LMFDB - Embedded newform 680.2.l.b.101.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(101,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.10
Character	$\chi$	$=$	680.101
Dual form			680.2.l.b.101.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.985753 + 1.01405i) q^{2} +1.46409 q^{3} +(-0.0565822 - 1.99920i) q^{4} -1.00000 q^{5} +(-1.44323 + 1.48466i) q^{6} +1.02762i q^{7} +(2.08306 + 1.91334i) q^{8} -0.856436 q^{9} +(0.985753 - 1.01405i) q^{10} +0.737326 q^{11} +(-0.0828415 - 2.92701i) q^{12} +4.98026i q^{13} +(-1.04205 - 1.01298i) q^{14} -1.46409 q^{15} +(-3.99360 + 0.226238i) q^{16} +(3.59849 + 2.01268i) q^{17} +(0.844234 - 0.868466i) q^{18} -2.82434i q^{19} +(0.0565822 + 1.99920i) q^{20} +1.50452i q^{21} +(-0.726822 + 0.747684i) q^{22} +4.95563i q^{23} +(3.04979 + 2.80130i) q^{24} +1.00000 q^{25} +(-5.05022 - 4.90931i) q^{26} -5.64618 q^{27} +(2.05441 - 0.0581448i) q^{28} +4.86957 q^{29} +(1.44323 - 1.48466i) q^{30} +7.67421i q^{31} +(3.70728 - 4.27271i) q^{32} +1.07951 q^{33} +(-5.58817 + 1.66503i) q^{34} -1.02762i q^{35} +(0.0484591 + 1.71219i) q^{36} -3.22579 q^{37} +(2.86402 + 2.78410i) q^{38} +7.29156i q^{39} +(-2.08306 - 1.91334i) q^{40} +4.45258i q^{41} +(-1.52566 - 1.48309i) q^{42} +5.96478i q^{43} +(-0.0417196 - 1.47406i) q^{44} +0.856436 q^{45} +(-5.02524 - 4.88502i) q^{46} +11.3771 q^{47} +(-5.84699 + 0.331234i) q^{48} +5.94401 q^{49} +(-0.985753 + 1.01405i) q^{50} +(5.26852 + 2.94675i) q^{51} +(9.95654 - 0.281794i) q^{52} +0.0517813i q^{53} +(5.56573 - 5.72549i) q^{54} -0.737326 q^{55} +(-1.96618 + 2.14058i) q^{56} -4.13510i q^{57} +(-4.80019 + 4.93797i) q^{58} -6.48292i q^{59} +(0.0828415 + 2.92701i) q^{60} -14.4629 q^{61} +(-7.78201 - 7.56487i) q^{62} -0.880087i q^{63} +(0.678262 + 7.97120i) q^{64} -4.98026i q^{65} +(-1.06413 + 1.09468i) q^{66} -4.56989i q^{67} +(3.82013 - 7.30798i) q^{68} +7.25549i q^{69} +(1.04205 + 1.01298i) q^{70} +12.9933i q^{71} +(-1.78401 - 1.63865i) q^{72} -0.800933i q^{73} +(3.17983 - 3.27110i) q^{74} +1.46409 q^{75} +(-5.64642 + 0.159808i) q^{76} +0.757688i q^{77} +(-7.39399 - 7.18768i) q^{78} -7.83068i q^{79} +(3.99360 - 0.226238i) q^{80} -5.69721 q^{81} +(-4.51512 - 4.38914i) q^{82} -10.7517i q^{83} +(3.00784 - 0.0851293i) q^{84} +(-3.59849 - 2.01268i) q^{85} +(-6.04856 - 5.87980i) q^{86} +7.12949 q^{87} +(1.53589 + 1.41076i) q^{88} -6.70231 q^{89} +(-0.844234 + 0.868466i) q^{90} -5.11780 q^{91} +(9.90729 - 0.280400i) q^{92} +11.2357i q^{93} +(-11.2150 + 11.5369i) q^{94} +2.82434i q^{95} +(5.42780 - 6.25564i) q^{96} +7.53723i q^{97} +(-5.85932 + 6.02750i) q^{98} -0.631473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 2 q^{4} - 36 q^{5} + 36 q^{9} + 8 q^{11} + 2 q^{12} - 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} - 2 q^{20} - 26 q^{24} + 36 q^{25} + 6 q^{26} + 16 q^{27} - 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots + 40 q^{99}+O(q^{100}) $ 36 * q + 4 * q^3 + 2 * q^4 - 36 * q^5 + 36 * q^9 + 8 * q^11 + 2 * q^12 - 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 - 2 * q^20 - 26 * q^24 + 36 * q^25 + 6 * q^26 + 16 * q^27 - 14 * q^28 - 10 * q^32 - 8 * q^33 + 12 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 - 6 * q^44 - 36 * q^45 - 24 * q^46 + 20 * q^47 + 4 * q^48 - 36 * q^49 + 6 * q^52 + 56 * q^54 - 8 * q^55 - 20 * q^56 + 18 * q^58 - 2 * q^60 + 24 * q^62 + 14 * q^64 - 16 * q^66 + 16 * q^68 + 2 * q^70 - 54 * q^72 - 6 * q^74 + 4 * q^75 + 2 * q^76 + 14 * q^78 - 6 * q^80 + 44 * q^81 - 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 + 58 * q^88 + 10 * q^90 + 56 * q^91 + 12 * q^92 + 14 * q^94 + 24 * q^96 + 10 * q^98 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−0.985753	+	1.01405i	−0.697033	+	0.717039i
$2$	−0.985753	+	1.01405i	−0.697033	+	0.717039i
$3$	1.46409			0.845294			0.422647	−	0.906294i	$-0.361101\pi$
$3$	1.46409			0.845294			0.422647	+	0.906294i	$0.361101\pi$
$4$	−0.0565822	−	1.99920i	−0.0282911	−	0.999600i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.44323	+	1.48466i	−0.589197	+	0.606109i
$7$			1.02762i			0.388402i	0.980962	+	0.194201i	$0.0622114\pi$
$7$			1.02762i			0.388402i	−0.980962	+	0.194201i	$0.937789\pi$
$8$	2.08306	+	1.91334i	0.736472	+	0.676468i
$9$	−0.856436			−0.285479
$10$	0.985753	−	1.01405i	0.311722	−	0.320670i
$11$	0.737326			0.222312			0.111156	−	0.993803i	$-0.464545\pi$
$11$	0.737326			0.222312			0.111156	+	0.993803i	$0.464545\pi$
$12$	−0.0828415	−	2.92701i	−0.0239143	−	0.844955i
$13$			4.98026i			1.38128i	0.723200	+	0.690638i	$0.242670\pi$
$13$			4.98026i			1.38128i	−0.723200	+	0.690638i	$0.757330\pi$
$14$	−1.04205	−	1.01298i	−0.278500	−	0.270729i
$15$	−1.46409			−0.378027
$16$	−3.99360	+	0.226238i	−0.998399	+	0.0565596i
$17$	3.59849	+	2.01268i	0.872762	+	0.488146i
$17$	3.59849	+	2.01268i	0.872762	+	0.488146i
$18$	0.844234	−	0.868466i	0.198988	−	0.204699i
$19$		−	2.82434i		−	0.647949i	−0.946066	−	0.323974i	$-0.894981\pi$
$19$		−	2.82434i		−	0.647949i	0.946066	−	0.323974i	$-0.105019\pi$
$20$	0.0565822	+	1.99920i	0.0126522	+	0.447035i
$21$			1.50452i			0.328314i
$22$	−0.726822	+	0.747684i	−0.154959	+	0.159407i
$23$			4.95563i			1.03332i	0.856191	+	0.516660i	$0.172825\pi$
$23$			4.95563i			1.03332i	−0.856191	+	0.516660i	$0.827175\pi$
$24$	3.04979	+	2.80130i	0.622535	+	0.571814i
$25$	1.00000			0.200000
$26$	−5.05022	−	4.90931i	−0.990430	−	0.962795i
$27$	−5.64618			−1.08661
$28$	2.05441	−	0.0581448i	0.388247	−	0.0109883i
$29$	4.86957			0.904256			0.452128	−	0.891953i	$-0.350665\pi$
$29$	4.86957			0.904256			0.452128	+	0.891953i	$0.350665\pi$
$30$	1.44323	−	1.48466i	0.263497	−	0.271060i
$31$			7.67421i			1.37833i	0.724605	+	0.689164i	$0.242022\pi$
$31$			7.67421i			1.37833i	−0.724605	+	0.689164i	$0.757978\pi$
$32$	3.70728	−	4.27271i	0.655361	−	0.755315i
$33$	1.07951			0.187919
$34$	−5.58817	+	1.66503i	−0.958364	+	0.285551i
$35$		−	1.02762i		−	0.173699i
$36$	0.0484591	+	1.71219i	0.00807651	+	0.285364i
$37$	−3.22579			−0.530316			−0.265158	−	0.964205i	$-0.585424\pi$
$37$	−3.22579			−0.530316			−0.265158	+	0.964205i	$0.585424\pi$
$38$	2.86402	+	2.78410i	0.464605	+	0.451641i
$39$			7.29156i			1.16758i
$40$	−2.08306	−	1.91334i	−0.329360	−	0.302526i
$41$			4.45258i			0.695376i	0.937610	+	0.347688i	$0.113033\pi$
$41$			4.45258i			0.695376i	−0.937610	+	0.347688i	$0.886967\pi$
$42$	−1.52566	−	1.48309i	−0.235414	−	0.228846i
$43$			5.96478i			0.909620i	0.890588	+	0.454810i	$0.150293\pi$
$43$			5.96478i			0.909620i	−0.890588	+	0.454810i	$0.849707\pi$
$44$	−0.0417196	−	1.47406i	−0.00628946	−	0.222223i
$45$	0.856436			0.127670
$46$	−5.02524	−	4.88502i	−0.740931	−	0.720258i
$47$	11.3771			1.65952			0.829761	−	0.558119i	$-0.188477\pi$
$47$	11.3771			1.65952			0.829761	+	0.558119i	$0.188477\pi$
$48$	−5.84699	+	0.331234i	−0.843940	+	0.0478094i
$49$	5.94401			0.849144
$50$	−0.985753	+	1.01405i	−0.139407	+	0.143408i
$51$	5.26852	+	2.94675i	0.737740	+	0.412627i
$52$	9.95654	−	0.281794i	1.38072	−	0.0390778i
$53$			0.0517813i			0.00711271i	0.999994	+	0.00355636i	$0.00113203\pi$
$53$			0.0517813i			0.00711271i	−0.999994	+	0.00355636i	$0.998868\pi$
$54$	5.56573	−	5.72549i	0.757400	−	0.779140i
$55$	−0.737326			−0.0994211
$56$	−1.96618	+	2.14058i	−0.262742	+	0.286047i
$57$		−	4.13510i		−	0.547707i
$58$	−4.80019	+	4.93797i	−0.630296	+	0.648387i
$59$		−	6.48292i		−	0.844005i	−0.906595	−	0.422002i	$-0.861327\pi$
$59$		−	6.48292i		−	0.844005i	0.906595	−	0.422002i	$-0.138673\pi$
$60$	0.0828415	+	2.92701i	0.0106948	+	0.377875i
$61$	−14.4629			−1.85178			−0.925890	−	0.377792i	$-0.876683\pi$
$61$	−14.4629			−1.85178			−0.925890	+	0.377792i	$0.876683\pi$
$62$	−7.78201	−	7.56487i	−0.988316	−	0.960740i
$63$		−	0.880087i		−	0.110881i
$64$	0.678262	+	7.97120i	0.0847827	+	0.996399i
$65$		−	4.98026i		−	0.617726i
$66$	−1.06413	+	1.09468i	−0.130986	+	0.134745i
$67$		−	4.56989i		−	0.558301i	−0.960247	−	0.279150i	$-0.909947\pi$
$67$		−	4.56989i		−	0.558301i	0.960247	−	0.279150i	$-0.0900528\pi$
$68$	3.82013	−	7.30798i	0.463259	−	0.886223i
