LMFDB - Embedded newform 1140.2.b.e.151.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1140,2,Mod(151,1140)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1140.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1140, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1140.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,-1,-20] 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:	$9.10294583043$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + x^{18} - 3 x^{17} + 5 x^{16} - 3 x^{15} + 5 x^{14} - 7 x^{13} - 4 x^{12} + 2 x^{11} + \cdots + 1024 $ x^20 - x^19 + x^18 - 3x^17 + 5x^16 - 3x^15 + 5x^14 - 7x^13 - 4x^12 + 2x^11 - 8x^10 + 4x^9 - 16x^8 - 56x^7 + 80x^6 - 96x^5 + 320x^4 - 384x^3 + 256x^2 - 512*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.20
Root			$-1.37956 - 0.311154i$ of defining polynomial
Character	$\chi$	$=$	1140.151
Dual form			1140.2.b.e.151.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37956 + 0.311154i) q^{2} -1.00000 q^{3} +(1.80637 + 0.858511i) q^{4} +1.00000 q^{5} +(-1.37956 - 0.311154i) q^{6} -0.407387i q^{7} +(2.22486 + 1.74642i) q^{8} +1.00000 q^{9} +(1.37956 + 0.311154i) q^{10} -3.16208i q^{11} +(-1.80637 - 0.858511i) q^{12} +0.0877418i q^{13} +(0.126760 - 0.562014i) q^{14} -1.00000 q^{15} +(2.52592 + 3.10157i) q^{16} +3.73926 q^{17} +(1.37956 + 0.311154i) q^{18} +(3.39555 - 2.73317i) q^{19} +(1.80637 + 0.858511i) q^{20} +0.407387i q^{21} +(0.983893 - 4.36227i) q^{22} -1.97278i q^{23} +(-2.22486 - 1.74642i) q^{24} +1.00000 q^{25} +(-0.0273012 + 0.121045i) q^{26} -1.00000 q^{27} +(0.349746 - 0.735890i) q^{28} +8.67924i q^{29} +(-1.37956 - 0.311154i) q^{30} -0.689183 q^{31} +(2.51959 + 5.06475i) q^{32} +3.16208i q^{33} +(5.15853 + 1.16349i) q^{34} -0.407387i q^{35} +(1.80637 + 0.858511i) q^{36} -3.46642i q^{37} +(5.53480 - 2.71404i) q^{38} -0.0877418i q^{39} +(2.22486 + 1.74642i) q^{40} +8.08486i q^{41} +(-0.126760 + 0.562014i) q^{42} +6.90046i q^{43} +(2.71468 - 5.71187i) q^{44} +1.00000 q^{45} +(0.613839 - 2.72157i) q^{46} -7.21521i q^{47} +(-2.52592 - 3.10157i) q^{48} +6.83404 q^{49} +(1.37956 + 0.311154i) q^{50} -3.73926 q^{51} +(-0.0753273 + 0.158494i) q^{52} -10.4335i q^{53} +(-1.37956 - 0.311154i) q^{54} -3.16208i q^{55} +(0.711470 - 0.906378i) q^{56} +(-3.39555 + 2.73317i) q^{57} +(-2.70058 + 11.9735i) q^{58} -0.925355 q^{59} +(-1.80637 - 0.858511i) q^{60} +0.385462 q^{61} +(-0.950768 - 0.214442i) q^{62} -0.407387i q^{63} +(1.90000 + 7.77110i) q^{64} +0.0877418i q^{65} +(-0.983893 + 4.36227i) q^{66} -5.36985 q^{67} +(6.75447 + 3.21020i) q^{68} +1.97278i q^{69} +(0.126760 - 0.562014i) q^{70} -6.13547 q^{71} +(2.22486 + 1.74642i) q^{72} -2.86281 q^{73} +(1.07859 - 4.78213i) q^{74} -1.00000 q^{75} +(8.48007 - 2.02200i) q^{76} -1.28819 q^{77} +(0.0273012 - 0.121045i) q^{78} +6.33459 q^{79} +(2.52592 + 3.10157i) q^{80} +1.00000 q^{81} +(-2.51564 + 11.1535i) q^{82} +4.89317i q^{83} +(-0.349746 + 0.735890i) q^{84} +3.73926 q^{85} +(-2.14711 + 9.51959i) q^{86} -8.67924i q^{87} +(5.52233 - 7.03518i) q^{88} -1.37139i