LMFDB - Embedded newform 280.2.l.a.29.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(29,280)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("280.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.l (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.33
Character	$\chi$	$=$	280.29
Dual form			280.2.l.a.29.34

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37343 - 0.337187i) q^{2} -3.10393 q^{3} +(1.77261 - 0.926204i) q^{4} +(0.0152300 + 2.23602i) q^{5} +(-4.26302 + 1.04660i) q^{6} +1.00000i q^{7} +(2.12225 - 1.86978i) q^{8} +6.63436 q^{9} +O(q^{10})$	\(q+(1.37343 - 0.337187i) q^{2} -3.10393 q^{3} +(1.77261 - 0.926204i) q^{4} +(0.0152300 + 2.23602i) q^{5} +(-4.26302 + 1.04660i) q^{6} +1.00000i q^{7} +(2.12225 - 1.86978i) q^{8} +6.63436 q^{9} +(0.774873 + 3.06587i) q^{10} +5.18387i q^{11} +(-5.50205 + 2.87487i) q^{12} +3.37714 q^{13} +(0.337187 + 1.37343i) q^{14} +(-0.0472728 - 6.94043i) q^{15} +(2.28429 - 3.28360i) q^{16} +4.40502i q^{17} +(9.11181 - 2.23702i) q^{18} -3.64185i q^{19} +(2.09800 + 3.94948i) q^{20} -3.10393i q^{21} +(1.74793 + 7.11967i) q^{22} +2.34219i q^{23} +(-6.58730 + 5.80365i) q^{24} +(-4.99954 + 0.0681090i) q^{25} +(4.63826 - 1.13873i) q^{26} -11.2808 q^{27} +(0.926204 + 1.77261i) q^{28} -2.80441i q^{29} +(-2.40515 - 9.51624i) q^{30} -0.829031 q^{31} +(2.03012 - 5.28002i) q^{32} -16.0903i q^{33} +(1.48532 + 6.04998i) q^{34} +(-2.23602 + 0.0152300i) q^{35} +(11.7601 - 6.14477i) q^{36} -7.31621 q^{37} +(-1.22798 - 5.00182i) q^{38} -10.4824 q^{39} +(4.21317 + 4.71690i) q^{40} +4.72862 q^{41} +(-1.04660 - 4.26302i) q^{42} +4.34414 q^{43} +(4.80132 + 9.18898i) q^{44} +(0.101041 + 14.8345i) q^{45} +(0.789756 + 3.21683i) q^{46} -3.33384i q^{47} +(-7.09027 + 10.1920i) q^{48} -1.00000 q^{49} +(-6.84354 + 1.77932i) q^{50} -13.6729i q^{51} +(5.98635 - 3.12792i) q^{52} -0.861277 q^{53} +(-15.4933 + 3.80373i) q^{54} +(-11.5912 + 0.0789503i) q^{55} +(1.86978 + 2.12225i) q^{56} +11.3040i q^{57} +(-0.945610 - 3.85165i) q^{58} -8.70012i q^{59} +(-6.51205 - 12.2589i) q^{60} -3.83271i q^{61} +(-1.13861 + 0.279539i) q^{62} +6.63436i q^{63} +(1.00788 - 7.93626i) q^{64} +(0.0514338 + 7.55134i) q^{65} +(-5.42546 - 22.0989i) q^{66} +6.66292 q^{67} +(4.07995 + 7.80839i) q^{68} -7.26998i q^{69} +(-3.06587 + 0.774873i) q^{70} -13.5671 q^{71} +(14.0798 - 12.4048i) q^{72} -2.29840i q^{73} +(-10.0483 + 2.46693i) q^{74} +(15.5182 - 0.211405i) q^{75} +(-3.37310 - 6.45558i) q^{76} -5.18387 q^{77} +(-14.3968 + 3.53453i) q^{78} +7.50450 q^{79} +(7.37697 + 5.05770i) q^{80} +15.1116 q^{81} +(6.49442 - 1.59443i) q^{82} +10.3268 q^{83} +(-2.87487 - 5.50205i) q^{84} +(-9.84970 + 0.0670885i) q^{85} +(5.96636 - 1.46479i) q^{86} +8.70467i q^{87} +(9.69268 + 11.0015i) q^{88} +7.26822 q^{89} +(5.14078 + 20.3401i) q^{90} +3.37714i q^{91} +(2.16935 + 4.15179i) q^{92} +2.57325 q^{93} +(-1.12413 - 4.57879i) q^{94} +(8.14323 - 0.0554653i) q^{95} +(-6.30135 + 16.3888i) q^{96} -0.793686i q^{97} +(-1.37343 + 0.337187i) q^{98} +34.3916i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	1.37343	−	0.337187i	0.971160	−	0.238427i
$2$	1.37343	−	0.337187i	0.971160	−	0.238427i
$3$	−3.10393			−1.79205			−0.896026	−	0.444001i	$-0.853559\pi$
$3$	−3.10393			−1.79205			−0.896026	+	0.444001i	$0.853559\pi$
$4$	1.77261	−	0.926204i	0.886305	−	0.463102i
$5$	0.0152300	+	2.23602i	0.00681106	+	0.999977i
$5$	0.0152300	+	2.23602i	0.00681106	+	0.999977i
$6$	−4.26302	+	1.04660i	−1.74037	+	0.427274i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.12225	−	1.86978i	0.750328	−	0.661066i
$9$	6.63436			2.21145
$10$	0.774873	+	3.06587i	0.245036	+	0.969514i
$11$			5.18387i			1.56300i	0.623908	+	0.781498i	$0.285544\pi$
$11$			5.18387i			1.56300i	−0.623908	+	0.781498i	$0.714456\pi$
$12$	−5.50205	+	2.87487i	−1.58831	+	0.829903i
$13$	3.37714			0.936650			0.468325	−	0.883556i	$-0.344858\pi$
$13$	3.37714			0.936650			0.468325	+	0.883556i	$0.344858\pi$
$14$	0.337187	+	1.37343i	0.0901170	+	0.367064i
$15$	−0.0472728	−	6.94043i	−0.0122058	−	1.79201i
$16$	2.28429	−	3.28360i	0.571073	−	0.820899i
$17$			4.40502i			1.06837i	0.845366	+	0.534187i	$0.179382\pi$
$17$			4.40502i			1.06837i	−0.845366	+	0.534187i	$0.820618\pi$
$18$	9.11181	−	2.23702i	2.14767	−	0.527270i
$19$		−	3.64185i		−	0.835497i	−0.908563	−	0.417749i	$-0.862819\pi$
$19$		−	3.64185i		−	0.835497i	0.908563	−	0.417749i	$-0.137181\pi$
$20$	2.09800	+	3.94948i	0.469128	+	0.883130i
$21$		−	3.10393i		−	0.677332i
$22$	1.74793	+	7.11967i	0.372661	+	1.51792i
$23$			2.34219i			0.488380i	0.969727	+	0.244190i	$0.0785221\pi$
$23$			2.34219i			0.488380i	−0.969727	+	0.244190i	$0.921478\pi$
$24$	−6.58730	+	5.80365i	−1.34463	+	1.18466i
$25$	−4.99954	+	0.0681090i	−0.999907	+	0.0136218i
$26$	4.63826	−	1.13873i	0.909638	−	0.223323i
$27$	−11.2808			−2.17099
$28$	0.926204	+	1.77261i	0.175036	+	0.334992i
$29$		−	2.80441i		−	0.520765i	−0.965505	−	0.260383i	$-0.916151\pi$
$29$		−	2.80441i		−	0.520765i	0.965505	−	0.260383i	$-0.0838487\pi$
$30$	−2.40515	−	9.51624i	−0.439118	−	1.73742i
$31$	−0.829031			−0.148898			−0.0744492	−	0.997225i	$-0.523720\pi$
$31$	−0.829031			−0.148898			−0.0744492	+	0.997225i	$0.523720\pi$
$32$	2.03012	−	5.28002i	0.358879	−	0.933384i
$33$		−	16.0903i		−	2.80097i
$34$	1.48532	+	6.04998i	0.254730	+	1.03756i
$35$	−2.23602	+	0.0152300i	−0.377956	+	0.00257434i
$36$	11.7601	−	6.14477i	1.96002	−	1.02413i
$37$	−7.31621			−1.20278			−0.601388	−	0.798957i	$-0.705386\pi$
$37$	−7.31621			−1.20278			−0.601388	+	0.798957i	$0.705386\pi$
$38$	−1.22798	−	5.00182i	−0.199205	−	0.811402i
$39$	−10.4824			−1.67853
$40$	4.21317	+	4.71690i	0.666161	+	0.745808i
$41$	4.72862			0.738487			0.369243	−	0.929333i	$-0.379617\pi$
$41$	4.72862			0.738487			0.369243	+	0.929333i	$0.379617\pi$
$42$	−1.04660	−	4.26302i	−0.161494	−	0.657798i
$43$	4.34414			0.662475			0.331237	−	0.943547i	$-0.392534\pi$
$43$	4.34414			0.662475			0.331237	+	0.943547i	$0.392534\pi$
$44$	4.80132	+	9.18898i	0.723827	+	1.38529i
$45$	0.101041	+	14.8345i	0.0150623	+	2.21140i
$46$	0.789756	+	3.21683i	0.116443	+	0.474296i
$47$		−	3.33384i		−	0.486291i	−0.969990	−	0.243145i	$-0.921821\pi$
$47$		−	3.33384i		−	0.486291i	0.969990	−	0.243145i	$-0.0781792\pi$
$48$	−7.09027	+	10.1920i	−1.02339	+	1.47109i
$49$	−1.00000			−0.142857
$50$	−6.84354	+	1.77932i	−0.967822	+	0.251634i
$51$		−	13.6729i		−	1.91458i
$52$	5.98635	−	3.12792i	0.830158	−	0.433765i
$53$	−0.861277			−0.118305			−0.0591527	−	0.998249i	$-0.518840\pi$
$53$	−0.861277			−0.118305			−0.0591527	+	0.998249i	$0.518840\pi$
$54$	−15.4933	+	3.80373i	−2.10838	+	0.517622i
$55$	−11.5912	+	0.0789503i	−1.56296	+	0.0106457i
$56$	1.86978	+	2.12225i	0.249859	+	0.283597i
$57$			11.3040i			1.49726i
$58$	−0.945610	−	3.85165i	−0.124165	−	0.505747i
$59$		−	8.70012i		−	1.13266i	−0.824179	−	0.566330i	$-0.808363\pi$
$59$		−	8.70012i		−	1.13266i	0.824179	−	0.566330i	$-0.191637\pi$
$60$	−6.51205	−	12.2589i	−0.840702	−	1.58262i
$61$		−	3.83271i		−	0.490729i	−0.969431	−	0.245364i	$-0.921092\pi$
$61$		−	3.83271i		−	0.490729i	0.969431	−	0.245364i	$-0.0789076\pi$
$62$	−1.13861	+	0.279539i	−0.144604	+	0.0355014i
$63$			6.63436i			0.835850i
$64$	1.00788	−	7.93626i	0.125985	−	0.992032i
$65$	0.0514338	+	7.55134i	0.00637958	+	0.936628i
$66$	−5.42546	−	22.0989i	−0.667828	−	2.72019i
$67$	6.66292			0.814006			0.407003	−	0.913427i	$-0.366574\pi$
$67$	6.66292			0.814006			0.407003	+	0.913427i	$0.366574\pi$
$68$	4.07995	+	7.80839i	0.494767	+	0.946906i
$69$		−	7.26998i		−	0.875203i
$70$	−3.06587	+	0.774873i	−0.366442	+	0.0926150i
$71$	−13.5671			−1.61012			−0.805060	−	0.593193i	$-0.797867\pi$
$71$	−13.5671			−1.61012			−0.805060	+	0.593193i	$0.797867\pi$
$72$	14.0798	−	12.4048i	1.65931	−	1.46192i
$73$		−	2.29840i		−	0.269007i	−0.990913	−	0.134504i	$-0.957056\pi$
$73$		−	2.29840i		−	0.269007i	0.990913	−	0.134504i	$-0.0429440\pi$
$74$	−10.0483	+	2.46693i	−1.16809	+	0.286775i
$75$	15.5182	−	0.211405i	1.79189	−	0.0244110i
$76$	−3.37310	−	6.45558i	−0.386921	−	0.740505i