$69$			7.25549i			0.873459i
$70$	1.04205	+	1.01298i	0.124549	+	0.121074i
$71$			12.9933i			1.54202i	0.636822	+	0.771010i	$0.280248\pi$
$71$			12.9933i			1.54202i	−0.636822	+	0.771010i	$0.719752\pi$
$72$	−1.78401	−	1.63865i	−0.210247	−	0.193117i
$73$		−	0.800933i		−	0.0937421i	−0.998901	−	0.0468710i	$-0.985075\pi$
$73$		−	0.800933i		−	0.0937421i	0.998901	−	0.0468710i	$-0.0149250\pi$
$74$	3.17983	−	3.27110i	0.369648	−	0.380258i
$75$	1.46409			0.169059
$76$	−5.64642	+	0.159808i	−0.647689	+	0.0183312i
$77$			0.757688i			0.0863466i
$78$	−7.39399	−	7.18768i	−0.837204	−	0.813844i
$79$		−	7.83068i		−	0.881020i	−0.897748	−	0.440510i	$-0.854798\pi$
$79$		−	7.83068i		−	0.881020i	0.897748	−	0.440510i	$-0.145202\pi$
$80$	3.99360	−	0.226238i	0.446498	−	0.0252942i
$81$	−5.69721			−0.633023
$82$	−4.51512	−	4.38914i	−0.498612	−	0.484700i
$83$		−	10.7517i		−	1.18016i	−0.807346	−	0.590078i	$-0.799097\pi$
$83$		−	10.7517i		−	1.18016i	0.807346	−	0.590078i	$-0.200903\pi$
$84$	3.00784	−	0.0851293i	0.328183	−	0.00928836i
$85$	−3.59849	−	2.01268i	−0.390311	−	0.218306i
$86$	−6.04856	−	5.87980i	−0.652233	−	0.634035i
$87$	7.12949			0.764362
$88$	1.53589	+	1.41076i	0.163727	+	0.150387i
$89$	−6.70231			−0.710443			−0.355222	−	0.934782i	$-0.615595\pi$
$89$	−6.70231			−0.710443			−0.355222	+	0.934782i	$0.615595\pi$
$90$	−0.844234	+	0.868466i	−0.0889901	+	0.0915444i
$91$	−5.11780			−0.536491
$92$	9.90729	−	0.280400i	1.03291	−	0.0292338i
$93$			11.2357i			1.16509i
$94$	−11.2150	+	11.5369i	−1.15674	+	1.18994i
$95$			2.82434i			0.289771i
$96$	5.42780	−	6.25564i	0.553973	−	0.638463i
$97$			7.53723i			0.765289i	0.923896	+	0.382645i	$0.124987\pi$
$97$			7.53723i			0.765289i	−0.923896	+	0.382645i	$0.875013\pi$
$98$	−5.85932	+	6.02750i	−0.591881	+	0.608870i
$99$	−0.631473			−0.0634654
$100$	−0.0565822	−	1.99920i	−0.00565822	−	0.199920i
$101$		−	1.99652i		−	0.198662i	−0.995054	−	0.0993308i	$-0.968330\pi$
$101$		−	1.99652i		−	0.198662i	0.995054	−	0.0993308i	$-0.0316702\pi$
$102$	−8.18159	+	2.43776i	−0.810099	+	0.241374i
$103$	1.44810			0.142685			0.0713426	−	0.997452i	$-0.477272\pi$
$103$	1.44810			0.142685			0.0713426	+	0.997452i	$0.477272\pi$
$104$	−9.52894	+	10.3742i	−0.934389	+	1.01727i
$105$		−	1.50452i		−	0.146826i
$106$	−0.0525087	−	0.0510436i	−0.00510010	−	0.00495779i
$107$	4.74210			0.458436			0.229218	−	0.973375i	$-0.426383\pi$
$107$	4.74210			0.458436			0.229218	+	0.973375i	$0.426383\pi$
$108$	0.319473	+	11.2878i	0.0307413	+	1.08617i
$109$	−18.6027			−1.78182			−0.890910	−	0.454180i	$-0.849932\pi$
$109$	−18.6027			−1.78182			−0.890910	+	0.454180i	$0.849932\pi$
$110$	0.726822	−	0.747684i	0.0692997	−	0.0712888i
$111$	−4.72285			−0.448273
$112$	−0.232486	−	4.10388i	−0.0219679	−	0.387781i
$113$		−	13.6404i		−	1.28319i	−0.767046	−	0.641593i	$-0.778274\pi$
$113$		−	13.6404i		−	1.28319i	0.767046	−	0.641593i	$-0.221726\pi$
$114$	4.19318	+	4.07618i	0.392727	+	0.381769i
$115$		−	4.95563i		−	0.462115i
$116$	−0.275531	−	9.73524i	−0.0255824	−	0.903894i
$117$		−	4.26528i		−	0.394325i
$118$	6.57399	+	6.39056i	0.605185	+	0.588299i
$119$	−2.06826	+	3.69786i	−0.189597	+	0.338983i
$120$	−3.04979	−	2.80130i	−0.278406	−	0.255723i
$121$	−10.4563			−0.950577
$122$	14.2568	−	14.6660i	1.29075	−	1.32780i
$123$			6.51898i			0.587797i
$124$	15.3423	−	0.434224i	1.37778	−	0.0389944i
$125$	−1.00000			−0.0894427
$126$	0.892450	+	0.867549i	0.0795057	+	0.0772874i
$127$	−3.25854			−0.289149			−0.144574	−	0.989494i	$-0.546181\pi$
$127$	−3.25854			−0.289149			−0.144574	+	0.989494i	$0.546181\pi$
$128$	−8.75176	−	7.16984i	−0.773554	−	0.633730i
$129$			8.73298i			0.768896i
$130$	5.05022	+	4.90931i	0.442934	+	0.430575i
$131$	19.1586			1.67390			0.836949	−	0.547282i	$-0.184337\pi$
$131$	19.1586			1.67390			0.836949	+	0.547282i	$0.184337\pi$
$132$	−0.0610813	−	2.15816i	−0.00531644	−	0.187844i
$133$	2.90234			0.251665
$134$	4.63408	+	4.50478i	0.400324	+	0.389154i
$135$	5.64618			0.485945
$136$	3.64493	+	11.0777i	0.312550	+	0.949901i
$137$	12.0129			1.02633			0.513164	−	0.858291i	$-0.328473\pi$
$137$	12.0129			1.02633			0.513164	+	0.858291i	$0.328473\pi$
$138$	−7.35741	−	7.15212i	−0.626304	−	0.608829i
$139$	8.85801			0.751326			0.375663	−	0.926756i	$-0.377415\pi$
$139$	8.85801			0.751326			0.375663	+	0.926756i	$0.377415\pi$
$140$	−2.05441	+	0.0581448i	−0.173629	+	0.00491413i
$141$	16.6571			1.40278
$142$	−13.1758	−	12.8082i	−1.10569	−	1.07484i
$143$			3.67208i			0.307075i
$144$	3.42026	−	0.193759i	0.285022	−	0.0161466i
$145$	−4.86957			−0.404396
$146$	0.812183	+	0.789522i	0.0672168	+	0.0653413i
$147$	8.70257			0.717776
$148$	0.182522	+	6.44899i	0.0150032	+	0.530104i
$149$		−	22.3957i		−	1.83472i	−0.398055	−	0.917362i	$-0.630315\pi$
$149$		−	22.3957i		−	1.83472i	0.398055	−	0.917362i	$-0.369685\pi$
$150$	−1.44323	+	1.48466i	−0.117839	+	0.121222i
$151$	15.4701			1.25894			0.629469	−	0.777025i	$-0.283272\pi$
$151$	15.4701			1.25894			0.629469	+	0.777025i	$0.283272\pi$
$152$	5.40393	−	5.88327i	0.438316	−	0.477196i
$153$	−3.08188	−	1.72373i	−0.249155	−	0.139355i
$154$	−0.768331	−	0.746893i	−0.0619139	−	0.0601864i
$155$		−	7.67421i		−	0.616407i
$156$	14.5773	−	0.412573i	1.16712	−	0.0330323i
$157$		−	11.0348i		−	0.880670i	−0.897833	−	0.440335i	$-0.854860\pi$
$157$		−	11.0348i		−	0.880670i	0.897833	−	0.440335i	$-0.145140\pi$
$158$	7.94068	+	7.71912i	0.631726	+	0.614100i
$159$			0.0758126i			0.00601233i
$160$	−3.70728	+	4.27271i	−0.293087	+	0.337787i
$161$	−5.09248			−0.401344
$162$	5.61604	−	5.77724i	0.441238	−	0.453903i
$163$	0.320808			0.0251276			0.0125638	−	0.999921i	$-0.496001\pi$
$163$	0.320808			0.0251276			0.0125638	+	0.999921i	$0.496001\pi$
$164$	8.90159	−	0.251937i	0.695098	−	0.0196730i
$165$	−1.07951			−0.0840400
$166$	10.9028	+	10.5986i	0.846219	+	0.822607i
$167$		−	14.3206i		−	1.10816i	−0.832463	−	0.554080i	$-0.813070\pi$
$167$		−	14.3206i		−	1.10816i	0.832463	−	0.554080i	$-0.186930\pi$
$168$	−2.87866	+	3.13401i	−0.222094	+	0.241794i
$169$	−11.8030			−0.907925
$170$	5.58817	−	1.66503i	0.428593	−	0.127702i
$171$			2.41887i			0.184976i
$172$	11.9248	−	0.337500i	0.909256	−	0.0257342i
$173$	17.4844			1.32932			0.664658	−	0.747148i	$-0.268577\pi$
$173$	17.4844			1.32932			0.664658	+	0.747148i	$0.268577\pi$
$174$	−7.02792	+	7.22964i	−0.532785	+	0.548078i
$175$			1.02762i			0.0776805i
$176$	−2.94458	+	0.166811i	−0.221956	+	0.0125739i
$177$		−	9.49159i		−	0.713432i
$178$	6.60682	−	6.79645i	0.495202	−	0.509416i
$179$			10.0384i			0.750308i	0.926962	+	0.375154i	$0.122410\pi$
$179$			10.0384i			0.750308i	−0.926962	+	0.375154i	$0.877590\pi$
$180$	−0.0484591	−	1.71219i	−0.00361192	−	0.127619i
$181$	−7.21688			−0.536427			−0.268213	−	0.963360i	$-0.586433\pi$
$181$	−7.21688			−0.536427			−0.268213	+	0.963360i	$0.586433\pi$
$182$	5.04488	−	5.18969i	0.373952	−	0.384685i
$183$	−21.1750			−1.56530
$184$	−9.48180	+	10.3229i	−0.699008	+	0.761011i
$185$	3.22579			0.237165
$186$	−11.3936	−	11.0757i	−0.835417	−	0.812107i
$187$	2.65326	+	1.48400i	0.194026	+	0.108521i
$188$	−0.643742	−	22.7451i	−0.0469497	−	1.65886i
$189$		−	5.80210i		−	0.422041i
$190$	−2.86402	−	2.78410i	−0.207778	−	0.201980i
$191$	16.2281			1.17423			0.587113	−	0.809505i	$-0.300264\pi$
$191$	16.2281			1.17423			0.587113	+	0.809505i	$0.300264\pi$
$192$	0.993038	+	11.6706i	0.0716663	+	0.842250i
$193$		−	18.4087i		−	1.32509i	−0.749022	−	0.662545i	$-0.769476\pi$
$193$		−	18.4087i		−	1.32509i	0.749022	−	0.662545i	$-0.230524\pi$
$194$	−7.64310	−	7.42984i	−0.548743	−	0.533432i
$195$		−	7.29156i		−	0.522160i
$196$	−0.336325	−	11.8833i	−0.0240232	−	0.848804i
$197$	−1.17821			−0.0839438			−0.0419719	−	0.999119i	$-0.513364\pi$
$197$	−1.17821			−0.0839438			−0.0419719	+	0.999119i	$0.513364\pi$
$198$	0.622476	−	0.640343i	0.0442375	−	0.0455072i
$199$			4.78744i			0.339373i	0.985498	+	0.169686i	$0.0542755\pi$
$199$			4.78744i			0.339373i	−0.985498	+	0.169686i	$0.945725\pi$
$200$	2.08306	+	1.91334i	0.147294	+	0.135294i
$201$		−	6.69073i		−	0.471928i
$202$	2.02457	+	1.96808i	0.142448	+	0.138474i
