LMFDB - Embedded newform 45.4.l.a.2.15

Newspace parameters

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.15
Character	$\chi$	$=$	45.2
Dual form			45.4.l.a.23.15

$q$-expansion

$f(q)$	$=$	$q+(1.15194 + 4.29910i) q^{2} +(-2.52446 + 4.54171i) q^{3} +(-10.2271 + 5.90461i) q^{4} +(10.7022 - 3.23468i) q^{5} +(-22.4333 - 5.62113i) q^{6} +(-7.13532 + 1.91190i) q^{7} +(-11.9883 - 11.9883i) q^{8} +(-14.2542 - 22.9307i) q^{9} +O(q^{10})$	\(q+(1.15194 + 4.29910i) q^{2} +(-2.52446 + 4.54171i) q^{3} +(-10.2271 + 5.90461i) q^{4} +(10.7022 - 3.23468i) q^{5} +(-22.4333 - 5.62113i) q^{6} +(-7.13532 + 1.91190i) q^{7} +(-11.9883 - 11.9883i) q^{8} +(-14.2542 - 22.9307i) q^{9} +(26.2345 + 42.2836i) q^{10} +(-7.55654 - 4.36277i) q^{11} +(-0.999152 - 61.3544i) q^{12} +(73.7842 + 19.7704i) q^{13} +(-16.4389 - 28.4731i) q^{14} +(-12.3263 + 56.7720i) q^{15} +(-9.50797 + 16.4683i) q^{16} +(-5.92131 + 5.92131i) q^{17} +(82.1614 - 87.6951i) q^{18} +106.718i q^{19} +(-90.3527 + 96.2737i) q^{20} +(9.32953 - 37.2331i) q^{21} +(10.0513 - 37.5120i) q^{22} +(27.4553 - 102.465i) q^{23} +(84.7110 - 24.1833i) q^{24} +(104.074 - 69.2363i) q^{25} +339.980i q^{26} +(140.129 - 6.85080i) q^{27} +(61.6846 - 61.6846i) q^{28} +(85.3380 - 147.810i) q^{29} +(-258.268 + 12.4061i) q^{30} +(-157.999 - 273.662i) q^{31} +(-212.761 - 57.0093i) q^{32} +(38.8906 - 23.3059i) q^{33} +(-32.2773 - 18.6353i) q^{34} +(-70.1792 + 43.5421i) q^{35} +(281.176 + 150.349i) q^{36} +(-31.7091 - 31.7091i) q^{37} +(-458.791 + 122.933i) q^{38} +(-276.057 + 285.197i) q^{39} +(-167.079 - 89.5224i) q^{40} +(298.272 - 172.207i) q^{41} +(170.816 - 2.78172i) q^{42} +(115.545 + 431.220i) q^{43} +103.042 q^{44} +(-226.725 - 199.301i) q^{45} +472.133 q^{46} +(-60.9929 - 227.629i) q^{47} +(-50.7917 - 84.7559i) q^{48} +(-249.789 + 144.216i) q^{49} +(417.541 + 367.667i) q^{50} +(-11.9448 - 41.8410i) q^{51} +(-871.335 + 233.473i) q^{52} +(-60.5508 - 60.5508i) q^{53} +(190.872 + 594.536i) q^{54} +(-94.9837 - 22.2482i) q^{55} +(108.460 + 62.6197i) q^{56} +(-484.682 - 269.405i) q^{57} +(733.754 + 196.609i) q^{58} +(-25.4427 - 44.0680i) q^{59} +(-209.155 - 653.395i) q^{60} +(-36.1174 + 62.5572i) q^{61} +(994.494 - 994.494i) q^{62} +(145.550 + 136.365i) q^{63} -828.227i q^{64} +(853.604 - 27.0816i) q^{65} +(144.994 + 140.347i) q^{66} +(4.59668 - 17.1550i) q^{67} +(25.5947 - 95.5208i) q^{68} +(396.055 + 383.362i) q^{69} +(-268.034 - 251.549i) q^{70} -109.592i q^{71} +(-104.016 + 445.782i) q^{72} +(-144.319 + 144.319i) q^{73} +(99.7935 - 172.847i) q^{74} +(51.7214 + 647.456i) q^{75} +(-630.128 - 1091.41i) q^{76} +(62.2595 + 16.6824i) q^{77} +(-1544.09 - 858.266i) q^{78} +(-140.624 - 81.1891i) q^{79} +(-48.4864 + 207.002i) q^{80} +(-322.635 + 653.718i) q^{81} +(1083.93 + 1083.93i) q^{82} +(279.860 - 74.9883i) q^{83} +(124.433 + 435.873i) q^{84} +(-44.2174 + 82.5245i) q^{85} +(-1720.76 + 993.479i) q^{86} +(455.877 + 760.720i) q^{87} +(38.2877 + 142.892i) q^{88} -1107.89 q^{89} +(595.641 - 1204.30i) q^{90} -564.273 q^{91} +(324.227 + 1210.03i) q^{92} +(1641.75 - 26.7358i) q^{93} +(908.339 - 524.430i) q^{94} +(345.199 + 1142.12i) q^{95} +(796.027 - 822.383i) q^{96} +(-197.725 + 52.9802i) q^{97} +(-907.741 - 907.741i) q^{98} +(7.67108 + 235.465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.15194	+	4.29910i	0.407272	+	1.51996i	0.799826	+	0.600232i	$0.204925\pi$
$2$	1.15194	+	4.29910i	0.407272	+	1.51996i	−0.392553	+	0.919729i	$0.628408\pi$
$3$	−2.52446	+	4.54171i	−0.485832	+	0.874052i
$3$	−2.52446	+	4.54171i	−0.485832	+	0.874052i
$4$	−10.2271	+	5.90461i	−1.27839	+	0.738077i
$5$	10.7022	−	3.23468i	0.957233	−	0.289319i
$5$	10.7022	−	3.23468i	0.957233	−	0.289319i
$6$	−22.4333	−	5.62113i	−1.52639	−	0.382469i
$7$	−7.13532	+	1.91190i	−0.385271	+	0.103233i	−0.446255	−	0.894906i	$-0.647243\pi$
$7$	−7.13532	+	1.91190i	−0.385271	+	0.103233i	0.0609842	+	0.998139i	$0.480576\pi$
$8$	−11.9883	−	11.9883i	−0.529811	−	0.529811i
$9$	−14.2542	−	22.9307i	−0.527934	−	0.849286i
$10$	26.2345	+	42.2836i	0.829608	+	1.33713i
$11$	−7.55654	−	4.36277i	−0.207126	−	0.119584i	0.392849	−	0.919603i	$-0.371489\pi$
$11$	−7.55654	−	4.36277i	−0.207126	−	0.119584i	−0.599975	+	0.800019i	$0.704823\pi$
$12$	−0.999152	−	61.3544i	−0.0240359	−	1.47596i
$13$	73.7842	+	19.7704i	1.57416	+	0.421794i	0.937111	−	0.349030i	$-0.113489\pi$
$13$	73.7842	+	19.7704i	1.57416	+	0.421794i	0.637047	+	0.770825i	$0.280156\pi$
$14$	−16.4389	−	28.4731i	−0.313821	−	0.543553i
$15$	−12.3263	+	56.7720i	−0.212175	+	0.977232i
$16$	−9.50797	+	16.4683i	−0.148562	+	0.257317i
$17$	−5.92131	+	5.92131i	−0.0844782	+	0.0844782i	−0.748083	−	0.663605i	$-0.769026\pi$
$17$	−5.92131	+	5.92131i	−0.0844782	+	0.0844782i	0.663605	+	0.748083i	$0.269026\pi$
$18$	82.1614	−	87.6951i	1.07587	−	1.14833i
$19$			106.718i			1.28857i	0.764787	+	0.644284i	$0.222844\pi$
$19$			106.718i			1.28857i	−0.764787	+	0.644284i	$0.777156\pi$
$20$	−90.3527	+	96.2737i	−1.01017	+	1.07637i
$21$	9.32953	−	37.2331i	0.0969462	−	0.386901i
$22$	10.0513	−	37.5120i	0.0974066	−	0.363526i
$23$	27.4553	−	102.465i	0.248906	−	0.928930i	−0.722474	−	0.691398i	$-0.756995\pi$
$23$	27.4553	−	102.465i	0.248906	−	0.928930i	0.971380	−	0.237531i	$-0.0763383\pi$
$24$	84.7110	−	24.1833i	0.720482	−	0.205683i
$25$	104.074	−	69.2363i	0.832589	−	0.553891i
$26$			339.980i			2.56445i
$27$	140.129	−	6.85080i	0.998807	−	0.0488310i
$28$	61.6846	−	61.6846i	0.416332	−	0.416332i
$29$	85.3380	−	147.810i	0.546444	−	0.946469i	−0.452070	−	0.891982i	$-0.649314\pi$
$29$	85.3380	−	147.810i	0.546444	−	0.946469i	0.998515	−	0.0544866i	$-0.0173522\pi$
$30$	−258.268	+	12.4061i	−1.57177	+	0.0755014i
$31$	−157.999	−	273.662i	−0.915400	−	1.58552i	−0.806315	−	0.591487i	$-0.798541\pi$
$31$	−157.999	−	273.662i	−0.915400	−	1.58552i	−0.109085	−	0.994032i	$-0.534792\pi$
$32$	−212.761	−	57.0093i	−1.17535	−	0.314935i
$33$	38.8906	−	23.3059i	0.205151	−	0.122941i
$34$	−32.2773	−	18.6353i	−0.162809	−	0.0939979i
$35$	−70.1792	+	43.5421i	−0.338927	+	0.210284i
$36$	281.176	+	150.349i	1.30174	+	0.696060i
$37$	−31.7091	−	31.7091i	−0.140890	−	0.140890i	0.633144	−	0.774034i	$-0.281764\pi$
$37$	−31.7091	−	31.7091i	−0.140890	−	0.140890i	−0.774034	+	0.633144i	$0.781764\pi$
$38$	−458.791	+	122.933i	−1.95857	+	0.524798i
$39$	−276.057	+	285.197i	−1.13345	+	1.17097i
$40$	−167.079	−	89.5224i	−0.660437	−	0.353868i
$41$	298.272	−	172.207i	1.13615	−	0.655958i	0.190677	−	0.981653i	$-0.438932\pi$
$41$	298.272	−	172.207i	1.13615	−	0.655958i	0.945475	+	0.325695i	$0.105598\pi$
$42$	170.816	−	2.78172i	0.627558	−	0.0102197i
$43$	115.545	+	431.220i	0.409778	+	1.52931i	0.795070	+	0.606517i	$0.207434\pi$
$43$	115.545	+	431.220i	0.409778	+	1.52931i	−0.385292	+	0.922795i	$0.625899\pi$
$44$	103.042			0.353049
$45$	−226.725	−	199.301i	−0.751070	−	0.660223i
$46$	472.133			1.51331
$47$	−60.9929	−	227.629i	−0.189292	−	0.706448i	−0.993671	−	0.112331i	$-0.964168\pi$
$47$	−60.9929	−	227.629i	−0.189292	−	0.706448i	0.804379	−	0.594117i	$-0.202498\pi$
$48$	−50.7917	−	84.7559i	−0.152732	−	0.254864i
$49$	−249.789	+	144.216i	−0.728249	+	0.420454i
$50$	417.541	+	367.667i	1.18098	+	1.03992i
$51$	−11.9448	−	41.8410i	−0.0327961	−	0.114881i
$52$	−871.335	+	233.473i	−2.32370	+	0.622633i
