940i	0.181873	+	0.171588i
$501$	289.218	+	32.7390i	0.577282	+	0.0653473i
$502$	−252.561	+	339.249i	−0.503110	+	0.675794i
$503$	187.418	+	33.0469i	0.372601	+	0.0656997i	0.356813	−	0.934176i	$-0.383863\pi$
$503$	187.418	+	33.0469i	0.372601	+	0.0656997i	0.0157880	+	0.999875i	$0.494974\pi$
$504$	−30.8466	+	134.504i	−0.0612035	+	0.266874i
$505$	−13.2310	−	75.0365i	−0.0261999	−	0.148587i
$506$	−202.963	+	404.133i	−0.401113	+	0.798682i
$507$	481.121	+	83.0315i	0.948956	+	0.163770i
$508$	441.868	−	51.6470i	0.869819	−	0.101667i
$509$	−174.534	+	265.366i	−0.342896	+	0.521348i	−0.965229	−	0.261405i	$-0.915814\pi$
$509$	−174.534	+	265.366i	−0.342896	+	0.521348i	0.622334	+	0.782752i	$0.286185\pi$
$510$	3.89488	−	71.3415i	0.00763702	−	0.139885i
$511$	−64.5404	+	215.580i	−0.126302	+	0.421878i
$512$	19.5959	−	11.3137i	0.0382733	−	0.0220971i
$513$	22.1779	+	12.4838i	0.0432318	+	0.0243349i
$514$	−184.741	+	319.981i	−0.359418	+	0.622531i
$515$	166.539	−	157.122i	0.323378	−	0.305091i
$516$	−4.49440	−	37.2759i	−0.00871008	−	0.0722400i
$517$	−27.3687	+	469.903i	−0.0529376	+	0.908904i
$518$	−136.658	−	58.9485i	−0.263819	−	0.113800i
$519$	−176.032	+	148.803i	−0.339176	+	0.286711i
$520$	0.532054	+	9.13502i	0.00102318	+	0.0175673i
$521$	35.6310	−	97.8954i	0.0683897	−	0.187899i	−0.900789	−	0.434256i	$-0.857011\pi$
$521$	35.6310	−	97.8954i	0.0683897	−	0.187899i	0.969179	+	0.246357i	$0.0792335\pi$
$522$	−91.2937	+	160.815i	−0.174892	+	0.308075i
$523$	−588.970	+	214.367i	−1.12614	+	0.409880i	−0.836888	−	0.547374i	$-0.815628\pi$
$523$	−588.970	+	214.367i	−1.12614	+	0.409880i	−0.289249	+	0.957254i	$0.593405\pi$
$524$	−47.5365	+	20.5053i	−0.0907186	+	0.0391322i
$525$	169.025	−	339.630i	0.321952	−	0.646914i
$526$	64.5515	+	15.2990i	0.122721	+	0.0290855i
$527$	−26.8598	+	113.330i	−0.0509674	+	0.215048i
$528$	5.44148	+	87.9169i	0.0103058	+	0.166509i
$529$	−542.167	−	1256.88i	−1.02489	−	2.37596i
$530$	−22.4342	−	61.6374i	−0.0423287	−	0.116297i
$531$	964.411	−	177.294i	1.81622	−	0.333887i
$532$	−9.60329	−	3.49531i	−0.0180513	−	0.00657013i
$533$	24.6340	−	1.43476i	0.0462175	−	0.00269187i
$534$	−50.7942	+	9.14698i	−0.0951202	+	0.0171292i
$535$	104.313	−	241.824i	0.194977	−	0.452007i
$536$	−36.2712	−	2.11256i	−0.0676702	−	0.00394134i
$537$	−14.6331	−	19.5071i	−0.0272497	−	0.0363261i
$538$	−324.655	−	344.114i	−0.603448	−	0.639617i
$539$	−124.678	−	71.9831i	−0.231314	−	0.133549i
$540$	28.3635	+	63.8300i	0.0525251	+	0.118204i
$541$	64.4137	+	111.568i	0.119064	+	0.206225i	0.919397	−	0.393331i	$-0.128677\pi$
$541$	64.4137	+	111.568i	0.119064	+	0.206225i	−0.800333	+	0.599556i	$0.795344\pi$
$542$	−708.312	−	212.055i	−1.30685	−	0.391245i
$543$	−13.8290	+	21.1935i	−0.0254678	+	0.0390304i
$544$	61.5327	+	40.4707i	0.113112	+	0.0743947i
$545$	23.6830	+	202.621i	0.0434551	+	0.371782i
