LMFDB - Embedded newform 240.2.bl.a.229.3

Newspace parameters

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			229.3
Character	$\chi$	$=$	240.229
Dual form			240.2.bl.a.109.3

$q$-expansion

$f(q)$	$=$	$q+(-1.36038 - 0.386472i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.70128 + 1.05150i) q^{4} +(-1.98421 - 1.03097i) q^{5} +(-0.688658 - 1.23521i) q^{6} -3.91927 q^{7} +(-1.90801 - 2.08794i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.36038 - 0.386472i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.70128 + 1.05150i) q^{4} +(-1.98421 - 1.03097i) q^{5} +(-0.688658 - 1.23521i) q^{6} -3.91927 q^{7} +(-1.90801 - 2.08794i) q^{8} +1.00000i q^{9} +(2.30085 + 2.16936i) q^{10} +(-2.93423 - 2.93423i) q^{11} +(0.459462 + 1.94651i) q^{12} +(-0.732828 - 0.732828i) q^{13} +(5.33170 + 1.51469i) q^{14} +(-0.674045 - 2.13206i) q^{15} +(1.78869 + 3.57779i) q^{16} -2.89302i q^{17} +(0.386472 - 1.36038i) q^{18} +(1.67534 - 1.67534i) q^{19} +(-2.29163 - 3.84037i) q^{20} +(-2.77134 - 2.77134i) q^{21} +(2.85767 + 5.12567i) q^{22} -1.73133 q^{23} +(0.127228 - 2.82556i) q^{24} +(2.87420 + 4.09133i) q^{25} +(0.713708 + 1.28014i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-6.66776 - 4.12111i) q^{28} +(-4.99003 + 4.99003i) q^{29} +(0.0929773 + 3.16091i) q^{30} -10.8149 q^{31} +(-1.05059 - 5.55844i) q^{32} -4.14963i q^{33} +(-1.11807 + 3.93561i) q^{34} +(7.77666 + 4.04065i) q^{35} +(-1.05150 + 1.70128i) q^{36} +(6.41524 - 6.41524i) q^{37} +(-2.92658 + 1.63163i) q^{38} -1.03637i q^{39} +(1.63330 + 6.11002i) q^{40} -0.00577512i q^{41} +(2.69904 + 4.84113i) q^{42} +(-2.23930 + 2.23930i) q^{43} +(-1.90660 - 8.07728i) q^{44} +(1.03097 - 1.98421i) q^{45} +(2.35527 + 0.669110i) q^{46} +11.6451i q^{47} +(-1.26508 + 3.79468i) q^{48} +8.36066 q^{49} +(-2.32883 - 6.67657i) q^{50} +(2.04567 - 2.04567i) q^{51} +(-0.476175 - 2.01731i) q^{52} +(5.55765 - 5.55765i) q^{53} +(1.23521 - 0.688658i) q^{54} +(2.79703 + 8.84724i) q^{55} +(7.47801 + 8.18319i) q^{56} +2.36929 q^{57} +(8.71685 - 4.85983i) q^{58} +(3.83290 + 3.83290i) q^{59} +(1.09512 - 4.33598i) q^{60} +(9.30595 - 9.30595i) q^{61} +(14.7123 + 4.17964i) q^{62} -3.91927i q^{63} +(-0.718981 + 7.96763i) q^{64} +(0.698563 + 2.20961i) q^{65} +(-1.60372 + 5.64508i) q^{66} +(-3.85243 - 3.85243i) q^{67} +(3.04201 - 4.92182i) q^{68} +(-1.22423 - 1.22423i) q^{69} +(-9.01763 - 8.50229i) q^{70} -1.15355i q^{71} +(2.08794 - 1.90801i) q^{72} -7.98713 q^{73} +(-11.2065 + 6.24786i) q^{74} +(-0.860637 + 4.92537i) q^{75} +(4.61185 - 1.08860i) q^{76} +(11.5000 + 11.5000i) q^{77} +(-0.400530 + 1.40987i) q^{78} +0.843960 q^{79} +(0.139442 - 8.94318i) q^{80} -1.00000 q^{81} +(-0.00223193 + 0.00785637i) q^{82} +(-5.20069 - 5.20069i) q^{83} +(-1.80076 - 7.62889i) q^{84} +(-2.98261 + 5.74036i) q^{85} +(3.91173 - 2.18088i) q^{86} -7.05696 q^{87} +(-0.527948 + 11.7250i) q^{88} +5.40896i q^{89} +(-2.16936 + 2.30085i) q^{90} +(2.87215 + 2.87215i) q^{91} +(-2.94547 - 1.82049i) q^{92} +(-7.64726 - 7.64726i) q^{93} +(4.50051 - 15.8418i) q^{94} +(-5.05147 + 1.59701i) q^{95} +(3.18753 - 4.67329i) q^{96} +2.24154i q^{97} +(-11.3737 - 3.23117i) q^{98} +(2.93423 - 2.93423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.36038	−	0.386472i	−0.961935	−	0.273277i
$2$	−1.36038	−	0.386472i	−0.961935	−	0.273277i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	1.70128	+	1.05150i	0.850639	+	0.525750i
$5$	−1.98421	−	1.03097i	−0.887367	−	0.461064i
$5$	−1.98421	−	1.03097i	−0.887367	−	0.461064i
$6$	−0.688658	−	1.23521i	−0.281143	−	0.504273i
$7$	−3.91927			−1.48134			−0.740672	−	0.671867i	$-0.765493\pi$
$7$	−3.91927			−1.48134			−0.740672	+	0.671867i	$0.765493\pi$
$8$	−1.90801	−	2.08794i	−0.674584	−	0.738198i
$9$			1.00000i			0.333333i
$10$	2.30085	+	2.16936i	0.727591	+	0.686011i
$11$	−2.93423	−	2.93423i	−0.884703	−	0.884703i	0.109305	−	0.994008i	$-0.465138\pi$
$11$	−2.93423	−	2.93423i	−0.884703	−	0.884703i	−0.994008	+	0.109305i	$0.965138\pi$
$12$	0.459462	+	1.94651i	0.132635	+	0.561909i
$13$	−0.732828	−	0.732828i	−0.203250	−	0.203250i	0.598141	−	0.801391i	$-0.295906\pi$
$13$	−0.732828	−	0.732828i	−0.203250	−	0.203250i	−0.801391	+	0.598141i	$0.795906\pi$
$14$	5.33170	+	1.51469i	1.42496	+	0.404818i
$15$	−0.674045	−	2.13206i	−0.174038	−	0.550495i
$16$	1.78869	+	3.57779i	0.447173	+	0.894447i
$17$		−	2.89302i		−	0.701659i	−0.936439	−	0.350830i	$-0.885900\pi$
$17$		−	2.89302i		−	0.701659i	0.936439	−	0.350830i	$-0.114100\pi$
$18$	0.386472	−	1.36038i	0.0910924	−	0.320645i
$19$	1.67534	−	1.67534i	0.384350	−	0.384350i	−0.488316	−	0.872667i	$-0.662389\pi$
$19$	1.67534	−	1.67534i	0.384350	−	0.384350i	0.872667	+	0.488316i	$0.162389\pi$
$20$	−2.29163	−	3.84037i	−0.512425	−	0.858732i
$21$	−2.77134	−	2.77134i	−0.604756	−	0.604756i
$22$	2.85767	+	5.12567i	0.609258	+	1.09280i
$23$	−1.73133			−0.361006			−0.180503	−	0.983574i	$-0.557773\pi$
$23$	−1.73133			−0.361006			−0.180503	+	0.983574i	$0.557773\pi$
$24$	0.127228	−	2.82556i	0.0259703	−	0.576766i
$25$	2.87420	+	4.09133i	0.574841	+	0.818265i
$26$	0.713708	+	1.28014i	0.139970	+	0.251057i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−6.66776	−	4.12111i	−1.26009	−	0.778817i
$29$	−4.99003	+	4.99003i	−0.926625	+	0.926625i	−0.997486	−	0.0708617i	$-0.977425\pi$
$29$	−4.99003	+	4.99003i	−0.926625	+	0.926625i	0.0708617	+	0.997486i	$0.477425\pi$
$30$	0.0929773	+	3.16091i	0.0169753	+	0.577101i
$31$	−10.8149			−1.94241			−0.971203	−	0.238254i	$-0.923425\pi$
$31$	−10.8149			−1.94241			−0.971203	+	0.238254i	$0.923425\pi$
$32$	−1.05059	−	5.55844i	−0.185720	−	0.982603i
$33$		−	4.14963i		−	0.722357i
$34$	−1.11807	+	3.93561i	−0.191748	+	0.674951i
$35$	7.77666	+	4.04065i	1.31450	+	0.682994i
$36$	−1.05150	+	1.70128i	−0.175250	+	0.283546i
$37$	6.41524	−	6.41524i	1.05466	−	1.05466i	0.0562413	−	0.998417i	$-0.482088\pi$
$37$	6.41524	−	6.41524i	1.05466	−	1.05466i	0.998417	−	0.0562413i	$-0.0179116\pi$
$38$	−2.92658	+	1.63163i	−0.474754	+	0.264686i
$39$		−	1.03637i		−	0.165953i
$40$	1.63330	+	6.11002i	0.258247	+	0.966079i
$41$		−	0.00577512i		−	0.000901923i	−1.00000		0.000450961i	$-0.999856\pi$
$41$		−	0.00577512i		−	0.000901923i	1.00000		0.000450961i	$-0.000143545\pi$
$42$	2.69904	+	4.84113i	0.416470	+	0.747002i
$43$	−2.23930	+	2.23930i	−0.341490	+	0.341490i	−0.856927	−	0.515437i	$-0.827630\pi$
$43$	−2.23930	+	2.23930i	−0.341490	+	0.341490i	0.515437	+	0.856927i	$0.327630\pi$
$44$	−1.90660	−	8.07728i	−0.287430	−	1.21770i
$45$	1.03097	−	1.98421i	0.153688	−	0.295789i
$46$	2.35527	+	0.669110i	0.347265	+	0.0986549i
$47$			11.6451i			1.69861i	0.527900	+	0.849307i	$0.322980\pi$
$47$			11.6451i			1.69861i	−0.527900	+	0.849307i	$0.677020\pi$
$48$	−1.26508	+	3.79468i	−0.182599	+	0.547714i
$49$	8.36066			1.19438
$50$	−2.32883	−	6.67657i	−0.329346	−	0.944209i
$51$	2.04567	−	2.04567i	0.286451	−	0.286451i
$52$	−0.476175	−	2.01731i	−0.0660336	−	0.279751i
$53$	5.55765	−	5.55765i	0.763402	−	0.763402i	−0.213533	−	0.976936i	$-0.568497\pi$