$77$	−5.18387			−0.590757
$78$	−14.3968	+	3.53453i	−1.63012	+	0.400206i
$79$	7.50450			0.844323			0.422161	−	0.906521i	$-0.361272\pi$
$79$	7.50450			0.844323			0.422161	+	0.906521i	$0.361272\pi$
$80$	7.37697	+	5.05770i	0.824770	+	0.565468i
$81$	15.1116			1.67907
$82$	6.49442	−	1.59443i	0.717189	−	0.176075i
$83$	10.3268			1.13352			0.566758	−	0.823885i	$-0.308198\pi$
$83$	10.3268			1.13352			0.566758	+	0.823885i	$0.308198\pi$
$84$	−2.87487	−	5.50205i	−0.313674	−	0.600323i
$85$	−9.84970	+	0.0670885i	−1.06835	+	0.00727676i
$86$	5.96636	−	1.46479i	0.643369	−	0.157952i
$87$			8.70467i			0.933239i
$88$	9.69268	+	11.0015i	1.03324	+	1.17276i
$89$	7.26822			0.770430			0.385215	−	0.922827i	$-0.374127\pi$
$89$	7.26822			0.770430			0.385215	+	0.922827i	$0.374127\pi$
$90$	5.14078	+	20.3401i	0.541886	+	2.14403i
$91$			3.37714i			0.354020i
$92$	2.16935	+	4.15179i	0.226170	+	0.432854i
$93$	2.57325			0.266834
$94$	−1.12413	−	4.57879i	−0.115945	−	0.472266i
$95$	8.14323	−	0.0554653i	0.835478	−	0.00569062i
$96$	−6.30135	+	16.3888i	−0.643129	+	1.67267i
$97$		−	0.793686i		−	0.0805866i	−0.999188	−	0.0402933i	$-0.987171\pi$
$97$		−	0.793686i		−	0.0805866i	0.999188	−	0.0402933i	$-0.0128292\pi$
$98$	−1.37343	+	0.337187i	−0.138737	+	0.0340610i
$99$			34.3916i			3.45649i
$100$	−8.79914	+	4.75132i	−0.879914	+	0.475132i
$101$			16.3504i			1.62693i	0.581616	+	0.813464i	$0.302421\pi$
$101$			16.3504i			1.62693i	−0.581616	+	0.813464i	$0.697579\pi$
$102$	−4.61031	−	18.7787i	−0.456489	−	1.85937i
$103$			0.405581i			0.0399631i	0.999800	+	0.0199815i	$0.00636074\pi$
$103$			0.405581i			0.0399631i	−0.999800	+	0.0199815i	$0.993639\pi$
$104$	7.16713	−	6.31450i	0.702795	−	0.619187i
$105$	6.94043	−	0.0472728i	0.677316	−	0.00461335i
$106$	−1.18290	+	0.290411i	−0.114894	+	0.0282072i
$107$	15.7118			1.51891			0.759457	−	0.650557i	$-0.225465\pi$
$107$	15.7118			1.51891			0.759457	+	0.650557i	$0.225465\pi$
$108$	−19.9964	+	10.4483i	−1.92416	+	1.00539i
$109$		−	14.9982i		−	1.43657i	−0.695750	−	0.718284i	$-0.744928\pi$
$109$		−	14.9982i		−	1.43657i	0.695750	−	0.718284i	$-0.255072\pi$
$110$	−15.8931	+	4.01684i	−1.51535	+	0.382991i
$111$	22.7090			2.15544
$112$	3.28360	+	2.28429i	0.310271	+	0.215845i
$113$		−	14.3451i		−	1.34948i	−0.738057	−	0.674738i	$-0.764256\pi$
$113$		−	14.3451i		−	1.34948i	0.738057	−	0.674738i	$-0.235744\pi$
$114$	3.81157	+	15.5253i	0.356986	+	1.45407i
$115$	−5.23717	+	0.0356715i	−0.488369	+	0.00332639i
$116$	−2.59745	−	4.97112i	−0.241168	−	0.461557i
$117$	22.4052			2.07136
$118$	−2.93357	−	11.9490i	−0.270057	−	1.09999i
$119$	−4.40502			−0.403808
$120$	−13.0774	−	14.6409i	−1.19380	−	1.33653i
$121$	−15.8725			−1.44296
$122$	−1.29234	−	5.26396i	−0.117003	−	0.476576i
$123$	−14.6773			−1.32341
$124$	−1.46955	+	0.767852i	−0.131969	+	0.0689552i
$125$	−0.228436	−	11.1780i	−0.0204319	−	0.999791i
$126$	2.23702	+	9.11181i	0.199289	+	0.811745i
$127$			5.49873i			0.487933i	0.969784	+	0.243967i	$0.0784488\pi$
$127$			5.49873i			0.487933i	−0.969784	+	0.243967i	$0.921551\pi$
$128$	−1.29176	−	11.2397i	−0.114176	−	0.993461i
$129$	−13.4839			−1.18719
$130$	2.61685	+	10.3539i	0.229513	+	0.908095i
$131$		−	14.8009i		−	1.29316i	−0.762846	−	0.646580i	$-0.776199\pi$
$131$		−	14.8009i		−	1.29316i	0.762846	−	0.646580i	$-0.223801\pi$
$132$	−14.9029	−	28.5219i	−1.29714	−	2.48251i
$133$	3.64185			0.315788
$134$	9.15105	−	2.24665i	0.790530	−	0.194081i
$135$	−0.171806	−	25.2240i	−0.0147867	−	2.17094i
$136$	8.23640	+	9.34855i	0.706266	+	0.801632i
$137$		−	4.98693i		−	0.426062i	−0.977045	−	0.213031i	$-0.931666\pi$
$137$		−	4.98693i		−	0.426062i	0.977045	−	0.213031i	$-0.0683336\pi$
$138$	−2.45134	−	9.98480i	−0.208672	−	0.849963i
$139$			7.27185i			0.616790i	0.951258	+	0.308395i	$0.0997918\pi$
$139$			7.27185i			0.616790i	−0.951258	+	0.308395i	$0.900208\pi$
$140$	−3.94948	+	2.09800i	−0.333792	+	0.177314i
$141$			10.3480i			0.871458i
$142$	−18.6335	+	4.57465i	−1.56368	+	0.383896i
$143$			17.5067i			1.46398i
$144$	15.1548	−	21.7846i	1.26290	−	1.81538i
$145$	6.27070	−	0.0427111i	0.520753	−	0.00354696i
$146$	−0.774990	−	3.15668i	−0.0641386	−	0.261249i
$147$	3.10393			0.256008
$148$	−12.9688	+	6.77630i	−1.06603	+	0.557008i
$149$			10.9797i			0.899491i	0.893157	+	0.449746i	$0.148485\pi$
$149$			10.9797i			0.899491i	−0.893157	+	0.449746i	$0.851515\pi$
$150$	21.2418	−	5.52288i	1.73439	−	0.450941i
$151$	0.287791			0.0234201			0.0117100	−	0.999931i	$-0.496272\pi$
$151$	0.287791			0.0234201			0.0117100	+	0.999931i	$0.496272\pi$
$152$	−6.80944	−	7.72891i	−0.552319	−	0.626897i
$153$			29.2245i			2.36266i
$154$	−7.11967	+	1.74793i	−0.573720	+	0.140852i
$155$	−0.0126261	−	1.85373i	−0.00101416	−	0.148895i
$156$	−18.5812	+	9.70884i	−1.48769	+	0.777329i
$157$	−22.3595			−1.78448			−0.892240	−	0.451562i	$-0.850867\pi$
$157$	−22.3595			−1.78448			−0.892240	+	0.451562i	$0.850867\pi$
$158$	10.3069	−	2.53042i	0.819973	−	0.201309i
$159$	2.67334			0.212010
$160$	11.8371	+	4.45898i	0.935807	+	0.352513i
$161$	−2.34219			−0.184590
$162$	20.7547	−	5.09544i	1.63065	−	0.400336i
$163$	−8.70628			−0.681929			−0.340964	−	0.940076i	$-0.610754\pi$
$163$	−8.70628			−0.681929			−0.340964	+	0.940076i	$0.610754\pi$
$164$	8.38200	−	4.37967i	0.654525	−	0.341995i
$165$	35.9783	−	0.245056i	2.80091	−	0.0190776i
$166$	14.1831	−	3.48207i	1.10083	−	0.270261i
$167$		−	9.32410i		−	0.721521i	−0.932659	−	0.360760i	$-0.882517\pi$
$167$		−	9.32410i		−	0.721521i	0.932659	−	0.360760i	$-0.117483\pi$
$168$	−5.80365	−	6.58730i	−0.447761	−	0.508221i
$169$	−1.59492			−0.122686
$170$	−13.5052	+	3.41333i	−1.03580	+	0.261791i
$171$		−	24.1613i		−	1.84766i
$172$	7.70046	−	4.02356i	0.587155	−	0.306793i
$173$	−16.4811			−1.25303			−0.626517	−	0.779408i	$-0.715520\pi$
$173$	−16.4811			−1.25303			−0.626517	+	0.779408i	$0.715520\pi$
$174$	2.93510	+	11.9552i	0.222510	+	0.906325i
$175$	−0.0681090	−	4.99954i	−0.00514856	−	0.377929i
$176$	17.0217	+	11.8415i	1.28306	+	0.892584i
$177$			27.0045i			2.02979i
$178$	9.98238	−	2.45075i	0.748211	−	0.183691i
$179$			19.6983i			1.47232i	0.676807	+	0.736161i	$0.263363\pi$
$179$			19.6983i			1.47232i	−0.676807	+	0.736161i	$0.736637\pi$
$180$	13.9189	+	26.2022i	1.03745	+	1.95300i
$181$		−	8.95860i		−	0.665887i	−0.942947	−	0.332944i	$-0.891958\pi$
$181$		−	8.95860i		−	0.665887i	0.942947	−	0.332944i	$-0.108042\pi$
$182$	1.13873	+	4.63826i	0.0844081	+	0.343811i
$183$			11.8965i			0.879411i
$184$	4.37937	+	4.97071i	0.322851	+	0.366445i
$185$	−0.111426	−	16.3592i	−0.00819218	−	1.20275i
$186$	3.53418	−	0.867667i	0.259138	−	0.0636204i
$187$	−22.8351			−1.66987
$188$	−3.08782	−	5.90960i	−0.225202	−	0.431002i
$189$		−	11.2808i		−	0.820556i
$190$	11.1654	−	2.82197i	0.810026	−	0.204727i
$191$	−5.45538			−0.394737			−0.197369	−	0.980329i	$-0.563240\pi$
$191$	−5.45538			−0.394737			−0.197369	+	0.980329i	$0.563240\pi$
$192$	−3.12837	+	24.6336i	−0.225771	+	1.77777i
$193$		−	21.0023i		−	1.51178i	−0.654698	−	0.755891i	$-0.727204\pi$
$193$		−	21.0023i		−	1.51178i	0.654698	−	0.755891i	$-0.272796\pi$
$194$	−0.267621	−	1.09007i	−0.0192140	−	0.0782626i
$195$	−0.159647	−	23.4388i	−0.0114325	−	1.67849i
$196$	−1.77261	+	0.926204i	−0.126615	+	0.0661574i
$197$	17.9206			1.27679			0.638396	−	0.769708i	$-0.279598\pi$
$197$	17.9206			1.27679			0.638396	+	0.769708i	$0.279598\pi$
$198$	11.5964	+	47.2345i	0.824121	+	3.35681i
$199$	−7.50754			−0.532195			−0.266098	−	0.963946i	$-0.585734\pi$
$199$	−7.50754			−0.532195			−0.266098	+	0.963946i	$0.585734\pi$
$200$	−10.4829	+	9.49256i	−0.741254	+	0.671225i
$201$	−20.6812			−1.45874
$202$	5.51315	+	22.4561i	0.387904	+	1.58001i
$203$	2.80441			0.196831
$204$	−12.6639	−	24.2367i	−0.886648	−	1.69691i
$205$	0.0720169	+	10.5733i	0.00502988	+	0.738470i
$206$	0.136757	+	0.557036i	0.00952828	+	0.0388105i
$207$			15.5389i			1.08003i
$208$	7.71437	−	11.0892i	0.534896	−	0.768896i
$209$	18.8789			1.30588
$210$	9.51624	−	2.40515i	0.656683	−	0.165971i