$203$			5.00405i			0.351215i
$204$	5.59303	−	10.6996i	0.391590	−	0.749118i
$205$		−	4.45258i		−	0.310982i
$206$	−1.42747	+	1.46844i	−0.0994563	+	0.102311i
$207$		−	4.24418i		−	0.294991i
$208$	−1.12673	−	19.8892i	−0.0781244	−	1.37907i
$209$		−	2.08246i		−	0.144047i
$210$	1.52566	+	1.48309i	0.105280	+	0.102343i
$211$	15.1007			1.03958			0.519788	−	0.854295i	$-0.326011\pi$
$211$	15.1007			1.03958			0.519788	+	0.854295i	$0.326011\pi$
$212$	0.103521	−	0.00292990i	0.00710987	−	0.000201227i
$213$			19.0234i			1.30346i
$214$	−4.67454	+	4.80871i	−0.319545	+	0.328717i
$215$		−	5.96478i		−	0.406794i
$216$	−11.7613	−	10.8031i	−0.800256	−	0.735055i
$217$	−7.88614			−0.535346
$218$	18.3377	−	18.8641i	1.24199	−	1.27763i
$219$		−	1.17264i		−	0.0792396i
$220$	0.0417196	+	1.47406i	0.00281273	+	0.0993813i
$221$	−10.0237	+	17.9214i	−0.674265	+	1.20553i
$222$	4.65556	−	4.78919i	0.312461	−	0.321429i
$223$	−9.12247			−0.610886			−0.305443	−	0.952210i	$-0.598805\pi$
$223$	−9.12247			−0.610886			−0.305443	+	0.952210i	$0.598805\pi$
$224$	4.39070	+	3.80966i	0.293366	+	0.254544i
$225$	−0.856436			−0.0570957
$226$	13.8321	+	13.4461i	0.920094	+	0.894422i
$227$	−5.42890			−0.360328			−0.180164	−	0.983637i	$-0.557663\pi$
$227$	−5.42890			−0.360328			−0.180164	+	0.983637i	$0.557663\pi$
$228$	−8.26688	+	0.233973i	−0.547488	+	0.0154952i
$229$			5.57938i			0.368696i	0.982861	+	0.184348i	$0.0590173\pi$
$229$			5.57938i			0.368696i	−0.982861	+	0.184348i	$0.940983\pi$
$230$	5.02524	+	4.88502i	0.331354	+	0.322109i
$231$			1.10932i			0.0729882i
$232$	10.1436	+	9.31714i	0.665960	+	0.611700i
$233$			19.6266i			1.28578i	0.765959	+	0.642889i	$0.222264\pi$
$233$			19.6266i			1.28578i	−0.765959	+	0.642889i	$0.777736\pi$
$234$	4.32519	+	4.20451i	0.282747	+	0.274857i
$235$	−11.3771			−0.742161
$236$	−12.9607	+	0.366818i	−0.843667	+	0.0238778i
$237$		−	11.4648i		−	0.744721i
$238$	−1.71101	−	5.74249i	−0.110909	−	0.372231i
$239$	−1.63097			−0.105499			−0.0527494	−	0.998608i	$-0.516798\pi$
$239$	−1.63097			−0.105499			−0.0527494	+	0.998608i	$0.516798\pi$
$240$	5.84699	−	0.331234i	0.377422	−	0.0213810i
$241$		−	20.9878i		−	1.35194i	−0.736927	−	0.675972i	$-0.763724\pi$
$241$		−	20.9878i		−	1.35194i	0.736927	−	0.675972i	$-0.236276\pi$
$242$	10.3074	−	10.6032i	0.662583	−	0.681601i
$243$	8.59729			0.551516
$244$	0.818341	+	28.9142i	0.0523889	+	1.85104i
$245$	−5.94401			−0.379749
$246$	−6.61055	−	6.42611i	−0.421473	−	0.409714i
$247$	14.0660			0.894996
$248$	−14.6834	+	15.9858i	−0.932395	+	1.01510i
$249$		−	15.7415i		−	0.997579i
$250$	0.985753	−	1.01405i	0.0623445	−	0.0641340i
$251$			7.63860i			0.482144i	0.970507	+	0.241072i	$0.0774990\pi$
$251$			7.63860i			0.482144i	−0.970507	+	0.241072i	$0.922501\pi$
$252$	−1.75947	+	0.0497973i	−0.110836	+	0.00313693i
$253$			3.65392i			0.229720i
$254$	3.21211	−	3.30431i	0.201546	−	0.207331i
$255$	−5.26852	−	2.94675i	−0.329927	−	0.184532i
$256$	15.8976	−	1.80701i	0.993602	−	0.112938i
$257$	1.38861			0.0866189			0.0433095	−	0.999062i	$-0.486210\pi$
$257$	1.38861			0.0866189			0.0433095	+	0.999062i	$0.486210\pi$
$258$	−8.85565	−	8.60856i	−0.551329	−	0.535946i
$259$		−	3.31487i		−	0.205976i
$260$	−9.95654	+	0.281794i	−0.617478	+	0.0174761i
$261$	−4.17048			−0.258146
$262$	−18.8857	+	19.4277i	−1.16676	+	1.20025i
$263$	−12.1867			−0.751464			−0.375732	−	0.926728i	$-0.622609\pi$
$263$	−12.1867			−0.751464			−0.375732	+	0.926728i	$0.622609\pi$
$264$	2.24869	+	2.06548i	0.138397	+	0.127121i
$265$		−	0.0517813i		−	0.00318090i
$266$	−2.86099	+	2.94311i	−0.175418	+	0.180453i
$267$	−9.81279			−0.600533
$268$	−9.13612	+	0.258574i	−0.558077	+	0.0157949i
$269$	−8.53409			−0.520333			−0.260166	−	0.965564i	$-0.583777\pi$
$269$	−8.53409			−0.520333			−0.260166	+	0.965564i	$0.583777\pi$
$270$	−5.56573	+	5.72549i	−0.338720	+	0.348442i
$271$	19.0473			1.15704			0.578522	−	0.815667i	$-0.303630\pi$
$271$	19.0473			1.15704			0.578522	+	0.815667i	$0.303630\pi$
$272$	−14.8263	−	7.22371i	−0.898974	−	0.438002i
$273$	−7.49292			−0.453492
$274$	−11.8417	+	12.1816i	−0.715384	+	0.735918i
$275$	0.737326			0.0444625
$276$	14.5052	−	0.410532i	0.873109	−	0.0247111i
$277$	−3.11221			−0.186994			−0.0934972	−	0.995620i	$-0.529805\pi$
$277$	−3.11221			−0.186994			−0.0934972	+	0.995620i	$0.529805\pi$
$278$	−8.73180	+	8.98243i	−0.523699	+	0.538731i
$279$		−	6.57247i		−	0.393483i
$280$	1.96618	−	2.14058i	0.117502	−	0.127924i
$281$	−28.7935			−1.71767			−0.858837	−	0.512249i	$-0.828813\pi$
$281$	−28.7935			−1.71767			−0.858837	+	0.512249i	$0.828813\pi$
$282$	−16.4198	+	16.8911i	−0.977786	+	1.00585i
$283$	19.7867			1.17620			0.588100	−	0.808788i	$-0.299876\pi$
$283$	19.7867			1.17620			0.588100	+	0.808788i	$0.299876\pi$
$284$	25.9762	−	0.735190i	1.54140	−	0.0436255i
$285$			4.13510i			0.244942i
$286$	−3.72366	−	3.61976i	−0.220185	−	0.214041i
$287$	−4.57554			−0.270086
$288$	−3.17505	+	3.65930i	−0.187092	+	0.215626i
$289$	8.89825	+	14.4852i	0.523427	+	0.852071i
$290$	4.80019	−	4.93797i	0.281877	−	0.289968i
$291$			11.0352i			0.646894i
$292$	−1.60122	+	0.0453186i	−0.0937046	+	0.00265207i
$293$			11.3185i			0.661232i	0.943765	+	0.330616i	$0.107256\pi$
$293$			11.3185i			0.661232i	−0.943765	+	0.330616i	$0.892744\pi$
$294$	−8.57858	+	8.82481i	−0.500313	+	0.514674i
$295$			6.48292i			0.377450i
$296$	−6.71950	−	6.17203i	−0.390563	−	0.358742i
$297$	−4.16307			−0.241566
$298$	22.7102	+	22.0766i	1.31557	+	1.27886i
$299$	−24.6803			−1.42730
$300$	−0.0828415	−	2.92701i	−0.00478286	−	0.168991i
$301$	−6.12950			−0.353298
$302$	−15.2497	+	15.6874i	−0.877521	+	0.902709i
$303$		−	2.92309i		−	0.167927i
$304$	0.638974	+	11.2793i	0.0366477	+	0.646911i
$305$	14.4629			0.828142
$306$	4.78591	−	1.42599i	0.273592	−	0.0815187i
$307$			34.8808i			1.99075i	0.0960443	+	0.995377i	$0.469381\pi$
$307$			34.8808i			1.99075i	−0.0960443	+	0.995377i	$0.530619\pi$
$308$	1.51477	−	0.0428717i	0.0863120	−	0.00244284i
$309$	2.12015			0.120611
$310$	7.78201	+	7.56487i	0.441988	+	0.429656i
$311$		−	28.9283i		−	1.64037i	−0.572096	−	0.820186i	$-0.693870\pi$
$311$		−	28.9283i		−	1.64037i	0.572096	−	0.820186i	$-0.306130\pi$
$312$	−13.9512	+	15.1887i	−0.789833	+	0.859893i
$313$		−	5.33643i		−	0.301633i	−0.988562	−	0.150816i	$-0.951810\pi$
$313$		−	5.33643i		−	0.301633i	0.988562	−	0.150816i	$-0.0481902\pi$
$314$	11.1898	+	10.8776i	0.631475	+	0.613856i
$315$			0.880087i			0.0495873i
$316$	−15.6551	+	0.443077i	−0.880668	+	0.0249250i
$317$	15.5468			0.873195			0.436598	−	0.899657i	$-0.356183\pi$
$317$	15.5468			0.873195			0.436598	+	0.899657i	$0.356183\pi$
$318$	−0.0768776	−	0.0747325i	−0.00431108	−	0.00419079i
$319$	3.59046			0.201027
$320$	−0.678262	−	7.97120i	−0.0379160	−	0.445603i
$321$	6.94286			0.387513
$322$	5.01993	−	5.16401i	0.279750	−	0.287779i
$323$	5.68449	−	10.1634i	0.316294	−	0.565505i
$324$	0.322361	+	11.3899i	0.0179089	+	0.632770i
$325$			4.98026i			0.276255i
$326$	−0.316237	+	0.325314i	−0.0175148	+	0.0180175i
$327$	−27.2361			−1.50616
$328$	−8.51929	+	9.27498i	−0.470399	+	0.512125i
$329$			11.6913i			0.644562i
$330$	1.06413	−	1.09468i	0.0585786	−	0.0602600i
$331$		−	0.824032i		−	0.0452929i	−0.999744	−	0.0226465i	$-0.992791\pi$
$331$		−	0.824032i		−	0.0452929i	0.999744	−	0.0226465i	$-0.00720921\pi$
$332$	−21.4949	+	0.608357i	−1.17968	+	0.0333879i
$333$	2.76268			0.151394
$334$	14.5217	+	14.1166i	0.794595	+	0.772424i
$335$			4.56989i			0.249680i
$336$	−0.340381	−	6.00846i	−0.0185693	−	0.327788i
$337$		−	10.3903i		−	0.565998i	−0.959120	−	0.282999i	$-0.908671\pi$
$337$		−	10.3903i		−	0.565998i	0.959120	−	0.282999i	$-0.0913294\pi$
$338$	11.6349	−	11.9688i	0.632853	−	0.651018i
$339$		−	19.9709i		−	1.08467i
$340$	−3.82013	+	7.30798i	−0.207176	+	0.396331i
$341$			5.65840i			0.306419i
$342$	−2.45285	−	2.38441i	−0.132635	−	0.128934i
$343$			13.3015i			0.718212i
$344$	−11.4126	+	12.4250i	−0.615329	+	0.669910i
$345$		−	7.25549i		−	0.390623i
$346$	−17.2353	+	17.7300i	−0.926576	+	0.953172i
$347$	−8.82570			−0.473789			−0.236894	−	0.971535i	$-0.576129\pi$