$53$	−60.5508	−	60.5508i	−0.156930	−	0.156930i	0.624275	−	0.781205i	$-0.285395\pi$
$53$	−60.5508	−	60.5508i	−0.156930	−	0.156930i	−0.781205	+	0.624275i	$0.785395\pi$
$54$	190.872	+	594.536i	0.481008	+	1.49826i
$55$	−94.9837	−	22.2482i	−0.232865	−	0.0545445i
$56$	108.460	+	62.6197i	0.258815	+	0.149427i
$57$	−484.682	−	269.405i	−1.12627	−	0.626028i
$58$	733.754	+	196.609i	1.66115	+	0.445103i
$59$	−25.4427	−	44.0680i	−0.0561416	−	0.0972401i	0.836589	−	0.547831i	$-0.184546\pi$
$59$	−25.4427	−	44.0680i	−0.0561416	−	0.0972401i	−0.892730	+	0.450591i	$0.851213\pi$
$60$	−209.155	−	653.395i	−0.450030	−	1.40588i
$61$	−36.1174	+	62.5572i	−0.0758092	+	0.131305i	−0.901438	−	0.432909i	$-0.857487\pi$
$61$	−36.1174	+	62.5572i	−0.0758092	+	0.131305i	0.825629	+	0.564214i	$0.190821\pi$
$62$	994.494	−	994.494i	2.03711	−	2.03711i
$63$	145.550	+	136.365i	0.291072	+	0.272705i
$64$		−	828.227i		−	1.61763i
$65$	853.604	−	27.0816i	1.62887	−	0.0516779i
$66$	144.994	+	140.347i	0.270418	+	0.261751i
$67$	4.59668	−	17.1550i	0.00838169	−	0.0312809i	−0.961608	−	0.274426i	$-0.911512\pi$
$67$	4.59668	−	17.1550i	0.00838169	−	0.0312809i	0.969990	+	0.243145i	$0.0781790\pi$
$68$	25.5947	−	95.5208i	0.0456444	−	0.170347i
$69$	396.055	+	383.362i	0.691006	+	0.668861i
$70$	−268.034	−	251.549i	−0.457660	−	0.429513i
$71$		−	109.592i		−	0.183185i	−0.995797	−	0.0915927i	$-0.970804\pi$
$71$		−	109.592i		−	0.183185i	0.995797	−	0.0915927i	$-0.0291958\pi$
$72$	−104.016	+	445.782i	−0.170256	+	0.729666i
$73$	−144.319	+	144.319i	−0.231387	+	0.231387i	−0.813271	−	0.581885i	$-0.802315\pi$
$73$	−144.319	+	144.319i	−0.231387	+	0.231387i	0.581885	+	0.813271i	$0.302315\pi$
$74$	99.7935	−	172.847i	0.156767	−	0.271529i
$75$	51.7214	+	647.456i	0.0796303	+	0.996824i
$76$	−630.128	−	1091.41i	−0.951062	−	1.64729i
$77$	62.2595	+	16.6824i	0.0921446	+	0.0246901i
$78$	−1544.09	−	858.266i	−2.24146	−	1.24589i
$79$	−140.624	−	81.1891i	−0.200271	−	0.115626i	0.396511	−	0.918030i	$-0.370221\pi$
$79$	−140.624	−	81.1891i	−0.200271	−	0.115626i	−0.596782	+	0.802404i	$0.703554\pi$
$80$	−48.4864	+	207.002i	−0.0677619	+	0.289294i
$81$	−322.635	+	653.718i	−0.442572	+	0.896733i
$82$	1083.93	+	1083.93i	1.45975	+	1.45975i
$83$	279.860	−	74.9883i	0.370104	−	0.0991691i	−0.0689728	−	0.997619i	$-0.521972\pi$
$83$	279.860	−	74.9883i	0.370104	−	0.0991691i	0.439077	+	0.898449i	$0.355306\pi$
$84$	124.433	+	435.873i	0.161628	+	0.566163i
$85$	−44.2174	+	82.5245i	−0.0564242	+	0.105306i
$86$	−1720.76	+	993.479i	−2.15760	+	1.24569i
$87$	455.877	+	760.720i	0.561783	+	0.937446i
$88$	38.2877	+	142.892i	0.0463805	+	0.173094i
$89$	−1107.89			−1.31950			−0.659751	−	0.751484i	$-0.729338\pi$
$89$	−1107.89			−1.31950			−0.659751	+	0.751484i	$0.729338\pi$
$90$	595.641	−	1204.30i	0.697624	−	1.41049i
$91$	−564.273			−0.650021
$92$	324.227	+	1210.03i	0.367423	+	1.37124i
$93$	1641.75	−	26.7358i	1.83056	−	0.0298105i
$94$	908.339	−	524.430i	0.996681	−	0.575434i
$95$	345.199	+	1142.12i	0.372807	+	1.23346i
$96$	796.027	−	822.383i	0.846294	−	0.874314i
$97$	−197.725	+	52.9802i	−0.206968	+	0.0554569i	−0.360813	−	0.932638i	$-0.617501\pi$
$97$	−197.725	+	52.9802i	−0.206968	+	0.0554569i	0.153845	+	0.988095i	$0.450834\pi$
$98$	−907.741	−	907.741i	−0.935670	−	0.935670i
$99$	7.67108	+	235.465i	0.00778760	+	0.239041i
$100$	−655.557	+	1322.60i	−0.655557	+	1.32260i
$101$	−960.085	−	554.305i	−0.945862	−	0.546093i	−0.0540686	−	0.998537i	$-0.517219\pi$
$101$	−960.085	−	554.305i	−0.945862	−	0.546093i	−0.891793	+	0.452444i	$0.850552\pi$
$102$	166.119	−	99.5500i	0.161257	−	0.0966364i
$103$	−276.457	−	74.0766i	−0.264468	−	0.0708639i	0.124148	−	0.992264i	$-0.460380\pi$
$103$	−276.457	−	74.0766i	−0.264468	−	0.0708639i	−0.388616	+	0.921400i	$0.627047\pi$
$104$	−647.531	−	1121.56i	−0.610535	−	1.05748i
$105$	−20.5908	−	428.653i	−0.0191377	−	0.398403i
$106$	190.563	−	330.065i	0.174614	−	0.302441i
$107$	−864.028	+	864.028i	−0.780643	+	0.780643i	−0.979939	−	0.199296i	$-0.936134\pi$
$107$	−864.028	+	864.028i	−0.780643	+	0.780643i	0.199296	+	0.979939i	$0.436134\pi$
$108$	−1392.66	+	897.470i	−1.24082	+	0.799621i
$109$		−	990.712i		−	0.870578i	−0.900291	−	0.435289i	$-0.856646\pi$
$109$		−	990.712i		−	0.870578i	0.900291	−	0.435289i	$-0.143354\pi$
$110$	−13.7683	−	433.973i	−0.0119342	−	0.376161i
$111$	224.062	−	63.9651i	0.191595	−	0.0546964i
$112$	36.3567	−	135.685i	0.0306730	−	0.114473i
$113$	19.6119	−	73.1927i	0.0163269	−	0.0609327i	−0.957282	−	0.289157i	$-0.906625\pi$
$113$	19.6119	−	73.1927i	0.0163269	−	0.0609327i	0.973609	+	0.228224i	$0.0732918\pi$
$114$	599.875	−	2394.03i	0.492837	−	1.96686i
$115$	−37.6085	−	1185.41i	−0.0304957	−	0.961215i
$116$			2015.55i			1.61327i
$117$	−598.386	−	1973.74i	−0.472827	−	1.55959i
$118$	160.144	−	160.144i	0.124936	−	0.124936i
$119$	30.9295	−	53.5714i	0.0238261	−	0.0412679i
$120$	828.368	−	532.827i	0.630161	−	0.405335i
$121$	−627.432	−	1086.74i	−0.471399	−	0.816488i
$122$	−310.545	−	83.2102i	−0.230454	−	0.0617500i
$123$	29.1401	+	1789.39i	0.0213616	+	1.31174i
$124$	3231.73	+	1865.84i	2.34047	+	1.35127i
$125$	889.859	−	1077.63i	0.636731	−	0.771086i
$126$	−418.584	+	782.818i	−0.295956	+	0.553484i
$127$	1084.18	+	1084.18i	0.757521	+	0.757521i	0.975871	−	0.218350i	$-0.0700674\pi$
$127$	1084.18	+	1084.18i	0.757521	+	0.757521i	−0.218350	+	0.975871i	$0.570067\pi$
$128$	1858.54	−	497.994i	1.28338	−	0.343882i
$129$	−2250.16	−	563.825i	−1.53578	−	0.384822i
$130$	1099.73	+	3638.53i	0.741942	+	2.45477i
$131$	1415.36	−	817.157i	0.943972	−	0.545003i	0.0527689	−	0.998607i	$-0.483195\pi$
$131$	1415.36	−	817.157i	0.943972	−	0.545003i	0.891203	+	0.453604i	$0.149862\pi$
$132$	−260.125	+	467.986i	−0.171523	+	0.308583i
$133$	−204.035	−	761.467i	−0.133023	−	0.496448i
$134$	79.0463			0.0509594
$135$	1477.52	−	526.590i	0.941963	−	0.335716i
$136$	141.972			0.0895149
$137$	591.988	+	2209.33i	0.369175	+	1.37778i	0.861672	+	0.507465i	$0.169417\pi$
$137$	591.988	+	2209.33i	0.369175	+	1.37778i	−0.492497	+	0.870314i	$0.663916\pi$
$138$	−1191.88	+	2144.29i	−0.735215	+	1.32271i
$139$	−1895.18	+	1094.18i	−1.15645	+	0.667678i	−0.950451	−	0.310874i	$-0.899378\pi$
$139$	−1895.18	+	1094.18i	−1.15645	+	0.667678i	−0.206001	+	0.978552i	$0.566045\pi$
$140$	460.630	−	859.690i	0.278074	−	0.518979i
$141$	1187.80	+	297.627i	0.709437	+	0.177764i
$142$	471.146	−	126.243i	0.278435	−	0.0746063i
$143$	−471.299	−	471.299i	−0.275609	−	0.275609i
$144$	513.158	−	16.7179i	0.296967	−	0.00967471i
$145$	435.186	−	1857.93i	0.249243	−	1.06409i
$146$	−786.687	−	454.194i	−0.445936	−	0.257461i
$147$	−24.4035	−	1498.54i	−0.0136923	−	0.840797i
$148$	511.522	+	137.062i	0.284100	+	0.0761244i
$149$	311.430	+	539.412i	0.171230	+	0.296580i	0.938850	−	0.344326i	$-0.111892\pi$
$149$	311.430	+	539.412i	0.171230	+	0.296580i	−0.767620	+	0.640905i	$0.778559\pi$
$150$	−2723.90	+	968.187i	−1.48270	+	0.527014i
$151$	−1009.02	+	1747.68i	−0.543795	+	0.941881i	0.454887	+	0.890549i	$0.349680\pi$
$151$	−1009.02	+	1747.68i	−0.543795	+	0.941881i	−0.998682	+	0.0513314i	$0.983654\pi$
$152$	1279.36	−	1279.36i	0.682697	−	0.682697i
$153$	220.183	+	51.3763i	0.116345	+	0.0271472i
$154$			286.877i			0.150112i
$155$	−2576.14	−	2417.70i	−1.33497	−	1.25287i