q^{89} +(1.37956 + 0.311154i) q^{90} +0.0357448 q^{91} +(1.69365 - 3.56357i) q^{92} +0.689183 q^{93} +(2.24504 - 9.95380i) q^{94} +(3.39555 - 2.73317i) q^{95} +(-2.51959 - 5.06475i) q^{96} +6.41554i q^{97} +(9.42796 + 2.12644i) q^{98} -3.16208i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} - 20 q^{3} - q^{4} + 20 q^{5} + q^{6} - 7 q^{8} + 20 q^{9} - q^{10} + q^{12} - 20 q^{15} - 9 q^{16} + 8 q^{17} - q^{18} - 2 q^{19} - q^{20} + 7 q^{24} + 20 q^{25} + 2 q^{26} - 20 q^{27}+ \cdots - 3 q^{98}+O(q^{100}) $ 20 * q - q^2 - 20 * q^3 - q^4 + 20 * q^5 + q^6 - 7 * q^8 + 20 * q^9 - q^10 + q^12 - 20 * q^15 - 9 * q^16 + 8 * q^17 - q^18 - 2 * q^19 - q^20 + 7 * q^24 + 20 * q^25 + 2 * q^26 - 20 * q^27 + 24 * q^28 + q^30 - 20 * q^31 + 9 * q^32 + 6 * q^34 - q^36 - 5 * q^38 - 7 * q^40 + 4 * q^44 + 20 * q^45 + 6 * q^46 + 9 * q^48 - 28 * q^49 - q^50 - 8 * q^51 + 22 * q^52 + q^54 - 24 * q^56 + 2 * q^57 + 10 * q^58 + 8 * q^59 + q^60 + 28 * q^61 - q^64 - 28 * q^67 - 6 * q^68 + 8 * q^71 - 7 * q^72 + 12 * q^73 + 14 * q^74 - 20 * q^75 + 11 * q^76 - 32 * q^77 - 2 * q^78 + 32 * q^79 - 9 * q^80 + 20 * q^81 - 22 * q^82 - 24 * q^84 + 8 * q^85 - 24 * q^86 + 16 * q^88 - q^90 - 24 * q^91 - 6 * q^92 + 20 * q^93 + 30 * q^94 - 2 * q^95 - 9 * q^96 - 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1140\mathbb{Z}\right)^\times$.

$n$	$457$	$571$	$761$	$781$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	1.37956	+	0.311154i	0.975496	+	0.220019i
$2$	1.37956	+	0.311154i	0.975496	+	0.220019i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.80637	+	0.858511i	0.903183	+	0.429255i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.37956	−	0.311154i	−0.563203	−	0.127028i
$7$		−	0.407387i		−	0.153978i	−0.997032	−	0.0769889i	$-0.975469\pi$
$7$		−	0.407387i		−	0.153978i	0.997032	−	0.0769889i	$-0.0245306\pi$
$8$	2.22486	+	1.74642i	0.786607	+	0.617454i
$9$	1.00000			0.333333
$10$	1.37956	+	0.311154i	0.436255	+	0.0983956i
$11$		−	3.16208i		−	0.953402i	−0.879065	−	0.476701i	$-0.841832\pi$
$11$		−	3.16208i		−	0.953402i	0.879065	−	0.476701i	$-0.158168\pi$
$12$	−1.80637	−	0.858511i	−0.521453	−	0.247831i
$13$			0.0877418i			0.0243352i	0.999926	+	0.0121676i	$0.00387316\pi$
$13$			0.0877418i			0.0243352i	−0.999926	+	0.0121676i	$0.996127\pi$
$14$	0.126760	−	0.562014i	0.0338780	−	0.150205i
$15$	−1.00000			−0.258199
$16$	2.52592	+	3.10157i	0.631479	+	0.775393i
$17$	3.73926			0.906904			0.453452	−	0.891281i	$-0.350192\pi$
$17$	3.73926			0.906904			0.453452	+	0.891281i	$0.350192\pi$
$18$	1.37956	+	0.311154i	0.325165	+	0.0733397i
$19$	3.39555	−	2.73317i	0.778993	−	0.627033i
$19$	3.39555	−	2.73317i	0.778993	−	0.627033i
$20$	1.80637	+	0.858511i	0.403916	+	0.191969i
$21$			0.407387i			0.0888991i
$22$	0.983893	−	4.36227i	0.209767	−	0.930040i
$23$		−	1.97278i		−	0.411354i	−0.978620	−	0.205677i	$-0.934060\pi$
$23$		−	1.97278i		−	0.411354i	0.978620	−	0.205677i	$-0.0659395\pi$
$24$	−2.22486	−	1.74642i	−0.454148	−	0.356487i
$25$	1.00000			0.200000
$26$	−0.0273012	+	0.121045i	−0.00535421	+	0.0237389i
$27$	−1.00000			−0.192450