$53$	5.55765	−	5.55765i	0.763402	−	0.763402i	0.976936	+	0.213533i	$0.0684972\pi$
$54$	1.23521	−	0.688658i	0.168091	−	0.0937145i
$55$	2.79703	+	8.84724i	0.377152	+	1.19296i
$56$	7.47801	+	8.18319i	0.999291	+	1.09353i
$57$	2.36929			0.313821
$58$	8.71685	−	4.85983i	1.14458	−	0.638127i
$59$	3.83290	+	3.83290i	0.499001	+	0.499001i	0.911127	−	0.412126i	$-0.135214\pi$
$59$	3.83290	+	3.83290i	0.499001	+	0.499001i	−0.412126	+	0.911127i	$0.635214\pi$
$60$	1.09512	−	4.33598i	0.141379	−	0.559772i
$61$	9.30595	−	9.30595i	1.19150	−	1.19150i	0.214859	−	0.976645i	$-0.431071\pi$
$61$	9.30595	−	9.30595i	1.19150	−	1.19150i	0.976645	−	0.214859i	$-0.0689293\pi$
$62$	14.7123	+	4.17964i	1.86847	+	0.530815i
$63$		−	3.91927i		−	0.493781i
$64$	−0.718981	+	7.96763i	−0.0898726	+	0.995953i
$65$	0.698563	+	2.20961i	0.0866461	+	0.274068i
$66$	−1.60372	+	5.64508i	−0.197404	+	0.694861i
$67$	−3.85243	−	3.85243i	−0.470649	−	0.470649i	0.431476	−	0.902124i	$-0.357993\pi$
$67$	−3.85243	−	3.85243i	−0.470649	−	0.470649i	−0.902124	+	0.431476i	$0.857993\pi$
$68$	3.04201	−	4.92182i	0.368898	−	0.596859i
$69$	−1.22423	−	1.22423i	−0.147380	−	0.147380i
$70$	−9.01763	−	8.50229i	−1.07781	−	1.01622i
$71$		−	1.15355i		−	0.136901i	−0.997655	−	0.0684504i	$-0.978195\pi$
$71$		−	1.15355i		−	0.136901i	0.997655	−	0.0684504i	$-0.0218055\pi$
$72$	2.08794	−	1.90801i	0.246066	−	0.224861i
$73$	−7.98713			−0.934823			−0.467411	−	0.884040i	$-0.654813\pi$
$73$	−7.98713			−0.934823			−0.467411	+	0.884040i	$0.654813\pi$
$74$	−11.2065	+	6.24786i	−1.30273	+	0.726299i
$75$	−0.860637	+	4.92537i	−0.0993778	+	0.568733i
$76$	4.61185	−	1.08860i	0.529016	−	0.124871i
$77$	11.5000	+	11.5000i	1.31055	+	1.31055i
$78$	−0.400530	+	1.40987i	−0.0453511	+	0.159636i
$79$	0.843960			0.0949529			0.0474765	−	0.998872i	$-0.484882\pi$
$79$	0.843960			0.0949529			0.0474765	+	0.998872i	$0.484882\pi$
$80$	0.139442	−	8.94318i	0.0155901	−	0.999878i
$81$	−1.00000			−0.111111
$82$	−0.00223193	+	0.00785637i	−0.000246475	+	0.000867591i
$83$	−5.20069	−	5.20069i	−0.570850	−	0.570850i	0.361516	−	0.932366i	$-0.382259\pi$
$83$	−5.20069	−	5.20069i	−0.570850	−	0.570850i	−0.932366	+	0.361516i	$0.882259\pi$
$84$	−1.80076	−	7.62889i	−0.196479	−	0.832380i
$85$	−2.98261	+	5.74036i	−0.323510	+	0.622629i
$86$	3.91173	−	2.18088i	0.421813	−	0.235170i
$87$	−7.05696			−0.756586
$88$	−0.527948	+	11.7250i	−0.0562794	+	1.24989i
$89$			5.40896i			0.573349i	0.958028	+	0.286674i	$0.0925498\pi$
$89$			5.40896i			0.573349i	−0.958028	+	0.286674i	$0.907450\pi$
$90$	−2.16936	+	2.30085i	−0.228670	+	0.242530i
$91$	2.87215	+	2.87215i	0.301083	+	0.301083i
$92$	−2.94547	−	1.82049i	−0.307086	−	0.189799i
$93$	−7.64726	−	7.64726i	−0.792984	−	0.792984i
$94$	4.50051	−	15.8418i	0.464193	−	1.63396i
$95$	−5.05147	+	1.59701i	−0.518270	+	0.163850i
$96$	3.18753	−	4.67329i	0.325326	−	0.476966i
$97$			2.24154i			0.227594i	0.993504	+	0.113797i	$0.0363013\pi$
$97$			2.24154i			0.227594i	−0.993504	+	0.113797i	$0.963699\pi$
$98$	−11.3737	−	3.23117i	−1.14892	−	0.326397i
$99$	2.93423	−	2.93423i	0.294901	−	0.294901i
$100$	0.587786	+	9.98271i	0.0587786	+	0.998271i
$101$	−7.50655	−	7.50655i	−0.746930	−	0.746930i	0.226972	−	0.973901i	$-0.427118\pi$
$101$	−7.50655	−	7.50655i	−0.746930	−	0.746930i	−0.973901	+	0.226972i	$0.927118\pi$
$102$	−3.57349	+	1.99230i	−0.353828	+	0.197267i
$103$	3.91110			0.385372			0.192686	−	0.981260i	$-0.438280\pi$
$103$	3.91110			0.385372			0.192686	+	0.981260i	$0.438280\pi$
$104$	−0.131856	+	2.92834i	−0.0129295	+	0.287148i
$105$	2.64176	+	8.35610i	0.257810	+	0.815472i
$106$	−9.70841	+	5.41265i	−0.942964	+	0.525723i
$107$	−2.60233	+	2.60233i	−0.251577	+	0.251577i	−0.821617	−	0.570040i	$-0.806928\pi$
$107$	−2.60233	+	2.60233i	−0.251577	+	0.251577i	0.570040	+	0.821617i	$0.306928\pi$
$108$	−1.94651	+	0.459462i	−0.187303	+	0.0442118i
$109$	−2.06635	+	2.06635i	−0.197920	+	0.197920i	−0.799108	−	0.601188i	$-0.794694\pi$
$109$	−2.06635	+	2.06635i	−0.197920	+	0.197920i	0.601188	+	0.799108i	$0.294694\pi$
$110$	−0.385821	−	13.1166i	−0.0367866	−	1.25062i
$111$	9.07252			0.861125
$112$	−7.01037	−	14.0223i	−0.662418	−	1.32498i
$113$			8.13610i			0.765380i	0.923877	+	0.382690i	$0.125002\pi$
$113$			8.13610i			0.765380i	−0.923877	+	0.382690i	$0.874998\pi$
$114$	−3.22315	−	0.915667i	−0.301875	−	0.0857601i
$115$	3.43532	+	1.78495i	0.320345	+	0.166447i
$116$	−13.7364	+	3.24241i	−1.27540	+	0.301050i
$117$	0.732828	−	0.732828i	0.0677500	−	0.0677500i
$118$	−3.73290	−	6.69551i	−0.343641	−	0.616372i
$119$			11.3385i			1.03940i
$120$	−3.16552	+	5.47535i	−0.288971	+	0.499829i
$121$			6.21941i			0.565401i
$122$	−16.2561	+	9.06315i	−1.47176	+	0.820539i
$123$	0.00408363	−	0.00408363i	0.000368208	−	0.000368208i
$124$	−18.3991	−	11.3718i	−1.65229	−	1.02122i
$125$	−1.48500	−	11.0813i	−0.132822	−	0.991140i
$126$	−1.51469	+	5.33170i	−0.134939	+	0.474986i
$127$		−	16.0862i		−	1.42742i	−0.700442	−	0.713709i	$-0.747014\pi$
$127$		−	16.0862i		−	1.42742i	0.700442	−	0.713709i	$-0.252986\pi$
$128$	4.05736	−	10.5611i	0.358623	−	0.933482i
$129$	−3.16685			−0.278826
$130$	−0.0963593	−	3.27589i	−0.00845127	−	0.287314i
$131$	13.0407	−	13.0407i	1.13937	−	1.13937i	0.150808	−	0.988563i	$-0.451813\pi$
$131$	13.0407	−	13.0407i	1.13937	−	1.13937i	0.988563	−	0.150808i	$-0.0481875\pi$
$132$	4.36333	−	7.05967i	0.379780	−	0.614465i
$133$	−6.56612	+	6.56612i	−0.569355	+	0.569355i
$134$	3.75191	+	6.72963i	0.324116	+	0.581351i
$135$	2.13206	−	0.674045i	0.183498	−	0.0580125i
$136$	−6.04044	+	5.51991i	−0.517964	+	0.473328i
$137$	−6.51614			−0.556711			−0.278356	−	0.960478i	$-0.589789\pi$
$137$	−6.51614			−0.556711			−0.278356	+	0.960478i	$0.589789\pi$
$138$	1.19229	+	2.13856i	0.101495	+	0.182046i
$139$	−15.0953	−	15.0953i	−1.28036	−	1.28036i	−0.940461	−	0.339902i	$-0.889606\pi$
$139$	−15.0953	−	15.0953i	−1.28036	−	1.28036i	−0.339902	−	0.940461i	$-0.610394\pi$
$140$	8.98152	+	15.0514i	0.759077	+	1.27208i
$141$	−8.23434	+	8.23434i	−0.693456	+	0.693456i
$142$	−0.445814	+	1.56926i	−0.0374119	+	0.131690i
$143$			4.30057i			0.359632i
$144$	−3.57779	+	1.78869i	−0.298149	+	0.149058i
$145$	15.0458	−	4.75671i	1.24949	−	0.395023i
$146$	10.8655	+	3.08681i	0.899239	+	0.255466i
$147$	5.91188	+	5.91188i	0.487604	+	0.487604i
$148$	17.6597	−	4.16848i	1.45162	−	0.342647i
$149$	4.27402	+	4.27402i	0.350141	+	0.350141i	0.860162	−	0.510021i	$-0.170362\pi$
$149$	4.27402	+	4.27402i	0.350141	+	0.350141i	−0.510021	+	0.860162i	$0.670362\pi$
$150$	3.07432	−	6.36778i	0.251017	−	0.519927i
$151$		−	8.39998i		−	0.683581i	−0.939776	−	0.341790i	$-0.888967\pi$
$151$		−	8.39998i		−	0.683581i	0.939776	−	0.341790i	$-0.111033\pi$
$152$	−6.69459	−	0.301440i	−0.543003	−	0.0244500i
$153$	2.89302			0.233886
$154$	−11.2000	−	20.0889i	−0.902521	−	1.61881i
$155$	21.4590	+	11.1498i	1.72363	+	0.895573i
$156$	1.08975	−	1.76316i	0.0872497	−	0.141166i
$157$	−5.68893	−	5.68893i	−0.454026	−	0.454026i	0.442662	−	0.896689i	$-0.354034\pi$