$211$			16.1667i			1.11296i	0.830860	+	0.556481i	$0.187849\pi$
$211$			16.1667i			1.11296i	−0.830860	+	0.556481i	$0.812151\pi$
$212$	−1.52671	+	0.797718i	−0.104855	+	0.0547875i
$213$	42.1113			2.88542
$214$	21.5790	−	5.29780i	1.47511	−	0.362150i
$215$	0.0661612	+	9.71356i	0.00451215	+	0.662459i
$216$	−23.9406	+	21.0925i	−1.62895	+	1.43516i
$217$		−	0.829031i		−	0.0562783i
$218$	−5.05720	−	20.5990i	−0.342517	−	1.39514i
$219$			7.13406i			0.482075i
$220$	−20.4736	+	10.8758i	−1.38033	+	0.733245i
$221$			14.8764i			1.00069i
$222$	31.1891	−	7.65717i	2.09328	−	0.513915i
$223$		−	17.0451i		−	1.14143i	−0.821150	−	0.570713i	$-0.806667\pi$
$223$		−	17.0451i		−	1.14143i	0.821150	−	0.570713i	$-0.193333\pi$
$224$	5.28002	+	2.03012i	0.352786	+	0.135643i
$225$	−33.1687	+	0.451860i	−2.21125	+	0.0301240i
$226$	−4.83699	−	19.7020i	−0.321752	−	1.31056i
$227$	−0.252426			−0.0167541			−0.00837704	−	0.999965i	$-0.502667\pi$
$227$	−0.252426			−0.0167541			−0.00837704	+	0.999965i	$0.502667\pi$
$228$	10.4698	+	20.0376i	0.693382	+	1.32702i
$229$		−	12.3663i		−	0.817188i	−0.912716	−	0.408594i	$-0.866019\pi$
$229$		−	12.3663i		−	0.817188i	0.912716	−	0.408594i	$-0.133981\pi$
$230$	−7.18085	+	1.81490i	−0.473491	+	0.119671i
$231$	16.0903			1.05867
$232$	−5.24361	−	5.95165i	−0.344260	−	0.390745i
$233$			5.38563i			0.352824i	0.984316	+	0.176412i	$0.0564491\pi$
$233$			5.38563i			0.352824i	−0.984316	+	0.176412i	$0.943551\pi$
$234$	30.7719	−	7.55473i	2.01162	−	0.493868i
$235$	7.45452	−	0.0507744i	0.486279	−	0.00331215i
$236$	−8.05809	−	15.4219i	−0.524537	−	1.00388i
$237$	−23.2934			−1.51307
$238$	−6.04998	+	1.48532i	−0.392162	+	0.0962787i
$239$	4.62605			0.299234			0.149617	−	0.988744i	$-0.452196\pi$
$239$	4.62605			0.299234			0.149617	+	0.988744i	$0.452196\pi$
$240$	−22.8976	−	15.6987i	−1.47803	−	1.01335i
$241$	−3.03593			−0.195561			−0.0977807	−	0.995208i	$-0.531174\pi$
$241$	−3.03593			−0.195561			−0.0977807	+	0.995208i	$0.531174\pi$
$242$	−21.7997	+	5.35200i	−1.40134	+	0.344040i
$243$	−13.0630			−0.837994
$244$	−3.54987	−	6.79390i	−0.227257	−	0.434935i
$245$	−0.0152300	−	2.23602i	−0.000973008	−	0.142854i
$246$	−20.1582	+	4.94899i	−1.28524	+	0.315536i
$247$		−	12.2990i		−	0.782569i
$248$	−1.75941	+	1.55010i	−0.111723	+	0.0984316i
$249$	−32.0537			−2.03132
$250$	−4.08282	−	15.2752i	−0.258220	−	0.966086i
$251$			15.2219i			0.960795i	0.877051	+	0.480398i	$0.159508\pi$
$251$			15.2219i			0.960795i	−0.877051	+	0.480398i	$0.840492\pi$
$252$	6.14477	+	11.7601i	0.387084	+	0.740818i
$253$	−12.1416			−0.763336
$254$	1.85410	+	7.55211i	0.116337	+	0.473862i
$255$	30.5727	−	0.208238i	1.91454	−	0.0130403i
$256$	−5.56402	−	15.0014i	−0.347752	−	0.937587i
$257$			24.6949i			1.54043i	0.637785	+	0.770214i	$0.279851\pi$
$257$			24.6949i			1.54043i	−0.637785	+	0.770214i	$0.720149\pi$
$258$	−18.5191	+	4.54659i	−1.15295	+	0.283058i
$259$		−	7.31621i		−	0.454607i
$260$	7.08525	+	13.3379i	0.439409	+	0.827184i
$261$		−	18.6054i		−	1.15165i
$262$	−4.99067	−	20.3280i	−0.308325	−	1.25587i
$263$		−	20.1124i		−	1.24018i	−0.784530	−	0.620091i	$-0.787096\pi$
$263$		−	20.1124i		−	1.24018i	0.784530	−	0.620091i	$-0.212904\pi$
$264$	−30.0853	−	34.1477i	−1.85163	−	2.10165i
$265$	−0.0131172	−	1.92583i	−0.000805785	−	0.118303i
$266$	5.00182	−	1.22798i	0.306681	−	0.0752925i
$267$	−22.5600			−1.38065
$268$	11.8108	−	6.17123i	0.721457	−	0.376968i
$269$		−	0.327378i		−	0.0199606i	−0.999950	−	0.00998030i	$-0.996823\pi$
$269$		−	0.327378i		−	0.0199606i	0.999950	−	0.00998030i	$-0.00317688\pi$
$270$	−8.74117	−	34.5854i	−0.531970	−	2.10480i
$271$	25.1226			1.52609			0.763044	−	0.646347i	$-0.223704\pi$
$271$	25.1226			1.52609			0.763044	+	0.646347i	$0.223704\pi$
$272$	14.4643	+	10.0624i	0.877028	+	0.610120i
$273$		−	10.4824i		−	0.634423i
$274$	−1.68153	−	6.84919i	−0.101585	−	0.413775i
$275$	−0.353068	−	25.9169i	−0.0212908	−	1.56285i
$276$	−6.73349	−	12.8868i	−0.405308	−	0.775697i
$277$	−18.9641			−1.13944			−0.569720	−	0.821839i	$-0.692948\pi$
$277$	−18.9641			−1.13944			−0.569720	+	0.821839i	$0.692948\pi$
$278$	2.45197	+	9.98736i	0.147059	+	0.599002i
$279$	−5.50009			−0.329282
$280$	−4.71690	+	4.21317i	−0.281889	+	0.251785i
$281$	25.2018			1.50342			0.751708	−	0.659497i	$-0.229230\pi$
$281$	25.2018			1.50342			0.751708	+	0.659497i	$0.229230\pi$
$282$	3.48921	+	14.2122i	0.207779	+	0.846326i
$283$	9.29944			0.552794			0.276397	−	0.961043i	$-0.410859\pi$
$283$	9.29944			0.552794			0.276397	+	0.961043i	$0.410859\pi$
$284$	−24.0492	+	12.5659i	−1.42706	+	0.745650i
$285$	−25.2760	+	0.172160i	−1.49722	+	0.0101979i
$286$	5.90302	+	24.0441i	0.349053	+	1.42176i
$287$			4.72862i			0.279122i
$288$	13.4686	−	35.0295i	0.793643	−	2.06413i
$289$	−2.40422			−0.141425
$290$	8.59796	−	2.17306i	0.504889	−	0.127606i
$291$			2.46354i			0.144416i
$292$	−2.12879	−	4.07416i	−0.124578	−	0.238422i
$293$	−1.23536			−0.0721706			−0.0360853	−	0.999349i	$-0.511489\pi$
$293$	−1.23536			−0.0721706			−0.0360853	+	0.999349i	$0.511489\pi$
$294$	4.26302	−	1.04660i	0.248624	−	0.0610392i
$295$	19.4536	−	0.132503i	1.13263	−	0.00771461i
$296$	−15.5268	+	13.6797i	−0.902477	+	0.795114i
$297$		−	58.4781i		−	3.39324i
$298$	3.70221	+	15.0798i	0.214463	+	0.873550i
$299$			7.90990i			0.457441i
$300$	27.3119	−	14.7478i	1.57685	−	0.851462i
$301$			4.34414i			0.250392i
$302$	0.395260	−	0.0970394i	0.0227447	−	0.00558399i
$303$		−	50.7505i		−	2.91554i
$304$	−11.9584	−	8.31904i	−0.685859	−	0.477130i
$305$	8.57001	−	0.0583722i	0.490717	−	0.00334238i
$306$	9.85412	+	40.1377i	0.563322	+	2.29452i
$307$	−12.6677			−0.722982			−0.361491	−	0.932376i	$-0.617732\pi$
$307$	−12.6677			−0.722982			−0.361491	+	0.932376i	$0.617732\pi$
$308$	−9.18898	+	4.80132i	−0.523591	+	0.273581i
$309$		−	1.25889i		−	0.0716159i
$310$	−0.642394	−	2.54170i	−0.0364855	−	0.144359i
$311$	−15.3688			−0.871482			−0.435741	−	0.900072i	$-0.643514\pi$
$311$	−15.3688			−0.871482			−0.435741	+	0.900072i	$0.643514\pi$
$312$	−22.2462	+	19.5997i	−1.25945	+	1.10962i
$313$		−	5.40865i		−	0.305715i	−0.988248	−	0.152858i	$-0.951152\pi$
$313$		−	5.40865i		−	0.305715i	0.988248	−	0.152858i	$-0.0488476\pi$
$314$	−30.7091	+	7.53932i	−1.73302	+	0.425469i
$315$	−14.8345	+	0.101041i	−0.835831	+	0.00569303i
$316$	13.3026	−	6.95070i	0.748327	−	0.391008i
$317$	−0.946780			−0.0531764			−0.0265882	−	0.999646i	$-0.508464\pi$
$317$	−0.946780			−0.0531764			−0.0265882	+	0.999646i	$0.508464\pi$
$318$	3.67164	−	0.901415i	0.205895	−	0.0505488i
$319$	14.5377			0.813954
$320$	17.7609	+	2.13276i	0.992867	+	0.119225i
$321$	−48.7682			−2.72197
$322$	−3.21683	+	0.789756i	−0.179267	+	0.0440114i
$323$	16.0424			0.892624
$324$	26.7870	−	13.9964i	1.48817	−	0.777580i
$325$	−16.8841	+	0.230014i	−0.936563	+	0.0127589i
$326$	−11.9575	+	2.93565i	−0.662262	+	0.162590i
$327$			46.5534i			2.57441i
$328$	10.0353	−	8.84147i	0.554107	−	0.488188i
$329$	3.33384			0.183801
$330$	49.3310	−	12.4680i	2.71558	−	0.686339i
$331$			19.3252i			1.06221i	0.847306	+	0.531105i	$0.178223\pi$
$331$			19.3252i			1.06221i	−0.847306	+	0.531105i	$0.821777\pi$
$332$	18.3054	−	9.56474i	1.00464	−	0.524933i
$333$	−48.5383			−2.65988
$334$	−3.14397	−	12.8060i	−0.172030	−	0.700712i
$335$	0.101476	+	14.8984i	0.00554424	+	0.813987i
$336$	−10.1920	−	7.09027i	−0.556022	−	0.386806i
$337$			6.21276i			0.338431i	0.985579	+	0.169215i	$0.0541233\pi$
$337$			6.21276i			0.338431i	−0.985579	+	0.169215i	$0.945877\pi$
$338$	−2.19051	+	0.537787i	−0.119148	+	0.0292518i
$339$			44.5262i			2.41833i
$340$	−17.3975	+	9.24176i	−0.943514	+	0.501205i
$341$		−	4.29759i		−	0.232728i
$342$	−8.14688	−	33.1838i	−0.440533	−	1.79438i
$343$		−	1.00000i		−	0.0539949i
$344$	9.21934	−	8.12256i	0.497073	−	0.437939i
$345$	16.2558	−	0.110722i	0.875183	−	0.00596106i
$346$	−22.6356	+	5.55721i	−1.21690	+	0.298757i
$347$	13.5979			0.729976			0.364988	−	0.931012i	$-0.381073\pi$
$347$	13.5979			0.729976			0.364988	+	0.931012i	$0.381073\pi$
$348$	8.06231	+	15.4300i	0.432185	+	0.827134i
$349$			6.23615i			0.333813i	0.985973	+	0.166907i	$0.0533779\pi$