$347$	−8.82570			−0.473789			−0.236894	+	0.971535i	$0.576129\pi$
$348$	−0.403403	−	14.2533i	−0.0216246	−	0.764056i
$349$		−	7.74760i		−	0.414720i	−0.978265	−	0.207360i	$-0.933513\pi$
$349$		−	7.74760i		−	0.414720i	0.978265	−	0.207360i	$-0.0664871\pi$
$350$	−1.04205	−	1.01298i	−0.0556999	−	0.0541458i
$351$		−	28.1194i		−	1.50090i
$352$	2.73348	−	3.15038i	0.145695	−	0.167916i
$353$	7.97452			0.424441			0.212221	−	0.977222i	$-0.431930\pi$
$353$	7.97452			0.424441			0.212221	+	0.977222i	$0.431930\pi$
$354$	9.62492	+	9.35636i	0.511559	+	0.497285i
$355$		−	12.9933i		−	0.689613i
$356$	0.379231	+	13.3992i	0.0200992	+	0.710159i
$357$	−3.02812	+	5.41401i	−0.160265	+	0.286540i
$358$	−10.1794	−	9.89542i	−0.538001	−	0.522989i
$359$	−19.2883			−1.01800			−0.508998	−	0.860767i	$-0.669984\pi$
$359$	−19.2883			−1.01800			−0.508998	+	0.860767i	$0.669984\pi$
$360$	1.78401	+	1.63865i	0.0940254	+	0.0863646i
$361$	11.0231			0.580163
$362$	7.11407	−	7.31826i	0.373907	−	0.384639i
$363$	−15.3091			−0.803517
$364$	0.289576	+	10.2315i	0.0151779	+	0.536276i
$365$			0.800933i			0.0419227i
$366$	20.8733	−	21.4724i	1.09106	−	1.12238i
$367$			15.8068i			0.825109i	0.910933	+	0.412555i	$0.135363\pi$
$367$			15.8068i			0.825109i	−0.910933	+	0.412555i	$0.864637\pi$
$368$	−1.12115	−	19.7908i	−0.0584441	−	1.03167i
$369$		−	3.81335i		−	0.198515i
$370$	−3.17983	+	3.27110i	−0.165311	+	0.170056i
$371$	−0.0532113			−0.00276259
$372$	22.4625	−	0.635743i	1.16463	−	0.0329617i
$373$			23.2547i			1.20408i	0.798466	+	0.602040i	$0.205645\pi$
$373$			23.2547i			1.20408i	−0.798466	+	0.602040i	$0.794355\pi$
$374$	−4.12031	+	1.22767i	−0.213056	+	0.0634815i
$375$	−1.46409			−0.0756054
$376$	23.6992	+	21.7683i	1.22219	+	1.12261i
$377$			24.2517i			1.24903i
$378$	5.88360	+	5.71944i	0.302620	+	0.294176i
$379$	−26.7603			−1.37458			−0.687292	−	0.726381i	$-0.741201\pi$
$379$	−26.7603			−1.37458			−0.687292	+	0.726381i	$0.741201\pi$
$380$	5.64642	−	0.159808i	0.289655	−	0.00819795i
$381$	−4.77080			−0.244415
$382$	−15.9969	+	16.4561i	−0.818474	+	0.841966i
$383$	8.46688			0.432638			0.216319	−	0.976323i	$-0.430595\pi$
$383$	8.46688			0.432638			0.216319	+	0.976323i	$0.430595\pi$
$384$	−12.8134	−	10.4973i	−0.653880	−	0.535688i
$385$		−	0.757688i		−	0.0386154i
$386$	18.6673	+	18.1465i	0.950141	+	0.923631i
$387$		−	5.10845i		−	0.259677i
$388$	15.0684	−	0.426473i	0.764983	−	0.0216509i
$389$		−	25.9652i		−	1.31649i	−0.752804	−	0.658245i	$-0.771299\pi$
$389$		−	25.9652i		−	1.31649i	0.752804	−	0.658245i	$-0.228701\pi$
$390$	7.39399	+	7.18768i	0.374409	+	0.363962i
$391$	−9.97408	+	17.8328i	−0.504411	+	0.901842i
$392$	12.3817	+	11.3729i	0.625371	+	0.574418i
$393$	28.0500			1.41493
$394$	1.16142	−	1.19476i	0.0585116	−	0.0601910i
$395$			7.83068i			0.394004i
$396$	0.0357301	+	1.26244i	0.00179551	+	0.0634400i
$397$	−22.6930			−1.13893			−0.569466	−	0.822015i	$-0.692850\pi$
$397$	−22.6930			−1.13893			−0.569466	+	0.822015i	$0.692850\pi$
$398$	−4.85469	−	4.71923i	−0.243344	−	0.236554i
$399$	4.24929			0.212731
$400$	−3.99360	+	0.226238i	−0.199680	+	0.0113119i
$401$			32.7100i			1.63346i	0.577019	+	0.816731i	$0.304216\pi$
$401$			32.7100i			1.63346i	−0.577019	+	0.816731i	$0.695784\pi$
$402$	6.78472	+	6.59541i	0.338391	+	0.328949i
$403$	−38.2196			−1.90385
$404$	−3.99145	+	0.112968i	−0.198582	+	0.00562035i
$405$	5.69721			0.283097
$406$	−5.07434	−	4.93275i	−0.251835	−	0.244808i
$407$	−2.37846			−0.117896
$408$	5.33650	+	16.2187i	0.264196	+	0.802946i
$409$	−25.3481			−1.25338			−0.626691	−	0.779268i	$-0.715591\pi$
$409$	−25.3481			−1.25338			−0.626691	+	0.779268i	$0.715591\pi$
$410$	4.51512	+	4.38914i	0.222986	+	0.216764i
$411$	17.5879			0.867549
$412$	−0.0819366	−	2.89504i	−0.00403672	−	0.142628i
$413$	6.66195			0.327813
$414$	4.30380	+	4.18371i	0.211520	+	0.205618i
$415$			10.7517i			0.527782i
$416$	21.2792	+	18.4633i	1.04330	+	0.905235i
$417$	12.9689			0.635091
$418$	2.11171	+	2.05279i	0.103287	+	0.100405i
$419$	2.11612			0.103379			0.0516897	−	0.998663i	$-0.483539\pi$
$419$	2.11612			0.103379			0.0516897	+	0.998663i	$0.483539\pi$
$420$	−3.00784	+	0.0851293i	−0.146768	+	0.00415388i
$421$		−	33.1164i		−	1.61399i	−0.590556	−	0.806996i	$-0.701092\pi$
$421$		−	33.1164i		−	1.61399i	0.590556	−	0.806996i	$-0.298908\pi$
$422$	−14.8856	+	15.3128i	−0.724619	+	0.745417i
$423$	−9.74377			−0.473758
$424$	−0.0990753	+	0.107864i	−0.00481152	+	0.00523832i
$425$	3.59849	+	2.01268i	0.174552	+	0.0976292i
$426$	−19.2906	−	18.7524i	−0.934633	−	0.908554i
$427$		−	14.8623i		−	0.719236i
$428$	−0.268318	−	9.48040i	−0.0129697	−	0.458252i
$429$			5.37626i			0.259568i
$430$	6.04856	+	5.87980i	0.291688	+	0.283549i
$431$			9.16433i			0.441430i	0.975338	+	0.220715i	$0.0708391\pi$
$431$			9.16433i			0.441430i	−0.975338	+	0.220715i	$0.929161\pi$
$432$	22.5485	−	1.27738i	1.08487	−	0.0614580i
$433$	28.6734			1.37796			0.688978	−	0.724783i	$-0.258060\pi$
$433$	28.6734			1.37796			0.688978	+	0.724783i	$0.258060\pi$
$434$	7.77378	−	7.99691i	0.373154	−	0.383864i
$435$	−7.12949			−0.341833
$436$	1.05258	+	37.1906i	0.0504096	+	1.78111i
$437$	13.9964			0.669538
$438$	1.18911	+	1.15593i	0.0568179	+	0.0552326i
$439$		−	25.2376i		−	1.20452i	−0.798299	−	0.602261i	$-0.794266\pi$
$439$		−	25.2376i		−	1.20452i	0.798299	−	0.602261i	$-0.205734\pi$
$440$	−1.53589	−	1.41076i	−0.0732209	−	0.0672551i
$441$	−5.09066			−0.242412
$442$	−8.29231	−	27.8306i	−0.394425	−	1.32377i
$443$			7.07363i			0.336078i	0.985780	+	0.168039i	$0.0537435\pi$
$443$			7.07363i			0.336078i	−0.985780	+	0.168039i	$0.946257\pi$
$444$	0.267229	+	9.44192i	0.0126821	+	0.448094i
$445$	6.70231			0.317720
$446$	8.99251	−	9.25062i	0.425807	−	0.438029i
$447$		−	32.7893i		−	1.55088i
$448$	−8.19133	+	0.696993i	−0.387004	+	0.0329298i
$449$		−	14.5442i		−	0.686382i	−0.939266	−	0.343191i	$-0.888492\pi$
$449$		−	14.5442i		−	0.686382i	0.939266	−	0.343191i	$-0.111508\pi$
$450$	0.844234	−	0.868466i	0.0397976	−	0.0409399i
$451$			3.28300i			0.154591i
$452$	−27.2700	+	0.771807i	−1.28267	+	0.0363027i
$453$	22.6496			1.06417
$454$	5.35155	−	5.50515i	0.251161	−	0.258370i
$455$	5.11780			0.239926
$456$	7.91184	−	8.61364i	0.370506	−	0.403371i
$457$	−36.1784			−1.69236			−0.846178	−	0.532901i	$-0.821102\pi$
$457$	−36.1784			−1.69236			−0.846178	+	0.532901i	$0.821102\pi$
$458$	−5.65775	−	5.49989i	−0.264369	−	0.256993i
$459$	−20.3177	−	11.3639i	−0.948349	−	0.530423i
$460$	−9.90729	+	0.280400i	−0.461930	+	0.0130737i
$461$			2.76009i			0.128550i	0.997932	+	0.0642751i	$0.0204735\pi$
$461$			2.76009i			0.128550i	−0.997932	+	0.0642751i	$0.979526\pi$
$462$	−1.12491	−	1.09352i	−0.0523354	−	0.0508752i
$463$	8.26733			0.384216			0.192108	−	0.981374i	$-0.438468\pi$
$463$	8.26733			0.384216			0.192108	+	0.981374i	$0.438468\pi$
$464$	−19.4471	+	1.10168i	−0.902809	+	0.0511443i
$465$		−	11.2357i		−	0.521045i
$466$	−19.9023	−	19.3469i	−0.921954	−	0.896230i
$467$		−	14.7543i		−	0.682748i	−0.939928	−	0.341374i	$-0.889108\pi$
$467$		−	14.7543i		−	0.682748i	0.939928	−	0.341374i	$-0.110892\pi$
$468$	−8.52714	+	0.241339i	−0.394167	+	0.0111559i
$469$	4.69609			0.216845
$470$	11.2150	−	11.5369i	0.517310	−	0.532159i
$471$		−	16.1559i		−	0.744425i
$472$	12.4040	−	13.5043i	0.570942	−	0.621586i
$473$			4.39799i			0.202220i
$474$	11.6259	+	11.3015i	0.533994	+	0.519095i
$475$		−	2.82434i		−	0.129590i
$476$	7.50980	+	3.92563i	0.344211	+	0.179931i
$477$		−	0.0443474i		−	0.00203053i
$478$	1.60774	−	1.65388i	0.0735361	−	0.0756468i
$479$			22.2732i			1.01769i	0.860859	+	0.508843i	$0.169927\pi$
$479$			22.2732i			1.01769i	−0.860859	+	0.508843i	$0.830073\pi$
$480$	−5.42780	+	6.25564i	−0.247744	+	0.285529i
$481$		−	16.0653i		−	0.732514i
$482$	21.2826	+	20.6888i	0.969398	+	0.942350i
$483$	−7.45586			−0.339253
$484$	0.591643	+	20.9043i	0.0268929	+	0.950197i
$485$		−	7.53723i		−	0.342248i
$486$	−8.47481	+	8.71806i	−0.384425	+	0.395459i
$487$		−	16.9274i		−	0.767055i	−0.923529	−	0.383528i	$-0.874709\pi$
$487$		−	16.9274i		−	0.767055i	0.923529	−	0.383528i	$-0.125291\pi$