$157$	−5.68893	−	5.68893i	−0.454026	−	0.454026i	−0.896689	+	0.442662i	$0.854034\pi$
$158$	−1.14811	−	0.326167i	−0.0913386	−	0.0259485i
$159$	7.85971			0.623315
$160$	−3.64599	+	12.1123i	−0.288241	+	0.957558i
$161$	6.78553			0.534775
$162$	1.36038	+	0.386472i	0.106882	+	0.0303641i
$163$	5.63869	+	5.63869i	0.441656	+	0.441656i	0.892568	−	0.450912i	$-0.148901\pi$
$163$	5.63869	+	5.63869i	0.441656	+	0.441656i	−0.450912	+	0.892568i	$0.648901\pi$
$164$	0.00607254	−	0.00982509i	0.000474186	−	0.000767211i
$165$	−4.27814	+	8.23374i	−0.333053	+	0.640996i
$166$	5.06500	+	9.08485i	0.393120	+	0.705121i
$167$	−6.45583			−0.499567			−0.249783	−	0.968302i	$-0.580359\pi$
$167$	−6.45583			−0.499567			−0.249783	+	0.968302i	$0.580359\pi$
$168$	−0.498640	+	11.0741i	−0.0384709	+	0.854389i
$169$		−	11.9259i		−	0.917379i
$170$	6.27598	−	6.65638i	0.481346	−	0.510521i
$171$	1.67534	+	1.67534i	0.128117	+	0.128117i
$172$	−6.16430	+	1.45505i	−0.470023	+	0.110946i
$173$	7.33664	+	7.33664i	0.557795	+	0.557795i	0.928679	−	0.370884i	$-0.120945\pi$
$173$	7.33664	+	7.33664i	0.557795	+	0.557795i	−0.370884	+	0.928679i	$0.620945\pi$
$174$	9.60016	+	2.72732i	0.727787	+	0.206758i
$175$	−11.2648	−	16.0350i	−0.851537	−	1.21213i
$176$	5.24962	−	15.7465i	0.395705	−	1.18694i
$177$			5.42054i			0.407432i
$178$	2.09042	−	7.35826i	0.156683	−	0.551525i
$179$	−1.04377	+	1.04377i	−0.0780153	+	0.0780153i	−0.745038	−	0.667022i	$-0.767569\pi$
$179$	−1.04377	+	1.04377i	−0.0780153	+	0.0780153i	0.667022	+	0.745038i	$0.267569\pi$
$180$	3.84037	−	2.29163i	0.286244	−	0.170808i
$181$	−12.1024	−	12.1024i	−0.899567	−	0.899567i	0.0958310	−	0.995398i	$-0.469449\pi$
$181$	−12.1024	−	12.1024i	−0.899567	−	0.899567i	−0.995398	+	0.0958310i	$0.969449\pi$
$182$	−2.79721	−	5.01723i	−0.207343	−	0.371901i
$183$	13.1606			0.972859
$184$	3.30339	+	3.61490i	0.243529	+	0.266494i
$185$	−19.3431	+	6.11528i	−1.42213	+	0.449604i
$186$	7.44774	+	13.3586i	0.546095	+	0.979504i
$187$	−8.48877	+	8.48877i	−0.620761	+	0.620761i
$188$	−12.2448	+	19.8116i	−0.893046	+	1.44491i
$189$	2.77134	−	2.77134i	0.201585	−	0.201585i
$190$	7.48913	−	0.220291i	0.543318	−	0.0159816i
$191$	−21.2273			−1.53596			−0.767978	−	0.640477i	$-0.778737\pi$
$191$	−21.2273			−1.53596			−0.767978	+	0.640477i	$0.778737\pi$
$192$	−6.14236	+	5.12557i	−0.443287	+	0.369906i
$193$			19.2782i			1.38767i	0.720132	+	0.693837i	$0.244081\pi$
$193$			19.2782i			1.38767i	−0.720132	+	0.693837i	$0.755919\pi$
$194$	0.866292	−	3.04935i	0.0621961	−	0.218930i
$195$	−1.06847	+	2.05639i	−0.0765148	+	0.147261i
$196$	14.2238	+	8.79124i	1.01599	+	0.627946i
$197$	9.48350	−	9.48350i	0.675672	−	0.675672i	−0.283346	−	0.959018i	$-0.591444\pi$
$197$	9.48350	−	9.48350i	0.675672	−	0.675672i	0.959018	+	0.283346i	$0.0914445\pi$
$198$	−5.12567	+	2.85767i	−0.364266	+	0.203086i
$199$			8.65421i			0.613481i	0.951793	+	0.306740i	$0.0992383\pi$
$199$			8.65421i			0.613481i	−0.951793	+	0.306740i	$0.900762\pi$
$200$	3.05843	−	13.8075i	0.216264	−	0.976335i
$201$		−	5.44815i		−	0.384283i
$202$	7.31070	+	13.1129i	0.514379	+	0.922617i
$203$	19.5572	−	19.5572i	1.37265	−	1.37265i
$204$	5.63128	−	1.32923i	0.394268	−	0.0930648i
$205$	−0.00595398	+	0.0114591i	−0.000415844	+	0.000800336i
$206$	−5.32059	−	1.51153i	−0.370703	−	0.105313i
$207$		−	1.73133i		−	0.120335i
$208$	1.31110	−	3.93271i	0.0909083	−	0.272684i
$209$	−9.83169			−0.680072
$210$	−0.364403	−	12.3885i	−0.0251462	−	0.854885i
$211$	−0.875946	+	0.875946i	−0.0603026	+	0.0603026i	−0.736615	−	0.676312i	$-0.763577\pi$
$211$	−0.875946	+	0.875946i	−0.0603026	+	0.0603026i	0.676312	+	0.736615i	$0.263577\pi$
$212$	15.2990	−	3.61124i	1.05074	−	0.248021i
$213$	0.815681	−	0.815681i	0.0558895	−	0.0558895i
$214$	4.54589	−	2.53443i	0.310751	−	0.173250i
$215$	6.75190	−	2.13460i	0.460476	−	0.145578i
$216$	2.82556	+	0.127228i	0.192255	+	0.00865675i
$217$	42.3863			2.87737
$218$	3.60961	−	2.01243i	0.244473	−	0.136299i
$219$	−5.64775	−	5.64775i	−0.381640	−	0.381640i
$220$	−4.54434	+	17.9927i	−0.306379	+	1.21307i
$221$	−2.12008	+	2.12008i	−0.142612	+	0.142612i
$222$	−12.3421	−	3.50628i	−0.828347	−	0.235326i
$223$			10.4375i			0.698946i	0.936946	+	0.349473i	$0.113639\pi$
$223$			10.4375i			0.698946i	−0.936946	+	0.349473i	$0.886361\pi$
$224$	4.11754	+	21.7850i	0.275115	+	1.45557i
$225$	−4.09133	+	2.87420i	−0.272755	+	0.191614i
$226$	3.14438	−	11.0682i	0.209161	−	0.736246i
$227$	−13.7218	−	13.7218i	−0.910747	−	0.910747i	0.0855842	−	0.996331i	$-0.472724\pi$
$227$	−13.7218	−	13.7218i	−0.910747	−	0.910747i	−0.996331	+	0.0855842i	$0.972724\pi$
$228$	4.03083	+	2.49131i	0.266948	+	0.164991i
$229$	8.43878	+	8.43878i	0.557651	+	0.557651i	0.928638	−	0.370987i	$-0.120981\pi$
$229$	8.43878	+	8.43878i	0.557651	+	0.557651i	−0.370987	+	0.928638i	$0.620981\pi$
$230$	−3.98352	−	3.75586i	−0.262665	−	0.247654i
$231$			16.2635i			1.07006i
$232$	19.9399	+	0.897842i	1.30912	+	0.0589462i
$233$	−28.6100			−1.87431			−0.937153	−	0.348919i	$-0.886549\pi$
$233$	−28.6100			−1.87431			−0.937153	+	0.348919i	$0.886549\pi$
$234$	−1.28014	+	0.713708i	−0.0836856	+	0.0466565i
$235$	12.0058	−	23.1064i	0.783169	−	1.50729i
$236$	2.49053	+	10.5511i	0.162120	+	0.686819i
$237$	0.596770	+	0.596770i	0.0387644	+	0.0387644i
$238$	4.38202	−	15.4247i	0.284044	−	0.999835i
$239$	21.4924			1.39023			0.695115	−	0.718899i	$-0.255354\pi$
$239$	21.4924			1.39023			0.695115	+	0.718899i	$0.255354\pi$
$240$	6.42239	−	6.22519i	0.414563	−	0.401834i
$241$	−19.5943			−1.26218			−0.631091	−	0.775709i	$-0.717393\pi$
$241$	−19.5943			−1.26218			−0.631091	+	0.775709i	$0.717393\pi$
$242$	2.40363	−	8.46077i	0.154511	−	0.543879i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	25.6172	−	6.04680i	1.63997	−	0.387106i
$245$	−16.5893	−	8.61959i	−1.05985	−	0.550685i
$246$	−0.00713350	+	0.00397708i	−0.000454816	+	0.000253570i
$247$	−2.45548			−0.156238
$248$	20.6349	+	22.5808i	1.31032	+	1.43388i
$249$		−	7.35489i		−	0.466097i
$250$	−2.26245	+	15.6487i	−0.143090	+	0.989710i
$251$	−9.58072	−	9.58072i	−0.604730	−	0.604730i	0.336834	−	0.941564i	$-0.390644\pi$
$251$	−9.58072	−	9.58072i	−0.604730	−	0.604730i	−0.941564	+	0.336834i	$0.890644\pi$
$252$	4.12111	−	6.66776i	0.259606	−	0.420030i
$253$	5.08011	+	5.08011i	0.319384	+	0.319384i
$254$	−6.21687	+	21.8834i	−0.390081	+	1.37308i
$255$	−6.16807	+	1.95002i	−0.386260	+	0.122115i
$256$	−9.60115	+	12.7991i	−0.600072	+	0.799946i
$257$		−	13.2730i		−	0.827946i	−0.910289	−	0.413973i	$-0.864141\pi$
$257$		−	13.2730i		−	0.827946i	0.910289	−	0.413973i	$-0.135859\pi$
$258$	4.30813	+	1.22390i	0.268212	+	0.0761967i
$259$	−25.1430	+	25.1430i	−1.56231	+	1.56231i
$260$	−1.13496	+	4.49370i	−0.0703869	+	0.278687i
$261$	−4.99003	−	4.99003i	−0.308875	−	0.308875i
$262$	−22.7802	+	12.7005i	−1.40737	+	0.784637i
$263$	13.0606			0.805349			0.402675	−	0.915343i	$-0.368081\pi$
$263$	13.0606			0.805349			0.402675	+	0.915343i	$0.368081\pi$
$264$	−8.66417	+	7.91754i	−0.533243	+	0.487291i
$265$	−16.7573	+	5.29780i	−1.02940	+	0.325441i