$349$			6.23615i			0.333813i	−0.985973	+	0.166907i	$0.946622\pi$
$350$	−1.77932	−	6.84354i	−0.0951087	−	0.365803i
$351$	−38.0968			−2.03345
$352$	27.3709	+	10.5239i	1.45888	+	0.560926i
$353$			23.2082i			1.23525i	0.786474	+	0.617623i	$0.211904\pi$
$353$			23.2082i			1.23525i	−0.786474	+	0.617623i	$0.788096\pi$
$354$	9.10558	+	37.0888i	0.483956	+	1.97125i
$355$	−0.206627	−	30.3363i	−0.0109666	−	1.61008i
$356$	12.8837	−	6.73185i	0.682836	−	0.356788i
$357$	13.6729			0.723645
$358$	6.64201	+	27.0542i	0.351041	+	1.42986i
$359$	−13.5024			−0.712628			−0.356314	−	0.934366i	$-0.615967\pi$
$359$	−13.5024			−0.712628			−0.356314	+	0.934366i	$0.615967\pi$
$360$	27.9517	+	31.2936i	1.47318	+	1.64932i
$361$	5.73694			0.301944
$362$	−3.02072	−	12.3040i	−0.158766	−	0.646683i
$363$	49.2671			2.58585
$364$	3.12792	+	5.98635i	0.163948	+	0.313770i
$365$	5.13926	−	0.0350046i	0.269001	−	0.00183222i
$366$	4.01133	+	16.3389i	0.209676	+	0.854049i
$367$			1.53267i			0.0800047i	0.999200	+	0.0400023i	$0.0127365\pi$
$367$			1.53267i			0.0800047i	−0.999200	+	0.0400023i	$0.987263\pi$
$368$	7.69081	+	5.35024i	0.400911	+	0.278901i
$369$	31.3714			1.63313
$370$	−5.66913	−	22.4306i	−0.294724	−	1.16611i
$371$		−	0.861277i		−	0.0447152i
$372$	4.56137	−	2.38336i	0.236496	−	0.123571i
$373$	−5.66044			−0.293087			−0.146543	−	0.989204i	$-0.546815\pi$
$373$	−5.66044			−0.293087			−0.146543	+	0.989204i	$0.546815\pi$
$374$	−31.3623	+	7.69969i	−1.62171	+	0.398141i
$375$	0.709048	+	34.6957i	0.0366151	+	1.79168i
$376$	−6.23353	−	7.07524i	−0.321470	−	0.364877i
$377$		−	9.47088i		−	0.487775i
$378$	−3.80373	−	15.4933i	−0.195643	−	0.796891i
$379$		−	33.5460i		−	1.72314i	−0.507636	−	0.861572i	$-0.669480\pi$
$379$		−	33.5460i		−	1.72314i	0.507636	−	0.861572i	$-0.330520\pi$
$380$	14.3834	−	7.64061i	0.737853	−	0.391955i
$381$		−	17.0677i		−	0.874402i
$382$	−7.49257	+	1.83948i	−0.383353	+	0.0941161i
$383$			24.6395i			1.25902i	0.776992	+	0.629511i	$0.216745\pi$
$383$			24.6395i			1.25902i	−0.776992	+	0.629511i	$0.783255\pi$
$384$	4.00952	+	34.8873i	0.204610	+	1.78033i
$385$	−0.0789503	−	11.5912i	−0.00402368	−	0.590743i
$386$	−7.08171	−	28.8452i	−0.360450	−	1.46818i
$387$	28.8206			1.46503
$388$	−0.735116	−	1.40690i	−0.0373198	−	0.0714243i
$389$		−	20.4599i		−	1.03736i	−0.854968	−	0.518680i	$-0.826424\pi$
$389$		−	20.4599i		−	1.03736i	0.854968	−	0.518680i	$-0.173576\pi$
$390$	−8.12252	−	32.1377i	−0.411300	−	1.62735i
$391$	−10.3174			−0.521773
$392$	−2.12225	+	1.86978i	−0.107190	+	0.0944379i
$393$			45.9409i			2.31741i
$394$	24.6127	−	6.04261i	1.23997	−	0.304422i
$395$	0.114294	+	16.7802i	0.00575073	+	0.844303i
$396$	31.8537	+	60.9630i	1.60071	+	3.06350i
$397$	23.0263			1.15566			0.577828	−	0.816159i	$-0.303901\pi$
$397$	23.0263			1.15566			0.577828	+	0.816159i	$0.303901\pi$
$398$	−10.3111	+	2.53144i	−0.516847	+	0.126890i
$399$	−11.3040			−0.565909
$400$	−11.1968	+	16.5720i	−0.559838	+	0.828602i
$401$	10.2348			0.511103			0.255552	−	0.966795i	$-0.417743\pi$
$401$	10.2348			0.511103			0.255552	+	0.966795i	$0.417743\pi$
$402$	−28.4042	+	6.97344i	−1.41667	+	0.347803i
$403$	−2.79975			−0.139466
$404$	15.1438	+	28.9829i	0.753434	+	1.44195i
$405$	0.230150	+	33.7898i	0.0114362	+	1.67903i
$406$	3.85165	−	0.945610i	0.191154	−	0.0469298i
$407$		−	37.9263i		−	1.87993i
$408$	−25.5652	−	29.0172i	−1.26567	−	1.43657i
$409$	3.38780			0.167516			0.0837580	−	0.996486i	$-0.473308\pi$
$409$	3.38780			0.167516			0.0837580	+	0.996486i	$0.473308\pi$
$410$	3.66408	+	14.4974i	0.180956	+	0.715973i
$411$			15.4791i			0.763526i
$412$	0.375651	+	0.718936i	0.0185070	+	0.0354194i
$413$	8.70012			0.428105
$414$	5.23952	+	21.3416i	0.257508	+	1.04888i
$415$	0.157277	+	23.0909i	0.00772044	+	1.13349i
$416$	6.85601	−	17.8314i	0.336144	−	0.874255i
$417$		−	22.5713i		−	1.10532i
$418$	25.9288	−	6.36571i	1.26822	−	0.311357i
$419$			0.0664449i			0.00324604i	0.999999	+	0.00162302i	$0.000516624\pi$
$419$			0.0664449i			0.00324604i	−0.999999	+	0.00162302i	$0.999483\pi$
$420$	12.2589	−	6.51205i	0.598172	−	0.317756i
$421$			33.7434i			1.64455i	0.569089	+	0.822276i	$0.307296\pi$
$421$			33.7434i			1.64455i	−0.569089	+	0.822276i	$0.692704\pi$
$422$	5.45120	+	22.2038i	0.265360	+	1.08086i
$423$		−	22.1179i		−	1.07541i
$424$	−1.82784	+	1.61039i	−0.0887679	+	0.0782077i
$425$	−0.300022	−	22.0231i	−0.0145532	−	1.06828i
$426$	57.8369	−	14.1994i	2.80221	−	0.687963i
$427$	3.83271			0.185478
$428$	27.8508	−	14.5523i	1.34622	−	0.703412i
$429$		−	54.3394i		−	2.62353i
$430$	3.36615	+	13.3186i	0.162330	+	0.642278i
$431$	−26.0512			−1.25484			−0.627421	−	0.778681i	$-0.715889\pi$
$431$	−26.0512			−1.25484			−0.627421	+	0.778681i	$0.715889\pi$
$432$	−25.7686	+	37.0415i	−1.23979	+	1.78216i
$433$			0.534216i			0.0256728i	0.999918	+	0.0128364i	$0.00408606\pi$
$433$			0.534216i			0.0256728i	−0.999918	+	0.0128364i	$0.995914\pi$
$434$	−0.279539	−	1.13861i	−0.0134183	−	0.0546553i
$435$	−19.4638	+	0.132572i	−0.933217	+	0.00635635i
$436$	−13.8914	−	26.5860i	−0.665278	−	1.27324i
$437$	8.52990			0.408040
$438$	2.40551	+	9.79812i	0.114940	+	0.468172i
$439$	25.7102			1.22708			0.613540	−	0.789664i	$-0.289745\pi$
$439$	25.7102			1.22708			0.613540	+	0.789664i	$0.289745\pi$
$440$	−24.4518	+	21.8405i	−1.16569	+	1.04121i
$441$	−6.63436			−0.315922
$442$	5.01612	+	20.4316i	0.238593	+	0.971834i
$443$	−32.9572			−1.56584			−0.782921	−	0.622121i	$-0.786271\pi$
$443$	−32.9572			−1.56584			−0.782921	+	0.622121i	$0.786271\pi$
$444$	40.2541	−	21.0331i	1.91038	−	0.998188i
$445$	0.110695	+	16.2519i	0.00524744	+	0.770412i
$446$	−5.74740	−	23.4103i	−0.272147	−	1.10851i
$447$		−	34.0802i		−	1.61194i
$448$	7.93626	+	1.00788i	0.374953	+	0.0476177i
$449$	−13.4009			−0.632428			−0.316214	−	0.948688i	$-0.602412\pi$
$449$	−13.4009			−0.632428			−0.316214	+	0.948688i	$0.602412\pi$
$450$	−45.4025	+	11.8047i	−2.14029	+	0.556477i
$451$			24.5126i			1.15425i
$452$	−13.2865	−	25.4283i	−0.624946	−	1.19605i
$453$	−0.893282			−0.0419700
$454$	−0.346689	+	0.0851147i	−0.0162709	+	0.00399463i
$455$	−7.55134	+	0.0514338i	−0.354012	+	0.00241125i
$456$	21.1360	+	23.9900i	0.989784	+	1.12343i
$457$			13.9220i			0.651242i	0.945500	+	0.325621i	$0.105573\pi$
$457$			13.9220i			0.651242i	−0.945500	+	0.325621i	$0.894427\pi$
$458$	−4.16976	−	16.9842i	−0.194840	−	0.793621i
$459$		−	49.6921i		−	2.31943i
$460$	−9.25043	+	4.91392i	−0.431303	+	0.229113i
$461$		−	0.352397i		−	0.0164128i	−0.999966	−	0.00820639i	$-0.997388\pi$
$461$		−	0.352397i		−	0.0164128i	0.999966	−	0.00820639i	$-0.00261221\pi$
$462$	22.0989	−	5.42546i	1.02814	−	0.252415i
$463$		−	28.3823i		−	1.31904i	−0.751688	−	0.659519i	$-0.770760\pi$
$463$		−	28.3823i		−	1.31904i	0.751688	−	0.659519i	$-0.229240\pi$
$464$	−9.20855	−	6.40609i	−0.427496	−	0.297395i
$465$	0.0391906	+	5.75383i	0.00181742	+	0.266828i
$466$	1.81596	+	7.39677i	0.0841229	+	0.342649i
$467$	13.7435			0.635972			0.317986	−	0.948095i	$-0.396994\pi$
$467$	13.7435			0.635972			0.317986	+	0.948095i	$0.396994\pi$
$468$	39.7156	−	20.7517i	1.83585	−	0.959250i
$469$			6.66292i			0.307665i
$470$	10.2211	−	2.58330i	0.471465	−	0.119159i
$471$	69.4021			3.19788
$472$	−16.2673	−	18.4638i	−0.748762	−	0.849866i
$473$			22.5194i			1.03544i
$474$	−31.9918	+	7.85424i	−1.46943	+	0.360757i
$475$	0.248043	+	18.2076i	0.0113810	+	0.835420i
$476$	−7.80839	+	4.07995i	−0.357897	+	0.187004i
$477$	−5.71402			−0.261627
$478$	6.35355	−	1.55984i	0.290604	−	0.0713456i
$479$	−7.79400			−0.356117			−0.178058	−	0.984020i	$-0.556982\pi$
$479$	−7.79400			−0.356117			−0.178058	+	0.984020i	$0.556982\pi$
$480$	−36.7416	−	13.8403i	−1.67702	−	0.631722i
$481$	−24.7079			−1.12658
$482$	−4.16963	+	1.02368i	−0.189921	+	0.0466272i
$483$	7.26998			0.330796
$484$	−28.1358	+	14.7012i	−1.27890	+	0.668236i
$485$	1.77470	−	0.0120878i	0.0805848	−	0.000548880i
$486$	−17.9411	+	4.40468i	−0.813826	+	0.199800i
$487$			0.760366i			0.0344555i	0.999852	+	0.0172277i	$0.00548403\pi$