$156$	1139.28	−	4546.74i	0.584715	−	2.33353i
$157$	182.444	−	680.891i	0.0927428	−	0.346121i	−0.903925	−	0.427692i	$-0.859327\pi$
$157$	182.444	−	680.891i	0.0927428	−	0.346121i	0.996668	+	0.0815706i	$0.0259936\pi$
$158$	187.050	−	698.080i	0.0941829	−	0.351495i
$159$	427.862	−	122.146i	0.213407	−	0.0609233i
$160$	−2461.42	+	78.0916i	−1.21620	+	0.0385855i
$161$			783.611i			0.383585i
$162$	−3182.06	−	633.996i	−1.54325	−	0.307478i
$163$	−426.426	+	426.426i	−0.204909	+	0.204909i	−0.802100	−	0.597190i	$-0.796284\pi$
$163$	−426.426	+	426.426i	−0.204909	+	0.204909i	0.597190	+	0.802100i	$0.296284\pi$
$164$	−2033.64	+	3522.36i	−0.968294	+	1.67714i
$165$	340.827	−	375.223i	0.160808	−	0.177037i
$166$	644.765	+	1116.77i	0.301467	+	0.522155i
$167$	613.477	+	164.381i	0.284265	+	0.0761686i	0.398134	−	0.917327i	$-0.369658\pi$
$167$	613.477	+	164.381i	0.284265	+	0.0761686i	−0.113869	+	0.993496i	$0.536324\pi$
$168$	−558.204	+	334.515i	−0.256348	+	0.153621i
$169$	3150.58	+	1818.99i	1.43404	+	0.827943i
$170$	−405.717	−	95.0318i	−0.183042	−	0.0428742i
$171$	2447.12	−	1521.18i	1.09436	−	0.680278i
$172$	−3727.88	−	3727.88i	−1.65260	−	1.65260i
$173$	686.713	−	184.004i	0.301791	−	0.0808646i	−0.104746	−	0.994499i	$-0.533403\pi$
$173$	686.713	−	184.004i	0.301791	−	0.0808646i	0.406537	+	0.913634i	$0.366736\pi$
$174$	−2745.27	+	2836.16i	−1.19608	+	1.23568i
$175$	−610.226	+	693.003i	−0.263593	+	0.299349i
$176$	143.695	−	82.9622i	0.0615420	−	0.0355313i
$177$	264.373	−	4.30529i	0.112268	−	0.00182828i
$178$	−1276.22	−	4762.91i	−0.537397	−	2.00559i
$179$	2690.52			1.12346			0.561730	−	0.827321i	$-0.310136\pi$
$179$	2690.52			1.12346			0.561730	+	0.827321i	$0.310136\pi$
$180$	3495.53	+	699.547i	1.44745	+	0.289673i
$181$	197.441			0.0810810			0.0405405	−	0.999178i	$-0.487092\pi$
$181$	197.441			0.0810810			0.0405405	+	0.999178i	$0.487092\pi$
$182$	−650.009	−	2425.87i	−0.264736	−	0.988007i
$183$	−192.939	−	321.958i	−0.0779371	−	0.130054i
$184$	−1557.52	+	899.232i	−0.624030	+	0.360284i
$185$	−441.925	−	236.788i	−0.175627	−	0.0941026i
$186$	2006.14	+	7027.26i	0.790846	+	2.77023i
$187$	70.5779	−	18.9113i	0.0275998	−	0.00739535i
$188$	1967.84	+	1967.84i	0.763402	+	0.763402i
$189$	−986.766	+	316.795i	−0.379771	+	0.121923i
$190$	−4512.42	+	2799.69i	−1.72298	+	1.06901i
$191$	306.085	+	176.718i	0.115956	+	0.0669470i	0.556856	−	0.830609i	$-0.312007\pi$
$191$	306.085	+	176.718i	0.115956	+	0.0669470i	−0.440900	+	0.897556i	$0.645341\pi$
$192$	3761.56	+	2090.82i	1.41389	+	0.785897i
$193$	1387.59	+	371.803i	0.517517	+	0.138668i	0.508118	−	0.861287i	$-0.330341\pi$
$193$	1387.59	+	371.803i	0.517517	+	0.138668i	0.00939936	+	0.999956i	$0.497008\pi$
$194$	−455.534	−	789.008i	−0.168585	−	0.291997i
$195$	−2031.89	+	3945.18i	−0.746188	+	1.44882i
$196$	1703.08	−	2949.82i	0.620655	−	1.07501i
$197$	−2647.40	+	2647.40i	−0.957458	+	0.957458i	−0.999131	−	0.0416736i	$-0.986731\pi$
$197$	−2647.40	+	2647.40i	−0.957458	+	0.957458i	0.0416736	+	0.999131i	$0.486731\pi$
$198$	−1003.45	+	304.220i	−0.360162	+	0.109192i
$199$		−	3785.65i		−	1.34853i	−0.738488	−	0.674266i	$-0.764460\pi$
$199$		−	3785.65i		−	1.34853i	0.738488	−	0.674266i	$-0.235540\pi$
$200$	−2077.68	−	417.639i	−0.734572	−	0.147658i
$201$	66.3090	+	64.1839i	0.0232690	+	0.0225233i
$202$	1277.05	−	4766.03i	0.444818	−	1.66008i
$203$	−326.316	+	1217.83i	−0.112822	+	0.421058i
$204$	369.215	+	357.382i	0.126717	+	0.122656i
$205$	2635.13	−	2807.81i	0.897781	−	0.956614i
$206$		−	1273.85i		−	0.430842i
$207$	−2740.94	+	830.983i	−0.920332	+	0.279021i
$208$	−1027.12	+	1027.12i	−0.342395	+	0.342395i
$209$	465.586	−	806.418i	0.154092	−	0.266895i
$210$	1819.10	−	582.305i	0.597763	−	0.191347i
$211$	676.890	+	1172.41i	0.220849	+	0.382521i	0.955066	−	0.296394i	$-0.0957840\pi$
$211$	676.890	+	1172.41i	0.220849	+	0.382521i	−0.734217	+	0.678915i	$0.762451\pi$
$212$	976.788	+	261.730i	0.316444	+	0.0847908i
$213$	497.734	+	276.660i	0.160114	+	0.0889974i
$214$	−4709.85	−	2719.24i	−1.50448	−	0.868613i
$215$	2631.44	+	4241.25i	0.834711	+	1.34535i
$216$	−1762.03	−	1597.77i	−0.555050	−	0.503308i
$217$	1650.59	+	1650.59i	0.516355	+	0.516355i
$218$	4259.17	−	1141.24i	1.32325	−	0.354563i
$219$	−291.126	−	1019.78i	−0.0898288	−	0.314659i
$220$	1102.77	−	333.308i	0.337950	−	0.102144i
$221$	−553.966	+	319.832i	−0.168614	+	0.0973496i
$222$	533.098	+	889.579i	0.161168	+	0.268940i
$223$	508.185	+	1896.57i	0.152604	+	0.569525i	0.999299	+	0.0374461i	$0.0119222\pi$
$223$	508.185	+	1896.57i	0.152604	+	0.569525i	−0.846695	+	0.532079i	$0.821411\pi$
$224$	1627.12			0.485341
$225$	−3071.13	−	1399.57i	−0.909963	−	0.414689i
$226$	337.255			0.0992648
$227$	−816.800	−	3048.34i	−0.238823	−	0.891301i	−0.976388	−	0.216025i	$-0.930691\pi$
$227$	−816.800	−	3048.34i	−0.238823	−	0.891301i	0.737564	−	0.675277i	$-0.235976\pi$
$228$	6547.62	−	106.627i	1.90187	−	0.0309718i
$229$	3455.23	−	1994.88i	0.997066	−	0.575656i	0.0896872	−	0.995970i	$-0.471413\pi$
$229$	3455.23	−	1994.88i	0.997066	−	0.575656i	0.907379	+	0.420314i	$0.138080\pi$
$230$	5052.86	−	1527.20i	1.44859	−	0.437829i
$231$	−232.938	+	240.651i	−0.0663472	+	0.0685439i
$232$	−2795.04	+	748.928i	−0.790962	+	0.211937i
$233$	−2166.38	−	2166.38i	−0.609118	−	0.609118i	0.333598	−	0.942715i	$-0.391737\pi$
$233$	−2166.38	−	2166.38i	−0.609118	−	0.609118i	−0.942715	+	0.333598i	$0.891737\pi$
$234$	7795.98	−	4846.15i	2.17795	−	1.35386i
$235$	−1389.06	−	2238.83i	−0.385585	−	0.621470i
$236$	520.409	+	300.458i	0.143541	+	0.0828736i
$237$	723.736	−	433.713i	0.198362	−	0.118872i
$238$	265.938	+	71.2579i	0.0724294	+	0.0194074i
$239$	−1946.01	−	3370.59i	−0.526682	−	0.912239i	−0.999517	−	0.0310884i	$-0.990103\pi$
$239$	−1946.01	−	3370.59i	−0.526682	−	0.912239i	0.472835	−	0.881151i	$-0.343231\pi$
$240$	−817.740	−	742.779i	−0.219937	−	0.199776i
$241$	−3291.66	+	5701.33i	−0.879812	+	1.52388i	−0.0282647	+	0.999600i	$0.508998\pi$
$241$	−3291.66	+	5701.33i	−0.879812	+	1.52388i	−0.851547	+	0.524278i	$0.824335\pi$
$242$	3949.26	−	3949.26i	1.04904	−	1.04904i
$243$	−2154.52	−	3115.60i	−0.568775	−	0.822493i
$244$		−	853.037i		−	0.223812i
$245$	−2206.80	+	2351.41i	−0.575458	+	0.613169i
$246$	−7659.22	+	2186.55i	−1.98510	+	0.566705i
$247$	−2109.86	+	7874.10i	−0.543511	+	2.02841i
$248$	−1386.60	+	5174.85i	−0.355036	+	1.32501i
$249$	−365.921	+	1460.35i	−0.0931297	+	0.371670i
$250$	5657.88	+	2584.23i	1.43134	+	0.653765i
$251$		−	6323.18i		−	1.59010i	−0.606543	−	0.795051i	$-0.707444\pi$
$251$		−	6323.18i		−	1.59010i	0.606543	−	0.795051i	$-0.292556\pi$
$252$	−2293.74	−	535.206i	−0.573380	−	0.133789i
$253$	−654.497	+	654.497i	−0.162640	+	0.162640i
$254$	−3412.08	+	5909.89i	−0.842885	+	1.45992i
$255$	−263.177	−	409.152i	−0.0646306	−	0.100479i
$256$	968.943	+	1678.26i	0.236558	+	0.409731i
$257$	−1363.16	−	365.257i	−0.330861	−	0.0886541i	0.0895642	−	0.995981i	$-0.471453\pi$
$257$	−1363.16	−	365.257i	−0.330861	−	0.0886541i	−0.420426	+	0.907327i	$0.638119\pi$
$258$	−168.112	−	10323.2i	−0.0405666	−	2.49106i
$259$	286.879	+	165.630i	0.0688255	+	0.0397364i
$260$	−8569.98	+	5317.17i	−2.04418	+	1.26829i
$261$	−4605.81	+	150.050i	−1.09231	+	0.0355857i
$262$	5143.45	+	5143.45i	1.21284	+	1.21284i
$263$	317.317	−	85.0248i	0.0743977	−	0.0199348i	−0.221428	−	0.975177i	$-0.571072\pi$