$266$	11.4701	−	6.39481i	0.703274	−	0.392091i
$267$	−3.82471	+	3.82471i	−0.234069	+	0.234069i
$268$	−2.50322	−	10.6049i	−0.152908	−	0.647796i
$269$	−12.4067	+	12.4067i	−0.756451	+	0.756451i	−0.975675	−	0.219224i	$-0.929647\pi$
$269$	−12.4067	+	12.4067i	−0.756451	+	0.756451i	0.219224	+	0.975675i	$0.429647\pi$
$270$	−3.16091	+	0.0929773i	−0.192367	+	0.00565842i
$271$	2.11193			0.128291			0.0641453	−	0.997941i	$-0.479568\pi$
$271$	2.11193			0.128291			0.0641453	+	0.997941i	$0.479568\pi$
$272$	10.3506	−	5.17472i	0.627597	−	0.313763i
$273$			4.06183i			0.245833i
$274$	8.86444	+	2.51831i	0.535520	+	0.152137i
$275$	3.57132	−	20.4385i	0.215359	−	1.23249i
$276$	−0.795479	−	3.37004i	−0.0478822	−	0.202853i
$277$	−13.2116	+	13.2116i	−0.793808	+	0.793808i	−0.982111	−	0.188303i	$-0.939701\pi$
$277$	−13.2116	+	13.2116i	−0.793808	+	0.793808i	0.188303	+	0.982111i	$0.439701\pi$
$278$	14.7014	+	26.3692i	0.881732	+	1.58152i
$279$		−	10.8149i		−	0.647469i
$280$	−6.40134	−	23.9468i	−0.382553	−	1.43110i
$281$		−	3.78786i		−	0.225965i	−0.993597	−	0.112982i	$-0.963960\pi$
$281$		−	3.78786i		−	0.225965i	0.993597	−	0.112982i	$-0.0360404\pi$
$282$	14.3842	−	8.01950i	0.856566	−	0.477554i
$283$	−3.16274	+	3.16274i	−0.188005	+	0.188005i	−0.794833	−	0.606828i	$-0.792442\pi$
$283$	−3.16274	+	3.16274i	−0.188005	+	0.188005i	0.606828	+	0.794833i	$0.292442\pi$
$284$	1.21295	−	1.96250i	0.0719756	−	0.116453i
$285$	−4.70118	−	2.44267i	−0.278474	−	0.144691i
$286$	1.66205	−	5.85042i	0.0982792	−	0.345942i
$287$			0.0226343i			0.00133606i
$288$	5.55844	−	1.05059i	0.327534	−	0.0619066i
$289$	8.63046			0.507674
$290$	−22.3064	+	0.656137i	−1.30988	+	0.0385297i
$291$	−1.58501	+	1.58501i	−0.0929147	+	0.0929147i
$292$	−13.5883	−	8.39847i	−0.795197	−	0.491483i
$293$	8.51339	−	8.51339i	0.497357	−	0.497357i	−0.413257	−	0.910614i	$-0.635609\pi$
$293$	8.51339	−	8.51339i	0.497357	−	0.497357i	0.910614	+	0.413257i	$0.135609\pi$
$294$	−5.75764	−	10.3272i	−0.335792	−	0.602294i
$295$	−3.65368	−	11.5569i	−0.212726	−	0.672868i
$296$	−25.6350	−	1.15428i	−1.49000	−	0.0670909i
$297$	4.14963			0.240786
$298$	−4.16251	−	7.46609i	−0.241128	−	0.432499i
$299$	1.26876	+	1.26876i	0.0733745	+	0.0733745i
$300$	−6.64321	+	7.47447i	−0.383546	+	0.431539i
$301$	8.77642	−	8.77642i	0.505864	−	0.505864i
$302$	−3.24636	+	11.4272i	−0.186807	+	0.657560i
$303$		−	10.6159i		−	0.609866i
$304$	8.99071	+	2.99735i	0.515652	+	0.171910i
$305$	−28.0591	+	8.87083i	−1.60666	+	0.507942i
$306$	−3.93561	−	1.11807i	−0.224984	−	0.0639159i
$307$	7.12093	+	7.12093i	0.406413	+	0.406413i	0.880486	−	0.474073i	$-0.157217\pi$
$307$	7.12093	+	7.12093i	0.406413	+	0.406413i	−0.474073	+	0.880486i	$0.657217\pi$
$308$	7.47246	+	31.6570i	0.425783	+	1.80383i
$309$	2.76557	+	2.76557i	0.157328	+	0.157328i
$310$	−24.8833	−	23.4613i	−1.41328	−	1.33251i
$311$		−	21.2980i		−	1.20770i	−0.797099	−	0.603849i	$-0.793633\pi$
$311$		−	21.2980i		−	1.20770i	0.797099	−	0.603849i	$-0.206367\pi$
$312$	−2.16389	+	1.97742i	−0.122506	+	0.111949i
$313$	7.49789			0.423806			0.211903	−	0.977291i	$-0.432034\pi$
$313$	7.49789			0.423806			0.211903	+	0.977291i	$0.432034\pi$
$314$	5.54051	+	9.93774i	0.312669	+	0.560819i
$315$	−4.04065	+	7.77666i	−0.227665	+	0.438165i
$316$	1.43581	+	0.887425i	0.0807707	+	0.0499215i
$317$	2.35354	+	2.35354i	0.132188	+	0.132188i	0.770105	−	0.637917i	$-0.220204\pi$
$317$	2.35354	+	2.35354i	0.132188	+	0.132188i	−0.637917	+	0.770105i	$0.720204\pi$
$318$	−10.6922	−	3.03756i	−0.599589	−	0.170338i
$319$	29.2838			1.63958
$320$	9.64099	−	15.0682i	0.538948	−	0.842339i
$321$	−3.68025			−0.205412
$322$	−9.23091	−	2.62242i	−0.514419	−	0.146142i
$323$	−4.84680	−	4.84680i	−0.269683	−	0.269683i
$324$	−1.70128	−	1.05150i	−0.0945154	−	0.0584167i
$325$	0.891943	−	5.10453i	0.0494761	−	0.283149i
$326$	−5.49157	−	9.84997i	−0.304150	−	0.545539i
$327$	−2.92226			−0.161601
$328$	−0.0120581	+	0.0110190i	−0.000665797	+	0.000608423i
$329$		−	45.6403i		−	2.51623i
$330$	9.00202	−	9.54765i	0.495545	−	0.525581i
$331$	22.6845	+	22.6845i	1.24685	+	1.24685i	0.957102	+	0.289753i	$0.0935730\pi$
$331$	22.6845	+	22.6845i	1.24685	+	1.24685i	0.289753	+	0.957102i	$0.406427\pi$
$332$	−3.37929	−	14.3163i	−0.185463	−	0.785712i
$333$	6.41524	+	6.41524i	0.351553	+	0.351553i
$334$	8.78239	+	2.49500i	0.480551	+	0.136520i
$335$	3.67230	+	11.6158i	0.200639	+	0.634637i
$336$	4.95819	−	14.8724i	0.270492	−	0.811353i
$337$			8.90357i			0.485008i	0.970150	+	0.242504i	$0.0779688\pi$
$337$			8.90357i			0.485008i	−0.970150	+	0.242504i	$0.922031\pi$
$338$	−4.60904	+	16.2238i	−0.250699	+	0.882459i
$339$	−5.75309	+	5.75309i	−0.312465	+	0.312465i
$340$	−11.1102	+	6.62973i	−0.602538	+	0.359548i
$341$	31.7333	+	31.7333i	1.71845	+	1.71845i
$342$	−1.63163	−	2.92658i	−0.0882286	−	0.158251i
$343$	−5.33279			−0.287944
$344$	8.94814	+	0.402911i	0.482451	+	0.0217235i
$345$	1.16699	+	3.69129i	0.0628287	+	0.198732i
$346$	−7.14523	−	12.8160i	−0.384130	−	0.688995i
$347$	8.87783	−	8.87783i	0.476587	−	0.476587i	−0.427451	−	0.904038i	$-0.640588\pi$
$347$	8.87783	−	8.87783i	0.476587	−	0.476587i	0.904038	+	0.427451i	$0.140588\pi$
$348$	−12.0059	−	7.42040i	−0.643581	−	0.397775i
$349$	−8.23040	+	8.23040i	−0.440563	+	0.440563i	−0.892201	−	0.451638i	$-0.850840\pi$
$349$	−8.23040	+	8.23040i	−0.440563	+	0.440563i	0.451638	+	0.892201i	$0.350840\pi$
$350$	9.12730	+	26.1673i	0.487875	+	1.39870i
$351$	1.03637			0.0553176
$352$	−13.2271	+	19.3924i	−0.705005	+	1.03362i
$353$		−	34.7125i		−	1.84756i	−0.382922	−	0.923781i	$-0.625082\pi$
$353$		−	34.7125i		−	1.84756i	0.382922	−	0.923781i	$-0.374918\pi$
$354$	2.09489	−	7.37400i	0.111342	−	0.391924i
$355$	−1.18927	+	2.28888i	−0.0631200	+	0.121481i
$356$	−5.68753	+	9.20215i	−0.301438	+	0.487713i
$357$	−8.01753	+	8.01753i	−0.424333	+	0.424333i
$358$	1.82332	−	1.01654i	0.0963655	−	0.0537259i
$359$		−	2.81082i		−	0.148350i	−0.997245	−	0.0741748i	$-0.976368\pi$
$359$		−	2.81082i		−	0.148350i	0.997245	−	0.0741748i	$-0.0236323\pi$
$360$	−6.11002	+	1.63330i	−0.322026	+	0.0860825i
$361$			13.3864i			0.704550i
$362$	11.7867	+	21.1412i	0.619494	+	1.11116i
$363$	−4.39778	+	4.39778i	−0.230824	+	0.230824i
$364$	1.86626	+	7.90639i	0.0978185	+	0.414407i
$365$	15.8482	+	8.23449i	0.829531	+	0.431013i
$366$	−17.9034	−	5.08621i	−0.935828	−	0.265860i
$367$		−	18.2835i		−	0.954392i	−0.878797	−	0.477196i	$-0.841653\pi$
$367$		−	18.2835i		−	0.954392i	0.878797	−	0.477196i	$-0.158347\pi$
$368$	−3.09681	−	6.19432i	−0.161433	−	0.322901i
$369$	0.00577512			0.000300641
$370$	28.6774	−	0.843538i	1.49087	−	0.0438534i
$371$	−21.7819	+	21.7819i	−1.13086	+	1.13086i
$372$	−4.96902	−	21.0512i	−0.257632	−	1.09145i
$373$	−23.4176	+	23.4176i	−1.21252	+	1.21252i	−0.242324	+	0.970195i	$0.577910\pi$
$373$	−23.4176	+	23.4176i	−1.21252	+	1.21252i	−0.970195	+	0.242324i	$0.922090\pi$
$374$	14.8287	−	8.26730i	0.766771	−	0.427492i
$375$	6.78560	−	8.88570i	0.350407	−	0.458856i
$376$	24.3143	−	22.2190i	1.25391	−	1.14586i
$377$	7.31366			0.376673