$487$			0.760366i			0.0344555i	−0.999852	+	0.0172277i	$0.994516\pi$
$488$	−7.16631	−	8.13397i	−0.324404	−	0.368207i
$489$	27.0237			1.22205
$490$	−0.774873	−	3.06587i	−0.0350052	−	0.138502i
$491$		−	29.9543i		−	1.35182i	−0.736986	−	0.675908i	$-0.763751\pi$
$491$		−	29.9543i		−	1.35182i	0.736986	−	0.675908i	$-0.236249\pi$
$492$	−26.0171	+	13.5942i	−1.17294	+	0.612873i
$493$	12.3535			0.556373
$494$	−4.14707	−	16.8918i	−0.186586	−	0.760000i
$495$	−76.9003	+	0.523784i	−3.45641	+	0.0235424i
$496$	−1.89375	+	2.72220i	−0.0850318	+	0.122231i
$497$		−	13.5671i		−	0.608568i
$498$	−44.0234	+	10.8081i	−1.97274	+	0.484322i
$499$			1.02152i			0.0457296i	0.999739	+	0.0228648i	$0.00727872\pi$
$499$			1.02152i			0.0457296i	−0.999739	+	0.0228648i	$0.992721\pi$
$500$	−10.7580	−	19.6027i	−0.481114	−	0.876658i
$501$			28.9413i			1.29300i
$502$	5.13261	+	20.9061i	0.229080	+	0.933086i
$503$			27.6606i			1.23332i	0.787228	+	0.616662i	$0.211516\pi$
$503$			27.6606i			1.23332i	−0.787228	+	0.616662i	$0.788484\pi$
$504$	12.4048	+	14.0798i	0.552552	+	0.627162i
$505$	−36.5598	+	0.249017i	−1.62689	+	0.0110811i
$506$	−16.6756	+	4.09399i	−0.741322	+	0.182000i
$507$	4.95052			0.219861
$508$	5.09295	+	9.74710i	0.225963	+	0.432458i
$509$			17.2309i			0.763745i	0.924215	+	0.381873i	$0.124721\pi$
$509$			17.2309i			0.763745i	−0.924215	+	0.381873i	$0.875279\pi$
$510$	41.9193	−	10.5947i	1.85622	−	0.469143i
$511$	2.29840			0.101675
$512$	−12.7001	−	18.7272i	−0.561269	−	0.827634i
$513$			41.0829i			1.81385i
$514$	8.32681	+	33.9167i	0.367280	+	1.49600i
$515$	−0.906885	+	0.00617699i	−0.0399621	+	0.000272191i
$516$	−23.9017	+	12.4888i	−1.05221	+	0.549790i
$517$	17.2822			0.760070
$518$	−2.46693	−	10.0483i	−0.108391	−	0.441496i
$519$	51.1561			2.24550
$520$	14.2285	+	15.9296i	0.623960	+	0.698561i
$521$	41.5623			1.82088			0.910440	−	0.413642i	$-0.135744\pi$
$521$	41.5623			1.82088			0.910440	+	0.413642i	$0.135744\pi$
$522$	−6.27351	−	25.5532i	−0.274584	−	1.11843i
$523$	−24.1828			−1.05744			−0.528719	−	0.848797i	$-0.677328\pi$
$523$	−24.1828			−1.05744			−0.528719	+	0.848797i	$0.677328\pi$
$524$	−13.7087	−	26.2362i	−0.598865	−	1.14613i
$525$	0.211405	+	15.5182i	0.00922649	+	0.677269i
$526$	−6.78163	−	27.6229i	−0.295693	−	1.20442i
$527$		−	3.65190i		−	0.159079i
$528$	−52.8342	−	36.7550i	−2.29931	−	1.59956i
$529$	17.5141			0.761485
$530$	−0.667380	−	2.64056i	−0.0289891	−	0.114699i
$531$		−	57.7197i		−	2.50482i
$532$	6.45558	−	3.37310i	0.279885	−	0.146242i
$533$	15.9692			0.691704
$534$	−30.9846	+	7.60694i	−1.34083	+	0.329185i
$535$	0.239290	+	35.1318i	0.0103454	+	1.51888i
$536$	14.1404	−	12.4582i	0.610771	−	0.538111i
$537$		−	61.1421i		−	2.63848i
$538$	−0.110388	−	0.449630i	−0.00475915	−	0.0193849i
$539$		−	5.18387i		−	0.223285i
$540$	−23.6671	−	44.5532i	−1.01847	−	1.91726i
$541$			40.5324i			1.74262i	0.490730	+	0.871312i	$0.336730\pi$
$541$			40.5324i			1.74262i	−0.490730	+	0.871312i	$0.663270\pi$
$542$	34.5041	−	8.47101i	1.48208	−	0.363861i
$543$			27.8068i			1.19331i
$544$	23.2586	+	8.94274i	0.997204	+	0.383417i
$545$	33.5363	−	0.228423i	1.43654	−	0.00978456i
$546$	−3.53453	−	14.3968i	−0.151264	−	0.616127i
$547$	24.6239			1.05284			0.526420	−	0.850225i	$-0.323534\pi$
$547$	24.6239			1.05284			0.526420	+	0.850225i	$0.323534\pi$
$548$	−4.61892	−	8.83988i	−0.197310	−	0.377621i
$549$		−	25.4276i		−	1.08522i
$550$	−9.22377	−	35.4760i	−0.393303	−	1.51270i
$551$	−10.2132			−0.435098
$552$	−13.5932	−	15.4287i	−0.578567	−	0.656689i
$553$			7.50450i			0.319124i
$554$	−26.0458	+	6.39443i	−1.10658	+	0.271673i
$555$	0.345857	+	50.7776i	0.0146808	+	2.15539i
$556$	6.73521	+	12.8901i	0.285637	+	0.546664i
$557$	38.4640			1.62977			0.814886	−	0.579622i	$-0.196800\pi$
$557$	38.4640			1.62977			0.814886	+	0.579622i	$0.196800\pi$
$558$	−7.55398	+	1.85456i	−0.319785	+	0.0785097i
$559$	14.6708			0.620507
$560$	−5.05770	+	7.37697i	−0.213727	+	0.311734i
$561$	70.8783			2.99249
$562$	34.6129	−	8.49773i	1.46006	−	0.358455i
$563$	−32.5851			−1.37330			−0.686650	−	0.726989i	$-0.740919\pi$
$563$	−32.5851			−1.37330			−0.686650	+	0.726989i	$0.740919\pi$
$564$	9.58435	+	18.3430i	0.403574	+	0.772378i
$565$	32.0760	−	0.218476i	1.34945	−	0.00919137i
$566$	12.7721	−	3.13565i	0.536852	−	0.131801i
$567$			15.1116i			0.634628i
$568$	−28.7928	+	25.3675i	−1.20812	+	1.06439i
$569$	−18.0015			−0.754661			−0.377330	−	0.926079i	$-0.623158\pi$
$569$	−18.0015			−0.754661			−0.377330	+	0.926079i	$0.623158\pi$
$570$	−34.6567	+	8.75918i	−1.45161	+	0.366882i
$571$		−	21.4418i		−	0.897310i	−0.893705	−	0.448655i	$-0.851903\pi$
$571$		−	21.4418i		−	0.897310i	0.893705	−	0.448655i	$-0.148097\pi$
$572$	16.2147	+	31.0325i	0.677972	+	1.29753i
$573$	16.9331			0.707390
$574$	1.59443	+	6.49442i	0.0665502	+	0.271072i
$575$	−0.159524	−	11.7099i	−0.00665262	−	0.488335i
$576$	6.68661	−	52.6520i	0.278609	−	2.19383i
$577$			34.6243i			1.44143i	0.693232	+	0.720715i	$0.256186\pi$
$577$			34.6243i			1.44143i	−0.693232	+	0.720715i	$0.743814\pi$
$578$	−3.30203	+	0.810672i	−0.137346	+	0.0337195i
$579$			65.1897i			2.70919i
$580$	11.0759	−	5.88366i	0.459904	−	0.244306i
$581$			10.3268i			0.428429i
$582$	0.830675	+	3.38350i	0.0344326	+	0.140251i
$583$		−	4.46475i		−	0.184911i
$584$	−4.29749	−	4.87777i	−0.177831	−	0.201844i
$585$	0.341230	+	50.0983i	0.0141081	+	2.07131i
$586$	−1.69668	+	0.416548i	−0.0700892	+	0.0172074i
$587$	−15.6163			−0.644555			−0.322278	−	0.946645i	$-0.604448\pi$
$587$	−15.6163			−0.644555			−0.322278	+	0.946645i	$0.604448\pi$
$588$	5.50205	−	2.87487i	0.226901	−	0.118558i
$589$			3.01921i			0.124404i
$590$	26.6735	−	6.74149i	1.09813	−	0.277543i
$591$	−55.6243			−2.28808
$592$	−16.7123	+	24.0235i	−0.686873	+	0.987359i
$593$			20.9845i			0.861731i	0.902416	+	0.430866i	$0.141792\pi$
$593$			20.9845i			0.861731i	−0.902416	+	0.430866i	$0.858208\pi$
$594$	−19.7180	−	80.3154i	−0.809041	−	3.29538i
$595$	−0.0670885	−	9.84970i	−0.00275036	−	0.403798i
$596$	10.1694	+	19.4627i	0.416556	+	0.797224i
$597$	23.3029			0.953722
$598$	2.66712	+	10.8637i	0.109066	+	0.444249i
$599$	−38.5614			−1.57557			−0.787787	−	0.615947i	$-0.788773\pi$
$599$	−38.5614			−1.57557			−0.787787	+	0.615947i	$0.788773\pi$
$600$	32.5382	−	29.4642i	1.32837	−	1.20287i
$601$	−6.94429			−0.283264			−0.141632	−	0.989919i	$-0.545235\pi$
$601$	−6.94429			−0.283264			−0.141632	+	0.989919i	$0.545235\pi$
$602$	1.46479	+	5.96636i	0.0597002	+	0.243171i
$603$	44.2042			1.80013
$604$	0.510141	−	0.266553i	0.0207573	−	0.0108459i
$605$	−0.241738	−	35.4912i	−0.00982805	−	1.44292i
$606$	−17.1124	−	69.7022i	−0.695144	−	2.83146i
$607$		−	18.8127i		−	0.763585i	−0.924248	−	0.381793i	$-0.875307\pi$
$607$		−	18.8127i		−	0.763585i	0.924248	−	0.381793i	$-0.124693\pi$
$608$	−19.2290	−	7.39340i	−0.779840	−	0.299842i
$609$	−8.70467			−0.352731
$610$	11.7506	−	2.96986i	0.475768	−	0.120246i
$611$		−	11.2588i		−	0.455484i
$612$	27.0678	+	51.8036i	1.09415	+	2.09404i
$613$	1.52584			0.0616279			0.0308140	−	0.999525i	$-0.490190\pi$
$613$	1.52584			0.0616279			0.0308140	+	0.999525i	$0.490190\pi$
$614$	−17.3981	+	4.27138i	−0.702132	+	0.172379i
$615$	−0.223535	−	32.8187i	−0.00901381	−	1.32338i
$616$	−11.0015	+	9.69268i	−0.443261	+	0.390529i
$617$		−	10.2687i		−	0.413401i	−0.978404	−	0.206700i	$-0.933727\pi$
$617$		−	10.2687i		−	0.413401i	0.978404	−	0.206700i	$-0.0662725\pi$
$618$	−0.424482	−	1.72900i	−0.0170752	−	0.0695505i
$619$		−	19.3595i		−	0.778122i	−0.921212	−	0.389061i	$-0.872800\pi$
$619$		−	19.3595i		−	0.778122i	0.921212	−	0.389061i	$-0.127200\pi$
$620$	−1.73931	−	3.27424i	−0.0698524	−	0.131497i
$621$		−	26.4217i		−	1.06027i
$622$	−21.1079	+	5.18215i	−0.846349	+	0.207785i
$623$			7.26822i			0.291195i
$624$	−23.9448	+	34.4200i	−0.958561	+	1.37790i
$625$	24.9907	−	0.681027i	0.999629	−	0.0272411i
$626$	−1.82373	−	7.42840i	−0.0728908	−	0.296898i
$627$	−58.5986			−2.34020
$628$	−39.6346	+	20.7094i	−1.58159	+	0.826396i
$629$		−	32.2280i		−	1.28502i
$630$	−20.3401	+	5.14078i	−0.810369	+	0.204814i