$488$	−30.1270	−	27.6724i	−1.36379	−	1.25267i
$489$	0.469692			0.0212402
$490$	5.85932	−	6.02750i	0.264697	−	0.272295i
$491$			10.4958i			0.473668i	0.971550	+	0.236834i	$0.0761098\pi$
$491$			10.4958i			0.473668i	−0.971550	+	0.236834i	$0.923890\pi$
$492$	13.0327	−	0.368858i	0.587562	−	0.0166294i
$493$	17.5231	+	9.80088i	0.789200	+	0.441409i
$494$	−13.8656	+	14.2636i	−0.623842	+	0.641748i
$495$	0.631473			0.0283826
$496$	−1.73620	−	30.6477i	−0.0779577	−	1.37612i
$497$	−13.3521			−0.598924
$498$	15.9626	+	15.5173i	0.715303	+	0.695345i
$499$	23.9095			1.07034			0.535168	−	0.844746i	$-0.320248\pi$
$499$	23.9095			1.07034			0.535168	+	0.844746i	$0.320248\pi$
$500$	0.0565822	+	1.99920i	0.00253043	+	0.0894069i
$501$		−	20.9666i		−	0.936721i
$502$	−7.74590	−	7.52977i	−0.345716	−	0.336070i
$503$		−	1.84621i		−	0.0823184i	−0.999153	−	0.0411592i	$-0.986895\pi$
$503$		−	1.84621i		−	0.0823184i	0.999153	−	0.0411592i	$-0.0131051\pi$
$504$	1.68391	−	1.83327i	0.0750071	−	0.0816605i
$505$			1.99652i			0.0888441i
$506$	−3.70524	−	3.60186i	−0.164718	−	0.160122i
$507$	−17.2807			−0.767463
$508$	0.184375	+	6.51447i	0.00818033	+	0.289033i
$509$		−	21.9087i		−	0.971086i	−0.874213	−	0.485543i	$-0.838622\pi$
$509$		−	21.9087i		−	0.971086i	0.874213	−	0.485543i	$-0.161378\pi$
$510$	8.18159	−	2.43776i	0.362287	−	0.107946i
$511$	0.823051			0.0364096
$512$	−13.8387	+	17.9022i	−0.611592	+	0.791173i
$513$			15.9467i			0.704065i
$514$	−1.36882	+	1.40811i	−0.0603762	+	0.0621092i
$515$	−1.44810			−0.0638108
$516$	17.4590	−	0.494131i	0.768588	−	0.0217529i
$517$	8.38865			0.368932
$518$	3.36143	+	3.26764i	0.147693	+	0.143572i
$519$	25.5988			1.12366
$520$	9.52894	−	10.3742i	0.417872	−	0.454938i
$521$		−	1.41157i		−	0.0618421i	−0.999522	−	0.0309211i	$-0.990156\pi$
$521$		−	1.41157i		−	0.0618421i	0.999522	−	0.0309211i	$-0.00984405\pi$
$522$	4.11106	−	4.22906i	0.179936	−	0.185101i
$523$			20.7749i			0.908421i	0.890894	+	0.454211i	$0.150079\pi$
$523$			20.7749i			0.908421i	−0.890894	+	0.454211i	$0.849921\pi$
$524$	−1.08404	−	38.3019i	−0.0473564	−	1.67323i
$525$			1.50452i			0.0656628i
$526$	12.0131	−	12.3579i	0.523795	−	0.538829i
$527$	−15.4457	+	27.6156i	−0.672826	+	1.20295i
$528$	−4.31114	+	0.244227i	−0.187618	+	0.0106286i
$529$	−1.55824			−0.0677498
$530$	0.0525087	+	0.0510436i	0.00228083	+	0.00221719i
$531$			5.55221i			0.240945i
$532$	−0.164221	−	5.80235i	−0.00711987	−	0.251564i
$533$	−22.1750			−0.960506
$534$	9.67299	−	9.95063i	0.418591	−	0.430606i
$535$	−4.74210			−0.205019
$536$	8.74375	−	9.51934i	0.377672	−	0.411173i
$537$			14.6972i			0.634231i
$538$	8.41250	−	8.65397i	0.362689	−	0.373099i
$539$	4.38267			0.188775
$540$	−0.319473	−	11.2878i	−0.0137479	−	0.485751i
$541$	4.03830			0.173620			0.0868101	−	0.996225i	$-0.472333\pi$
$541$	4.03830			0.173620			0.0868101	+	0.996225i	$0.472333\pi$
$542$	−18.7760	+	19.3149i	−0.806497	+	0.829646i
$543$	−10.5662			−0.453438
$544$	21.9402	−	7.91373i	0.940679	−	0.339298i
$545$	18.6027			0.796854
$546$	7.38617	−	7.59818i	0.316099	−	0.325172i
$547$	41.2053			1.76181			0.880906	−	0.473290i	$-0.156934\pi$
$547$	41.2053			1.76181			0.880906	+	0.473290i	$0.156934\pi$
$548$	−0.679714	−	24.0161i	−0.0290360	−	1.02592i
$549$	12.3865			0.528644
$550$	−0.726822	+	0.747684i	−0.0309918	+	0.0318813i
$551$		−	13.7533i		−	0.585912i
$552$	−13.8822	+	15.1136i	−0.590867	+	0.643278i
$553$	8.04693			0.342190
$554$	3.06787	−	3.15592i	0.130341	−	0.134082i
$555$	4.72285			0.200474
$556$	−0.501206	−	17.7089i	−0.0212558	−	0.751025i
$557$		−	13.9646i		−	0.591699i	−0.955235	−	0.295849i	$-0.904397\pi$
$557$		−	13.9646i		−	0.591699i	0.955235	−	0.295849i	$-0.0956027\pi$
$558$	6.66479	+	6.47883i	0.282143	+	0.274271i
$559$	−29.7062			−1.25644
$560$	0.232486	+	4.10388i	0.00982433	+	0.173421i
$561$	3.88462	+	2.17271i	0.164009	+	0.0917320i
$562$	28.3832	−	29.1979i	1.19727	−	1.23164i
$563$		−	39.0610i		−	1.64622i	−0.567880	−	0.823111i	$-0.692236\pi$
$563$		−	39.0610i		−	1.64622i	0.567880	−	0.823111i	$-0.307764\pi$
$564$	−0.942497	−	33.3009i	−0.0396863	−	1.40222i
$565$			13.6404i			0.573858i
$566$	−19.5048	+	20.0647i	−0.819850	+	0.843382i
$567$		−	5.85454i		−	0.245868i
$568$	−24.8606	+	27.0658i	−1.04313	+	1.13566i
$569$	40.3237			1.69046			0.845228	−	0.534405i	$-0.179464\pi$
$569$	40.3237			1.69046			0.845228	+	0.534405i	$0.179464\pi$
$570$	−4.19318	−	4.07618i	−0.175633	−	0.170732i
$571$	−27.1177			−1.13484			−0.567421	−	0.823428i	$-0.692059\pi$
$571$	−27.1177			−1.13484			−0.567421	+	0.823428i	$0.692059\pi$
$572$	7.34122	−	0.207774i	0.306952	−	0.00868748i
$573$	23.7595			0.992566
$574$	4.51035	−	4.63981i	0.188258	−	0.193662i
$575$			4.95563i			0.206664i
$576$	−0.580888	−	6.82682i	−0.0242037	−	0.284451i
$577$	−7.77551			−0.323699			−0.161849	−	0.986815i	$-0.551746\pi$
$577$	−7.77551			−0.323699			−0.161849	+	0.986815i	$0.551746\pi$
$578$	−23.4602	−	5.25559i	−0.975814	−	0.218604i
$579$		−	26.9521i		−	1.12009i
$580$	0.275531	+	9.73524i	0.0114408	+	0.404234i
$581$	11.0487			0.458375
$582$	−11.1902	−	10.8780i	−0.463849	−	0.450906i
$583$			0.0381798i			0.00158124i
$584$	1.53246	−	1.66839i	0.0634135	−	0.0690385i
$585$			4.26528i			0.176348i
$586$	−11.4775	−	11.1572i	−0.474129	−	0.460900i
$587$			35.6192i			1.47016i	0.677980	+	0.735080i	$0.262855\pi$
$587$			35.6192i			1.47016i	−0.677980	+	0.735080i	$0.737145\pi$
$588$	−0.492411	−	17.3982i	−0.0203067	−	0.717488i
$589$	21.6746			0.893086
$590$	−6.57399	−	6.39056i	−0.270647	−	0.263095i
$591$	−1.72500			−0.0709572
$592$	12.8825	−	0.729797i	0.529467	−	0.0299945i
$593$	35.3602			1.45207			0.726035	−	0.687658i	$-0.241361\pi$
$593$	35.3602			1.45207			0.726035	+	0.687658i	$0.241361\pi$
$594$	4.10376	−	4.22155i	0.168379	−	0.173212i
$595$	2.06826	−	3.69786i	0.0847904	−	0.151598i
$596$	−44.7734	+	1.26720i	−1.83399	+	0.0519064i
$597$			7.00925i			0.286870i
$598$	24.3287	−	25.0270i	0.994875	−	1.02343i
$599$	25.3800			1.03700			0.518500	−	0.855078i	$-0.326491\pi$
$599$	25.3800			1.03700			0.518500	+	0.855078i	$0.326491\pi$
$600$	3.04979	+	2.80130i	0.124507	+	0.114363i
$601$			0.940741i			0.0383736i	0.999816	+	0.0191868i	$0.00610773\pi$
$601$			0.940741i			0.0383736i	−0.999816	+	0.0191868i	$0.993892\pi$
$602$	6.04217	−	6.21560i	0.246261	−	0.253329i
$603$			3.91382i			0.159383i
$604$	−0.875332	−	30.9278i	−0.0356168	−	1.25843i
$605$	10.4563			0.425111
$606$	2.96415	+	2.88145i	0.120410	+	0.117051i
$607$		−	9.70858i		−	0.394059i	−0.980398	−	0.197030i	$-0.936871\pi$
$607$		−	9.70858i		−	0.394059i	0.980398	−	0.197030i	$-0.0631295\pi$
$608$	−12.0676	−	10.4706i	−0.489406	−	0.424640i
$609$			7.32638i			0.296880i
$610$	−14.2568	+	14.6660i	−0.577242	+	0.593810i
$611$			56.6610i			2.29226i
$612$	−3.27170	+	6.25882i	−0.132251	+	0.252998i
$613$			30.1125i			1.21623i	0.793848	+	0.608116i	$0.208075\pi$
$613$			30.1125i			1.21623i	−0.793848	+	0.608116i	$0.791925\pi$
$614$	−35.3708	−	34.3839i	−1.42745	−	1.38762i
$615$		−	6.51898i		−	0.262871i
$616$	−1.44972	+	1.57831i	−0.0584107	+	0.0635919i
$617$			33.4173i			1.34533i	0.739947	+	0.672665i	$0.234850\pi$
$617$			33.4173i			1.34533i	−0.739947	+	0.672665i	$0.765150\pi$
$618$	−2.08994	+	2.14993i	−0.0840698	+	0.0864828i
$619$	−5.48862			−0.220606			−0.110303	−	0.993898i	$-0.535182\pi$
$619$	−5.48862			−0.220606			−0.110303	+	0.993898i	$0.535182\pi$
$620$	−15.3423	+	0.434224i	−0.616160	+	0.0174388i
$621$		−	27.9803i		−	1.12281i
$622$	29.3346	+	28.5161i	1.17621	+	1.14339i
$623$		−	6.88740i		−	0.275938i
$624$	−1.64963	−	29.1196i	−0.0660381	−	1.16572i
$625$	1.00000			0.0400000
$626$	5.41139	+	5.26040i	0.216282	+	0.210248i
$627$		−	3.04892i		−	0.121762i
$628$	−22.0607	+	0.624372i	−0.880318	+	0.0249151i
$629$	−11.6080	−	6.49247i	−0.462840	−	0.258872i
$630$	−0.892450	−	0.867549i	−0.0355560	−	0.0345640i
$631$	0.444706			0.0177035			0.00885173	−	0.999961i	$-0.497182\pi$
$631$	0.444706			0.0177035			0.00885173	+	0.999961i	$0.497182\pi$
$632$	14.9828	−	16.3118i	0.595982	−	0.648847i