$378$	−4.84113	+	2.69904i	−0.249001	+	0.138823i
$379$	−6.20944	−	6.20944i	−0.318957	−	0.318957i	0.529409	−	0.848367i	$-0.322414\pi$
$379$	−6.20944	−	6.20944i	−0.318957	−	0.318957i	−0.848367	+	0.529409i	$0.822414\pi$
$380$	−10.2732	−	2.59466i	−0.527005	−	0.133103i
$381$	11.3746	−	11.3746i	0.582741	−	0.582741i
$382$	28.8773	+	8.20378i	1.47749	+	0.419742i
$383$			14.4005i			0.735832i	0.929859	+	0.367916i	$0.119929\pi$
$383$			14.4005i			0.735832i	−0.929859	+	0.367916i	$0.880071\pi$
$384$	10.3368	−	4.59888i	0.527500	−	0.234685i
$385$	−10.9623	−	34.6747i	−0.558692	−	1.76719i
$386$	7.45049	−	26.2257i	0.379220	−	1.33485i
$387$	−2.23930	−	2.23930i	−0.113830	−	0.113830i
$388$	−2.35698	+	3.81348i	−0.119657	+	0.193600i
$389$	15.4753	+	15.4753i	0.784630	+	0.784630i	0.980608	−	0.195978i	$-0.0627882\pi$
$389$	15.4753	+	15.4753i	0.784630	+	0.784630i	−0.195978	+	0.980608i	$0.562788\pi$
$390$	2.24827	−	2.38454i	0.113845	−	0.120746i
$391$			5.00875i			0.253304i
$392$	−15.9522	−	17.4566i	−0.805710	−	0.881689i
$393$	18.4423			0.930292
$394$	−16.5663	+	9.23607i	−0.834598	+	0.465307i
$395$	−1.67460	−	0.870098i	−0.0842581	−	0.0437794i
$396$	8.07728	−	1.90660i	0.405899	−	0.0958101i
$397$	−15.0440	−	15.0440i	−0.755036	−	0.755036i	0.220378	−	0.975414i	$-0.429271\pi$
$397$	−15.0440	−	15.0440i	−0.755036	−	0.755036i	−0.975414	+	0.220378i	$0.929271\pi$
$398$	3.34461	−	11.7730i	0.167650	−	0.590129i
$399$	−9.28590			−0.464876
$400$	−9.49684	+	17.6014i	−0.474842	+	0.880071i
$401$	28.7953			1.43797			0.718985	−	0.695026i	$-0.244607\pi$
$401$	28.7953			1.43797			0.718985	+	0.695026i	$0.244607\pi$
$402$	−2.10556	+	7.41157i	−0.105016	+	0.369655i
$403$	7.92543	+	7.92543i	0.394794	+	0.394794i
$404$	−4.87759	−	20.6639i	−0.242669	−	1.02807i
$405$	1.98421	+	1.03097i	0.0985963	+	0.0512293i
$406$	−34.1637	+	19.0470i	−1.69551	+	0.945286i
$407$	−37.6476			−1.86612
$408$	−8.17440	−	0.368072i	−0.404693	−	0.0182223i
$409$		−	23.3562i		−	1.15489i	−0.816430	−	0.577444i	$-0.804050\pi$
$409$		−	23.3562i		−	1.15489i	0.816430	−	0.577444i	$-0.195950\pi$
$410$	0.0125283	−	0.0132877i	0.000618729	−	0.000656231i
$411$	−4.60760	−	4.60760i	−0.227276	−	0.227276i
$412$	6.65387	+	4.11252i	0.327813	+	0.202610i
$413$	−15.0222	−	15.0222i	−0.739192	−	0.739192i
$414$	−0.669110	+	2.35527i	−0.0328850	+	0.115755i
$415$	4.95752	+	15.6810i	0.243355	+	0.769751i
$416$	−3.30348	+	4.84328i	−0.161966	+	0.237461i
$417$		−	21.3479i		−	1.04541i
$418$	13.3749	+	3.79968i	0.654185	+	0.185848i
$419$	−22.4332	+	22.4332i	−1.09594	+	1.09594i	−0.101055	+	0.994881i	$0.532222\pi$
$419$	−22.4332	+	22.4332i	−1.09594	+	1.09594i	−0.994881	+	0.101055i	$0.967778\pi$
$420$	−4.29207	+	16.9939i	−0.209432	+	0.829216i
$421$	14.7632	+	14.7632i	0.719513	+	0.719513i	0.968505	−	0.248993i	$-0.0800995\pi$
$421$	14.7632	+	14.7632i	0.719513	+	0.719513i	−0.248993	+	0.968505i	$0.580100\pi$
$422$	1.53015	−	0.853092i	0.0744865	−	0.0415279i
$423$	−11.6451			−0.566205
$424$	−22.2081	−	0.999973i	−1.07852	−	0.0485630i
$425$	11.8363	−	8.31511i	0.574144	−	0.403342i
$426$	−1.42488	+	0.794399i	−0.0690354	+	0.0384888i
$427$	−36.4725	+	36.4725i	−1.76503	+	1.76503i
$428$	−7.16364	+	1.69094i	−0.346268	+	0.0817345i
$429$	−3.04096	+	3.04096i	−0.146819	+	0.146819i
$430$	−10.0101	+	0.294445i	−0.482731	+	0.0141994i
$431$	5.92220			0.285262			0.142631	−	0.989776i	$-0.454444\pi$
$431$	5.92220			0.285262			0.142631	+	0.989776i	$0.454444\pi$
$432$	−3.79468	−	1.26508i	−0.182571	−	0.0608662i
$433$		−	5.27026i		−	0.253272i	−0.991949	−	0.126636i	$-0.959582\pi$
$433$		−	5.27026i		−	0.253272i	0.991949	−	0.126636i	$-0.0404181\pi$
$434$	−57.6616	−	16.3811i	−2.76784	−	0.786320i
$435$	14.0025	+	7.27551i	0.671369	+	0.348834i
$436$	−5.68819	+	1.34267i	−0.272415	+	0.0643020i
$437$	−2.90057	+	2.90057i	−0.138753	+	0.138753i
$438$	5.50040	+	9.86580i	0.262819	+	0.471406i
$439$		−	17.8427i		−	0.851587i	−0.904820	−	0.425793i	$-0.859995\pi$
$439$		−	17.8427i		−	0.851587i	0.904820	−	0.425793i	$-0.140005\pi$
$440$	13.1357	−	22.7207i	0.626221	−	1.08317i
$441$			8.36066i			0.398127i
$442$	3.70348	−	2.06477i	0.176156	−	0.0982110i
$443$	−5.89855	+	5.89855i	−0.280248	+	0.280248i	−0.833208	−	0.552960i	$-0.813498\pi$
$443$	−5.89855	+	5.89855i	−0.280248	+	0.280248i	0.552960	+	0.833208i	$0.313498\pi$
$444$	15.4349	+	9.53975i	0.732507	+	0.452737i
$445$	5.57648	−	10.7325i	0.264350	−	0.508771i
$446$	4.03380	−	14.1990i	0.191006	−	0.672341i
$447$			6.04438i			0.285889i
$448$	2.81788	−	31.2273i	0.133132	−	1.47535i
$449$	8.12803			0.383586			0.191793	−	0.981435i	$-0.438570\pi$
$449$	8.12803			0.383586			0.191793	+	0.981435i	$0.438570\pi$
$450$	6.67657	−	2.32883i	0.314736	−	0.109782i
$451$	−0.0169455	+	0.0169455i	−0.000797934	+	0.000797934i
$452$	−8.55511	+	13.8418i	−0.402399	+	0.651062i
$453$	5.93968	−	5.93968i	0.279071	−	0.279071i
$454$	13.3638	+	23.9700i	0.627193	+	1.12497i
$455$	−2.73786	−	8.66005i	−0.128353	−	0.405990i
$456$	−4.52064	−	4.94694i	−0.211698	−	0.231662i
$457$	−6.35488			−0.297269			−0.148634	−	0.988892i	$-0.547488\pi$
$457$	−6.35488			−0.297269			−0.148634	+	0.988892i	$0.547488\pi$
$458$	−8.21861	−	14.7413i	−0.384030	−	0.688817i
$459$	2.04567	+	2.04567i	0.0954838	+	0.0954838i
$460$	3.96756	+	6.64893i	0.184989	+	0.310008i
$461$	2.13085	−	2.13085i	0.0992438	−	0.0992438i	−0.655742	−	0.754985i	$-0.727644\pi$
$461$	2.13085	−	2.13085i	0.0992438	−	0.0992438i	0.754985	+	0.655742i	$0.227644\pi$
$462$	6.28540	−	22.1246i	0.292423	−	1.02933i
$463$			18.4540i			0.857630i	0.903392	+	0.428815i	$0.141069\pi$
$463$			18.4540i			0.857630i	−0.903392	+	0.428815i	$0.858931\pi$
$464$	−26.7789	−	8.92763i	−1.24318	−	0.414455i
$465$	7.28970	+	23.0579i	0.338052	+	1.06928i
$466$	38.9206	+	11.0570i	1.80296	+	0.512205i
$467$	−5.63243	−	5.63243i	−0.260638	−	0.260638i	0.564675	−	0.825313i	$-0.309001\pi$
$467$	−5.63243	−	5.63243i	−0.260638	−	0.260638i	−0.825313	+	0.564675i	$0.809001\pi$
$468$	2.01731	−	0.476175i	0.0932503	−	0.0220112i
$469$	15.0987	+	15.0987i	0.697193	+	0.697193i
$470$	−25.2624	+	26.7936i	−1.16527	+	1.23590i
$471$		−	8.04537i		−	0.370711i
$472$	0.689643	−	15.3161i	0.0317434	−	0.704979i
$473$	13.1412			0.604235
$474$	−0.581200	−	1.04247i	−0.0266954	−	0.0478822i
$475$	11.6697	+	2.03910i	0.535441	+	0.0935604i
$476$	−11.9224	+	19.2899i	−0.546464	+	0.884153i
$477$	5.55765	+	5.55765i	0.254467	+	0.254467i
$478$	−29.2379	−	8.30623i	−1.33731	−	0.379918i
$479$	21.4860			0.981720			0.490860	−	0.871239i	$-0.336683\pi$
$479$	21.4860			0.981720			0.490860	+	0.871239i	$0.336683\pi$
$480$	−11.1428	+	5.98655i	−0.508595	+	0.273248i
$481$	−9.40253			−0.428718
$482$	26.6558	+	7.57267i	1.21414	+	0.344926i
$483$	4.79810	+	4.79810i	0.218321	+	0.218321i
$484$	−6.53971	+	10.5809i	−0.297259	+	0.480952i
$485$	2.31096	−	4.44769i	0.104935	−	0.201959i
$486$	0.688658	+	1.23521i	0.0312382	+	0.0560304i
$487$	36.3297			1.64626			0.823128	−	0.567856i	$-0.192227\pi$
$487$	36.3297			1.64626			0.823128	+	0.567856i	$0.192227\pi$