$631$	−36.1089			−1.43747			−0.718736	−	0.695283i	$-0.755279\pi$
$631$	−36.1089			−1.43747			−0.718736	+	0.695283i	$0.755279\pi$
$632$	15.9264	−	14.0317i	0.633519	−	0.558153i
$633$		−	50.1803i		−	1.99449i
$634$	−1.30033	+	0.319242i	−0.0516428	+	0.0126787i
$635$	−12.2952	+	0.0837456i	−0.487922	+	0.00332334i
$636$	4.73879	−	2.47606i	0.187905	−	0.0981821i
$637$	−3.37714			−0.133807
$638$	19.9665	−	4.90192i	0.790480	−	0.194069i
$639$	−90.0091			−3.56070
$640$	25.1125	−	3.05957i	0.992660	−	0.120940i
$641$	−23.8187			−0.940783			−0.470392	−	0.882458i	$-0.655887\pi$
$641$	−23.8187			−0.940783			−0.470392	+	0.882458i	$0.655887\pi$
$642$	−66.9796	+	16.4440i	−2.64347	+	0.648993i
$643$	−1.59037			−0.0627182			−0.0313591	−	0.999508i	$-0.509984\pi$
$643$	−1.59037			−0.0627182			−0.0313591	+	0.999508i	$0.509984\pi$
$644$	−4.15179	+	2.16935i	−0.163603	+	0.0854842i
$645$	−0.205359	−	30.1502i	−0.00808602	−	1.18716i
$646$	22.0331	−	5.40930i	0.866881	−	0.212826i
$647$			6.20233i			0.243839i	0.992540	+	0.121919i	$0.0389049\pi$
$647$			6.20233i			0.243839i	−0.992540	+	0.121919i	$0.961095\pi$
$648$	32.0706	−	28.2553i	1.25985	−	1.10997i
$649$	45.1003			1.77034
$650$	−23.1116	+	6.00902i	−0.906511	+	0.235693i
$651$			2.57325i			0.100854i
$652$	−15.4328	+	8.06380i	−0.604397	+	0.315803i
$653$	−22.1560			−0.867030			−0.433515	−	0.901146i	$-0.642727\pi$
$653$	−22.1560			−0.867030			−0.433515	+	0.901146i	$0.642727\pi$
$654$	15.6972	+	63.9377i	0.613809	+	2.50016i
$655$	33.0950	−	0.225418i	1.29313	−	0.00880779i
$656$	10.8016	−	15.5269i	0.421730	−	0.606223i
$657$		−	15.2484i		−	0.594896i
$658$	4.57879	−	1.12413i	0.178500	−	0.0438231i
$659$		−	9.72044i		−	0.378655i	−0.981914	−	0.189327i	$-0.939369\pi$
$659$		−	9.72044i		−	0.378655i	0.981914	−	0.189327i	$-0.0606307\pi$
$660$	63.5485	−	33.7576i	2.47362	−	1.31401i
$661$		−	44.7566i		−	1.74083i	−0.492320	−	0.870414i	$-0.663851\pi$
$661$		−	44.7566i		−	1.74083i	0.492320	−	0.870414i	$-0.336149\pi$
$662$	6.51622	+	26.5418i	0.253260	+	1.03158i
$663$		−	46.1752i		−	1.79330i
$664$	21.9161	−	19.3088i	0.850508	−	0.749328i
$665$	0.0554653	+	8.14323i	0.00215085	+	0.315781i
$666$	−66.6639	+	16.3665i	−2.58317	+	0.634189i
$667$	6.56845			0.254332
$668$	−8.63602	−	16.5280i	−0.334138	−	0.639487i
$669$			52.9068i			2.04550i
$670$	5.16292	+	20.4277i	0.199461	+	0.789190i
$671$	19.8683			0.767007
$672$	−16.3888	−	6.30135i	−0.632211	−	0.243080i
$673$		−	26.9330i		−	1.03819i	−0.854716	−	0.519095i	$-0.826269\pi$
$673$		−	26.9330i		−	1.03819i	0.854716	−	0.519095i	$-0.173731\pi$
$674$	2.09486	+	8.53278i	0.0806911	+	0.328670i
$675$	56.3986	−	0.768322i	2.17078	−	0.0295727i
$676$	−2.82718	+	1.47722i	−0.108738	+	0.0568163i
$677$	−41.0899			−1.57921			−0.789606	−	0.613614i	$-0.789715\pi$
$677$	−41.0899			−1.57921			−0.789606	+	0.613614i	$0.789715\pi$
$678$	15.0137	+	61.1536i	0.576597	+	2.34859i
$679$	0.793686			0.0304589
$680$	−20.7781	+	18.5591i	−0.796803	+	0.711709i
$681$	0.783511			0.0300242
$682$	−1.44909	−	5.90243i	−0.0554886	−	0.226016i
$683$	−13.7037			−0.524356			−0.262178	−	0.965019i	$-0.584441\pi$
$683$	−13.7037			−0.524356			−0.262178	+	0.965019i	$0.584441\pi$
$684$	−22.3783	−	42.8286i	−0.855656	−	1.63759i
$685$	11.1509	−	0.0759509i	0.426052	−	0.00290194i
$686$	−0.337187	−	1.37343i	−0.0128739	−	0.0524377i
$687$			38.3841i			1.46444i
$688$	9.92327	−	14.2644i	0.378321	−	0.543825i
$689$	−2.90865			−0.110811
$690$	22.2888	−	5.63331i	0.848522	−	0.214457i
$691$			21.3102i			0.810680i	0.914166	+	0.405340i	$0.132847\pi$
$691$			21.3102i			0.810680i	−0.914166	+	0.405340i	$0.867153\pi$
$692$	−29.2145	+	15.2649i	−1.11057	+	0.580283i
$693$	−34.3916			−1.30643
$694$	18.6758	−	4.58505i	0.708923	−	0.174046i
$695$	−16.2600	+	0.110750i	−0.616776	+	0.00420099i
$696$	16.2758	+	18.4735i	0.616932	+	0.700235i
$697$			20.8297i			0.788981i
$698$	2.10275	+	8.56490i	0.0795902	+	0.324186i
$699$		−	16.7166i		−	0.632279i
$700$	−4.75132	−	8.79914i	−0.179583	−	0.332576i
$701$			1.69034i			0.0638434i	0.999490	+	0.0319217i	$0.0101627\pi$
$701$			1.69034i			0.0638434i	−0.999490	+	0.0319217i	$0.989837\pi$
$702$	−52.3232	+	12.8457i	−1.97481	+	0.484831i
$703$			26.6445i			1.00492i
$704$	41.1405	+	5.22470i	1.55054	+	0.196913i
$705$	−23.1383	+	0.157600i	−0.871438	+	0.00593555i
$706$	7.82549	+	31.8747i	0.294516	+	1.19962i
$707$	−16.3504			−0.614921
$708$	25.0117	+	47.8685i	0.939998	+	1.79901i
$709$			5.51528i			0.207131i	0.994623	+	0.103565i	$0.0330251\pi$
$709$			5.51528i			0.207131i	−0.994623	+	0.103565i	$0.966975\pi$
$710$	−10.5128	−	41.5950i	−0.394538	−	1.56103i
$711$	49.7876			1.86718
$712$	15.4250	−	13.5899i	0.578075	−	0.509305i
$713$		−	1.94175i		−	0.0727190i
$714$	18.7787	−	4.61031i	0.702775	−	0.172537i
$715$	−39.1452	+	0.266626i	−1.46395	+	0.00997126i
$716$	18.2447	+	34.9174i	0.681835	+	1.30493i
$717$	−14.3589			−0.536243
$718$	−18.5446	+	4.55283i	−0.692077	+	0.169910i
$719$	−28.4731			−1.06187			−0.530934	−	0.847413i	$-0.678159\pi$
$719$	−28.4731			−1.06187			−0.530934	+	0.847413i	$0.678159\pi$
$720$	48.9414	+	33.5546i	1.82394	+	1.25051i
$721$	−0.405581			−0.0151046
$722$	7.87927	−	1.93442i	0.293236	−	0.0719917i
$723$	9.42330			0.350456
$724$	−8.29749	−	15.8801i	−0.308374	−	0.590179i
$725$	0.191005	+	14.0207i	0.00709376	+	0.520717i
$726$	67.6648	−	16.6122i	2.51128	−	0.616537i
$727$		−	37.0230i		−	1.37311i	−0.727080	−	0.686553i	$-0.759123\pi$
$727$		−	37.0230i		−	1.37311i	0.727080	−	0.686553i	$-0.240877\pi$
$728$	6.31450	+	7.16713i	0.234031	+	0.265632i
$729$	−4.78819			−0.177340
$730$	7.04659	−	1.78097i	0.260806	−	0.0659165i
$731$			19.1360i			0.707771i
$732$	11.0185	+	21.0878i	0.407257	+	0.779427i
$733$	36.2958			1.34062			0.670308	−	0.742083i	$-0.266162\pi$
$733$	36.2958			1.34062			0.670308	+	0.742083i	$0.266162\pi$
$734$	0.516796	+	2.10501i	0.0190753	+	0.0776974i
$735$	0.0472728	+	6.94043i	0.00174368	+	0.256002i
$736$	12.3668	+	4.75493i	0.455846	+	0.175269i
$737$			34.5397i			1.27229i
$738$	43.0863	−	10.5780i	1.58603	−	0.389382i
$739$			12.9184i			0.475212i	0.971362	+	0.237606i	$0.0763627\pi$
$739$			12.9184i			0.475212i	−0.971362	+	0.237606i	$0.923637\pi$
$740$	−15.3494	−	28.8952i	−0.564256	−	1.06221i
$741$			38.1753i			1.40240i
$742$	−0.290411	−	1.18290i	−0.0106613	−	0.0434257i
$743$			15.7477i			0.577728i	0.957370	+	0.288864i	$0.0932775\pi$
$743$			15.7477i			0.577728i	−0.957370	+	0.288864i	$0.906722\pi$
$744$	5.46108	−	4.81140i	0.200213	−	0.176395i
$745$	−24.5508	+	0.167221i	−0.899471	+	0.00612649i
$746$	−7.77421	+	1.90863i	−0.284634	+	0.0698798i
$747$	68.5118			2.50672
$748$	−40.4777	+	21.1499i	−1.48001	+	0.773318i
$749$			15.7118i			0.574096i
$750$	12.6728	+	47.4130i	0.462744	+	1.73128i
$751$	−20.2202			−0.737846			−0.368923	−	0.929460i	$-0.620273\pi$
$751$	−20.2202			−0.737846			−0.368923	+	0.929460i	$0.620273\pi$
$752$	−10.9470	−	7.61546i	−0.399196	−	0.277707i
$753$		−	47.2475i		−	1.72180i
$754$	−3.19346	−	13.0076i	−0.116299	−	0.473708i
$755$	0.00438305	+	0.643505i	0.000159516	+	0.0234196i
$756$	−10.4483	−	19.9964i	−0.380001	−	0.727263i
$757$	16.2961			0.592293			0.296147	−	0.955143i	$-0.404298\pi$
$757$	16.2961			0.592293			0.296147	+	0.955143i	$0.404298\pi$
$758$	−11.3113	−	46.0731i	−0.410844	−	1.67345i
$759$	37.6866			1.36794
$760$	17.1783	−	15.3437i	0.623121	−	0.556576i
$761$	−48.4529			−1.75642			−0.878208	−	0.478280i	$-0.841261\pi$
$761$	−48.4529			−1.75642			−0.878208	+	0.478280i	$0.841261\pi$
$762$	−5.75499	−	23.4412i	−0.208481	−	0.849185i
$763$	14.9982			0.542972
$764$	−9.67026	+	5.05280i	−0.349858	+	0.182804i
$765$	−65.3464	+	0.445089i	−2.36261	+	0.0160922i
$766$	8.30813	+	33.8406i	0.300185	+	1.22271i
$767$		−	29.3815i		−	1.06091i
$768$	17.2703	+	46.5632i	0.623189	+	1.68020i
$769$	−43.3554			−1.56343			−0.781717	−	0.623633i	$-0.785656\pi$
$769$	−43.3554			−1.56343			−0.781717	+	0.623633i	$0.785656\pi$
$770$	−4.01684	−	15.8931i	−0.144757	−	0.572747i
$771$		−	76.6513i		−	2.76053i
$772$	−19.4525	−	37.2289i	−0.700109	−	1.33990i