$633$	22.1088			0.878747
$634$	−15.3253	+	15.7652i	−0.608646	+	0.626116i
$635$	3.25854			0.129311
$636$	0.151565	−	0.00428965i	0.00600993	−	0.000170096i
$637$			29.6027i			1.17290i
$638$	−3.53931	+	3.64090i	−0.140123	+	0.144144i
$639$		−	11.1279i		−	0.440214i
$640$	8.75176	+	7.16984i	0.345944	+	0.283413i
$641$			24.5740i			0.970616i	0.874343	+	0.485308i	$0.161292\pi$
$641$			24.5740i			0.970616i	−0.874343	+	0.485308i	$0.838708\pi$
$642$	−6.84395	+	7.04039i	−0.270109	+	0.277862i
$643$	37.3639			1.47349			0.736743	−	0.676173i	$-0.236363\pi$
$643$	37.3639			1.47349			0.736743	+	0.676173i	$0.236363\pi$
$644$	0.288144	+	10.1809i	0.0113545	+	0.401183i
$645$		−	8.73298i		−	0.343861i
$646$	4.70262	+	15.7829i	0.185022	+	0.620970i
$647$	−1.14820			−0.0451405			−0.0225703	−	0.999745i	$-0.507185\pi$
$647$	−1.14820			−0.0451405			−0.0225703	+	0.999745i	$0.507185\pi$
$648$	−11.8676	−	10.9007i	−0.466204	−	0.428220i
$649$		−	4.78003i		−	0.187633i
$650$	−5.05022	−	4.90931i	−0.198086	−	0.192559i
$651$	−11.5460			−0.452524
$652$	−0.0181520	−	0.641359i	−0.000710888	−	0.0251175i
$653$	−4.48681			−0.175582			−0.0877912	−	0.996139i	$-0.527981\pi$
$653$	−4.48681			−0.175582			−0.0877912	+	0.996139i	$0.527981\pi$
$654$	26.8481	−	27.6187i	1.04984	−	1.07998i
$655$	−19.1586			−0.748590
$656$	−1.00734	−	17.7818i	−0.0393302	−	0.694263i
$657$			0.685948i			0.0267614i
$658$	−11.8555	−	11.5247i	−0.462177	−	0.449281i
$659$		−	0.209907i		−	0.00817683i	−0.999992	−	0.00408841i	$-0.998699\pi$
$659$		−	0.209907i		−	0.00817683i	0.999992	−	0.00408841i	$-0.00130139\pi$
$660$	0.0610813	+	2.15816i	0.00237758	+	0.0840064i
$661$		−	0.915250i		−	0.0355991i	−0.999842	−	0.0177996i	$-0.994334\pi$
$661$		−	0.915250i		−	0.0355991i	0.999842	−	0.0177996i	$-0.00566607\pi$
$662$	0.835608	+	0.812292i	0.0324768	+	0.0315706i
$663$	−14.6756	+	26.2386i	−0.569952	+	1.01902i
$664$	20.5717	−	22.3965i	0.798338	−	0.869152i
$665$	−2.90234			−0.112548
$666$	−2.72332	+	2.80149i	−0.105527	+	0.108555i
$667$			24.1318i			0.934386i
$668$	−28.6297	+	0.810291i	−1.10772	+	0.0313511i
$669$	−13.3561			−0.516378
$670$	−4.63408	−	4.50478i	−0.179030	−	0.174035i
$671$	−10.6639			−0.411674
$672$	6.42839	+	5.57770i	0.247981	+	0.215164i
$673$			28.6506i			1.10440i	0.833712	+	0.552199i	$0.186211\pi$
$673$			28.6506i			1.10440i	−0.833712	+	0.552199i	$0.813789\pi$
$674$	10.5363	+	10.2423i	0.405843	+	0.394519i
$675$	−5.64618			−0.217321
$676$	0.667841	+	23.5966i	0.0256862	+	0.907562i
$677$	27.5070			1.05718			0.528590	−	0.848877i	$-0.322721\pi$
$677$	27.5070			1.05718			0.528590	+	0.848877i	$0.322721\pi$
$678$	20.2514	+	19.6863i	0.777750	+	0.756049i
$679$	−7.74537			−0.297240
$680$	−3.64493	−	11.0777i	−0.139777	−	0.424809i
$681$	−7.94840			−0.304583
$682$	−5.73788	−	5.57778i	−0.219715	−	0.213584i
$683$	−28.8188			−1.10272			−0.551361	−	0.834267i	$-0.685891\pi$
$683$	−28.8188			−1.10272			−0.551361	+	0.834267i	$0.685891\pi$
$684$	4.83580	−	0.136865i	0.184901	−	0.00523316i
$685$	−12.0129			−0.458988
$686$	−13.4883	−	13.1120i	−0.514986	−	0.500617i
$687$			8.16872i			0.311656i
$688$	−1.34946	−	23.8209i	−0.0514477	−	0.908164i
$689$	−0.257885			−0.00982463
$690$	7.35741	+	7.15212i	0.280092	+	0.272277i
$691$	30.2174			1.14952			0.574761	−	0.818321i	$-0.305095\pi$
$691$	30.2174			1.14952			0.574761	+	0.818321i	$0.305095\pi$
$692$	−0.989307	−	34.9548i	−0.0376078	−	1.32878i
$693$		−	0.648912i		−	0.0246501i
$694$	8.69996	−	8.94968i	0.330246	−	0.339725i
$695$	−8.85801			−0.336003
$696$	14.8512	+	13.6411i	0.562931	+	0.517066i
$697$	−8.96161	+	16.0226i	−0.339445	+	0.606898i
$698$	7.85643	+	7.63722i	0.297370	+	0.289073i
$699$			28.7351i			1.08686i
$700$	2.05441	−	0.0581448i	0.0776494	−	0.00219767i
$701$		−	15.1682i		−	0.572893i	−0.958096	−	0.286447i	$-0.907526\pi$
$701$		−	15.1682i		−	0.572893i	0.958096	−	0.286447i	$-0.0924741\pi$
$702$	28.5144	+	27.7188i	1.07621	+	1.04618i
$703$			9.11073i			0.343618i
$704$	0.500100	+	5.87737i	0.0188482	+	0.221512i
$705$	−16.6571			−0.627344
$706$	−7.86091	+	8.08654i	−0.295849	+	0.304341i
$707$	2.05166			0.0771606
$708$	−18.9756	+	0.537055i	−0.713146	+	0.0201838i
$709$	1.02190			0.0383782			0.0191891	−	0.999816i	$-0.493892\pi$
$709$	1.02190			0.0383782			0.0191891	+	0.999816i	$0.493892\pi$
$710$	13.1758	+	12.8082i	0.494480	+	0.480683i
$711$			6.70648i			0.251513i
$712$	−13.9613	−	12.8238i	−0.523222	−	0.480592i
$713$	−38.0305			−1.42425
$714$	−2.50508	−	8.40754i	−0.0937503	−	0.314644i
$715$		−	3.67208i		−	0.137328i
$716$	20.0688	−	0.567997i	0.750008	−	0.0212270i
$717$	−2.38789			−0.0891775
$718$	19.0135	−	19.5592i	0.709577	−	0.729944i
$719$		−	46.2539i		−	1.72498i	−0.506073	−	0.862491i	$-0.668903\pi$
$719$		−	46.2539i		−	1.72498i	0.506073	−	0.862491i	$-0.331097\pi$
$720$	−3.42026	+	0.193759i	−0.127466	+	0.00722096i
$721$			1.48809i			0.0554193i
$722$	−10.8660	+	11.1779i	−0.404392	+	0.416000i
$723$		−	30.7281i		−	1.14279i
$724$	0.408347	+	14.4280i	0.0151761	+	0.536212i
$725$	4.86957			0.180851
$726$	15.0909	−	15.5241i	0.560077	−	0.576153i
$727$	43.5602			1.61556			0.807779	−	0.589485i	$-0.200669\pi$
$727$	43.5602			1.61556			0.807779	+	0.589485i	$0.200669\pi$
$728$	−10.6607	−	9.79209i	−0.395111	−	0.362919i
$729$	29.6788			1.09922
$730$	−0.812183	−	0.789522i	−0.0300603	−	0.0292215i
$731$	−12.0052	+	21.4642i	−0.444028	+	0.793882i
$732$	1.19813	+	42.3330i	0.0442840	+	1.56467i
$733$		−	5.12531i		−	0.189308i	−0.995510	−	0.0946538i	$-0.969826\pi$
$733$		−	5.12531i		−	0.189308i	0.995510	−	0.0946538i	$-0.0301744\pi$
$734$	−16.0289	−	15.5816i	−0.591636	−	0.575128i
$735$	−8.70257			−0.320999
$736$	21.1740	+	18.3719i	0.780482	+	0.677198i
$737$		−	3.36950i		−	0.124117i
$738$	3.86691	+	3.75902i	0.142343	+	0.138371i
$739$		−	15.8626i		−	0.583514i	−0.956493	−	0.291757i	$-0.905760\pi$
$739$		−	15.8626i		−	0.583514i	0.956493	−	0.291757i	$-0.0942398\pi$
$740$	−0.182522	−	6.44899i	−0.00670965	−	0.237070i
$741$	20.5939			0.756535
$742$	0.0524532	−	0.0539588i	0.00192562	−	0.00198089i
$743$			28.3848i			1.04134i	0.853759	+	0.520668i	$0.174317\pi$
$743$			28.3848i			1.04134i	−0.853759	+	0.520668i	$0.825683\pi$
$744$	−21.4978	+	23.4047i	−0.788147	+	0.858058i
$745$			22.3957i			0.820513i
$746$	−23.5813	−	22.9233i	−0.863373	−	0.839283i
$747$			9.20817i			0.336909i
$748$	2.81669	−	5.38837i	0.102988	−	0.197018i
$749$			4.87305i			0.178058i
$750$	1.44323	−	1.48466i	0.0526994	−	0.0542120i
$751$		−	31.5903i		−	1.15275i	−0.817187	−	0.576373i	$-0.804467\pi$
$751$		−	31.5903i		−	1.15275i	0.817187	−	0.576373i	$-0.195533\pi$
$752$	−45.4356	+	2.57394i	−1.65687	+	0.0938619i
$753$			11.1836i			0.407553i
$754$	−24.5924	−	23.9062i	−0.895602	−	0.870613i
$755$	−15.4701			−0.563014
$756$	−11.5996	+	0.328296i	−0.421872	+	0.0119400i
$757$		−	15.9749i		−	0.580619i	−0.956933	−	0.290309i	$-0.906242\pi$
$757$		−	15.9749i		−	0.580619i	0.956933	−	0.290309i	$-0.0937582\pi$
$758$	26.3790	−	27.1362i	0.958130	−	0.985631i
$759$			5.34967i			0.194181i
$760$	−5.40393	+	5.88327i	−0.196021	+	0.213409i
$761$	−0.0742013			−0.00268979			−0.00134490	−	0.999999i	$-0.500428\pi$
$761$	−0.0742013			−0.00268979			−0.00134490	+	0.999999i	$0.500428\pi$
$762$	4.70283	−	4.83781i	0.170366	−	0.175256i
$763$		−	19.1165i		−	0.692063i
$764$	−0.918223	−	32.4433i	−0.0332202	−	1.17376i
$765$	3.08188	+	1.72373i	0.111425	+	0.0623216i
$766$	−8.34626	+	8.58582i	−0.301562	+	0.310218i
$767$	32.2867			1.16580
$768$	23.2756	−	2.64563i	0.839885	−	0.0954658i
$769$	−37.0122			−1.33470			−0.667348	−	0.744746i	$-0.732571\pi$
$769$	−37.0122			−1.33470			−0.667348	+	0.744746i	$0.732571\pi$
$770$	0.768331	+	0.746893i	0.0276887	+	0.0269162i
$771$	2.03305			0.0732184
$772$	−36.8027	+	1.04161i	−1.32456	+	0.0374882i
$773$			22.3692i			0.804563i	0.915516	+	0.402282i	$0.131783\pi$
$773$			22.3692i			0.804563i	−0.915516	+	0.402282i	$0.868217\pi$
$774$	5.18021	+	5.03567i	0.186199	+	0.181003i
$775$			7.67421i			0.275666i
$776$	−14.4213	+	15.7005i	−0.517694	+	0.563614i
$777$		−	4.85327i		−	0.174110i