$263$	317.317	−	85.0248i	0.0743977	−	0.0199348i	0.295826	+	0.955242i	$0.404405\pi$
$264$	−745.628	−	186.833i	−0.173827	−	0.0435559i
$265$	−843.889	−	452.164i	−0.195621	−	0.104816i
$266$	3038.59	−	1754.33i	0.700405	−	0.404379i
$267$	2796.81	−	5031.70i	0.641057	−	1.15331i
$268$	54.2832	+	202.588i	0.0123727	+	0.0461754i
$269$	764.226			0.173218			0.0866091	−	0.996242i	$-0.472397\pi$
$269$	764.226			0.173218			0.0866091	+	0.996242i	$0.472397\pi$
$270$	3965.88	+	5745.42i	0.893911	+	1.29502i
$271$	4645.09			1.04121			0.520607	−	0.853797i	$-0.325706\pi$
$271$	4645.09			1.04121			0.520607	+	0.853797i	$0.325706\pi$
$272$	−41.2142	−	153.813i	−0.00918742	−	0.0342879i
$273$	1424.49	−	2562.76i	0.315801	−	0.568152i
$274$	−8816.19	+	5090.03i	−1.94382	+	1.12226i
$275$	−1088.50	+	69.1375i	−0.238687	+	0.0151605i
$276$	−6314.10	−	1582.13i	−1.37704	−	0.345047i
$277$	5783.77	−	1549.76i	1.25456	−	0.336158i	0.430463	−	0.902608i	$-0.358350\pi$
$277$	5783.77	−	1549.76i	1.25456	−	0.336158i	0.824096	+	0.566450i	$0.191684\pi$
$278$	−6887.13	−	6887.13i	−1.48584	−	1.48584i
$279$	−4023.11	+	7523.85i	−0.863288	+	1.61448i
$280$	1363.32	+	319.333i	0.290978	+	0.0681563i
$281$	4201.11	+	2425.51i	0.891877	+	0.514925i	0.874556	−	0.484925i	$-0.161153\pi$
$281$	4201.11	+	2425.51i	0.891877	+	0.514925i	0.0173209	+	0.999850i	$0.494486\pi$
$282$	88.7415	+	5449.31i	0.0187393	+	1.15071i
$283$	−345.530	−	92.5845i	−0.0725782	−	0.0194473i	0.222347	−	0.974968i	$-0.428628\pi$
$283$	−345.530	−	92.5845i	−0.0725782	−	0.0194473i	−0.294925	+	0.955520i	$0.595295\pi$
$284$	647.098	+	1120.81i	0.135205	+	0.234182i
$285$	−6058.60	−	1315.43i	−1.25923	−	0.273402i
$286$	1483.25	−	2569.07i	0.306667	−	0.531162i
$287$	−1799.02	+	1799.02i	−0.370010	+	0.370010i
$288$	1725.48	+	5691.39i	0.353039	+	1.16447i
$289$			4842.88i			0.985727i
$290$	8488.74	−	269.316i	1.71888	−	0.0545336i
$291$	258.528	−	1031.75i	0.0520796	−	0.207844i
$292$	623.814	−	2328.11i	0.125020	−	0.466582i
$293$	−2206.15	+	8233.45i	−0.439879	+	1.64165i	0.289236	+	0.957258i	$0.406599\pi$
$293$	−2206.15	+	8233.45i	−0.439879	+	1.64165i	−0.729114	+	0.684392i	$0.760068\pi$
$294$	6414.25	−	1831.14i	1.27240	−	0.363245i
$295$	−414.838	−	389.325i	−0.0818740	−	0.0768386i
$296$			760.273i			0.149290i
$297$	−1088.78	−	559.581i	−0.212718	−	0.109327i
$298$	−1960.24	+	1960.24i	−0.381052	+	0.381052i
$299$	4051.54	−	7017.48i	0.783635	−	1.35730i
$300$	−4351.94	−	6316.20i	−0.837531	−	1.21555i
$301$	−1648.90	−	2855.98i	−0.315751	−	0.546897i
$302$	−8675.77	−	2324.67i	−1.65310	−	0.442946i
$303$	4941.19	−	2961.10i	0.936844	−	0.561422i
$304$	−1757.46	−	1014.67i	−0.331570	−	0.191432i
$305$	−184.183	+	786.327i	−0.0345779	+	0.147623i
$306$	32.7665	+	1005.77i	0.00612137	+	0.187896i
$307$	−6239.03	−	6239.03i	−1.15987	−	1.15987i	−0.984503	−	0.175367i	$-0.943889\pi$
$307$	−6239.03	−	6239.03i	−1.15987	−	1.15987i	−0.175367	−	0.984503i	$-0.556111\pi$
$308$	−735.237	+	197.006i	−0.136020	+	0.0364463i
$309$	1034.34	−	1068.59i	0.190426	−	0.196730i
$310$	7426.39	−	13860.1i	1.36062	−	2.53936i
$311$	−1983.11	+	1144.95i	−0.361582	+	0.208760i	−0.669775	−	0.742565i	$-0.733609\pi$
$311$	−1983.11	+	1144.95i	−0.361582	+	0.208760i	0.308192	+	0.951324i	$0.400276\pi$
$312$	6728.45	−	109.572i	1.22091	−	0.0198824i
$313$	1583.94	+	5911.34i	0.286037	+	1.06750i	0.948079	+	0.318036i	$0.103023\pi$
$313$	1583.94	+	5911.34i	0.286037	+	1.06750i	−0.662042	+	0.749467i	$0.730310\pi$
$314$	3137.38			0.563862
$315$	1998.80	+	988.601i	0.357522	+	0.176830i
$316$	1917.56			0.341365
$317$	2327.37	+	8685.87i	0.412361	+	1.53895i	0.790064	+	0.613024i	$0.210047\pi$
$317$	2327.37	+	8685.87i	0.412361	+	1.53895i	−0.377704	+	0.925927i	$0.623286\pi$
$318$	1017.99	+	1698.72i	0.179516	+	0.299558i
$319$	−1289.72	+	744.620i	−0.226365	+	0.130692i
$320$	−2679.05	−	8863.84i	−0.468011	−	1.54845i
$321$	−1742.96	−	6105.37i	−0.303061	−	1.06158i
$322$	−3368.82	+	902.673i	−0.583035	+	0.156224i
$323$	−631.910	−	631.910i	−0.108856	−	0.108856i
$324$	−560.337	−	8590.67i	−0.0960797	−	1.47302i
$325$	9047.83	−	3050.97i	1.54426	−	0.520730i
$326$	−2324.46	−	1342.03i	−0.394909	−	0.228001i
$327$	4499.53	+	2501.01i	0.760931	+	0.422955i
$328$	−5640.22	−	1511.29i	−0.949479	−	0.254412i
$329$	870.409	+	1507.59i	0.145858	+	0.252633i
$330$	2005.74	+	1033.02i	0.334582	+	0.172320i
$331$	368.018	−	637.425i	0.0611120	−	0.105849i	−0.833851	−	0.551990i	$-0.813869\pi$
$331$	368.018	−	637.425i	0.0611120	−	0.105849i	0.894963	+	0.446141i	$0.147202\pi$
$332$	−2419.38	+	2419.38i	−0.399942	+	0.399942i
$333$	−275.124	+	1179.10i	−0.0452754	+	0.194037i
$334$			2826.75i			0.463093i
$335$	−6.29655	−	198.465i	−0.00102692	−	0.0323681i
$336$	524.460	+	507.652i	0.0851537	+	0.0824247i
$337$	1168.46	−	4360.75i	0.188873	−	0.704883i	−0.804896	−	0.593417i	$-0.797779\pi$
$337$	1168.46	−	4360.75i	0.188873	−	0.704883i	0.993768	−	0.111466i	$-0.0355546\pi$
$338$	−4190.74	+	15640.0i	−0.674396	+	2.51688i
$339$	282.910	+	273.844i	0.0453262	+	0.0438736i
$340$	−35.0598	−	1105.07i	−0.00559231	−	0.176268i
$341$			2757.25i			0.437869i
$342$	9358.64	+	8768.10i	1.47970	+	1.38633i
$343$	3298.23	−	3298.23i	0.519207	−	0.519207i
$344$	3784.39	−	6554.76i	0.593141	−	1.02735i
$345$	5478.71	+	2821.70i	0.854968	+	0.440335i
$346$	1582.11	+	2740.29i	0.245822	+	0.425777i
$347$	−3929.82	−	1052.99i	−0.607964	−	0.162904i	−0.0583140	−	0.998298i	$-0.518572\pi$
$347$	−3929.82	−	1052.99i	−0.607964	−	0.162904i	−0.549651	+	0.835395i	$0.685239\pi$
$348$	−9154.05	−	5088.18i	−1.41008	−	0.783779i
$349$	−2120.49	−	1224.26i	−0.325235	−	0.187775i	0.328489	−	0.944508i	$-0.393461\pi$
$349$	−2120.49	−	1224.26i	−0.325235	−	0.187775i	−0.653724	+	0.756733i	$0.726794\pi$
$350$	−3682.23	−	1825.13i	−0.562353	−	0.278735i
$351$	10474.7	+	2264.92i	1.59288	+	0.344424i
$352$	1359.02	+	1359.02i	0.205784	+	0.205784i
$353$	−10497.9	+	2812.90i	−1.58285	+	0.424123i	−0.939807	−	0.341707i	$-0.888995\pi$
$353$	−10497.9	+	2812.90i	−1.58285	+	0.424123i	−0.643043	+	0.765830i	$0.722328\pi$
$354$	323.051	+	1131.61i	0.0485027	+	0.169899i
$355$	−354.495	−	1172.87i	−0.0529989	−	0.175351i
$356$	11330.5	−	6541.64i	1.68683	−	0.973894i
$357$	165.226	+	275.712i	0.0244949	+	0.0408745i
$358$	3099.32	+	11566.8i	0.457554	+	1.70762i
$359$	6928.63			1.01861			0.509303	−	0.860587i	$-0.329903\pi$
$359$	6928.63			1.01861			0.509303	+	0.860587i	$0.329903\pi$
$360$	328.763	+	5107.30i	0.0481315	+	0.747718i
$361$	−4529.72			−0.660406
$362$	227.440	+	848.818i	0.0330221	+	0.123240i
$363$	6519.61	−	106.171i	0.942674	−	0.0153514i
$364$	5770.88	−	3331.82i	0.830978	−	0.479766i
$365$	−1077.70	+	2011.35i	−0.154546	+	0.288435i
$366$	1161.87	−	1200.34i	0.165935	−	0.171429i
$367$	−9084.65	+	2434.22i	−1.29214	+	0.346227i	−0.838472	−	0.544944i	$-0.816551\pi$
$367$	−9084.65	+	2434.22i	−1.29214	+	0.346227i	−0.453666	+	0.891172i	$0.649884\pi$
$368$	1426.37	+	1426.37i	0.202051	+	0.202051i
$369$	−8200.47	−	4384.91i	−1.15691	−	0.618615i
$370$	508.903	−	2172.65i	0.0715043	−	0.305272i
$371$	547.817	+	316.282i	0.0766610	+	0.0442603i
$372$	−16632.5	+	9967.34i	−2.31816	+	1.38920i
$373$	−5601.71	−	1500.97i	−0.777602	−	0.208358i	−0.151875	−	0.988400i	$-0.548531\pi$
$373$	−5601.71	−	1500.97i	−0.777602	−	0.208358i	−0.625727	+	0.780042i	$0.715198\pi$