$773$	17.9136			0.644308			0.322154	−	0.946687i	$-0.395593\pi$
$773$	17.9136			0.644308			0.322154	+	0.946687i	$0.395593\pi$
$774$	39.5830	−	9.71791i	1.42278	−	0.349303i
$775$	4.14477	−	0.0564645i	0.148885	−	0.00202826i
$776$	−1.48402	−	1.68440i	−0.0532731	−	0.0604664i
$777$			22.7090i			0.814679i
$778$	−6.89883	−	28.1003i	−0.247335	−	1.00744i
$779$		−	17.2209i		−	0.617004i
$780$	−21.9921	−	41.4000i	−0.787444	−	1.48236i
$781$		−	70.3301i		−	2.51661i
$782$	−14.1702	+	3.47889i	−0.506725	+	0.124405i
$783$			31.6359i			1.13057i
$784$	−2.28429	+	3.28360i	−0.0815818	+	0.117271i
$785$	−0.340535	−	49.9961i	−0.0121542	−	1.78444i
$786$	15.4907	+	63.0965i	0.552534	+	2.25058i
$787$	0.886662			0.0316061			0.0158030	−	0.999875i	$-0.494970\pi$
$787$	0.886662			0.0316061			0.0158030	+	0.999875i	$0.494970\pi$
$788$	31.7663	−	16.5982i	1.13163	−	0.591285i
$789$			62.4273i			2.22247i
$790$	5.81504	+	23.0078i	0.206890	+	0.818582i
$791$	14.3451			0.510054
$792$	64.3047	+	72.9876i	2.28497	+	2.59350i
$793$		−	12.9436i		−	0.459641i
$794$	31.6249	−	7.76416i	1.12233	−	0.275540i
$795$	0.0407149	+	5.97763i	0.00144401	+	0.212005i
$796$	−13.3079	+	6.95352i	−0.471687	+	0.246461i
$797$	−54.5088			−1.93080			−0.965401	−	0.260771i	$-0.916023\pi$
$797$	−54.5088			−1.93080			−0.965401	+	0.260771i	$0.916023\pi$
$798$	−15.5253	+	3.81157i	−0.549589	+	0.134928i
$799$	14.6856			0.519541
$800$	−9.79006	+	26.5359i	−0.346131	+	0.938186i
$801$	48.2200			1.70377
$802$	14.0568	−	3.45105i	0.496363	−	0.121861i
$803$	11.9146			0.420457
$804$	−36.6597	+	19.1550i	−1.29289	+	0.675546i
$805$	−0.0356715	−	5.23717i	−0.00125726	−	0.184586i
$806$	−3.84526	+	0.944041i	−0.135444	+	0.0332524i
$807$			1.01616i			0.0357704i
$808$	30.5716	+	34.6997i	1.07551	+	1.22073i
$809$	18.3920			0.646629			0.323315	−	0.946292i	$-0.395203\pi$
$809$	18.3920			0.646629			0.323315	+	0.946292i	$0.395203\pi$
$810$	11.7096	+	46.3303i	0.411433	+	1.62788i
$811$			56.3877i			1.98004i	0.140924	+	0.990020i	$0.454993\pi$
$811$			56.3877i			1.98004i	−0.140924	+	0.990020i	$0.545007\pi$
$812$	4.97112	−	2.59745i	0.174452	−	0.0911528i
$813$	−77.9786			−2.73483
$814$	−12.7882	−	52.0890i	−0.448228	−	1.82572i
$815$	−0.132597	−	19.4674i	−0.00464466	−	0.681913i
$816$	−44.8962	−	31.2328i	−1.57168	−	1.09337i
$817$		−	15.8207i		−	0.553496i
$818$	4.65290	−	1.14232i	0.162685	−	0.0399404i
$819$			22.4052i			0.782899i
$820$	9.92067	+	18.6756i	0.346445	+	0.652180i
$821$		−	25.8495i		−	0.902154i	−0.892485	−	0.451077i	$-0.851040\pi$
$821$		−	25.8495i		−	0.902154i	0.892485	−	0.451077i	$-0.148960\pi$
$822$	5.21934	+	21.2594i	0.182045	+	0.741506i
$823$			50.3544i			1.75524i	0.479352	+	0.877622i	$0.340872\pi$
$823$			50.3544i			1.75524i	−0.479352	+	0.877622i	$0.659128\pi$
$824$	0.758345	+	0.860743i	0.0264182	+	0.0299854i
$825$	1.09590	+	80.4443i	0.0381543	+	2.80071i
$826$	11.9490	−	2.93357i	0.415759	−	0.102072i
$827$	49.4285			1.71880			0.859398	−	0.511307i	$-0.170838\pi$
$827$	49.4285			1.71880			0.859398	+	0.511307i	$0.170838\pi$
$828$	14.3922	+	27.5444i	0.500164	+	0.957236i
$829$		−	17.6066i		−	0.611502i	−0.952112	−	0.305751i	$-0.901092\pi$
$829$		−	17.6066i		−	0.611502i	0.952112	−	0.305751i	$-0.0989075\pi$
$830$	8.00197	+	31.6607i	0.277752	+	1.09896i
$831$	58.8630			2.04194
$832$	3.40374	−	26.8019i	0.118003	−	0.929187i
$833$		−	4.40502i		−	0.152625i
$834$	−7.61074	−	31.0000i	−0.263538	−	1.07344i
$835$	20.8488	−	0.142006i	0.721504	−	0.00491432i
$836$	33.4649	−	17.4857i	1.15741	−	0.604755i
$837$	9.35212			0.323256
$838$	0.0224043	+	0.0912573i	0.000773945	+	0.00315243i
$839$	−37.3694			−1.29014			−0.645068	−	0.764125i	$-0.723171\pi$
$839$	−37.3694			−1.29014			−0.645068	+	0.764125i	$0.723171\pi$
$840$	14.6409	−	13.0774i	0.505160	−	0.451212i
$841$	21.1353			0.728803
$842$	11.3778	+	46.3441i	0.392106	+	1.59712i
$843$	−78.2246			−2.69420
$844$	14.9737	+	28.6573i	0.515415	+	0.986424i
$845$	−0.0242907	−	3.56627i	−0.000835625	−	0.122684i
$846$	−7.45786	−	30.3773i	−0.256407	−	1.04439i
$847$		−	15.8725i		−	0.545386i
$848$	−1.96741	+	2.82809i	−0.0675610	+	0.0971169i
$849$	−28.8648			−0.990637
$850$	−7.83795	−	30.1459i	−0.268839	−	1.03400i
$851$		−	17.1359i		−	0.587412i
$852$	74.6469	−	39.0037i	2.55736	−	1.33624i
$853$	−12.0171			−0.411457			−0.205728	−	0.978609i	$-0.565956\pi$
$853$	−12.0171			−0.411457			−0.205728	+	0.978609i	$0.565956\pi$
$854$	5.26396	−	1.29234i	0.180129	−	0.0442230i
$855$	54.0251	−	0.367977i	1.84762	−	0.0125845i
$856$	33.3443	−	29.3775i	1.13968	−	1.00410i
$857$		−	33.8023i		−	1.15466i	−0.816510	−	0.577332i	$-0.804094\pi$
$857$		−	33.8023i		−	1.15466i	0.816510	−	0.577332i	$-0.195906\pi$
$858$	−18.3225	−	74.6312i	−0.625521	−	2.54787i
$859$		−	37.4256i		−	1.27694i	−0.769645	−	0.638472i	$-0.779567\pi$
$859$		−	37.4256i		−	1.27694i	0.769645	−	0.638472i	$-0.220433\pi$
$860$	9.11402	+	17.1571i	0.310785	+	0.585051i
$861$		−	14.6773i		−	0.500201i
$862$	−35.7794	+	8.78412i	−1.21865	+	0.299188i
$863$		−	1.60011i		−	0.0544685i	−0.999629	−	0.0272343i	$-0.991330\pi$
$863$		−	1.60011i		−	0.0544685i	0.999629	−	0.0272343i	$-0.00867001\pi$
$864$	−22.9014	+	59.5627i	−0.779121	+	2.02636i
$865$	−0.251007	−	36.8520i	−0.00853449	−	1.25301i
$866$	0.180131	+	0.733707i	0.00612109	+	0.0249324i
$867$	7.46252			0.253441
$868$	−0.767852	−	1.46955i	−0.0260626	−	0.0498797i
$869$			38.9024i			1.31967i
$870$	−26.6874	+	6.74502i	−0.904788	+	0.228677i
$871$	22.5016			0.762439
$872$	−28.0433	−	31.8299i	−0.949666	−	1.07790i
$873$		−	5.26560i		−	0.178214i
$874$	11.7152	−	2.87617i	0.396273	−	0.0972879i
$875$	11.1780	−	0.228436i	0.377886	−	0.00772254i
$876$	6.60759	+	12.6459i	0.223250	+	0.427265i
$877$	−15.6288			−0.527746			−0.263873	−	0.964557i	$-0.585000\pi$
$877$	−15.6288			−0.527746			−0.263873	+	0.964557i	$0.585000\pi$
$878$	35.3111	−	8.66914i	1.19169	−	0.292569i
$879$	3.83447			0.129333
$880$	−26.2185	+	38.2412i	−0.883825	+	1.28911i
$881$	10.5860			0.356650			0.178325	−	0.983972i	$-0.442932\pi$
$881$	10.5860			0.356650			0.178325	+	0.983972i	$0.442932\pi$
$882$	−9.11181	+	2.23702i	−0.306811	+	0.0753243i
$883$	−34.6354			−1.16557			−0.582787	−	0.812625i	$-0.698038\pi$
$883$	−34.6354			−1.16557			−0.582787	+	0.812625i	$0.698038\pi$
$884$	13.7786	+	26.3700i	0.463423	+	0.886920i
$885$	−60.3826	+	0.411279i	−2.02974	+	0.0138250i
$886$	−45.2643	+	11.1127i	−1.52068	+	0.373339i
$887$		−	52.0583i		−	1.74795i	−0.485973	−	0.873974i	$-0.661535\pi$
$887$		−	52.0583i		−	1.74795i	0.485973	−	0.873974i	$-0.338465\pi$
$888$	48.1941	−	42.4607i	1.61729	−	1.42489i
$889$	−5.49873			−0.184421
$890$	5.63195	+	22.2834i	0.188783	+	0.746942i
$891$			78.3367i			2.62438i
$892$	−15.7873	−	30.2144i	−0.528597	−	1.01165i
$893$	−12.1413			−0.406294
$894$	−11.4914	−	46.8066i	−0.384329	−	1.56545i
$895$	−44.0457	+	0.300005i	−1.47229	+	0.0100281i
$896$	11.2397	−	1.29176i	0.375493	−	0.0431546i
$897$		−	24.5518i		−	0.819759i
$898$	−18.4052	+	4.51861i	−0.614189	+	0.150788i
$899$			2.32494i			0.0775412i
$900$	−58.3767	+	31.5220i	−1.94589	+	1.05073i
$901$		−	3.79394i		−	0.126395i
$902$	8.26532	+	33.6663i	0.275205	+	1.12096i
$903$		−	13.4839i		−	0.448715i
$904$	−26.8222	−	30.4439i	−0.892093	−	1.01255i
$905$	20.0316	−	0.136439i	0.665872	−	0.00453540i
$906$	−1.22686	+	0.301203i	−0.0407596	+	0.0100068i
$907$	−7.85182			−0.260715			−0.130358	−	0.991467i	$-0.541613\pi$
$907$	−7.85182			−0.260715			−0.130358	+	0.991467i	$0.541613\pi$
$908$	−0.447452	+	0.233798i	−0.0148492	+	0.00775885i
$909$			108.475i			3.59787i
$910$	−10.3539	+	2.61685i	−0.343228	+	0.0867479i
$911$	−6.43493			−0.213199			−0.106599	−	0.994302i	$-0.533996\pi$
$911$	−6.43493			−0.213199			−0.106599	+	0.994302i	$0.533996\pi$
$912$	37.1179	+	25.8217i	1.22910	+	0.855042i
$913$			53.5329i			1.77168i
$914$	4.69431	+	19.1208i	0.155274	+	0.632461i
$915$	−26.6007	+	0.181183i	−0.879391	+	0.00598972i
$916$	−11.4537	−	21.9206i	−0.378442	−	0.724278i
$917$	14.8009			0.488769
$918$	−16.7555	−	68.2485i	−0.553014	−	2.25254i