$778$	26.3300	+	25.5953i	0.943975	+	0.917636i
$779$	12.5756			0.450568
$780$	−14.5773	+	0.412573i	−0.521951	+	0.0147725i
$781$			9.58030i			0.342810i
$782$	−8.25129	−	27.6929i	−0.295065	−	0.990296i
$783$	−27.4944			−0.982571
$784$	−23.7380	+	1.34476i	−0.847784	+	0.0480272i
$785$			11.0348i			0.393848i
$786$	−27.6504	+	28.4440i	−0.986256	+	1.01456i
$787$	−10.9625			−0.390769			−0.195385	−	0.980727i	$-0.562596\pi$
$787$	−10.9625			−0.390769			−0.195385	+	0.980727i	$0.562596\pi$
$788$	0.0666656	+	2.35547i	0.00237486	+	0.0839102i
$789$	−17.8424			−0.635208
$790$	−7.94068	−	7.71912i	−0.282517	−	0.274634i
$791$	14.0171			0.498392
$792$	−1.31539	−	1.20822i	−0.0467405	−	0.0429323i
$793$		−	72.0289i		−	2.55782i
$794$	22.3697	−	23.0118i	0.793872	−	0.816658i
$795$		−	0.0758126i		−	0.00268880i
$796$	9.57105	−	0.270884i	0.339237	−	0.00960123i
$797$			39.0009i			1.38148i	0.723102	+	0.690741i	$0.242716\pi$
$797$			39.0009i			1.38148i	−0.723102	+	0.690741i	$0.757284\pi$
$798$	−4.18875	+	4.30898i	−0.148280	+	0.152536i
$799$	40.9404	+	22.8985i	1.44837	+	0.810090i
$800$	3.70728	−	4.27271i	0.131072	−	0.151063i
$801$	5.74010			0.202816
$802$	−33.1695	−	32.2440i	−1.17126	−	1.13858i
$803$		−	0.590549i		−	0.0208400i
$804$	−13.3761	+	0.378577i	−0.471739	+	0.0133514i
$805$	5.09248			0.179486
$806$	37.6751	−	38.7564i	1.32705	−	1.36514i
$807$	−12.4947			−0.439834
$808$	3.82003	−	4.15887i	0.134388	−	0.146309i
$809$			39.1418i			1.37615i	0.725638	+	0.688077i	$0.241545\pi$
$809$			39.1418i			1.37615i	−0.725638	+	0.688077i	$0.758455\pi$
$810$	−5.61604	+	5.77724i	−0.197328	+	0.202991i
$811$	−18.0496			−0.633809			−0.316904	−	0.948458i	$-0.602643\pi$
$811$	−18.0496			−0.633809			−0.316904	+	0.948458i	$0.602643\pi$
$812$	10.0041	−	0.283140i	0.351075	−	0.00993627i
$813$	27.8871			0.978042
$814$	2.34457	−	2.41187i	0.0821772	−	0.0845360i
$815$	−0.320808			−0.0112374
$816$	−21.7070	−	10.5762i	−0.759897	−	0.370240i
$817$	16.8466			0.589387
$818$	24.9869	−	25.7041i	0.873648	−	0.898724i
$819$	4.38307			0.153157
$820$	−8.90159	+	0.251937i	−0.310857	+	0.00879801i
$821$	4.04733			0.141253			0.0706263	−	0.997503i	$-0.477500\pi$
$821$	4.04733			0.141253			0.0706263	+	0.997503i	$0.477500\pi$
$822$	−17.3374	+	17.8350i	−0.604710	+	0.622067i
$823$			10.4958i			0.365862i	0.983126	+	0.182931i	$0.0585585\pi$
$823$			10.4958i			0.365862i	−0.983126	+	0.182931i	$0.941441\pi$
$824$	3.01647	+	2.77070i	0.105084	+	0.0965220i
$825$	1.07951			0.0375838
$826$	−6.56704	+	6.75553i	−0.228497	+	0.235055i
$827$	−35.2909			−1.22719			−0.613593	−	0.789623i	$-0.710276\pi$
$827$	−35.2909			−1.22719			−0.613593	+	0.789623i	$0.710276\pi$
$828$	−8.48496	+	0.240145i	−0.294873	+	0.00834562i
$829$		−	30.4113i		−	1.05623i	−0.849173	−	0.528114i	$-0.822899\pi$
$829$		−	30.4113i		−	1.05623i	0.849173	−	0.528114i	$-0.177101\pi$
$830$	−10.9028	−	10.5986i	−0.378440	−	0.367881i
$831$	−4.55656			−0.158065
$832$	−39.6987	+	3.37792i	−1.37630	+	0.117108i
$833$	21.3894	+	11.9634i	0.741100	+	0.414506i
$834$	−12.7842	+	13.1511i	−0.442679	+	0.455385i
$835$			14.3206i			0.495584i
$836$	−4.16326	+	0.117830i	−0.143989	+	0.00407525i
$837$		−	43.3299i		−	1.49770i
$838$	−2.08597	+	2.14585i	−0.0720588	+	0.0741271i
$839$		−	28.3278i		−	0.977985i	−0.872288	−	0.488992i	$-0.837365\pi$
$839$		−	28.3278i		−	0.977985i	0.872288	−	0.488992i	$-0.162635\pi$
$840$	2.87866	−	3.13401i	0.0993234	−	0.108134i
$841$	−5.28730			−0.182321
$842$	33.5815	+	32.6446i	1.15730	+	1.12501i
$843$	−42.1563			−1.45194
$844$	−0.854432	−	30.1893i	−0.0294108	−	1.03916i
$845$	11.8030			0.406036
$846$	9.60495	−	9.88064i	0.330225	−	0.339703i
$847$		−	10.7451i		−	0.369206i
$848$	−0.0117149	−	0.206794i	−0.000402292	−	0.00710133i
$849$	28.9696			0.994234
$850$	−5.58817	+	1.66503i	−0.191673	+	0.0571102i
$851$		−	15.9858i		−	0.547986i
$852$	38.0315	−	1.07638i	1.30294	−	0.0368763i
$853$	−49.3618			−1.69011			−0.845057	−	0.534676i	$-0.820434\pi$
$853$	−49.3618			−1.69011			−0.845057	+	0.534676i	$0.820434\pi$
$854$	15.0710	+	14.6505i	0.515720	+	0.501331i
$855$		−	2.41887i		−	0.0827236i
$856$	9.87806	+	9.07324i	0.337625	+	0.310117i
$857$		−	56.3068i		−	1.92340i	−0.274099	−	0.961701i	$-0.588380\pi$
$857$		−	56.3068i		−	1.92340i	0.274099	−	0.961701i	$-0.411620\pi$
$858$	−5.45178	−	5.29967i	−0.186121	−	0.180928i
$859$			4.79059i			0.163453i	0.996655	+	0.0817264i	$0.0260434\pi$
$859$			4.79059i			0.163453i	−0.996655	+	0.0817264i	$0.973957\pi$
$860$	−11.9248	+	0.337500i	−0.406632	+	0.0115087i
$861$	−6.69901			−0.228302
$862$	−9.29306	−	9.03376i	−0.316523	−	0.307691i
$863$	21.3707			0.727469			0.363734	−	0.931503i	$-0.381502\pi$
$863$	21.3707			0.727469			0.363734	+	0.931503i	$0.381502\pi$
$864$	−20.9320	+	24.1245i	−0.712120	+	0.820731i
$865$	−17.4844			−0.594488
$866$	−28.2649	+	29.0762i	−0.960480	+	0.988048i
$867$	13.0279	+	21.2077i	0.442449	+	0.720250i
$868$	0.446215	+	15.7660i	0.0151455	+	0.535132i
$869$		−	5.77377i		−	0.195862i
$870$	7.02792	−	7.22964i	0.238269	−	0.245108i
$871$	22.7592			0.771168
$872$	−38.7506	−	35.5934i	−1.31226	−	1.20534i
$873$		−	6.45515i		−	0.218474i
$874$	−13.7970	+	14.1930i	−0.466690	+	0.480085i
$875$		−	1.02762i		−	0.0347398i
$876$	−2.34434	+	0.0663505i	−0.0792079	+	0.00224178i
$877$	−13.8064			−0.466208			−0.233104	−	0.972452i	$-0.574888\pi$
$877$	−13.8064			−0.466208			−0.233104	+	0.972452i	$0.574888\pi$
$878$	25.5921	+	24.8780i	0.863690	+	0.839592i
$879$			16.5713i			0.558935i
$880$	2.94458	−	0.166811i	0.0992619	−	0.00562321i
$881$			53.3373i			1.79698i	0.438996	+	0.898489i	$0.355334\pi$
$881$			53.3373i			1.79698i	−0.438996	+	0.898489i	$0.644666\pi$
$882$	5.01813	−	5.16217i	0.168969	−	0.173819i
$883$		−	17.6643i		−	0.594452i	−0.954807	−	0.297226i	$-0.903939\pi$
$883$		−	17.6643i		−	0.594452i	0.954807	−	0.297226i	$-0.0960614\pi$
$884$	36.3957	+	19.0253i	1.22412	+	0.639889i
$885$			9.49159i			0.319056i
$886$	−7.17299	−	6.97285i	−0.240981	−	0.234257i
$887$			54.2478i			1.82146i	0.413001	+	0.910731i	$0.364481\pi$
$887$			54.2478i			1.82146i	−0.413001	+	0.910731i	$0.635519\pi$
$888$	−9.83797	−	9.03641i	−0.330141	−	0.303242i
$889$		−	3.34853i		−	0.112306i
$890$	−6.60682	+	6.79645i	−0.221461	+	0.227818i
$891$	−4.20070			−0.140729
$892$	0.516170	+	18.2376i	0.0172826	+	0.610642i
$893$		−	32.1329i		−	1.07529i
$894$	33.2499	+	32.3221i	1.11204	+	1.08101i
$895$		−	10.0384i		−	0.335548i
$896$	7.36784	−	8.99345i	0.246142	−	0.300450i
$897$	−36.1343			−1.20649
$898$	14.7485	+	14.3370i	0.492163	+	0.478431i
$899$			37.3701i			1.24636i
$900$	0.0484591	+	1.71219i	0.00161530	+	0.0570729i
$901$	−0.104219	+	0.186335i	−0.00347204	+	0.00620771i
$902$	−3.32912	−	3.23623i	−0.110848	−	0.107755i
$903$	−8.97415			−0.298641
$904$	26.0988	−	28.4138i	0.868033	−	0.945030i
$905$	7.21688			0.239897
$906$	−22.3269	+	22.9678i	−0.741763	+	0.763054i
$907$	53.1016			1.76321			0.881605	−	0.471989i	$-0.156464\pi$
$907$	53.1016			1.76321			0.881605	+	0.471989i	$0.156464\pi$
$908$	0.307179	+	10.8534i	0.0101941	+	0.360184i
$909$			1.70989i			0.0567136i
$910$	−5.04488	+	5.18969i	−0.167236	+	0.172036i
$911$			22.4664i			0.744344i	0.928164	+	0.372172i	$0.121387\pi$
$911$			22.4664i			0.744344i	−0.928164	+	0.372172i	$0.878613\pi$
$912$	0.935517	+	16.5139i	0.0309781	+	0.546830i
$913$		−	7.92754i		−	0.262363i
$914$	35.6630	−	36.6866i	1.17963	−	1.21349i
$915$	21.1750			0.700023
$916$	11.1543	−	0.315694i	0.368548	−	0.0104308i
$917$			19.6877i			0.650145i
$918$	31.5518	−	9.40107i	1.04136	−	0.310282i
$919$	17.5340			0.578393			0.289197	−	0.957270i	$-0.406612\pi$
$919$	17.5340			0.578393			0.289197	+	0.957270i	$0.406612\pi$
$920$	9.48180	−	10.3229i	0.312606	−	0.340335i
$921$			51.0687i			1.68277i
$922$	−2.79886	−	2.72077i	−0.0921756	−	0.0896037i
$923$	−64.7101			−2.12996
$924$	2.21776	−	0.0627681i	0.0729590	−	0.00206492i
$925$	−3.22579			−0.106063
$926$	−8.14955	+	8.38346i	−0.267811	+	0.275498i
$927$	−1.24020			−0.0407336
$928$	18.0529	−	20.8063i	0.592615	−	0.682999i
$929$		−	11.8068i		−	0.387369i	−0.981064	−	0.193684i	$-0.937956\pi$