$374$	162.603	+	281.637i	0.0224813	+	0.0389388i
$375$	2647.85	+	6761.90i	0.364625	+	0.931155i
$376$	−1997.67	+	3460.07i	−0.273995	+	0.474573i
$377$	9218.86	−	9218.86i	1.25940	−	1.25940i
$378$	−2498.63	−	3877.28i	−0.339989	−	0.527581i
$379$			6617.31i			0.896856i	0.893819	+	0.448428i	$0.148016\pi$
$379$			6617.31i			0.896856i	−0.893819	+	0.448428i	$0.851984\pi$
$380$	−10274.1	−	9642.26i	−1.38698	−	1.30168i
$381$	−7660.97	+	2187.05i	−1.03014	+	0.294084i
$382$	−407.137	+	1519.46i	−0.0545313	+	0.203514i
$383$	3218.73	−	12012.4i	0.429423	−	1.60263i	−0.324646	−	0.945836i	$-0.605245\pi$
$383$	3218.73	−	12012.4i	0.429423	−	1.60263i	0.754070	−	0.656795i	$-0.228088\pi$
$384$	−2430.06	+	9698.10i	−0.322939	+	1.28881i
$385$	720.276	−	22.8516i	0.0953471	−	0.00302500i
$386$			6393.68i			0.843082i
$387$	8241.18	−	8796.23i	1.08249	−	1.15539i
$388$	1709.32	−	1709.32i	0.223654	−	0.223654i
$389$	−4995.39	+	8652.28i	−0.651096	+	1.12773i	0.331761	+	0.943364i	$0.392357\pi$
$389$	−4995.39	+	8652.28i	−0.651096	+	1.12773i	−0.982857	+	0.184369i	$0.940976\pi$
$390$	−19301.4	−	4190.69i	−2.50606	−	0.544112i
$391$	444.154	+	769.297i	0.0574471	+	0.0995014i
$392$	4723.43	+	1265.64i	0.608595	+	0.163073i
$393$	138.276	+	8491.02i	0.0177483	+	1.08986i
$394$	−14431.1	−	8331.78i	−1.84524	−	1.06535i
$395$	−1767.60	−	414.029i	−0.225159	−	0.0527393i
$396$	−1468.78	−	2362.82i	−0.186386	−	0.299839i
$397$	1248.70	+	1248.70i	0.157860	+	0.157860i	0.781618	−	0.623758i	$-0.214395\pi$
$397$	1248.70	+	1248.70i	0.157860	+	0.157860i	−0.623758	+	0.781618i	$0.714395\pi$
$398$	16274.9	−	4360.85i	2.04972	−	0.549220i
$399$	3973.44	+	995.628i	0.498548	+	0.124922i
$400$	150.674	+	2372.21i	0.0188343	+	0.296527i
$401$	7999.65	−	4618.60i	0.996218	−	0.575166i	0.0890905	−	0.996024i	$-0.471604\pi$
$401$	7999.65	−	4618.60i	0.996218	−	0.575166i	0.907127	+	0.420857i	$0.138271\pi$
$402$	−199.549	+	359.005i	−0.0247577	+	0.0445412i
$403$	−6247.40	−	23315.6i	−0.772221	−	2.88197i
$404$	13091.8			1.61224
$405$	−1338.33	+	8039.84i	−0.164203	+	0.986427i
$406$	−5611.47			−0.685942
$407$	101.271	+	377.950i	0.0123338	+	0.0460302i
$408$	−358.403	+	644.797i	−0.0434892	+	0.0782407i
$409$	2817.50	−	1626.68i	0.340626	−	0.196661i	−0.319923	−	0.947444i	$-0.603657\pi$
$409$	2817.50	−	1626.68i	0.340626	−	0.196661i	0.660549	+	0.750783i	$0.270324\pi$
$410$	15106.6	+	8094.24i	1.81966	+	0.974990i
$411$	−11528.6	−	2888.73i	−1.38361	−	0.346692i
$412$	3264.75	−	874.787i	0.390395	−	0.104606i
$413$	265.796	+	265.796i	0.0316681	+	0.0316681i
$414$	−6729.89	−	10826.3i	−0.798927	−	1.28523i
$415$	2752.55	−	1707.80i	0.325584	−	0.202006i
$416$	−14571.3	−	8412.77i	−1.71735	−	0.991514i
$417$	−185.152	−	11369.6i	−0.0217433	−	1.33518i
$418$	4003.20	+	1072.65i	0.468428	+	0.125515i
$419$	−1840.03	−	3187.02i	−0.214537	−	0.371590i	0.738592	−	0.674153i	$-0.235491\pi$
$419$	−1840.03	−	3187.02i	−0.214537	−	0.371590i	−0.953129	+	0.302563i	$0.902158\pi$
$420$	2741.62	+	4262.30i	0.318517	+	0.495188i
$421$	−3430.26	+	5941.39i	−0.397104	+	0.687804i	−0.993367	−	0.114985i	$-0.963318\pi$
$421$	−3430.26	+	5941.39i	−0.397104	+	0.687804i	0.596263	+	0.802789i	$0.296651\pi$
$422$	−4260.56	+	4260.56i	−0.491472	+	0.491472i
$423$	−4350.28	+	4643.28i	−0.500043	+	0.533721i
$424$			1451.80i			0.166287i
$425$	−206.283	+	1026.22i	−0.0235440	+	0.117127i
$426$	−616.030	+	2458.50i	−0.0700628	+	0.279613i
$427$	138.106	−	515.419i	0.0156520	−	0.0584142i
$428$	3734.74	−	13938.3i	0.421789	−	1.57414i
$429$	3330.28	−	950.728i	0.374796	−	0.106997i
$430$	−15202.3	+	16198.5i	−1.70493	+	1.81665i
$431$		−	3116.28i		−	0.348273i	−0.984722	−	0.174137i	$-0.944287\pi$
$431$		−	3116.28i		−	0.348273i	0.984722	−	0.174137i	$-0.0557134\pi$
$432$	−1219.52	+	2372.82i	−0.135820	+	0.264264i
$433$	526.507	−	526.507i	0.0584349	−	0.0584349i	−0.677285	−	0.735720i	$-0.736844\pi$
$433$	526.507	−	526.507i	0.0584349	−	0.0584349i	0.735720	+	0.677285i	$0.236844\pi$
$434$	−5194.66	+	8997.41i	−0.574543	+	0.995137i
$435$	7339.56	+	6666.76i	0.808977	+	0.734820i
$436$	5849.77	+	10132.1i	0.642554	+	1.11294i
$437$	10934.8	+	2929.98i	1.19699	+	0.320732i
$438$	4048.77	−	2426.31i	0.441685	−	0.264688i
$439$	3213.40	+	1855.26i	0.349356	+	0.201701i	0.664401	−	0.747376i	$-0.268687\pi$
$439$	3213.40	+	1855.26i	0.349356	+	0.201701i	−0.315046	+	0.949076i	$0.602020\pi$
$440$	871.971	+	1405.41i	0.0944764	+	0.152273i
$441$	6867.52	+	3672.16i	0.741553	+	0.396519i
$442$	−2013.13	−	2013.13i	−0.216640	−	0.216640i
$443$	−1898.77	+	508.773i	−0.203641	+	0.0545655i	−0.359198	−	0.933261i	$-0.616950\pi$
$443$	−1898.77	+	508.773i	−0.203641	+	0.0545655i	0.155556	+	0.987827i	$0.450283\pi$
$444$	−1913.81	+	1977.17i	−0.204562	+	0.211335i
$445$	−11856.8	+	3583.66i	−1.26307	+	0.381757i
$446$	−7568.16	+	4369.48i	−0.803504	+	0.463903i
$447$	−3236.05	+	52.6987i	−0.342415	+	0.00557621i
$448$	1583.49	+	5909.67i	0.166993	+	0.623226i
$449$	−6556.48			−0.689131			−0.344565	−	0.938762i	$-0.611974\pi$
$449$	−6556.48			−0.689131			−0.344565	+	0.938762i	$0.611974\pi$
$450$	2479.16	−	14815.3i	0.259708	−	1.55200i
$451$	−3005.20			−0.313768
$452$	231.602	+	864.350i	0.0241010	+	0.0899460i
$453$	−5390.20	−	8994.62i	−0.559059	−	0.932901i
$454$	12164.2	−	7023.01i	1.25748	−	0.726005i
$455$	−6038.96	+	1825.24i	−0.622222	+	0.188063i
$456$	2580.79	+	9040.18i	0.265036	+	0.928389i
$457$	12355.7	−	3310.69i	1.26471	−	0.338879i	0.436710	−	0.899603i	$-0.356144\pi$
$457$	12355.7	−	3310.69i	1.26471	−	0.338879i	0.828003	+	0.560724i	$0.189477\pi$
$458$	12556.4	+	12556.4i	1.28105	+	1.28105i
$459$	−789.180	+	870.311i	−0.0802522	+	0.0885025i
$460$	7383.99	+	11901.2i	0.748436	+	1.20630i
$461$	−1996.02	−	1152.40i	−0.201657	−	0.116427i	0.395771	−	0.918349i	$-0.370477\pi$
$461$	−1996.02	−	1152.40i	−0.201657	−	0.116427i	−0.597428	+	0.801922i	$0.703811\pi$
$462$	−1302.91	−	724.210i	−0.131206	−	0.0729292i
$463$	−1195.40	−	320.306i	−0.119989	−	0.0321509i	0.198325	−	0.980136i	$-0.436450\pi$
$463$	−1195.40	−	320.306i	−0.119989	−	0.0321509i	−0.318314	+	0.947985i	$0.603117\pi$
$464$	1622.78	+	2810.74i	0.162362	+	0.281219i
$465$	17483.9	−	5596.68i	1.74364	−	0.558150i
$466$	6817.95	−	11809.0i	0.677759	−	1.17391i
$467$	3769.54	−	3769.54i	0.373519	−	0.373519i	−0.495238	−	0.868757i	$-0.664919\pi$
$467$	3769.54	−	3769.54i	0.373519	−	0.373519i	0.868757	+	0.495238i	$0.164919\pi$
$468$	17773.9	+	16652.3i	1.75555	+	1.64478i
$469$			131.195i			0.0129169i
$470$	8024.85	−	8550.73i	0.787572	−	0.839182i
$471$	2631.83	+	2547.49i	0.257470	+	0.249219i
$472$	−223.285	+	833.312i	−0.0217744	+	0.0812633i
$473$	1008.19	−	3762.63i	0.0980058	−	0.365763i
$474$	2698.28	+	2611.80i	0.261468	+	0.253089i
$475$	7388.76	+	11106.5i	0.713725	+	1.07285i
$476$			730.507i			0.0703419i
$477$	−525.369	+	2251.58i	−0.0504298	+	0.216127i
$478$	12248.8	−	12248.8i	1.17207	−	1.17207i
$479$	−1205.53	+	2088.04i	−0.114994	+	0.199175i	−0.917777	−	0.397096i	$-0.870018\pi$
$479$	−1205.53	+	2088.04i	−0.114994	+	0.199175i	0.802783	+	0.596271i	$0.203352\pi$
$480$	5859.09	−	11376.2i	0.557145	−	1.08177i
$481$	−1712.73	−	2966.53i	−0.162357	−	0.281210i
$482$	−28302.4	−	7583.60i	−2.67456	−	0.716646i
$483$	−3558.93	−	1978.19i	−0.335273	−	0.186358i