$546$	53.9836	−	19.8711i	0.0988711	−	0.0363939i
$547$	−643.326	−	323.090i	−1.17610	−	0.590659i	−0.250113	−	0.968217i	$-0.580468\pi$
$547$	−643.326	−	323.090i	−1.17610	−	0.590659i	−0.925986	+	0.377558i	$0.876764\pi$
$548$	−310.999	+	54.8375i	−0.567516	+	0.100068i
$549$	−216.661	+	512.495i	−0.394647	+	0.933507i
$550$	42.0498	−	238.476i	0.0764542	−	0.433593i
$551$	−10.9849	−	8.17797i	−0.0199363	−	0.0148420i
$552$	−297.309	−	219.662i	−0.538603	−	0.397939i
$553$	292.901	−	310.457i	0.529658	−	0.561404i
$554$	−527.611	+	157.956i	−0.952366	+	0.285120i
$555$	−73.2376	+	17.6392i	−0.131960	+	0.0317823i
$556$	425.695	+	49.7566i	0.765638	+	0.0894903i
$557$	−152.233	+	181.424i	−0.273309	+	0.325717i	−0.885187	−	0.465235i	$-0.845970\pi$
$557$	−152.233	+	181.424i	−0.273309	+	0.325717i	0.611878	+	0.790952i	$0.290414\pi$
$558$	−27.0637	−	110.599i	−0.0485012	−	0.198207i
$559$	−11.9896	+	10.0604i	−0.0214482	+	0.0179972i
$560$	−15.4126	−	23.4337i	−0.0275224	−	0.0418458i
$561$	−247.770	+	144.254i	−0.441658	+	0.257137i
$562$	−270.593	−	363.470i	−0.481483	−	0.646743i
$563$	−286.091	−	569.655i	−0.508155	−	1.01182i	−0.990715	−	0.135957i	$-0.956589\pi$
$563$	−286.091	−	569.655i	−0.508155	−	1.01182i	0.482559	−	0.875863i	$-0.339707\pi$
$564$	−374.695	−	87.3663i	−0.664352	−	0.154905i
$565$	93.4219	−	22.1414i	0.165348	−	0.0391883i
$566$			483.590i			0.854399i
$567$	332.229	−	287.112i	0.585942	−	0.506370i
$568$	−40.2007			−0.0707759
$569$	−9.06503	−	38.2484i	−0.0159315	−	0.0672203i	0.964498	−	0.264088i	$-0.0850711\pi$
$569$	−9.06503	−	38.2484i	−0.0159315	−	0.0672203i	−0.980430	+	0.196868i	$0.936923\pi$
$570$	−4.95002	+	1.50158i	−0.00868424	+	0.00263434i
$571$	−507.151	+	254.701i	−0.888181	+	0.446061i	−0.833549	−	0.552446i	$-0.813695\pi$
$571$	−507.151	+	254.701i	−0.888181	+	0.446061i	−0.0546316	+	0.998507i	$0.517398\pi$
$572$	29.4531	−	21.9270i	0.0514915	−	0.0383340i
$573$	430.755	−	1.56662i	0.751754	−	0.00273406i
$574$	−63.1924	+	41.5623i	−0.110091	+	0.0724082i
$575$	653.211	+	778.466i	1.13602	+	1.35385i
$576$	−71.5721	−	7.83830i	−0.124257	−	0.0136082i
$577$	789.057	+	662.098i	1.36752	+	1.14748i	0.973580	+	0.228345i	$0.0733315\pi$
$577$	789.057	+	662.098i	1.36752	+	1.14748i	0.393937	+	0.919138i	$0.371113\pi$
$578$	19.6187	−	167.849i	0.0339425	−	0.290396i
$579$	−215.612	+	204.906i	−0.372386	+	0.353897i
$580$	−10.7797	−	36.0067i	−0.0185857	−	0.0620804i
$581$	15.2032	+	14.3435i	0.0261673	+	0.0246876i
$582$	−72.4493	−	166.291i	−0.124483	−	0.285723i
$583$	−157.179	+	211.128i	−0.269603	+	0.362140i
$584$	−115.628	−	20.3884i	−0.197994	−	0.0349117i
$585$	15.8225	−	24.4424i	0.0270471	−	0.0417819i
$586$	−14.7541	−	83.6747i	−0.0251776	−	0.142790i
$587$	−344.039	+	685.037i	−0.586097	+	1.16701i	0.383782	+	0.923424i	$0.374622\pi$
$587$	−344.039	+	685.037i	−0.586097	+	1.16701i	−0.969878	+	0.243590i	$0.921675\pi$