$488$	−37.1861	−	1.67439i	−1.68334	−	0.0757962i
$489$			7.97431i			0.360611i
$490$	19.2366	+	18.1373i	0.869021	+	0.819358i
$491$	1.63599	+	1.63599i	0.0738313	+	0.0738313i	0.743058	−	0.669227i	$-0.233375\pi$
$491$	1.63599	+	1.63599i	0.0738313	+	0.0738313i	−0.669227	+	0.743058i	$0.733375\pi$
$492$	0.0112413	−	0.00265345i	0.000506798	−	0.000119627i
$493$	14.4362	+	14.4362i	0.650175	+	0.650175i
$494$	3.34039	+	0.948974i	0.150291	+	0.0426964i
$495$	−8.84724	+	2.79703i	−0.397654	+	0.125717i
$496$	−19.3445	−	38.6933i	−0.868592	−	1.73738i
$497$			4.52106i			0.202797i
$498$	−2.84246	+	10.0055i	−0.127374	+	0.448355i
$499$	18.7955	−	18.7955i	0.841402	−	0.841402i	−0.147639	−	0.989041i	$-0.547167\pi$
$499$	18.7955	−	18.7955i	0.841402	−	0.841402i	0.989041	+	0.147639i	$0.0471674\pi$
$500$	9.12558	−	20.4138i	0.408108	−	0.912933i
$501$	−4.56496	−	4.56496i	−0.203947	−	0.203947i
$502$	9.33076	+	16.7361i	0.416452	+	0.746970i
$503$	13.8118			0.615838			0.307919	−	0.951413i	$-0.400367\pi$
$503$	13.8118			0.615838			0.307919	+	0.951413i	$0.400367\pi$
$504$	−8.18319	+	7.47801i	−0.364508	+	0.333097i
$505$	7.15557	+	22.6336i	0.318419	+	1.00718i
$506$	−4.94757	−	8.87421i	−0.219946	−	0.394507i
$507$	8.43290	−	8.43290i	0.374518	−	0.374518i
$508$	16.9146	−	27.3671i	0.750465	−	1.21422i
$509$	−5.40184	+	5.40184i	−0.239432	+	0.239432i	−0.816615	−	0.577183i	$-0.804152\pi$
$509$	−5.40184	+	5.40184i	−0.239432	+	0.239432i	0.577183	+	0.816615i	$0.304152\pi$
$510$	9.14456	−	0.268985i	0.404928	−	0.0119108i
$511$	31.3037			1.38479
$512$	18.0077	−	13.7011i	0.795837	−	0.605510i
$513$			2.36929i			0.104607i
$514$	−5.12964	+	18.0563i	−0.226259	+	0.796431i
$515$	−7.76046	−	4.03223i	−0.341967	−	0.177681i
$516$	−5.38769	−	3.32994i	−0.237180	−	0.146593i
$517$	34.1694	−	34.1694i	1.50277	−	1.50277i
$518$	43.9212	−	24.4870i	1.92979	−	1.07590i
$519$			10.3756i			0.455437i
$520$	3.28066	−	5.67452i	0.143867	−	0.248844i
$521$			33.6969i			1.47629i	0.674642	+	0.738145i	$0.264298\pi$
$521$			33.6969i			1.47629i	−0.674642	+	0.738145i	$0.735702\pi$
$522$	4.85983	+	8.71685i	0.212709	+	0.381526i
$523$	−4.31481	+	4.31481i	−0.188673	+	0.188673i	−0.795122	−	0.606449i	$-0.792593\pi$
$523$	−4.31481	+	4.31481i	−0.188673	+	0.188673i	0.606449	+	0.795122i	$0.292593\pi$
$524$	35.8981	−	8.47355i	1.56822	−	0.370169i
$525$	3.37307	−	19.3039i	0.147213	−	0.842489i
$526$	−17.7674	−	5.04755i	−0.774694	−	0.220084i
$527$			31.2876i			1.36291i
$528$	14.8465	−	7.42241i	0.646111	−	0.323019i
$529$	−20.0025			−0.869674
$530$	24.8438	−	0.730774i	1.07915	−	0.0317428i
$531$	−3.83290	+	3.83290i	−0.166334	+	0.166334i
$532$	−18.0751	+	4.26652i	−0.783654	+	0.184977i
$533$	−0.00423217	+	0.00423217i	−0.000183316	+	0.000183316i
$534$	6.68122	−	3.72493i	0.289125	−	0.161193i
$535$	7.84650	−	2.48065i	0.339234	−	0.107248i
$536$	−0.693156	+	15.3941i	−0.0299398	+	0.664924i
$537$	−1.47612			−0.0636993
$538$	21.6727	−	12.0830i	0.934377	−	0.520936i
$539$	−24.5321	−	24.5321i	−1.05667	−	1.05667i
$540$	4.33598	+	1.09512i	0.186591	+	0.0471265i
$541$	−22.8010	+	22.8010i	−0.980290	+	0.980290i	−0.999809	−	0.0195198i	$-0.993786\pi$
$541$	−22.8010	+	22.8010i	−0.980290	+	0.980290i	0.0195198	+	0.999809i	$0.493786\pi$
$542$	−2.87303	−	0.816203i	−0.123407	−	0.0350589i
$543$		−	17.1154i		−	0.734493i
$544$	−16.0807	+	3.03937i	−0.689452	+	0.130312i
$545$	6.23041	−	1.96973i	0.266882	−	0.0843740i
$546$	1.56979	−	5.52564i	0.0671806	−	0.236476i
$547$	−5.56014	−	5.56014i	−0.237735	−	0.237735i	0.578177	−	0.815911i	$-0.303764\pi$
$547$	−5.56014	−	5.56014i	−0.237735	−	0.237735i	−0.815911	+	0.578177i	$0.803764\pi$
$548$	−11.0858	−	6.85172i	−0.473560	−	0.292691i
$549$	9.30595	+	9.30595i	0.397168	+	0.397168i
$550$	−12.7573	+	26.4239i	−0.543972	+	1.12672i
$551$			16.7200i			0.712297i
$552$	−0.220273	+	4.89197i	−0.00937543	+	0.208216i
$553$	−3.30771			−0.140658
$554$	23.0787	−	12.8669i	0.980521	−	0.546662i
$555$	−18.0018	−	9.35349i	−0.764134	−	0.397034i
$556$	−9.80856	−	41.5539i	−0.415976	−	1.76228i
$557$	12.2628	+	12.2628i	0.519591	+	0.519591i	0.917447	−	0.397857i	$-0.130246\pi$
$557$	12.2628	+	12.2628i	0.519591	+	0.519591i	−0.397857	+	0.917447i	$0.630246\pi$
$558$	−4.17964	+	14.7123i	−0.176938	+	0.622823i
$559$	3.28204			0.138816
$560$	−0.546512	+	35.0507i	−0.0230943	+	1.48116i
$561$	−12.0049			−0.506849
$562$	−1.46390	+	5.15294i	−0.0617510	+	0.217363i
$563$	0.327630	+	0.327630i	0.0138079	+	0.0138079i	0.713977	−	0.700169i	$-0.246892\pi$
$563$	0.327630	+	0.327630i	0.0138079	+	0.0138079i	−0.700169	+	0.713977i	$0.746892\pi$
$564$	−22.6673	+	5.35049i	−0.954465	+	0.225296i
$565$	8.38807	−	16.1438i	0.352889	−	0.679173i
$566$	5.52484	−	3.08022i	0.232226	−	0.129471i
$567$	3.91927			0.164594
$568$	−2.40853	+	2.20098i	−0.101060	+	0.0923511i
$569$		−	35.6010i		−	1.49247i	−0.665681	−	0.746237i	$-0.731859\pi$
$569$		−	35.6010i		−	1.49247i	0.665681	−	0.746237i	$-0.268141\pi$
$570$	5.45138	+	5.13984i	0.228333	+	0.215284i
$571$	3.57427	+	3.57427i	0.149579	+	0.149579i	0.777930	−	0.628351i	$-0.216270\pi$
$571$	3.57427	+	3.57427i	0.149579	+	0.149579i	−0.628351	+	0.777930i	$0.716270\pi$
$572$	−4.52205	+	7.31646i	−0.189076	+	0.305917i
$573$	−15.0100	−	15.0100i	−0.627051	−	0.627051i
$574$	0.00874752	−	0.0307912i	0.000365114	−	0.00128520i
$575$	−4.97618	−	7.08342i	−0.207521	−	0.295399i
$576$	−7.96763	−	0.718981i	−0.331984	−	0.0299575i
$577$			8.80260i			0.366457i	0.983070	+	0.183229i	$0.0586548\pi$
$577$			8.80260i			0.366457i	−0.983070	+	0.183229i	$0.941345\pi$
$578$	−11.7407	−	3.33543i	−0.488350	−	0.138736i
$579$	−13.6317	+	13.6317i	−0.566515	+	0.566515i
$580$	30.5988	+	7.72822i	1.27055	+	0.320897i
$581$	20.3829	+	20.3829i	0.845625	+	0.845625i
$582$	2.76877	−	1.54365i	0.114769	−	0.0639864i
$583$	−32.6149			−1.35077
$584$	15.2395	+	16.6766i	0.630616	+	0.690084i
$585$	−2.20961	+	0.698563i	−0.0913561	+	0.0288820i
$586$	−14.8716	+	8.29127i	−0.614342	+	0.342509i
$587$	17.9887	−	17.9887i	0.742475	−	0.742475i	−0.230579	−	0.973054i	$-0.574062\pi$
$587$	17.9887	−	17.9887i	0.742475	−	0.742475i	0.973054	+	0.230579i	$0.0740619\pi$
$588$	3.84141	+	16.2741i	0.158417	+	0.671132i
$589$	−18.1186	+	18.1186i	−0.746564	+	0.746564i
$590$	0.503987	+	17.1338i	0.0207488	+	0.705389i
$591$	13.4117			0.551684
$592$	34.4273	+	11.4775i	1.41495	+	0.471721i
$593$			25.4791i			1.04630i	0.852240	+	0.523150i	$0.175243\pi$
$593$			25.4791i			1.04630i	−0.852240	+	0.523150i	$0.824757\pi$
$594$	−5.64508	−	1.60372i	−0.231620	−	0.0658013i
$595$	11.6897	−	22.4980i	0.479229	−	0.922328i
$596$	2.77716	+	11.7654i	0.113757	+	0.481931i
$597$	−6.11945	+	6.11945i	−0.250452	+	0.250452i
$598$	−1.23566	−	2.21635i	−0.0505299	−	0.0906331i
$599$		−	14.6977i		−	0.600532i	−0.953856	−	0.300266i	$-0.902925\pi$
$599$		−	14.6977i		−	0.600532i	0.953856	−	0.300266i	$-0.0970754\pi$
$600$	11.9260	−	7.60071i	0.486876	−	0.310298i
$601$		−	12.2790i		−	0.500869i	−0.968134	−	0.250434i	$-0.919427\pi$
$601$		−	12.2790i		−	0.500869i	0.968134	−	0.250434i	$-0.0805735\pi$