$484$	12833.6	+	7409.49i	1.20526	+	0.695858i
$485$	−1944.71	+	1206.58i	−0.182072	+	0.112965i
$486$	10912.4	−	12851.5i	1.01851	−	1.19950i
$487$	−13278.0	−	13278.0i	−1.23549	−	1.23549i	−0.961825	−	0.273666i	$-0.911764\pi$
$487$	−13278.0	−	13278.0i	−1.23549	−	1.23549i	−0.273666	−	0.961825i	$-0.588236\pi$
$488$	1182.94	−	316.967i	0.109732	−	0.0294025i
$489$	−860.207	−	3013.20i	−0.0795499	−	0.278653i
$490$	−12651.1	−	6778.56i	−1.16636	−	0.624947i
$491$	−4882.30	+	2818.80i	−0.448748	+	0.259085i	−0.707301	−	0.706912i	$-0.750088\pi$
$491$	−4882.30	+	2818.80i	−0.448748	+	0.259085i	0.258553	+	0.965997i	$0.416754\pi$
$492$	−10863.7	−	18128.2i	−0.995474	−	1.66115i
$493$	369.915	+	1380.54i	0.0337934	+	0.126119i
$494$	−36282.0			−3.30446
$495$	843.750	+	2495.17i	0.0766136	+	0.226565i
$496$	6008.99			0.543975
$497$	209.529	+	781.973i	0.0189108	+	0.0705760i
$498$	−6699.70	+	109.104i	−0.602853	+	0.00981741i
$499$	5518.24	−	3185.96i	0.495051	−	0.285818i	−0.231617	−	0.972807i	$-0.574402\pi$
$499$	5518.24	−	3185.96i	0.495051	−	0.285818i	0.726667	+	0.686990i	$0.241068\pi$
$500$	−2737.70	+	16275.2i	−0.244868	+	1.45570i
$501$	−2295.27	+	2371.26i	−0.204680	+	0.211457i
$502$	27184.0	−	7283.92i	2.41689	−	0.647604i
$503$	5861.56	+	5861.56i	0.519591	+	0.519591i	0.917448	−	0.397857i	$-0.130246\pi$
$503$	5861.56	+	5861.56i	0.519591	+	0.519591i	−0.397857	+	0.917448i	$0.630246\pi$
$504$	−110.104	−	3379.67i	−0.00973104	−	0.298695i
$505$	−12068.0	−	2826.71i	−1.06340	−	0.249083i
$506$	−3567.69	−	2059.81i	−0.313445	−	0.180968i
$507$	−16214.8	+	9717.06i	−1.42037	+	0.851183i
$508$	−17489.6	−	4686.33i	−1.52751	−	0.409296i
$509$	−10716.8	−	18562.0i	−0.933228	−	1.61640i	−0.777763	−	0.628557i	$-0.783646\pi$
$509$	−10716.8	−	18562.0i	−0.933228	−	1.61640i	−0.155465	−	0.987841i	$-0.549688\pi$
$510$	1455.82	−	1602.74i	0.126402	−	0.139158i
$511$	753.837	−	1305.68i	0.0652598	−	0.113033i
$512$	4785.52	−	4785.52i	0.413070	−	0.413070i
$513$	731.103	+	14954.3i	0.0629220	+	1.28703i
$514$		−	6281.10i		−	0.539003i
$515$	−3198.31	+	101.470i	−0.273659	+	0.00868218i
$516$	26341.8	−	7520.05i	2.24735	−	0.641573i
$517$	−532.196	+	1986.18i	−0.0452727	+	0.168960i
$518$	−381.591	+	1424.12i	−0.0323671	+	0.120796i
$519$	−897.886	+	3583.36i	−0.0759399	+	0.303068i
$520$	−10557.9	−	9908.55i	−0.890372	−	0.835613i
$521$			18398.8i			1.54715i	0.633703	+	0.773577i	$0.281534\pi$
$521$			18398.8i			1.54715i	−0.633703	+	0.773577i	$0.718466\pi$
$522$	−5950.70	−	19628.0i	−0.498956	−	1.64577i
$523$	−12039.3	+	12039.3i	−1.00658	+	1.00658i	−0.00659910	+	0.999978i	$0.502101\pi$
$523$	−12039.3	+	12039.3i	−1.00658	+	1.00658i	−0.999978	+	0.00659910i	$0.997899\pi$
$524$	−9649.99	+	16714.3i	−0.804508	+	1.39345i
$525$	−1606.92	−	4520.93i	−0.133585	−	0.375827i
$526$	731.060	+	1266.23i	0.0606003	+	0.104963i
$527$	2555.99	+	684.877i	0.211273	+	0.0566104i
$528$	14.0385	+	862.054i	0.00115709	+	0.0710532i
$529$	791.700	+	457.088i	0.0650695	+	0.0375679i
$530$	971.787	−	4148.83i	0.0796448	−	0.340026i
$531$	−647.846	+	1211.57i	−0.0529456	+	0.0990166i
$532$	6582.85	+	6582.85i	0.536471	+	0.536471i
$533$	25412.4	−	6809.22i	2.06516	−	0.553359i
$534$	24853.5	+	6227.57i	2.01408	+	0.504669i
$535$	−6452.14	+	12041.9i	−0.521402	+	0.973112i
$536$	−260.765	+	150.553i	−0.0210137	+	0.0121322i
$537$	−6792.12	+	12219.6i	−0.545813	+	0.981962i
$538$	880.343	+	3285.49i	0.0705470	+	0.263285i
$539$	2516.72			0.201119
$540$	−12001.5	+	14109.7i	−0.956409	+	1.12442i
$541$	11737.9			0.932811			0.466405	−	0.884571i	$-0.345549\pi$
$541$	11737.9			0.932811			0.466405	+	0.884571i	$0.345549\pi$
$542$	5350.86	+	19969.7i	0.424058	+	1.58260i
$543$	−498.431	+	896.719i	−0.0393918	+	0.0708690i
$544$	1597.40	−	922.257i	0.125897	−	0.0726865i
$545$	−3204.64	−	10602.8i	−0.251875	−	0.833346i
$546$	12658.5	+	3171.85i	0.992187	+	0.248613i
$547$	−8392.40	+	2248.74i	−0.656002	+	0.175775i	−0.571441	−	0.820643i	$-0.693615\pi$
$547$	−8392.40	+	2248.74i	−0.656002	+	0.175775i	−0.0845610	+	0.996418i	$0.526949\pi$
$548$	−19099.6	−	19099.6i	−1.48886	−	1.48886i
$549$	1949.31	−	63.5054i	0.151538	−	0.00493687i
$550$	−1551.11	−	4599.92i	−0.120254	−	0.356621i
$551$	15774.0	+	9107.10i	1.21959	+	0.704130i
$552$	−152.164	−	9343.85i	−0.0117328	−	0.720472i
$553$	1158.62	+	310.452i	0.0890951	+	0.0238730i
$554$	13325.1	+	23079.8i	1.02189	+	1.76997i
$555$	2191.04	−	1409.33i	0.167576	−	0.107789i
$556$	12921.4	−	22380.6i	0.985595	−	1.70710i
$557$	−3736.22	+	3736.22i	−0.284217	+	0.284217i	−0.834788	−	0.550571i	$-0.814410\pi$
$557$	−3736.22	+	3736.22i	−0.284217	+	0.284217i	0.550571	+	0.834788i	$0.314410\pi$
$558$	−36980.2	−	8628.73i	−2.80555	−	0.654629i
$559$			34101.6i			2.58022i
$560$	−49.8015	−	1569.73i	−0.00375803	−	0.118452i
$561$	−92.2815	+	368.285i	−0.00694497	+	0.0277166i
$562$	−5588.10	+	20855.1i	−0.419430	+	1.56533i
$563$	−2537.76	+	9471.07i	−0.189972	+	0.708984i	0.803540	+	0.595251i	$0.202947\pi$
$563$	−2537.76	+	9471.07i	−0.189972	+	0.708984i	−0.993511	+	0.113733i	$0.963719\pi$
$564$	−13905.1	+	3969.62i	−1.03814	+	0.296367i
$565$	−26.8645	−	846.761i	−0.00200035	−	0.0630504i
$566$		−	1592.12i		−	0.118236i
$567$	1052.26	−	5281.34i	0.0779377	−	0.391174i
$568$	−1313.81	+	1313.81i	−0.0970536	+	0.0970536i
$569$	5188.49	−	8986.72i	0.382272	−	0.662114i	−0.609115	−	0.793082i	$-0.708475\pi$
$569$	5188.49	−	8986.72i	0.382272	−	0.662114i	0.991387	+	0.130968i	$0.0418084\pi$
$570$	−1323.96	−	27561.8i	−0.0972886	−	2.02533i
$571$	2372.48	+	4109.26i	0.173880	+	0.301168i	0.939773	−	0.341799i	$-0.111036\pi$
$571$	2372.48	+	4109.26i	0.173880	+	0.301168i	−0.765893	+	0.642968i	$0.777703\pi$
$572$	7602.86	+	2037.18i	0.555755	+	0.148914i
$573$	−1575.30	+	944.030i	−0.114850	+	0.0688262i
$574$	−9806.54	−	5661.81i	−0.713096	−	0.411706i
$575$	−4236.90	−	12564.8i	−0.307289	−	0.911284i
$576$	−18991.8	+	11805.7i	−1.37383	+	0.854002i
$577$	2575.02	+	2575.02i	0.185788	+	0.185788i	0.793872	−	0.608085i	$-0.208062\pi$
$577$	2575.02	+	2575.02i	0.185788	+	0.185788i	−0.608085	+	0.793872i	$0.708062\pi$
$578$	−20820.0	+	5578.70i	−1.49827	+	0.401459i
$579$	−5191.53	+	5363.42i	−0.372630	+	0.384967i
$580$	6519.67	+	21570.8i	0.466749	+	1.54428i
$581$	−1853.52	+	1070.13i	−0.132353	+	0.0764140i
$582$	4733.42	−	77.0834i	0.337125	−	0.00549005i
$583$	193.385	+	721.724i	0.0137379	+	0.0512706i
$584$	3460.26			0.245182
$585$	−12788.4	−	19187.7i	−0.903824	−	1.35609i
$586$	−37937.8			−2.67439
$587$	−2355.29	−	8790.07i	−0.165610	−	0.618067i	−0.997962	−	0.0638179i	$-0.979672\pi$
$587$	−2355.29	−	8790.07i	−0.165610	−	0.618067i	0.832351	−	0.554249i	$-0.186994\pi$
$588$	9097.86	+	15181.6i	0.638077	+	1.06476i
$589$	29204.6	−	16861.3i	2.04305	−	1.17955i
$590$	1195.88	−	2231.91i	0.0834467	−	0.155740i
$591$	−5340.45	−	18706.9i	−0.371704	−	1.30203i
$592$	823.683	−	220.705i	0.0571844	−	0.0153225i
$593$	−9619.29	−	9619.29i	−0.666133	−	0.666133i	0.290686	−	0.956819i	$-0.406117\pi$
$593$	−9619.29	−	9619.29i	−0.666133	−	0.666133i	−0.956819	+	0.290686i	$0.906117\pi$
$594$	1151.49	−	5325.36i	0.0795390	−	0.367849i
$595$	157.727	−	673.379i	0.0108675	−	0.0463964i
$596$	−6370.05	−	3677.75i	−0.437797	−	0.252762i
$597$	17193.3	+	9556.73i	1.17869	+	0.655161i
$598$	34836.0	+	9334.27i	2.38219	+	0.638306i