$588$	75.3128	−	90.4201i	0.128083	−	0.153776i
$589$	8.37531	−	0.978934i	0.0142195	−	0.00166203i
$590$	−109.519	+	166.515i	−0.185625	+	0.282229i
$591$	34.9385	−	17.7062i	0.0591175	−	0.0299597i
$592$	22.2710	−	74.3904i	0.0376200	−	0.125659i
$593$	−705.224	+	407.161i	−1.18925	+	0.686613i	−0.958136	−	0.286314i	$-0.907570\pi$
$593$	−705.224	+	407.161i	−1.18925	+	0.686613i	−0.231113	+	0.972927i	$0.574237\pi$
$594$	151.455	−	235.841i	0.254975	−	0.397039i
$595$	45.6459	−	79.0609i	0.0767157	−	0.132876i
$596$	−310.562	+	293.000i	−0.521077	+	0.491611i
$597$	760.918	+	324.951i	1.27457	+	0.544306i
$598$	−8.95971	+	153.832i	−0.0149828	+	0.257245i
$599$	−154.561	−	66.6709i	−0.258031	−	0.111304i	0.263135	−	0.964759i	$-0.415244\pi$
$599$	−154.561	−	66.6709i	−0.258031	−	0.111304i	−0.521166	+	0.853455i	$0.674503\pi$
$600$	186.243	+	67.0210i	0.310406	+	0.111702i
$601$	−1.98819	−	34.1359i	−0.00330814	−	0.0567986i	0.996250	−	0.0865206i	$-0.0275748\pi$
$601$	−1.98819	−	34.1359i	−0.00330814	−	0.0567986i	−0.999558	+	0.0297220i	$0.990538\pi$
$602$	16.4080	−	45.0807i	0.0272559	−	0.0748848i
$603$	89.1005	+	73.6665i	0.147762	+	0.122167i
$604$	−294.268	+	107.105i	−0.487198	+	0.177326i
$605$	−79.7160	+	34.3861i	−0.131762	+	0.0568366i
$606$	−138.090	−	208.302i	−0.227872	−	0.343733i
$607$	525.024	+	124.433i	0.864949	+	0.204997i	0.639060	−	0.769156i	$-0.279323\pi$
$607$	525.024	+	124.433i	0.864949	+	0.204997i	0.225888	+	0.974153i	$0.427472\pi$
$608$	1.22967	−	5.18839i	0.00202249	−	0.00853354i
$609$	−196.938	+	130.556i	−0.323379	+	0.214378i
$610$	−44.7932	−	103.842i	−0.0734315	−	0.170233i
$611$	54.8546	+	150.712i	0.0897783	+	0.246664i
$612$	−81.7518	−	219.627i	−0.133581	−	0.358868i
$613$	−753.560	−	274.274i	−1.22930	−	0.447428i	−0.355942	−	0.934508i	$-0.615840\pi$
$613$	−753.560	−	274.274i	−1.22930	−	0.447428i	−0.873357	+	0.487080i	$0.838062\pi$
$614$	−543.323	+	31.6450i	−0.884891	+	0.0515391i
$615$	−12.9628	+	36.0222i	−0.0210778	+	0.0585727i
$616$	−44.5788	+	103.345i	−0.0723682	+	0.167768i
$617$	1006.43	+	58.6179i	1.63117	+	0.0950047i	0.849115	−	0.528208i	$-0.177136\pi$
$617$	1006.43	+	58.6179i	1.63117	+	0.0950047i	0.782052	+	0.623213i	$0.214173\pi$
$618$	294.943	−	690.649i	0.477253	−	1.11756i
$619$	390.000	+	413.376i	0.630049	+	0.667813i	0.961228	−	0.275755i	$-0.0889279\pi$
$619$	390.000	+	413.376i	0.630049	+	0.667813i	−0.331179	+	0.943568i	$0.607446\pi$
$620$	20.0422	+	11.5713i	0.0323261	+	0.0186635i
$621$	349.621	+	1123.07i	0.562997	+	1.80849i
$622$	246.762	+	427.404i	0.396723	+	0.687144i
$623$	−63.1753	−	18.9135i	−0.101405	−	0.0303587i
$624$	13.5676	+	26.7721i	0.0217429	+	0.0429040i
$625$	−419.679	−	276.028i	−0.671487	−	0.441644i
$626$	84.9990	+	727.213i	0.135781	+	1.16168i
$627$	15.9493	+	13.2845i	0.0254375	+	0.0211874i