$919$	2.00694			0.0662028			0.0331014	−	0.999452i	$-0.489462\pi$
$919$	2.00694			0.0662028			0.0331014	+	0.999452i	$0.489462\pi$
$920$	−11.0479	+	9.86804i	−0.364238	+	0.325340i
$921$	39.3195			1.29562
$922$	−0.118824	−	0.483993i	−0.00391326	−	0.0159394i
$923$	−45.8180			−1.50812
$924$	28.5219	−	14.9029i	0.938302	−	0.490271i
$925$	36.5776	−	0.498300i	1.20267	−	0.0163840i
$926$	−9.57015	−	38.9811i	−0.314495	−	1.28100i
$927$			2.69077i			0.0883764i
$928$	−14.8073	−	5.69330i	−0.486074	−	0.186892i
$929$	38.3180			1.25717			0.628587	−	0.777740i	$-0.283634\pi$
$929$	38.3180			1.25717			0.628587	+	0.777740i	$0.283634\pi$
$930$	1.99394	+	7.88926i	0.0653840	+	0.258699i
$931$			3.64185i			0.119357i
$932$	4.98819	+	9.54661i	0.163394	+	0.312710i
$933$	47.7035			1.56174
$934$	18.8757	−	4.63412i	0.617631	−	0.151633i
$935$	−0.347778	−	51.0596i	−0.0113736	−	1.66983i
$936$	47.5493	−	41.8926i	1.55420	−	1.36930i
$937$			20.9563i			0.684613i	0.939588	+	0.342306i	$0.111208\pi$
$937$			20.9563i			0.684613i	−0.939588	+	0.342306i	$0.888792\pi$
$938$	2.24665	+	9.15105i	0.0733558	+	0.298792i
$939$			16.7881i			0.547858i
$940$	13.1669	−	6.99441i	0.429458	−	0.228133i
$941$			39.1317i			1.27566i	0.770179	+	0.637828i	$0.220167\pi$
$941$			39.1317i			1.27566i	−0.770179	+	0.637828i	$0.779833\pi$
$942$	95.3188	−	23.4015i	3.10566	−	0.762462i
$943$			11.0753i			0.360662i
$944$	−28.5677	−	19.8736i	−0.929800	−	0.646831i
$945$	25.2240	−	0.171806i	0.820537	−	0.00558885i
$946$	7.59326	+	30.9288i	0.246878	+	1.00558i
$947$	−58.5981			−1.90418			−0.952092	−	0.305813i	$-0.901072\pi$
$947$	−58.5981			−1.90418			−0.952092	+	0.305813i	$0.901072\pi$
$948$	−41.2901	+	21.5745i	−1.34104	+	0.700706i
$949$		−	7.76201i		−	0.251966i
$950$	6.48002	+	24.9231i	0.210240	+	0.808613i
$951$	2.93873			0.0952950
$952$	−9.34855	+	8.23640i	−0.302988	+	0.266943i
$953$		−	14.2681i		−	0.462191i	−0.972931	−	0.231095i	$-0.925769\pi$
$953$		−	14.2681i		−	0.462191i	0.972931	−	0.231095i	$-0.0742309\pi$
$954$	−7.84779	+	1.92669i	−0.254082	+	0.0623789i
$955$	−0.0830854	−	12.1983i	−0.00268858	−	0.394728i
$956$	8.20018	−	4.28467i	0.265213	−	0.138576i
$957$	−45.1239			−1.45865
$958$	−10.7045	+	2.62804i	−0.345847	+	0.0849080i
$959$	4.98693			0.161036
$960$	−55.1287	−	6.61992i	−1.77927	−	0.213657i
$961$	−30.3127			−0.977829
$962$	−33.9345	+	8.33117i	−1.09409	+	0.268608i
$963$	104.237			3.35901
$964$	−5.38152	+	2.81189i	−0.173327	+	0.0905649i
$965$	46.9616	−	0.319865i	1.51175	−	0.0102968i
$966$	9.98480	−	2.45134i	0.321256	−	0.0788707i
$967$			35.2254i			1.13277i	0.824140	+	0.566386i	$0.191659\pi$
$967$			35.2254i			1.13277i	−0.824140	+	0.566386i	$0.808341\pi$
$968$	−33.6854	+	29.6780i	−1.08269	+	0.953888i
$969$	−49.7945			−1.59963
$970$	2.43334	−	0.615006i	0.0781299	−	0.0197467i
$971$		−	29.7498i		−	0.954715i	−0.878709	−	0.477358i	$-0.841595\pi$
$971$		−	29.7498i		−	0.954715i	0.878709	−	0.477358i	$-0.158405\pi$
$972$	−23.1557	+	12.0990i	−0.742718	+	0.388077i
$973$	−7.27185			−0.233125
$974$	0.256385	+	1.04431i	0.00821512	+	0.0334618i
$975$	52.4071	−	0.713945i	1.67837	−	0.0228646i
$976$	−12.5851	−	8.75503i	−0.402839	−	0.280242i
$977$			9.93339i			0.317797i	0.987295	+	0.158899i	$0.0507943\pi$
$977$			9.93339i			0.317797i	−0.987295	+	0.158899i	$0.949206\pi$
$978$	37.1151	−	9.11203i	1.18681	−	0.291370i
$979$			37.6775i			1.20418i
$980$	−2.09800	−	3.94948i	−0.0670183	−	0.126161i
$981$		−	99.5035i		−	3.17690i
$982$	−10.1002	−	41.1400i	−0.322310	−	1.31283i
$983$			31.7247i			1.01186i	0.862575	+	0.505930i	$0.168850\pi$
$983$			31.7247i			1.01186i	−0.862575	+	0.505930i	$0.831150\pi$
$984$	−31.1489	+	27.4433i	−0.992990	+	0.874859i
$985$	0.272931	+	40.0708i	0.00869631	+	1.27676i
$986$	16.9666	−	4.16543i	0.540327	−	0.132654i
$987$	−10.3480			−0.329380
$988$	−11.3914	−	21.8014i	−0.362409	−	0.693595i
$989$			10.1748i			0.323539i
$990$	−105.440	+	26.6492i	−3.35112	+	0.846966i
$991$	−19.2232			−0.610647			−0.305323	−	0.952249i	$-0.598765\pi$
$991$	−19.2232			−0.610647			−0.305323	+	0.952249i	$0.598765\pi$
$992$	−1.68304	+	4.37730i	−0.0534365	+	0.138979i
$993$		−	59.9841i		−	1.90354i
$994$	−4.57465	−	18.6335i	−0.145099	−	0.591017i
$995$	−0.114340	−	16.7870i	−0.00362481	−	0.532183i
$996$	−56.8187	+	29.6882i	−1.80037	+	0.940708i
$997$	7.11548			0.225350			0.112675	−	0.993632i	$-0.464058\pi$
$997$	7.11548			0.225350			0.112675	+	0.993632i	$0.464058\pi$
$998$	0.344444	+	1.40299i	0.0109032	+	0.0444108i
$999$	82.5325			2.61121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.l.a.29.33	yes	36
4.3	odd	2		1120.2.l.a.1009.35		36
5.4	even	2	inner	280.2.l.a.29.4	yes	36
8.3	odd	2		1120.2.l.a.1009.2		36
8.5	even	2	inner	280.2.l.a.29.3	✓	36
20.19	odd	2		1120.2.l.a.1009.1		36
40.19	odd	2		1120.2.l.a.1009.36		36
40.29	even	2	inner	280.2.l.a.29.34	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.l.a.29.3	✓	36	8.5	even	2	inner
280.2.l.a.29.4	yes	36	5.4	even	2	inner
280.2.l.a.29.33	yes	36	1.1	even	1	trivial
280.2.l.a.29.34	yes	36	40.29	even	2	inner
1120.2.l.a.1009.1		36	20.19	odd	2
1120.2.l.a.1009.2		36	8.3	odd	2
1120.2.l.a.1009.35		36	4.3	odd	2
1120.2.l.a.1009.36		36	40.19	odd	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37343 - 0.337187i) q^{2} -3.10393 q^{3} +(1.77261 - 0.926204i) q^{4} +(0.0152300 + 2.23602i) q^{5} +(-4.26302 + 1.04660i) q^{6} +1.00000i q^{7} +(2.12225 - 1.86978i) q^{8} +6.63436 q^{9} +O(q^{10})\)	\(q+(1.37343 - 0.337187i) q^{2} -3.10393 q^{3} +(1.77261 - 0.926204i) q^{4} +(0.0152300 + 2.23602i) q^{5} +(-4.26302 + 1.04660i) q^{6} +1.00000i q^{7} +(2.12225 - 1.86978i) q^{8} +6.63436 q^{9} +(0.774873 + 3.06587i) q^{10} +5.18387i q^{11} +(-5.50205 + 2.87487i) q^{12} +3.37714 q^{13} +(0.337187 + 1.37343i) q^{14} +(-0.0472728 - 6.94043i) q^{15} +(2.28429 - 3.28360i) q^{16} +4.40502i q^{17} +(9.11181 - 2.23702i) q^{18} -3.64185i q^{19} +(2.09800 + 3.94948i) q^{20} -3.10393i q^{21} +(1.74793 + 7.11967i) q^{22} +2.34219i q^{23} +(-6.58730 + 5.80365i) q^{24} +(-4.99954 + 0.0681090i) q^{25} +(4.63826 - 1.13873i) q^{26} -11.2808 q^{27} +(0.926204 + 1.77261i) q^{28} -2.80441i q^{29} +(-2.40515 - 9.51624i) q^{30} -0.829031 q^{31} +(2.03012 - 5.28002i) q^{32} -16.0903i q^{33} +(1.48532 + 6.04998i) q^{34} +(-2.23602 + 0.0152300i) q^{35} +(11.7601 - 6.14477i) q^{36} -7.31621 q^{37} +(-1.22798 - 5.00182i) q^{38} -10.4824 q^{39} +(4.21317 + 4.71690i) q^{40} +4.72862 q^{41} +(-1.04660 - 4.26302i) q^{42} +4.34414 q^{43} +(4.80132 + 9.18898i) q^{44} +(0.101041 + 14.8345i) q^{45} +(0.789756 + 3.21683i) q^{46} -3.33384i q^{47} +(-7.09027 + 10.1920i) q^{48} -1.00000 q^{49} +(-6.84354 + 1.77932i) q^{50} -13.6729i q^{51} +(5.98635 - 3.12792i) q^{52} -0.861277 q^{53} +(-15.4933 + 3.80373i) q^{54} +(-11.5912 + 0.0789503i) q^{55} +(1.86978 + 2.12225i) q^{56} +11.3040i q^{57} +(-0.945610 - 3.85165i) q^{58} -8.70012i q^{59} +(-6.51205 - 12.2589i) q^{60} -3.83271i q^{61} +(-1.13861 + 0.279539i) q^{62} +6.63436i q^{63} +(1.00788 - 7.93626i) q^{64} +(0.0514338 + 7.55134i) q^{65} +(-5.42546 - 22.0989i) q^{66} +6.66292 q^{67} +(4.07995 + 7.80839i) q^{68} -7.26998i q^{69} +(-3.06587 + 0.774873i) q^{70} -13.5671 q^{71} +(14.0798 - 12.4048i) q^{72} -2.29840i q^{73} +(-10.0483 + 2.46693i) q^{74} +(15.5182 - 0.211405i) q^{75} +(-3.37310 - 6.45558i) q^{76} -5.18387 q^{77} +(-14.3968 + 3.53453i) q^{78} +7.50450 q^{79} +(7.37697 + 5.05770i) q^{80} +15.1116 q^{81} +(6.49442 - 1.59443i) q^{82} +10.3268 q^{83} +(-2.87487 - 5.50205i) q^{84} +(-9.84970 + 0.0670885i) q^{85} +(5.96636 - 1.46479i) q^{86} +8.70467i q^{87} +(9.69268 + 11.0015i) q^{88} +7.26822 q^{89} +(5.14078 + 20.3401i) q^{90} +3.37714i q^{91} +(2.16935 + 4.15179i) q^{92} +2.57325 q^{93} +(-1.12413 - 4.57879i) q^{94} +(8.14323 - 0.0554653i) q^{95} +(-6.30135 + 16.3888i) q^{96} -0.793686i q^{97} +(-1.37343 + 0.337187i) q^{98} +34.3916i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Introduction

L-functions

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