$599$	339.119	+	587.372i	0.0231320	+	0.0400657i	0.877360	−	0.479833i	$-0.159303\pi$
$599$	339.119	+	587.372i	0.0231320	+	0.0400657i	−0.854228	+	0.519899i	$0.825970\pi$
$600$	7141.82	−	8381.92i	0.485940	−	0.570317i
$601$	−4560.19	+	7898.48i	−0.309508	+	0.536083i	−0.978255	−	0.207407i	$-0.933498\pi$
$601$	−4560.19	+	7898.48i	−0.309508	+	0.536083i	0.668747	+	0.743490i	$0.266831\pi$
$602$	10378.7	−	10378.7i	0.702666	−	0.702666i
$603$	−458.899	+	139.126i	−0.0309914	+	0.00939579i
$604$		−	23831.5i		−	1.60545i
$605$	−10230.2	−	9601.01i	−0.687464	−	0.645184i
$606$	18422.0	+	17831.6i	1.23489	+	1.19532i
$607$	−3566.69	+	13311.1i	−0.238497	+	0.890082i	0.738045	+	0.674752i	$0.235749\pi$
$607$	−3566.69	+	13311.1i	−0.238497	+	0.890082i	−0.976541	+	0.215330i	$0.930917\pi$
$608$	6083.91	−	22705.5i	0.405815	−	1.51452i
$609$	−4707.25	−	4556.39i	−0.313214	−	0.303176i
$610$	−3592.67	+	113.982i	−0.238464	+	0.00756555i
$611$		−	18001.3i		−	1.19190i
$612$	−2555.19	+	774.669i	−0.168771	+	0.0511669i
$613$	7501.39	−	7501.39i	0.494255	−	0.494255i	−0.415389	−	0.909644i	$-0.636355\pi$
$613$	7501.39	−	7501.39i	0.494255	−	0.494255i	0.909644	+	0.415389i	$0.136355\pi$
$614$	19635.2	−	34009.2i	1.29057	−	2.23534i
$615$	6099.98	+	19056.2i	0.399959	+	1.24946i
$616$	−546.390	−	946.376i	−0.0357381	−	0.0619003i
$617$	21447.4	+	5746.81i	1.39942	+	0.374972i	0.878135	−	0.478413i	$-0.158788\pi$
$617$	21447.4	+	5746.81i	1.39942	+	0.374972i	0.521281	+	0.853385i	$0.325454\pi$
$618$	5785.46	+	3215.78i	0.376578	+	0.209317i
$619$	6003.77	+	3466.28i	0.389841	+	0.225075i	0.682091	−	0.731267i	$-0.261071\pi$
$619$	6003.77	+	3466.28i	0.389841	+	0.225075i	−0.292250	+	0.956342i	$0.594404\pi$
$620$	40622.0	+	9514.97i	2.63132	+	0.616339i
$621$	3145.32	−	14546.3i	0.203248	−	0.939976i
$622$	−7206.69	−	7206.69i	−0.464569	−	0.464569i
$623$	7905.13	−	2118.17i	0.508366	−	0.136216i
$624$	−2071.96	−	7257.82i	−0.132924	−	0.465618i
$625$	6037.66	−	14411.4i	0.386410	−	0.922327i
$626$	−23588.8	+	13619.0i	−1.50607	+	0.869529i
$627$	2487.16	+	4150.33i	0.158417	+	0.264351i
$628$	2154.52	+	8040.79i	0.136903	+	0.510928i
$629$	375.519			0.0238043
$630$	−1947.60	+	9731.85i	−0.123165	+	0.615438i
$631$	5174.87			0.326479			0.163239	−	0.986586i	$-0.447806\pi$
$631$	5174.87			0.326479			0.163239	+	0.986586i	$0.447806\pi$
$632$	712.516	+	2659.15i	0.0448455	+	0.167366i
$633$	−7033.52	+	114.540i	−0.441639	+	0.00719205i
$634$	−34660.5	+	20011.2i	−2.17120	+	1.25354i
$635$	15110.0	+	8096.10i	0.944288	+	0.505959i
$636$	−3654.56	+	3775.56i	−0.227850	+	0.235394i
$637$	−21281.7	+	5702.42i	−1.32372	+	0.354691i
$638$	−4686.88	−	4686.88i	−0.290839	−	0.290839i
$639$	−2513.02	+	1562.15i	−0.155577	+	0.0967097i
$640$	18279.6	−	11341.4i	1.12901	−	0.700482i
$641$	1800.01	+	1039.24i	0.110914	+	0.0640365i	0.554431	−	0.832230i	$-0.312936\pi$
$641$	1800.01	+	1039.24i	0.110914	+	0.0640365i	−0.443517	+	0.896266i	$0.646269\pi$
$642$	24239.8	−	14526.2i	1.49014	−	0.892995i
$643$	8982.29	+	2406.80i	0.550898	+	0.147613i	0.523521	−	0.852013i	$-0.324618\pi$
$643$	8982.29	+	2406.80i	0.550898	+	0.147613i	0.0273763	+	0.999625i	$0.491285\pi$
$644$	−4626.92	−	8014.06i	−0.283115	−	0.490370i
$645$	−25905.5	+	1244.39i	−1.58144	+	0.0759658i
$646$	1988.72	−	3444.57i	0.121123	−	0.209791i
$647$	−12361.4	+	12361.4i	−0.751125	+	0.751125i	−0.974689	−	0.223564i	$-0.928231\pi$
$647$	−12361.4	+	12361.4i	−0.751125	+	0.751125i	0.223564	+	0.974689i	$0.428231\pi$
$648$	11704.8	−	3969.11i	0.709578	−	0.240619i
$649$			444.002i			0.0268546i
$650$	23539.0	+	35383.0i	1.42042	+	2.13513i
$651$	−11663.3	+	3329.64i	−0.702184	+	0.200459i
$652$	1843.22	−	6878.98i	0.110715	−	0.413192i
$653$	−7383.03	+	27553.8i	−0.442450	+	1.65125i	0.280131	+	0.959962i	$0.409622\pi$
$653$	−7383.03	+	27553.8i	−0.442450	+	1.65125i	−0.722581	+	0.691286i	$0.757045\pi$
$654$	−5568.92	+	22224.9i	−0.332969	+	1.32884i
$655$	12504.2	−	13323.6i	0.745922	−	0.794803i
$656$			6549.37i			0.389802i
$657$	5366.48	+	1252.18i	0.318670	+	0.0743565i
$658$	−5478.63	+	5478.63i	−0.324589	+	0.324589i
$659$	5594.17	−	9689.39i	0.330680	−	0.572754i	−0.651966	−	0.758249i	$-0.726055\pi$
$659$	5594.17	−	9689.39i	0.330680	−	0.572754i	0.982645	+	0.185494i	$0.0593887\pi$
$660$	−1270.12	+	5849.90i	−0.0749082	+	0.345010i
$661$	−12520.6	−	21686.4i	−0.736757	−	1.27610i	−0.953948	−	0.299972i	$-0.903023\pi$
$661$	−12520.6	−	21686.4i	−0.736757	−	1.27610i	0.217190	−	0.976129i	$-0.430311\pi$
$662$	3164.29	+	847.869i	0.185776	+	0.0497785i
$663$	−54.1206	−	3323.36i	−0.00317024	−	0.194673i
$664$	−4254.01	−	2456.06i	−0.248626	−	0.143544i
$665$	−4646.72	−	7489.38i	−0.270966	−	0.436730i
$666$	−5385.99	+	175.467i	−0.313368	+	0.0102090i
$667$	−12802.3	−	12802.3i	−0.743190	−	0.743190i
$668$	−7244.69	+	1941.21i	−0.419619	+	0.112437i
$669$	−9896.58	−	2479.79i	−0.571934	−	0.143310i
$670$	845.968	−	255.689i	0.0487800	−	0.0147435i
$671$	545.845	−	315.144i	0.0314040	−	0.0181311i
$672$	−4107.59	+	7389.90i	−0.235794	+	0.424213i
$673$	−4660.65	−	17393.8i	−0.266946	−	0.996257i	−0.961048	−	0.276381i	$-0.910865\pi$
$673$	−4660.65	−	17393.8i	−0.266946	−	0.996257i	0.694102	−	0.719877i	$-0.255802\pi$
$674$	20093.3			1.14832
$675$	14109.4	−	10415.0i	0.804549	−	0.593886i
$676$	−42961.7			−2.44434
$677$	−5566.38	−	20774.0i	−0.316002	−	1.17934i	−0.923053	−	0.384673i	$-0.874314\pi$
$677$	−5566.38	−	20774.0i	−0.316002	−	1.17934i	0.607051	−	0.794663i	$-0.292352\pi$
$678$	−851.386	+	1531.71i	−0.0482261	+	0.0867626i
$679$	1309.54	−	756.062i	0.0740139	−	0.0427319i
$680$	1519.41	−	459.235i	0.0856866	−	0.0258983i
$681$	15906.6	+	3985.74i	0.895072	+	0.224279i
$682$	−11853.7	+	3176.18i	−0.665544	+	0.178332i
$683$	−4348.95	−	4348.95i	−0.243643	−	0.243643i	0.574713	−	0.818355i	$-0.305114\pi$
$683$	−4348.95	−	4348.95i	−0.243643	−	0.243643i	−0.818355	+	0.574713i	$0.805114\pi$
$684$	−16044.9	+	30006.5i	−0.896920	+	1.67738i
$685$	13482.0	+	21729.8i	0.752003	+	1.21205i
$686$	17978.8	+	10380.1i	1.00063	+	0.577715i
$687$	337.564	+	20728.6i	0.0187465	+	1.15116i
$688$	−8200.05	−	2197.20i	−0.454395	−	0.121755i
$689$	−3270.58	−	5664.81i	−0.180841	−	0.313225i
$690$	−5819.64	+	26804.0i	−0.321087	+	1.47885i
$691$	7927.92	−	13731.6i	0.436458	−	0.755967i	−0.560955	−	0.827846i	$-0.689566\pi$
$691$	7927.92	−	13731.6i	0.436458	−	0.755967i	0.997413	+	0.0718787i	$0.0228994\pi$
$692$	−5936.61	+	5936.61i	−0.326121	+	0.326121i
$693$	−504.921	−	1665.45i	−0.0276773	−	0.0912918i
$694$		−	18107.7i		−	0.990429i
$695$	−16743.2	+	17840.4i	−0.913822	+	0.973706i
$696$	3654.54	−	14584.9i	0.199030	−	0.794308i
$697$	−746.467	+	2785.85i	−0.0405659	+	0.151394i
$698$	2820.56	−	10526.5i	0.152951	−	0.570820i
$699$	15308.0	−	4370.13i	0.828330	−	0.236471i
$700$	2148.93	−	10690.6i	0.116031	−	0.577236i
$701$			21918.5i			1.18096i	0.807054	+	0.590478i	$0.201061\pi$
$701$			21918.5i			1.18096i	−0.807054	+	0.590478i	$0.798939\pi$
$702$	2329.14	+	47641.0i	0.125224	+	2.56139i
$703$	3383.93	−	3383.93i	0.181547	−	0.181547i
$704$	−3613.36	+	6258.53i	−0.193443	+	0.335053i
$705$	13674.8	−	656.880i	0.730527	−	0.0350915i
$706$	−24185.9	−	41891.2i	−1.28930	−	2.23314i
$707$	7910.29	+	2119.56i	0.420788	+	0.112750i
$708$	−2678.35	+	1605.05i	−0.142173	+	0.0851999i