$628$	419.256	+	210.558i	0.667605	+	0.335284i
$629$	248.908	−	43.8892i	0.395720	−	0.0697761i
$630$	−4.54110	+	89.1323i	−0.00720809	+	0.141480i
$631$	71.9673	−	408.147i	0.114053	−	0.646826i	−0.873162	−	0.487430i	$-0.837934\pi$
$631$	71.9673	−	408.147i	0.114053	−	0.646826i	0.987215	−	0.159395i	$-0.0509545\pi$
$632$	178.628	+	132.984i	0.282640	+	0.210417i
$633$	501.205	−	218.364i	0.791793	−	0.344967i
$634$	192.664	−	204.212i	0.303886	−	0.322100i
$635$	275.633	−	82.5191i	0.434068	−	0.129951i
$636$	−148.211	−	155.954i	−0.233035	−	0.245210i
$637$	−48.7227	−	5.69487i	−0.0764878	−	0.00894014i
$638$	−96.9471	+	115.537i	−0.151955	+	0.181093i
$639$	103.159	+	75.6389i	0.161438	+	0.118371i
$640$	11.2104	−	9.40662i	0.0175162	−	0.0146978i
$641$	63.7621	+	96.9455i	0.0994728	+	0.151241i	0.881795	−	0.471633i	$-0.156335\pi$
$641$	63.7621	+	96.9455i	0.0994728	+	0.151241i	−0.782322	+	0.622874i	$0.785965\pi$
$642$	−3.14166	−	863.827i	−0.00489355	−	1.34552i
$643$	126.717	+	170.211i	0.197072	+	0.264713i	0.889664	−	0.456616i	$-0.150939\pi$
$643$	126.717	+	170.211i	0.197072	+	0.264713i	−0.692592	+	0.721330i	$0.743531\pi$
$644$	−211.978	−	422.082i	−0.329158	−	0.655407i
$645$	−7.04884	−	23.2369i	−0.0109284	−	0.0360261i
$646$	16.8874	−	4.00240i	0.0261415	−	0.00619566i
$647$		−	518.388i		−	0.801219i	−0.916249	−	0.400609i	$-0.868798\pi$
$647$		−	518.388i		−	0.801219i	0.916249	−	0.400609i	$-0.131202\pi$
$648$	168.913	+	154.779i	0.260668	+	0.238856i
$649$	799.758			1.23229
$650$	−19.0283	−	80.2867i	−0.0292743	−	0.123518i
$651$	33.0365	−	141.686i	0.0507473	−	0.217644i
$652$	291.415	−	146.354i	0.446956	−	0.224470i
$653$	−386.369	+	287.641i	−0.591683	+	0.440492i	−0.850900	−	0.525327i	$-0.823943\pi$
$653$	−386.369	+	287.641i	−0.591683	+	0.440492i	0.259217	+	0.965819i	$0.416535\pi$
$654$	336.667	+	578.258i	0.514782	+	0.884186i
$655$	−27.9739	+	18.3988i	−0.0427083	+	0.0280897i
$656$	−25.3664	−	30.2305i	−0.0386682	−	0.0460830i
$657$	258.352	+	269.877i	0.393230	+	0.410772i
$658$	−376.591	−	315.998i	−0.572327	−	0.480240i
$659$	19.5434	−	167.204i	0.0296561	−	0.253724i	−0.970275	−	0.242004i	$-0.922195\pi$
$659$	19.5434	−	167.204i	0.0296561	−	0.253724i	0.999931	−	0.0117201i	$-0.00373071\pi$
$660$	13.3393	+	55.3846i	0.0202111	+	0.0839161i
$661$	−30.1720	−	100.782i	−0.0456460	−	0.152468i	0.932128	−	0.362128i	$-0.117950\pi$
$661$	−30.1720	−	100.782i	−0.0456460	−	0.152468i	−0.977774	+	0.209659i	$0.932764\pi$
$662$	−185.522	−	175.031i	−0.280245	−	0.264397i
$663$	−58.0512	+	78.5712i	−0.0875583	+	0.118509i
$664$	−6.51229	+	8.74752i	−0.00980766	+	0.0131740i
$665$	−6.50903	−	1.14772i	−0.00978802	−	0.00172589i
$666$	−197.117	+	148.989i	−0.295972	+	0.223707i
$667$	−109.908	−	623.320i	−0.164780	−	0.934513i
$668$	−87.0866	+	173.404i	−0.130369	+	0.259586i
$669$	219.626	+	596.656i	0.328289	+	0.891862i