$602$	−15.3311	+	8.54744i	−0.624850	+	0.348368i
$603$	3.85243	−	3.85243i	0.156883	−	0.156883i
$604$	8.83258	−	14.2907i	0.359393	−	0.581480i
$605$	6.41202	−	12.3406i	0.260686	−	0.501718i
$606$	−4.10274	+	14.4416i	−0.166662	+	0.586651i
$607$			26.2195i			1.06421i	0.846677	+	0.532107i	$0.178600\pi$
$607$			26.2195i			1.06421i	−0.846677	+	0.532107i	$0.821400\pi$
$608$	−11.0724	−	7.55220i	−0.449045	−	0.306282i
$609$	27.6581			1.12076
$610$	41.5995	−	1.22364i	1.68431	−	0.0495436i
$611$	8.53386	−	8.53386i	0.345243	−	0.345243i
$612$	4.92182	+	3.04201i	0.198953	+	0.122966i
$613$	23.4055	−	23.4055i	0.945340	−	0.945340i	−0.0532416	−	0.998582i	$-0.516955\pi$
$613$	23.4055	−	23.4055i	0.945340	−	0.945340i	0.998582	+	0.0532416i	$0.0169553\pi$
$614$	−6.93514	−	12.4392i	−0.279880	−	0.502007i
$615$	−0.0123129	+	0.00389269i	−0.000496503	+	0.000156968i
$616$	2.06917	−	45.9536i	0.0833692	−	1.85152i
$617$	−27.5735			−1.11007			−0.555033	−	0.831828i	$-0.687294\pi$
$617$	−27.5735			−1.11007			−0.555033	+	0.831828i	$0.687294\pi$
$618$	−2.69341	−	4.83104i	−0.108345	−	0.194333i
$619$	−12.2452	−	12.2452i	−0.492176	−	0.492176i	0.416815	−	0.908991i	$-0.363146\pi$
$619$	−12.2452	−	12.2452i	−0.492176	−	0.492176i	−0.908991	+	0.416815i	$0.863146\pi$
$620$	24.7837	+	41.5330i	0.995337	+	1.66801i
$621$	1.22423	−	1.22423i	0.0491268	−	0.0491268i
$622$	−8.23108	+	28.9734i	−0.330036	+	1.16173i
$623$		−	21.1992i		−	0.849327i
$624$	3.70793	−	1.85376i	0.148436	−	0.0742097i
$625$	−8.47792	+	23.5186i	−0.339117	+	0.940744i
$626$	−10.2000	−	2.89773i	−0.407673	−	0.115816i
$627$	−6.95205	−	6.95205i	−0.277638	−	0.277638i
$628$	−3.69654	−	15.6604i	−0.147508	−	0.624917i
$629$	−18.5594	−	18.5594i	−0.740011	−	0.740011i
$630$	8.50229	−	9.01763i	0.338739	−	0.359271i
$631$			25.5846i			1.01851i	0.860617	+	0.509253i	$0.170078\pi$
$631$			25.5846i			1.01851i	−0.860617	+	0.509253i	$0.829922\pi$
$632$	−1.61029	−	1.76214i	−0.0640537	−	0.0700941i
$633$	−1.23877			−0.0492369
$634$	−2.29214	−	4.11130i	−0.0910324	−	0.163281i
$635$	−16.5844	+	31.9184i	−0.658131	+	1.26664i
$636$	13.3716	+	8.26449i	0.530216	+	0.327708i
$637$	−6.12692	−	6.12692i	−0.242758	−	0.242758i
$638$	−39.8371	−	11.3174i	−1.57717	−	0.448059i
$639$	1.15355			0.0456336
$640$	−18.9389	+	16.7726i	−0.748625	+	0.662994i
$641$	−3.52020			−0.139040			−0.0695198	−	0.997581i	$-0.522147\pi$
$641$	−3.52020			−0.139040			−0.0695198	+	0.997581i	$0.522147\pi$
$642$	5.00655	+	1.42232i	0.197593	+	0.0561343i
$643$	−19.0869	−	19.0869i	−0.752715	−	0.752715i	0.222270	−	0.974985i	$-0.428653\pi$
$643$	−19.0869	−	19.0869i	−0.752715	−	0.752715i	−0.974985	+	0.222270i	$0.928653\pi$
$644$	11.5441	+	7.13499i	0.454900	+	0.281158i
$645$	6.28370	+	3.26493i	0.247421	+	0.128556i
$646$	4.72034	+	8.46665i	0.185719	+	0.333116i
$647$	5.02456			0.197536			0.0987678	−	0.995111i	$-0.468510\pi$
$647$	5.02456			0.197536			0.0987678	+	0.995111i	$0.468510\pi$
$648$	1.90801	+	2.08794i	0.0749538	+	0.0820220i
$649$		−	22.4932i		−	0.882935i
$650$	−3.18614	+	6.59940i	−0.124971	+	0.258850i
$651$	29.9717	+	29.9717i	1.17468	+	1.17468i
$652$	3.66389	+	15.5221i	0.143489	+	0.607891i
$653$	−6.07220	−	6.07220i	−0.237623	−	0.237623i	0.578242	−	0.815865i	$-0.303739\pi$
$653$	−6.07220	−	6.07220i	−0.237623	−	0.237623i	−0.815865	+	0.578242i	$0.803739\pi$
$654$	3.97538	+	1.12937i	0.155450	+	0.0441619i
$655$	−39.3201	+	12.4310i	−1.53636	+	0.485718i
$656$	0.0206622	−	0.0103299i	0.000806722	−	0.000403316i
$657$		−	7.98713i		−	0.311608i
$658$	−17.6387	+	62.0882i	−0.687629	+	2.42045i
$659$	−5.88182	+	5.88182i	−0.229123	+	0.229123i	−0.812326	−	0.583203i	$-0.801799\pi$
$659$	−5.88182	+	5.88182i	−0.229123	+	0.229123i	0.583203	+	0.812326i	$0.301799\pi$
$660$	−15.9361	+	9.50942i	−0.620312	+	0.370154i
$661$	−24.0275	−	24.0275i	−0.934562	−	0.934562i	0.0634242	−	0.997987i	$-0.479798\pi$
$661$	−24.0275	−	24.0275i	−0.934562	−	0.934562i	−0.997987	+	0.0634242i	$0.979798\pi$
$662$	−22.0927	−	39.6266i	−0.858656	−	1.54013i
$663$	−2.99825			−0.116442
$664$	−0.935746	+	20.7817i	−0.0363140	+	0.806486i
$665$	19.7981	−	6.25911i	0.767736	−	0.242718i
$666$	−6.24786	−	11.2065i	−0.242100	−	0.434243i
$667$	8.63936	−	8.63936i	0.334517	−	0.334517i
$668$	−10.9832	−	6.78831i	−0.424951	−	0.262647i
$669$	−7.38042	+	7.38042i	−0.285344	+	0.285344i
$670$	−0.506554	−	17.2211i	−0.0195699	−	0.665310i
$671$	−54.6116			−2.10826
$672$	−12.4928	+	18.3159i	−0.481920	+	0.706550i
$673$		−	36.5327i		−	1.40823i	−0.710084	−	0.704117i	$-0.751343\pi$
$673$		−	36.5327i		−	1.40823i	0.710084	−	0.704117i	$-0.248657\pi$
$674$	3.44098	−	12.1123i	0.132542	−	0.466546i
$675$	−4.92537	−	0.860637i	−0.189578	−	0.0331259i
$676$	12.5401	−	20.2893i	0.482312	−	0.780358i
$677$	20.5460	−	20.5460i	0.789645	−	0.789645i	−0.191791	−	0.981436i	$-0.561429\pi$
$677$	20.5460	−	20.5460i	0.789645	−	0.789645i	0.981436	+	0.191791i	$0.0614294\pi$
$678$	10.0498	−	5.60299i	0.385961	−	0.215182i
$679$		−	8.78518i		−	0.337144i
$680$	17.6764	−	4.72516i	0.677858	−	0.181202i
$681$		−	19.4055i		−	0.743622i
$682$	−30.9053	−	55.4334i	−1.18343	−	2.12265i
$683$	−18.2074	+	18.2074i	−0.696688	+	0.696688i	−0.963695	−	0.267007i	$-0.913965\pi$
$683$	−18.2074	+	18.2074i	−0.696688	+	0.696688i	0.267007	+	0.963695i	$0.413965\pi$
$684$	1.08860	+	4.61185i	0.0416237	+	0.176339i
$685$	12.9294	+	6.71794i	0.494007	+	0.256679i
$686$	7.25464	+	2.06098i	0.276983	+	0.0786885i
$687$			11.9342i			0.455320i
$688$	−12.0172	−	4.00632i	−0.458150	−	0.152740i
$689$	−8.14561			−0.310323
$690$	−0.160974	−	5.47257i	−0.00612818	−	0.208337i
$691$	11.5350	−	11.5350i	0.438811	−	0.438811i	−0.452801	−	0.891612i	$-0.649575\pi$
$691$	11.5350	−	11.5350i	0.438811	−	0.438811i	0.891612	+	0.452801i	$0.149575\pi$
$692$	4.76719	+	20.1962i	0.181221	+	0.767743i
$693$	−11.5000	+	11.5000i	−0.436850	+	0.436850i
$694$	−15.5083	+	8.64620i	−0.588686	+	0.328205i
$695$	14.3894	+	45.5149i	0.545823	+	1.72648i
$696$	13.4648	+	14.7345i	0.510381	+	0.558510i
$697$	−0.0167075			−0.000632842
$698$	14.3773	−	8.01567i	0.544189	−	0.303397i
$699$	−20.2304	−	20.2304i	−0.765182	−	0.765182i
$700$	−2.30369	−	39.1249i	−0.0870713	−	1.47878i
$701$	16.5440	−	16.5440i	0.624859	−	0.624859i	−0.321911	−	0.946770i	$-0.604325\pi$
$701$	16.5440	−	16.5440i	0.624859	−	0.624859i	0.946770	+	0.321911i	$0.104325\pi$
$702$	−1.40987	−	0.400530i	−0.0532120	−	0.0151170i
$703$		−	21.4955i		−	0.810717i
$704$	25.4885	−	21.2692i	0.960634	−	0.801613i
$705$	24.8280	−	7.84932i	0.935078	−	0.295623i
$706$	−13.4154	+	47.2223i	−0.504897	+	1.77723i
$707$	29.4202	+	29.4202i	1.10646	+	1.10646i
$708$	−5.69970	+	9.22184i	−0.214208	+	0.346578i
$709$	−8.47518	−	8.47518i	−0.318292	−	0.318292i	0.529819	−	0.848111i	$-0.322260\pi$
$709$	−8.47518	−	8.47518i	−0.318292	−	0.318292i	−0.848111	+	0.529819i	$0.822260\pi$
$710$	2.50245	−	2.65413i	0.0939154	−	0.0996078i
$711$			0.843960i			0.0316510i
$712$	11.2936	−	10.3204i	0.423245	−	0.386772i
$713$	18.7240			0.701221
$714$	14.0055	−	7.80835i	0.524141	−	0.292220i