$709$	−25661.5	−	14815.7i	−1.35929	−	0.784787i	−0.369763	−	0.929126i	$-0.620561\pi$
$709$	−25661.5	−	14815.7i	−1.35929	−	0.784787i	−0.989528	+	0.144338i	$0.953895\pi$
$710$	4633.94	−	2875.09i	0.244942	−	0.151972i
$711$	142.755	+	4381.89i	0.00752987	+	0.231130i
$712$	13281.6	+	13281.6i	0.699087	+	0.699087i
$713$	−32378.6	+	8675.82i	−1.70068	+	0.455697i
$714$	−994.982	+	1027.92i	−0.0521516	+	0.0538783i
$715$	−6568.44	−	3519.43i	−0.343560	−	0.184083i
$716$	−27516.2	+	15886.5i	−1.43622	+	0.829199i
$717$	20220.8	−	329.295i	1.05322	−	0.0171517i
$718$	7981.37	+	29786.9i	0.414850	+	1.54824i
$719$	5855.14			0.303700			0.151850	−	0.988404i	$-0.451477\pi$
$719$	5855.14			0.303700			0.151850	+	0.988404i	$0.451477\pi$
$720$	5437.84	−	1838.82i	0.281467	−	0.0951789i
$721$	2114.24			0.109207
$722$	−5217.97	−	19473.7i	−0.268965	−	1.00379i
$723$	−17584.1	−	29342.5i	−0.904508	−	1.50935i
$724$	−2019.25	+	1165.81i	−0.103653	+	0.0598440i
$725$	−1352.37	−	21291.6i	−0.0692767	−	1.09069i
$726$	7966.64	+	27906.1i	0.407258	+	1.42658i
$727$	17456.9	−	4677.55i	0.890563	−	0.238626i	0.215604	−	0.976481i	$-0.430828\pi$
$727$	17456.9	−	4677.55i	0.890563	−	0.238626i	0.674959	+	0.737855i	$0.264161\pi$
$728$	6764.65	+	6764.65i	0.344388	+	0.344388i
$729$	19589.1	−	1919.99i	0.995231	−	0.0975455i
$730$	−9888.44	−	2316.19i	−0.501353	−	0.117433i
$731$	−3237.56	−	1869.21i	−0.163811	−	0.0945762i
$732$	3874.25	+	2153.46i	0.195623	+	0.108735i
$733$	35884.0	+	9615.09i	1.80819	+	0.484504i	0.995208	−	0.0977795i	$-0.0311740\pi$
$733$	35884.0	+	9615.09i	1.80819	+	0.484504i	0.812986	+	0.582284i	$0.197841\pi$
$734$	−20929.9	−	36251.7i	−1.05250	−	1.82299i
$735$	−5108.46	−	15958.7i	−0.256365	−	0.800878i
$736$	−11682.9	+	20235.3i	−0.585104	+	1.01343i
$737$	−109.578	+	109.578i	−0.00547676	+	0.00547676i
$738$	9404.70	−	40305.8i	0.469095	−	2.01040i
$739$		−	16862.4i		−	0.839371i	−0.907670	−	0.419686i	$-0.862140\pi$
$739$		−	16862.4i		−	0.839371i	0.907670	−	0.419686i	$-0.137860\pi$
$740$	5917.75	−	187.748i	0.293974	−	0.00932669i
$741$	−30435.6	−	29460.2i	−1.50888	−	1.46052i
$742$	−728.677	+	2719.46i	−0.0360520	+	0.134548i
$743$	−2026.03	+	7561.26i	−0.100038	+	0.373345i	−0.997735	−	0.0672671i	$-0.978572\pi$
$743$	−2026.03	+	7561.26i	−0.100038	+	0.373345i	0.897697	+	0.440613i	$0.145239\pi$
$744$	−20002.3	−	19361.2i	−0.985643	−	0.954055i
$745$	5077.81	+	4765.52i	0.249713	+	0.234356i
$746$		−	25811.4i		−	1.26678i
$747$	−5708.72	−	5348.49i	−0.279613	−	0.261969i
$748$	−610.143	+	610.143i	−0.0298249	+	0.0298249i
$749$	4513.18	−	7817.06i	0.220171	−	0.381347i
$750$	−26019.9	+	19172.7i	−1.26682	+	0.933449i
$751$	9768.62	+	16919.7i	0.474650	+	0.822117i	0.999579	−	0.0290288i	$-0.00924145\pi$
$751$	9768.62	+	16919.7i	0.474650	+	0.822117i	−0.524929	+	0.851146i	$0.675908\pi$
$752$	4328.57	+	1159.84i	0.209903	+	0.0562433i
$753$	28718.0	+	15962.6i	1.38983	+	0.772523i
$754$	50252.4	+	29013.2i	2.42717	+	1.40133i
$755$	−5145.57	+	21967.8i	−0.248035	+	1.05893i
$756$	8221.19	−	9066.37i	0.395505	−	0.436165i
$757$	10039.5	+	10039.5i	0.482024	+	0.482024i	0.905777	−	0.423754i	$-0.139288\pi$
$757$	10039.5	+	10039.5i	0.482024	+	0.482024i	−0.423754	+	0.905777i	$0.639288\pi$
$758$	−28448.5	+	7622.74i	−1.36319	+	0.365265i
$759$	−1320.28	−	4624.79i	−0.0631400	−	0.221172i
$760$	9553.65	−	17830.3i	0.455983	−	0.851017i
$761$	−20084.8	+	11595.9i	−0.956731	+	0.552369i	−0.895165	−	0.445734i	$-0.852943\pi$
$761$	−20084.8	+	11595.9i	−0.956731	+	0.552369i	−0.0615654	+	0.998103i	$0.519609\pi$
$762$	−18227.3	−	30415.9i	−0.866545	−	1.44600i
$763$	1894.15	+	7069.05i	0.0898725	+	0.335409i
$764$	−4173.81			−0.197648
$765$	2522.63	−	162.385i	0.119223	−	0.00767456i
$766$	55350.5			2.61083
$767$	−1006.02	−	3754.54i	−0.0473604	−	0.176752i
$768$	−10068.2	+	163.960i	−0.473054	+	0.00770364i
$769$	−30950.8	+	17869.4i	−1.45138	+	0.837956i	−0.998560	−	0.0536450i	$-0.982916\pi$
$769$	−30950.8	+	17869.4i	−1.45138	+	0.837956i	−0.452822	+	0.891601i	$0.649583\pi$
$770$	927.956	+

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15194 + 4.29910i) q^{2} +(-2.52446 + 4.54171i) q^{3} +(-10.2271 + 5.90461i) q^{4} +(10.7022 - 3.23468i) q^{5} +(-22.4333 - 5.62113i) q^{6} +(-7.13532 + 1.91190i) q^{7} +(-11.9883 - 11.9883i) q^{8} +(-14.2542 - 22.9307i) q^{9} +O(q^{10})\)	\(q+(1.15194 + 4.29910i) q^{2} +(-2.52446 + 4.54171i) q^{3} +(-10.2271 + 5.90461i) q^{4} +(10.7022 - 3.23468i) q^{5} +(-22.4333 - 5.62113i) q^{6} +(-7.13532 + 1.91190i) q^{7} +(-11.9883 - 11.9883i) q^{8} +(-14.2542 - 22.9307i) q^{9} +(26.2345 + 42.2836i) q^{10} +(-7.55654 - 4.36277i) q^{11} +(-0.999152 - 61.3544i) q^{12} +(73.7842 + 19.7704i) q^{13} +(-16.4389 - 28.4731i) q^{14} +(-12.3263 + 56.7720i) q^{15} +(-9.50797 + 16.4683i) q^{16} +(-5.92131 + 5.92131i) q^{17} +(82.1614 - 87.6951i) q^{18} +106.718i q^{19} +(-90.3527 + 96.2737i) q^{20} +(9.32953 - 37.2331i) q^{21} +(10.0513 - 37.5120i) q^{22} +(27.4553 - 102.465i) q^{23} +(84.7110 - 24.1833i) q^{24} +(104.074 - 69.2363i) q^{25} +339.980i q^{26} +(140.129 - 6.85080i) q^{27} +(61.6846 - 61.6846i) q^{28} +(85.3380 - 147.810i) q^{29} +(-258.268 + 12.4061i) q^{30} +(-157.999 - 273.662i) q^{31} +(-212.761 - 57.0093i) q^{32} +(38.8906 - 23.3059i) q^{33} +(-32.2773 - 18.6353i) q^{34} +(-70.1792 + 43.5421i) q^{35} +(281.176 + 150.349i) q^{36} +(-31.7091 - 31.7091i) q^{37} +(-458.791 + 122.933i) q^{38} +(-276.057 + 285.197i) q^{39} +(-167.079 - 89.5224i) q^{40} +(298.272 - 172.207i) q^{41} +(170.816 - 2.78172i) q^{42} +(115.545 + 431.220i) q^{43} +103.042 q^{44} +(-226.725 - 199.301i) q^{45} +472.133 q^{46} +(-60.9929 - 227.629i) q^{47} +(-50.7917 - 84.7559i) q^{48} +(-249.789 + 144.216i) q^{49} +(417.541 + 367.667i) q^{50} +(-11.9448 - 41.8410i) q^{51} +(-871.335 + 233.473i) q^{52} +(-60.5508 - 60.5508i) q^{53} +(190.872 + 594.536i) q^{54} +(-94.9837 - 22.2482i) q^{55} +(108.460 + 62.6197i) q^{56} +(-484.682 - 269.405i) q^{57} +(733.754 + 196.609i) q^{58} +(-25.4427 - 44.0680i) q^{59} +(-209.155 - 653.395i) q^{60} +(-36.1174 + 62.5572i) q^{61} +(994.494 - 994.494i) q^{62} +(145.550 + 136.365i) q^{63} -828.227i q^{64} +(853.604 - 27.0816i) q^{65} +(144.994 + 140.347i) q^{66} +(4.59668 - 17.1550i) q^{67} +(25.5947 - 95.5208i) q^{68} +(396.055 + 383.362i) q^{69} +(-268.034 - 251.549i) q^{70} -109.592i q^{71} +(-104.016 + 445.782i) q^{72} +(-144.319 + 144.319i) q^{73} +(99.7935 - 172.847i) q^{74} +(51.7214 + 647.456i) q^{75} +(-630.128 - 1091.41i) q^{76} +(62.2595 + 16.6824i) q^{77} +(-1544.09 - 858.266i) q^{78} +(-140.624 - 81.1891i) q^{79} +(-48.4864 + 207.002i) q^{80} +(-322.635 + 653.718i) q^{81} +(1083.93 + 1083.93i) q^{82} +(279.860 - 74.9883i) q^{83} +(124.433 + 435.873i) q^{84} +(-44.2174 + 82.5245i) q^{85} +(-1720.76 + 993.479i) q^{86} +(455.877 + 760.720i) q^{87} +(38.2877 + 142.892i) q^{88} -1107.89 q^{89} +(595.641 - 1204.30i) q^{90} -564.273 q^{91} +(324.227 + 1210.03i) q^{92} +(1641.75 - 26.7358i) q^{93} +(908.339 - 524.430i) q^{94} +(345.199 + 1142.12i) q^{95} +(796.027 - 822.383i) q^{96} +(-197.725 + 52.9802i) q^{97} +(-907.741 - 907.741i) q^{98} +(7.67108 + 235.465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Introduction

L-functions

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