$670$	−23.3390	+	2.72794i	−0.0348343	+	0.00407155i
$671$	−249.373	+	379.154i	−0.371644	+	0.565058i
$672$	−77.0460	−	50.2735i	−0.114652	−	0.0748118i
$673$	−240.747	+	804.151i	−0.357722	+	1.19487i	0.570013	+	0.821636i	$0.306938\pi$
$673$	−240.747	+	804.151i	−0.357722	+	1.19487i	−0.927735	+	0.373239i	$0.878247\pi$
$674$	−385.268	+	222.434i	−0.571614	+	0.330021i
$675$	−351.816	−	522.405i	−0.521209	−	0.773933i
$676$	−162.744	+	281.881i	−0.240746	+	0.416984i
$677$	240.251	−	226.665i	0.354876	−	0.334809i	−0.488072	−	0.872804i	$-0.662300\pi$
$677$	240.251	−	226.665i	0.354876	−	0.334809i	0.842948	+	0.537995i	$0.180818\pi$
$678$	251.914	−	188.971i	0.371554	−	0.278718i
$679$	13.4760	−	231.375i	0.0198469	−	0.340758i
$680$	43.7363	+	18.8660i	0.0643181	+	0.0277441i
$681$	−152.385	−	846.212i	−0.223767	−	1.24260i
$682$	−5.39971	−	92.7094i	−0.00791746	−	0.135938i
$683$	396.847	−	1090.33i	0.581035	−	1.59638i	−0.205380	−	0.978682i	$-0.565843\pi$
$683$	396.847	−	1090.33i	0.581035	−	1.59638i	0.786415	−	0.617698i	$-0.211935\pi$
$684$	−12.9176	+	11.0002i	−0.0188853	+	0.0160822i
$685$	−191.922	+	69.8538i	−0.280178	+	0.101976i
$686$	482.997	−	208.344i	0.704077	−	0.303709i
$687$	838.225	−	51.8806i	1.22012	−	0.0755176i
$688$	24.3558	+	5.77244i	0.0354009	+	0.00839018i
$689$	−20.6829	+	87.2679i	−0.0300187	+	0.126659i
$690$	−214.030	−	106.517i	−0.310189	−	0.154372i
$691$	−378.801	−	878.160i	−0.548193	−	1.27085i	−0.936934	−	0.349507i	$-0.886349\pi$
$691$	−378.801	−	878.160i	−0.548193	−	1.27085i	0.388741	−	0.921347i	$-0.372910\pi$
$692$	−52.5568	−	144.399i	−0.0759491	−	0.208669i
$693$	308.841	−	181.317i	0.445658	−	0.261641i
$694$	742.679	+	270.313i	1.07014	+	0.389500i
$695$	276.720	−	16.1171i	0.398158	−	0.0231901i
$696$	−79.5866	−	94.1501i	−0.114349	−	0.135273i
$697$	50.8750	−	117.941i	0.0729914	−	0.169213i
$698$	114.533	+	6.67077i	0.164087	+	0.00955698i
$699$	−667.054	+	80.4276i	−0.954297	+	0.115061i
$700$	173.557	+	183.960i	0.247939	+	0.262800i
$701$	−125.935	−	72.7086i	−0.179650	−	0.103721i	0.407478	−	0.913215i	$-0.366408\pi$
$701$	−125.935	−	72.7086i	−0.179650	−	0.103721i	−0.587128	+	0.809494i	$0.699742\pi$
$702$	15.5568	−	94.2275i	0.0221607	−	0.134227i
$703$	−9.14936	−	15.8472i	−0.0130147	−	0.0225422i
$704$	−56.2564	−	16.8421i	−0.0799097	−	0.0239234i
$705$	−248.461	−	13.5647i	−0.352427	−	0.0192407i
$706$	430.174	+	282.930i	0.609312	+	0.400751i
$707$	−37.0719	−	317.170i	−0.0524355	−	0.448615i
$708$	−111.174	+	644.192i	−0.157026	+	0.909875i
$709$	−651.404	−	327.147i	−0.918765	−	0.461421i	−0.0744233	−	0.997227i	$-0.523712\pi$
$709$	−651.404	−	327.147i	−0.918765	−	0.461421i	−0.844341	+	0.535806i	$0.820008\pi$
$710$	−25.6045	+	4.51476i	−0.0360627	+	0.00635882i
$711$	−208.164	−	677.344i	−0.292776	−	0.952663i
$712$	5.97479	−	33.8847i	0.00839156	−	0.0475909i
$713$	312.603	+	232.724i	0.438433	+	0.326401i