$929$		−	11.8068i		−	0.387369i	0.981064	−	0.193684i	$-0.0620438\pi$
$930$	11.3936	+	11.0757i	0.373610	+	0.363185i
$931$		−	16.7879i		−	0.550201i
$932$	39.2374	−	1.11051i	1.28526	−	0.0363761i
$933$		−	42.3537i		−	1.38660i
$934$	14.9616	+	14.5441i	0.489557	+	0.475898i
$935$	−2.65326	−	1.48400i	−0.0867709	−	0.0485320i
$936$	8.16093	−	8.88482i	0.266748	−	0.290409i
$937$	42.2046			1.37876			0.689381	−	0.724398i	$-0.257882\pi$
$937$	42.2046			1.37876			0.689381	+	0.724398i	$0.257882\pi$
$938$	−4.62918	+	4.76205i	−0.151148	+	0.155487i
$939$		−	7.81302i		−	0.254968i
$940$	0.643742	+	22.7451i	0.0209966	+	0.741864i
$941$	−42.9773			−1.40102			−0.700510	−	0.713643i	$-0.747044\pi$
$941$	−42.9773			−1.40102			−0.700510	+	0.713643i	$0.747044\pi$
$942$	16.3828	+	15.9257i	0.533782	+	0.518889i
$943$	−22.0653			−0.718546
$944$	1.46668	+	25.8902i	0.0477365	+	0.842653i
$945$			5.80210i			0.188742i
$946$	−4.45977	−	4.33533i	−0.144999	−	0.140954i
$947$	23.7141			0.770605			0.385302	−	0.922790i	$-0.374097\pi$
$947$	23.7141			0.770605			0.385302	+	0.922790i	$0.374097\pi$
$948$	−22.9205	+	0.648706i	−0.744423	+	0.0210690i
$949$	3.98886			0.129484
$950$	2.86402	+	2.78410i	0.0929209	+	0.0903283i
$951$	22.7619			0.738106
$952$	−11.3836	+	3.74558i	−0.368944	+	0.121395i
$953$	25.3815			0.822186			0.411093	−	0.911593i	$-0.365147\pi$
$953$	25.3815			0.822186			0.411093	+	0.911593i	$0.365147\pi$
$954$	0.0449704	+	0.0437156i	0.00145597	+	0.00141534i
$955$	−16.2281			−0.525130
$956$	0.0922840	+	3.26064i	0.00298468	+	0.105457i
$957$	5.25676			0.169927
$958$	−22.5860	−	21.9558i	−0.729721	−	0.709361i
$959$			12.3446i			0.398628i
$960$	−0.993038	−	11.6706i	−0.0320501	−	0.376666i
$961$	−27.8935			−0.899789
$962$	16.2909	+	15.8364i	0.525241	+	0.510586i
$963$	−4.06130			−0.130874
$964$	−41.9589	+	1.18754i	−1.35140	+	0.0382480i
$965$			18.4087i			0.592598i
$966$	7.34963	−	7.56059i	0.236471	−	0.243258i
$967$	−9.84890			−0.316719			−0.158360	−	0.987382i	$-0.550621\pi$
$967$	−9.84890			−0.316719			−0.158360	+	0.987382i	$0.550621\pi$
$968$	−21.7812	−	20.0065i	−0.700074	−	0.643035i
$969$	8.32262	−	14.8801i	0.267361	−	0.478018i
$970$	7.64310	+	7.42984i	0.245405	+	0.238558i
$971$		−	15.5359i		−	0.498572i	−0.968430	−	0.249286i	$-0.919804\pi$
$971$		−	15.5359i		−	0.498572i	0.968430	−	0.249286i	$-0.0801959\pi$
$972$	−0.486454	−	17.1877i	−0.0156030	−	0.551296i
$973$			9.10263i			0.291817i
$974$	17.1652	+	16.6863i	0.550009	+	0.534662i
$975$			7.29156i			0.233517i
$976$	57.7589	−	3.27205i	1.84882	−	0.104736i
$977$	−11.3011			−0.361556			−0.180778	−	0.983524i	$-0.557861\pi$
$977$	−11.3011			−0.361556			−0.180778	+	0.983524i	$0.557861\pi$
$978$	−0.463000	+	0.476290i	−0.0148051	+	0.0152301i
$979$	−4.94179			−0.157940
$980$	0.336325	+	11.8833i	0.0107435	+	0.379597i
$981$	15.9321			0.508672
$982$	−10.6432	−	10.3463i	−0.339639	−	0.330162i
$983$		−	44.2735i		−	1.41210i	−0.708160	−	0.706052i	$-0.750474\pi$
$983$		−	44.2735i		−	1.41210i	0.708160	−	0.706052i	$-0.249526\pi$
$984$	−12.4730	+	13.5794i	−0.397626	+	0.432896i
$985$	1.17821			0.0375408
$986$	−27.2120	+	8.10800i	−0.866606	+	0.258211i
$987$			17.1171i			0.544844i
$988$	−0.795884	−	28.1207i	−0.0253204	−	0.894638i
$989$	−29.5592			−0.939928
$990$	−0.622476	+	0.640343i	−0.0197836	+	0.0203514i
$991$		−	52.0174i		−	1.65239i	−0.563386	−	0.826194i	$-0.690502\pi$
$991$		−	52.0174i		−	1.65239i	0.563386	−	0.826194i	$-0.309498\pi$
$992$	32.7897	+	28.4505i	1.04107	+	0.903303i
$993$		−	1.20646i		−	0.0382858i
$994$	13.1619	−	13.5397i	0.417470	−	0.429452i
$995$		−	4.78744i		−	0.151772i
$996$	−31.4704	+	0.890690i	−0.997179	+	0.0282226i
$997$	−5.37281			−0.170159			−0.0850793	−	0.996374i	$-0.527114\pi$
$997$	−5.37281			−0.170159			−0.0850793	+	0.996374i	$0.527114\pi$
$998$	−23.5689	+	24.2454i	−0.746059	+	0.767473i
$999$	18.2134			0.576245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.l.b.101.10	yes	36
4.3	odd	2		2720.2.l.a.2481.11		36
8.3	odd	2		2720.2.l.b.2481.25		36
8.5	even	2		680.2.l.a.101.9	✓	36
17.16	even	2		680.2.l.a.101.10	yes	36
68.67	odd	2		2720.2.l.b.2481.26		36
136.67	odd	2		2720.2.l.a.2481.12		36
136.101	even	2	inner	680.2.l.b.101.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.l.a.101.9	✓	36	8.5	even	2
680.2.l.a.101.10	yes	36	17.16	even	2
680.2.l.b.101.9	yes	36	136.101	even	2	inner
680.2.l.b.101.10	yes	36	1.1	even	1	trivial
2720.2.l.a.2481.11		36	4.3	odd	2
2720.2.l.a.2481.12		36	136.67	odd	2
2720.2.l.b.2481.25		36	8.3	odd	2
2720.2.l.b.2481.26		36	68.67	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.985753 + 1.01405i) q^{2} +1.46409 q^{3} +(-0.0565822 - 1.99920i) q^{4} -1.00000 q^{5} +(-1.44323 + 1.48466i) q^{6} +1.02762i q^{7} +(2.08306 + 1.91334i) q^{8} -0.856436 q^{9} +(0.985753 - 1.01405i) q^{10} +0.737326 q^{11} +(-0.0828415 - 2.92701i) q^{12} +4.98026i q^{13} +(-1.04205 - 1.01298i) q^{14} -1.46409 q^{15} +(-3.99360 + 0.226238i) q^{16} +(3.59849 + 2.01268i) q^{17} +(0.844234 - 0.868466i) q^{18} -2.82434i q^{19} +(0.0565822 + 1.99920i) q^{20} +1.50452i q^{21} +(-0.726822 + 0.747684i) q^{22} +4.95563i q^{23} +(3.04979 + 2.80130i) q^{24} +1.00000 q^{25} +(-5.05022 - 4.90931i) q^{26} -5.64618 q^{27} +(2.05441 - 0.0581448i) q^{28} +4.86957 q^{29} +(1.44323 - 1.48466i) q^{30} +7.67421i q^{31} +(3.70728 - 4.27271i) q^{32} +1.07951 q^{33} +(-5.58817 + 1.66503i) q^{34} -1.02762i q^{35} +(0.0484591 + 1.71219i) q^{36} -3.22579 q^{37} +(2.86402 + 2.78410i) q^{38} +7.29156i q^{39} +(-2.08306 - 1.91334i) q^{40} +4.45258i q^{41} +(-1.52566 - 1.48309i) q^{42} +5.96478i q^{43} +(-0.0417196 - 1.47406i) q^{44} +0.856436 q^{45} +(-5.02524 - 4.88502i) q^{46} +11.3771 q^{47} +(-5.84699 + 0.331234i) q^{48} +5.94401 q^{49} +(-0.985753 + 1.01405i) q^{50} +(5.26852 + 2.94675i) q^{51} +(9.95654 - 0.281794i) q^{52} +0.0517813i q^{53} +(5.56573 - 5.72549i) q^{54} -0.737326 q^{55} +(-1.96618 + 2.14058i) q^{56} -4.13510i q^{57} +(-4.80019 + 4.93797i) q^{58} -6.48292i q^{59} +(0.0828415 + 2.92701i) q^{60} -14.4629 q^{61} +(-7.78201 - 7.56487i) q^{62} -0.880087i q^{63} +(0.678262 + 7.97120i) q^{64} -4.98026i q^{65} +(-1.06413 + 1.09468i) q^{66} -4.56989i q^{67} +(3.82013 - 7.30798i) q^{68} +7.25549i q^{69} +(1.04205 + 1.01298i) q^{70} +12.9933i q^{71} +(-1.78401 - 1.63865i) q^{72} -0.800933i q^{73} +(3.17983 - 3.27110i) q^{74} +1.46409 q^{75} +(-5.64642 + 0.159808i) q^{76} +0.757688i q^{77} +(-7.39399 - 7.18768i) q^{78} -7.83068i q^{79} +(3.99360 - 0.226238i) q^{80} -5.69721 q^{81} +(-4.51512 - 4.38914i) q^{82} -10.7517i q^{83} +(3.00784 - 0.0851293i) q^{84} +(-3.59849 - 2.01268i) q^{85} +(-6.04856 - 5.87980i) q^{86} +7.12949 q^{87} +(1.53589 + 1.41076i) q^{88} -6.70231 q^{89} +(-0.844234 + 0.868466i) q^{90} -5.11780 q^{91} +(9.90729 - 0.280400i) q^{92} +11.2357i q^{93} +(-11.2150 + 11.5369i) q^{94} +2.82434i q^{95} +(5.42780 - 6.25564i) q^{96} +7.53723i q^{97} +(-5.85932 + 6.02750i) q^{98} -0.631473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 2 q^{4} - 36 q^{5} + 36 q^{9} + 8 q^{11} + 2 q^{12} - 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} - 2 q^{20} - 26 q^{24} + 36 q^{25} + 6 q^{26} + 16 q^{27} - 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots + 40 q^{99}+O(q^{100}) \) 36 * q + 4 * q^3 + 2 * q^4 - 36 * q^5 + 36 * q^9 + 8 * q^11 + 2 * q^12 - 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 - 2 * q^20 - 26 * q^24 + 36 * q^25 + 6 * q^26 + 16 * q^27 - 14 * q^28 - 10 * q^32 - 8 * q^33 + 12 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 - 6 * q^44 - 36 * q^45 - 24 * q^46 + 20 * q^47 + 4 * q^48 - 36 * q^49 + 6 * q^52 + 56 * q^54 - 8 * q^55 - 20 * q^56 + 18 * q^58 - 2 * q^60 + 24 * q^62 + 14 * q^64 - 16 * q^66 + 16 * q^68 + 2 * q^70 - 54 * q^72 - 6 * q^74 + 4 * q^75 + 2 * q^76 + 14 * q^78 - 6 * q^80 + 44 * q^81 - 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 + 58 * q^88 + 10 * q^90 + 56 * q^91 + 12 * q^92 + 14 * q^94 + 24 * q^96 + 10 * q^98 + 40 * q^99

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