$715$	4.43376	−	8.53325i	0.165813	−	0.319125i
$716$	−2.87328	+	0.678221i	−0.107379	+	0.0253463i
$717$	15.1974	+	15.1974i	0.567559	+	0.567559i
$718$	−1.08631	+	3.82380i	−0.0405406	+	0.142703i
$719$	−11.5303			−0.430008			−0.215004	−	0.976613i	$-0.568976\pi$
$719$	−11.5303			−0.430008			−0.215004	+	0.976613i	$0.568976\pi$
$720$	8.94318	+	0.139442i	0.333293	+	0.00519671i
$721$	−15.3287			−0.570869
$722$	5.17349	−	18.2107i	0.192537	−	0.677731i
$723$	−13.8553	−	13.8553i	−0.515284	−	0.515284i
$724$	−7.86389	−	33.3153i	−0.292259	−	1.23815i
$725$	−34.7582	−	6.07348i	−1.29089	−	0.225564i
$726$	7.68229	−	4.28304i	0.285116	−	0.158959i
$727$	32.2855			1.19740			0.598702	−	0.800972i	$-0.295684\pi$
$727$	32.2855			1.19740			0.598702	+	0.800972i	$0.295684\pi$
$728$	0.516778	−	11.4770i	0.0191531	−	0.425365i
$729$		−	1.00000i		−	0.0370370i
$730$	−18.3772	−	17.3269i	−0.680169	−	0.641298i
$731$	6.47833	+	6.47833i	0.239610	+	0.239610i
$732$	22.3898	+	13.8384i	0.827552	+	0.511481i
$733$	−33.6309	−	33.6309i	−1.24219	−	1.24219i	−0.959092	−	0.283094i	$-0.908639\pi$
$733$	−33.6309	−	33.6309i	−1.24219	−	1.24219i	−0.283094	−	0.959092i	$-0.591361\pi$
$734$	−7.06607	+	24.8726i	−0.260814	+	0.918063i
$735$	−5.63546	−	17.8254i	−0.207867	−	0.657500i
$736$	1.81891	+	9.62347i	0.0670461	+	0.354726i
$737$			22.6078i			0.832769i
$738$	−0.00785637	−	0.00223193i	−0.000289197	−	8.21583e-5i
$739$	−11.6806	+	11.6806i	−0.429676	+	0.429676i	−0.888518	−	0.458842i	$-0.848264\pi$
$739$	−11.6806	+	11.6806i	−0.429676	+	0.429676i	0.458842	+	0.888518i	$0.348264\pi$
$740$	−39.3382	−	9.93550i	−1.44610	−	0.365236i
$741$	−1.73628	−	1.73628i	−0.0637840	−	0.0637840i
$742$	38.0499	−	21.2136i	1.39685	−	0.778777i
$743$	−11.7641			−0.431582			−0.215791	−	0.976440i	$-0.569233\pi$
$743$	−11.7641			−0.431582			−0.215791	+	0.976440i	$0.569233\pi$
$744$	−1.37595	+	30.5581i	−0.0504448	+	1.12031i
$745$	−4.07418	−	12.8870i	−0.149266	−	0.472142i
$746$	40.9072	−	22.8067i	1.49772	−	0.835011i
$747$	5.20069	−	5.20069i	0.190283	−	0.190283i
$748$	−23.3677	+	5.51582i	−0.854408	+	0.201678i
$749$	10.1992	−	10.1992i	0.372672	−	0.372672i
$750$	−12.6651	+	9.46550i	−0.462463	+	0.345631i
$751$	9.89062			0.360914			0.180457	−	0.983583i	$-0.442242\pi$
$751$	9.89062			0.360914			0.180457	+	0.983583i	$0.442242\pi$
$752$	−41.6637	+	20.8295i	−1.51932	+	0.759575i
$753$		−	13.5492i		−	0.493760i
$754$	−9.94937	−	2.82653i	−0.362335	−	0.102936i
$755$	−8.66012	+	16.6673i	−0.315174	+	0.606587i
$756$	7.62889	−	1.80076i	0.277460	−	0.0654928i
$757$	−19.7078	+	19.7078i	−0.716291	+	0.716291i	−0.967844	−	0.251553i	$-0.919059\pi$
$757$	−19.7078	+	19.7078i	−0.716291	+	0.716291i	0.251553	+	0.967844i	$0.419059\pi$
$758$	6.04743	+	10.8470i	0.219653	+	0.393980i
$759$			7.18436i			0.260776i
$760$	12.9727	+	7.50004i	0.470570	+	0.272055i
$761$			48.2102i			1.74762i	0.486270	+	0.873808i	$0.338357\pi$
$761$			48.2102i			1.74762i	−0.486270	+	0.873808i	$0.661643\pi$
$762$	−19.8699	+	11.0779i	−0.719809	+	0.401309i
$763$	8.09857	−	8.09857i	0.293188	−	0.293188i
$764$	−36.1136	−	22.3205i	−1.30654	−	0.807529i
$765$	−5.74036	−	2.98261i	−0.207543	−	0.107837i
$766$	5.56540	−	19.5902i	0.201086	−	0.707823i
$767$		−	5.61771i		−	0.202844i
$768$	−15.8394	+	2.26132i	−0.571555	+	0.0815984i
$769$	−30.7814			−1.11000			−0.555002	−	0.831849i	$-0.687283\pi$
$769$	−30.7814			−1.11000			−0.555002	+	0.831849i	$0.687283\pi$
$770$	1.51214	+	51.4075i	0.0544936	+	1.85260i
$771$	9.38542	−	9.38542i	0.338008	−	0.338008i
$772$	−20.2710	+	32.7975i	−0.729570	+	1.18041i
$773$	−31.7802	+	31.7802i	−1.14306	+	1.14306i	−0.155167	+	0.987888i	$0.549592\pi$
$773$	−31.7802	+	31.7802i	−1.14306	+	1.14306i	−0.987888	+	0.155167i	$0.950408\pi$
$774$	2.18088	+	3.91173i	0.0783900	+	0.140604i
$775$	−31.0841	−

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36038 - 0.386472i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.70128 + 1.05150i) q^{4} +(-1.98421 - 1.03097i) q^{5} +(-0.688658 - 1.23521i) q^{6} -3.91927 q^{7} +(-1.90801 - 2.08794i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.36038 - 0.386472i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.70128 + 1.05150i) q^{4} +(-1.98421 - 1.03097i) q^{5} +(-0.688658 - 1.23521i) q^{6} -3.91927 q^{7} +(-1.90801 - 2.08794i) q^{8} +1.00000i q^{9} +(2.30085 + 2.16936i) q^{10} +(-2.93423 - 2.93423i) q^{11} +(0.459462 + 1.94651i) q^{12} +(-0.732828 - 0.732828i) q^{13} +(5.33170 + 1.51469i) q^{14} +(-0.674045 - 2.13206i) q^{15} +(1.78869 + 3.57779i) q^{16} -2.89302i q^{17} +(0.386472 - 1.36038i) q^{18} +(1.67534 - 1.67534i) q^{19} +(-2.29163 - 3.84037i) q^{20} +(-2.77134 - 2.77134i) q^{21} +(2.85767 + 5.12567i) q^{22} -1.73133 q^{23} +(0.127228 - 2.82556i) q^{24} +(2.87420 + 4.09133i) q^{25} +(0.713708 + 1.28014i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-6.66776 - 4.12111i) q^{28} +(-4.99003 + 4.99003i) q^{29} +(0.0929773 + 3.16091i) q^{30} -10.8149 q^{31} +(-1.05059 - 5.55844i) q^{32} -4.14963i q^{33} +(-1.11807 + 3.93561i) q^{34} +(7.77666 + 4.04065i) q^{35} +(-1.05150 + 1.70128i) q^{36} +(6.41524 - 6.41524i) q^{37} +(-2.92658 + 1.63163i) q^{38} -1.03637i q^{39} +(1.63330 + 6.11002i) q^{40} -0.00577512i q^{41} +(2.69904 + 4.84113i) q^{42} +(-2.23930 + 2.23930i) q^{43} +(-1.90660 - 8.07728i) q^{44} +(1.03097 - 1.98421i) q^{45} +(2.35527 + 0.669110i) q^{46} +11.6451i q^{47} +(-1.26508 + 3.79468i) q^{48} +8.36066 q^{49} +(-2.32883 - 6.67657i) q^{50} +(2.04567 - 2.04567i) q^{51} +(-0.476175 - 2.01731i) q^{52} +(5.55765 - 5.55765i) q^{53} +(1.23521 - 0.688658i) q^{54} +(2.79703 + 8.84724i) q^{55} +(7.47801 + 8.18319i) q^{56} +2.36929 q^{57} +(8.71685 - 4.85983i) q^{58} +(3.83290 + 3.83290i) q^{59} +(1.09512 - 4.33598i) q^{60} +(9.30595 - 9.30595i) q^{61} +(14.7123 + 4.17964i) q^{62} -3.91927i q^{63} +(-0.718981 + 7.96763i) q^{64} +(0.698563 + 2.20961i) q^{65} +(-1.60372 + 5.64508i) q^{66} +(-3.85243 - 3.85243i) q^{67} +(3.04201 - 4.92182i) q^{68} +(-1.22423 - 1.22423i) q^{69} +(-9.01763 - 8.50229i) q^{70} -1.15355i q^{71} +(2.08794 - 1.90801i) q^{72} -7.98713 q^{73} +(-11.2065 + 6.24786i) q^{74} +(-0.860637 + 4.92537i) q^{75} +(4.61185 - 1.08860i) q^{76} +(11.5000 + 11.5000i) q^{77} +(-0.400530 + 1.40987i) q^{78} +0.843960 q^{79} +(0.139442 - 8.94318i) q^{80} -1.00000 q^{81} +(-0.00223193 + 0.00785637i) q^{82} +(-5.20069 - 5.20069i) q^{83} +(-1.80076 - 7.62889i) q^{84} +(-2.98261 + 5.74036i) q^{85} +(3.91173 - 2.18088i) q^{86} -7.05696 q^{87} +(-0.527948 + 11.7250i) q^{88} +5.40896i q^{89} +(-2.16936 + 2.30085i) q^{90} +(2.87215 + 2.87215i) q^{91} +(-2.94547 - 1.82049i) q^{92} +(-7.64726 - 7.64726i) q^{93} +(4.50051 - 15.8418i) q^{94} +(-5.05147 + 1.59701i) q^{95} +(3.18753 - 4.67329i) q^{96} +2.24154i q^{97} +(-11.3737 - 3.23117i) q^{98} +(2.93423 - 2.93423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Introduction

L-functions

Modular forms

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