$714$	33.6807	−	297.537i	0.0471719	−	0.416719i
$715$	16.2967	−	17.2734i	0.0227925	−	0.0241587i
$716$	15.5741	−	4.66257i	0.0217515	−	0.00651197i
$717$	190.170	−	643.723i	0.265230	−	0.897800i
$718$	898.937	+	105.071i	1.25200	+	0.146338i
$719$	−354.890	+	422.941i	−0.493588	+	0.588235i	−0.954126	−	0.299405i	$-0.903212\pi$
$719$	−354.890	+	422.941i	−0.493588	+	0.588235i	0.460538	+	0.887640i	$0.347656\pi$
$720$	−46.4657	+	3.04560i	−0.0645357	+	0.00423000i
$721$	735.075	−	616.801i	1.01952	−	0.855480i
$722$	279.851	+	425.493i	0.387605	+	0.589325i
$723$	−4.38835	−	2.51238i	−0.00606964	−	0.00347494i
$724$	−10.0746	−	13.5325i	−0.0139151	−	0.0186913i
$725$	152.104	+	302.864i	0.209798	+	0.417743i
$726$	−194.658	+	207.835i	−0.268124	+	0.286274i
$727$	368.240	−	87.2746i	0.506520	−	0.120048i	0.0305927	−	0.999532i	$-0.490261\pi$
$727$	368.240	−	87.2746i	0.506520	−	0.120048i	0.475928	+	0.879484i	$0.342112\pi$
$728$			38.3498i			0.0526783i
$729$	−142.224	−	714.992i	−0.195095	−	0.980784i
$730$	−75.9354			−0.104021
$731$	18.7884	+	79.2746i	0.0257024	+	0.108447i
$732$	−270.737	−	253.572i	−0.369859	−	0.346410i
$733$	−1170.46	+	587.828i	−1.59681	+	0.801948i	−1.00000		0.000434361i	$-0.999862\pi$
$733$	−1170.46	+	587.828i	−1.59681	+	0.801948i	−0.596810	+	0.802382i	$0.703565\pi$
$734$	726.230	−	540.658i	0.989414	−	0.736591i
$735$	37.8133	−	66.0481i	0.0514466	−	0.0898614i
$736$	205.894	−	135.419i	0.279748	−	0.183993i
$737$	60.6096	+	72.2317i	0.0822383	+	0.0980078i
$738$	8.21291	+	125.302i	0.0111286	+	0.169786i
$739$	−199.148	−	167.105i	−0.269483	−	0.226123i	0.498024	−	0.867163i	$-0.334059\pi$
$739$	−199.148	−	167.105i	−0.269483	−	0.226123i	−0.767508	+	0.641040i	$0.778503\pi$
$740$	5.83033	−	49.8816i	0.00787882	−	0.0674076i
$741$	6.78290	+	2.00382i	0.00915371	+	0.00270421i
$742$	−78.8426	−	263.353i	−0.106257	−	0.354923i
$743$	−762.210	−	719.108i	−1.02585	−	0.967844i	−0.0263604	−	0.999653i	$-0.508392\pi$
$743$	−762.210	−	719.108i	−1.02585	−	0.967844i	−0.999494	+	0.0318088i	$0.989873\pi$
$744$	75.4266	+	8.53815i	0.101380	+	0.0114760i
$745$	−164.897	+	221.494i	−0.221338	+	0.297308i
$746$	−453.631	−	79.9873i	−0.608084	−	0.107222i
$747$	33.1699	−	10.1939i	0.0444041	−	0.0136464i
$748$	−33.1904	−	188.232i	−0.0443722	−	0.251647i
$749$	495.364	−	986.351i	0.661367	−	1.31689i
$750$	261.344	+	45.1027i	0.348459	+	0.0601369i
$751$	411.074	−	48.0477i	0.547369	−	0.0639783i	0.162086	−	0.986777i	$-0.448178\pi$
$751$	411.074	−	48.0477i	0.547369	−	0.0639783i	0.385283	+	0.922798i	$0.374104\pi$
$752$	140.947	−	214.300i	0.187430	−	0.284974i
$753$	−48.9091	+	895.854i	−0.0649523	+	1.18971i
$754$	−14.7390	+	49.2318i	−0.0195478	+	0.0652941i
$755$	−175.396	+	101.265i	−0.232312	+	0.134125i
$756$	103.116	+	273.971i	0.136397	+	0.362396i
$757$	1.71841	−	2.97637i	0.00227002	−	0.00393180i	−0.864888	−	0.501965i	$-0.832611\pi$
$757$	1.71841	−	2.97637i	0.00227002	−	0.00393180i	0.867158	+	0.498033i	$0.165944\pi$
$758$	170.166	−	160.543i	0.224493	−	0.211799i
$759$	114.837	+	952.440i	0.151300	+	1.25486i
$760$	0.200513	−	3.44267i	0.000263833	−	0.00452983i
$761$	197.037	+	84.9934i	0.258918	+	0.111686i	0.521582	−	0.853201i	$-0.325342\pi$
$761$	197.037	+	84.9934i	0.258918	+	0.111686i	−0.262664	+	0.964887i	$0.584601\pi$
$762$	720.724	−	609.240i	0.945832	−	0.799528i
$763$	49.7119	+	853.521i	0.0651533	+	1.11864i
$764$	−98.2186	+	269.853i	−0.128558	+	0.353211i
$765$	−76.7345	−	130.703i	−0.100307	−	0.170854i
$766$	64.8121	−	23.5897i	0.0846111	−	0.0307959i
$767$	250.219	−	107.934i	0.326231	−	0.140722i
$768$	21.3862	−	42.9724i	0.0278466	−	0.0559537i
$769$	−161.842	−	38.3573i	−0.210458	−	0.0498795i	0.124034	−	0.992278i	$-0.460417\pi$
$769$	−161.842	−	38.3573i	−0.210458	−	0.0498795i	−0.334492	+	0.942398i	$0.608565\pi$
$770$	−16.7867	+	70.8288i	−0.0218009	+	0.0919854i
$771$	48.4187	+

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.h (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.326140 + 1.37609i) q^{2} +(2.18959 + 2.05078i) q^{3} +(-1.78727 + 0.897598i) q^{4} +(-1.03753 + 0.772415i) q^{5} +(-2.10794 + 3.68193i) q^{6} +(-4.52918 + 2.97889i) q^{7} +(-1.81808 - 2.16670i) q^{8} +(0.588642 + 8.98073i) q^{9} +O(q^{10})\)	\(q+(0.326140 + 1.37609i) q^{2} +(2.18959 + 2.05078i) q^{3} +(-1.78727 + 0.897598i) q^{4} +(-1.03753 + 0.772415i) q^{5} +(-2.10794 + 3.68193i) q^{6} +(-4.52918 + 2.97889i) q^{7} +(-1.81808 - 2.16670i) q^{8} +(0.588642 + 8.98073i) q^{9} +(-1.40130 - 1.17583i) q^{10} +(-0.852172 + 7.29080i) q^{11} +(-5.75416 - 1.69990i) q^{12} +(0.717336 + 2.39607i) q^{13} +(-5.57637 - 5.26104i) q^{14} +(-3.85583 - 0.436473i) q^{15} +(2.38863 - 3.20849i) q^{16} +(12.8216 + 2.26080i) q^{17} +(-12.1663 + 3.73900i) q^{18} +(-0.163680 - 0.928274i) q^{19} +(1.16103 - 2.31180i) q^{20} +(-16.0261 - 2.76577i) q^{21} +(-10.3107 + 1.20515i) q^{22} +(23.9389 - 36.3973i) q^{23} +(0.462564 - 8.47266i) q^{24} +(-6.69023 + 22.3469i) q^{25} +(-3.06326 + 1.76858i) q^{26} +(-17.1286 + 20.8713i) q^{27} +(5.42100 - 9.38944i) q^{28} +(10.5679 - 9.97029i) q^{29} +(-0.656913 - 5.44833i) q^{30} +(-0.520156 + 8.93074i) q^{31} +(5.19421 + 2.24057i) q^{32} +(-16.8177 + 14.2163i) q^{33} +(1.07058 + 18.3811i) q^{34} +(2.39824 - 6.58910i) q^{35} +(-9.11315 - 15.5226i) q^{36} +(18.2424 - 6.63969i) q^{37} +(1.22401 - 0.527986i) q^{38} +(-3.34313 + 6.71752i) q^{39} +(3.55991 + 0.843714i) q^{40} +(2.27520 - 9.59983i) q^{41} +(-1.42079 - 22.9554i) q^{42} +(2.47852 + 5.74586i) q^{43} +(-5.02115 - 13.7955i) q^{44} +(-7.54759 - 8.86313i) q^{45} +(57.8935 + 21.0715i) q^{46} +(64.0157 - 3.72849i) q^{47} +(11.8100 - 2.12674i) q^{48} +(-7.76823 + 18.0088i) q^{49} +(-32.9334 - 1.91815i) q^{50} +(23.4377 + 31.2445i) q^{51} +(-3.43278 - 3.63853i) q^{52} +(31.0537 + 17.9289i) q^{53} +(-34.3072 - 16.7635i) q^{54} +(-4.74737 - 8.22268i) q^{55} +(14.6888 + 4.39752i) q^{56} +(1.54529 - 2.36821i) q^{57} +(17.1667 + 11.2907i) q^{58} +(-12.6486 - 108.216i) q^{59} +(7.28316 - 2.68089i) q^{60} +(55.2475 + 27.7463i) q^{61} +(-12.4592 + 2.19689i) q^{62} +(-29.4186 - 38.9218i) q^{63} +(-1.38919 + 7.87846i) q^{64} +(-2.59502 - 1.93192i) q^{65} +(-25.0478 - 18.5062i) q^{66} +(8.81515 - 9.34351i) q^{67} +(-24.9449 + 7.46801i) q^{68} +(127.059 - 30.6020i) q^{69} +(9.84938 + 1.15123i) q^{70} +(9.13600 - 10.8879i) q^{71} +(18.3884 - 17.6031i) q^{72} +(31.7996 - 26.6831i) q^{73} +(15.0864 + 22.9378i) q^{74} +(-60.4774 + 35.2105i) q^{75} +(1.12576 + 1.51215i) q^{76} +(-17.8588 - 35.5598i) q^{77} +(-10.3343 - 2.40960i) q^{78} +(-76.6120 + 18.1574i) q^{79} +5.17394i q^{80} +(-80.3070 + 10.5729i) q^{81} +13.9523 q^{82} +(-0.889177 - 3.75173i) q^{83} +(31.1254 - 9.44182i) q^{84} +(-15.0491 + 7.55795i) q^{85} +(-7.09850 + 5.28464i) q^{86} +(43.5862 - 0.158519i) q^{87} +(17.3463 - 11.4088i) q^{88} +(7.81943 + 9.31884i) q^{89} +(9.73493 - 13.2768i) q^{90} +(-10.3866 - 8.71536i) q^{91} +(-10.1150 + 86.5391i) q^{92} +(-19.4539 + 18.4880i) q^{93} +(26.0089 + 86.8756i) q^{94} +(0.886836 + 0.836687i) q^{95} +(6.77832 + 15.5581i) q^{96} +(-25.5306 + 34.2936i) q^{97} +(-27.3153 - 4.81642i) q^{98} +(-65.9783 - 3.36145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q + 72 q^{18} + 108 q^{20} + 270 q^{21} + 162 q^{23} - 54 q^{27} - 162 q^{29} - 216 q^{30} - 378 q^{33} - 486 q^{35} - 180 q^{36} - 108 q^{38} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 1728 q^{65} - 1008 q^{66} + 702 q^{67} - 216 q^{68} - 1872 q^{69} + 540 q^{70} - 1296 q^{71} - 576 q^{72} - 864 q^{74} - 900 q^{75} + 108 q^{76} - 864 q^{77} - 288 q^{78} + 108 q^{79} + 144 q^{81} + 432 q^{83} + 144 q^{84} - 540 q^{85} + 864 q^{86} + 2016 q^{87} - 216 q^{88} + 1782 q^{89} + 1440 q^{90} + 864 q^{92} + 2124 q^{93} - 756 q^{94} + 2808 q^{95} + 288 q^{96} - 918 q^{97} + 1296 q^{98} + 1800 q^{99}+O(q^{100}) \) 324 * q + 72 * q^18 + 108 * q^20 + 270 * q^21 + 162 * q^23 - 54 * q^27 - 162 * q^29 - 216 * q^30 - 378 * q^33 - 486 * q^35 - 180 * q^36 - 108 * q^38 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 1728 * q^65 - 1008 * q^66 + 702 * q^67 - 216 * q^68 - 1872 * q^69 + 540 * q^70 - 1296 * q^71 - 576 * q^72 - 864 * q^74 - 900 * q^75 + 108 * q^76 - 864 * q^77 - 288 * q^78 + 108 * q^79 + 144 * q^81 + 432 * q^83 + 144 * q^84 - 540 * q^85 + 864 * q^86 + 2016 * q^87 - 216 * q^88 + 1782 * q^89 + 1440 * q^90 + 864 * q^92 + 2124 * q^93 - 756 * q^94 + 2808 * q^95 + 288 * q^96 - 918 * q^97 + 1296 * q^98 + 1800 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more