$28$	0.349746	−	0.735890i	0.0660958	−	0.139070i
$29$			8.67924i			1.61169i	0.592124	+	0.805847i	$0.298290\pi$
$29$			8.67924i			1.61169i	−0.592124	+	0.805847i	$0.701710\pi$
$30$	−1.37956	−	0.311154i	−0.251872	−	0.0568087i
$31$	−0.689183			−0.123781			−0.0618904	−	0.998083i	$-0.519713\pi$
$31$	−0.689183			−0.123781			−0.0618904	+	0.998083i	$0.519713\pi$
$32$	2.51959	+	5.06475i	0.445404	+	0.895330i
$33$			3.16208i			0.550447i
$34$	5.15853	+	1.16349i	0.884681	+	0.199536i
$35$		−	0.407387i		−	0.0688609i
$36$	1.80637	+	0.858511i	0.301061	+	0.143085i
$37$		−	3.46642i		−	0.569875i	−0.958546	−	0.284938i	$-0.908027\pi$
$37$		−	3.46642i		−	0.569875i	0.958546	−	0.284938i	$-0.0919729\pi$
$38$	5.53480	−	2.71404i	0.897863	−	0.440275i
$39$		−	0.0877418i		−	0.0140499i
$40$	2.22486	+	1.74642i	0.351781	+	0.276134i
$41$			8.08486i			1.26264i	0.775521	+	0.631321i	$0.217487\pi$
$41$			8.08486i			1.26264i	−0.775521	+	0.631321i	$0.782513\pi$
$42$	−0.126760	+	0.562014i	−0.0195595	+	0.0867206i
$43$			6.90046i			1.05231i	0.850389	+	0.526155i	$0.176367\pi$
$43$			6.90046i			1.05231i	−0.850389	+	0.526155i	$0.823633\pi$
$44$	2.71468	−	5.71187i	0.409253	−	0.861097i
$45$	1.00000			0.149071
$46$	0.613839	−	2.72157i	0.0905057	−	0.401274i
$47$		−	7.21521i		−	1.05245i	−0.850347	−	0.526223i	$-0.823608\pi$
$47$		−	7.21521i		−	1.05245i	0.850347	−	0.526223i	$-0.176392\pi$
$48$	−2.52592	−	3.10157i	−0.364585	−	0.447673i
$49$	6.83404			0.976291
$50$	1.37956	+	0.311154i	0.195099	+	0.0440038i
$51$	−3.73926			−0.523601
$52$	−0.0753273	+	0.158494i	−0.0104460	+	0.0219791i
$53$		−	10.4335i		−	1.43315i	−0.697509	−	0.716576i	$-0.745708\pi$
$53$		−	10.4335i		−	1.43315i	0.697509	−	0.716576i	$-0.254292\pi$
$54$	−1.37956	−	0.311154i	−0.187734	−	0.0423427i
$55$		−	3.16208i		−	0.426374i
$56$	0.711470	−	0.906378i	0.0950742	−	0.121120i
$57$	−3.39555	+	2.73317i	−0.449752	+	0.362018i
$58$	−2.70058	+	11.9735i	−0.354604	+	1.57220i
$59$	−0.925355			−0.120471			−0.0602355	−	0.998184i	$-0.519185\pi$
$59$	−0.925355			−0.120471			−0.0602355	+	0.998184i	$0.519185\pi$
$60$	−1.80637	−	0.858511i	−0.233201	−	0.110833i
$61$	0.385462			0.0493533			0.0246767	−	0.999695i	$-0.492144\pi$
$61$	0.385462			0.0493533			0.0246767	+	0.999695i	$0.492144\pi$
$62$	−0.950768	−	0.214442i	−0.120748	−	0.0272342i
$63$		−	0.407387i		−	0.0513259i
$64$	1.90000	+	7.77110i	0.237500	+	0.971388i
$65$			0.0877418i			0.0108830i
$66$	−0.983893	+	4.36227i	−0.121109	+	0.536959i
$67$	−5.36985			−0.656031			−0.328016	−	0.944672i	$-0.606380\pi$
$67$	−5.36985			−0.656031			−0.328016	+	0.944672i	$0.606380\pi$
$68$	6.75447	+	3.21020i	0.819100	+	0.389293i
$69$			1.97278i			0.237495i
$70$	0.126760	−	0.562014i	0.0151507	−	0.0671735i
$71$	−6.13547			−0.728146			−0.364073	−	0.931370i	$-0.618614\pi$
$71$	−6.13547			−0.728146			−0.364073	+	0.931370i	$0.618614\pi$
$72$	2.22486	+	1.74642i	0.262202	+	0.205818i
$73$	−2.86281			−0.335066			−0.167533	−	0.985866i	$-0.553580\pi$
$73$	−2.86281			−0.335066			−0.167533	+	0.985866i	$0.553580\pi$
$74$	1.07859	−	4.78213i	0.125384	−	0.555911i
$75$	−1.00000			−0.115470
$76$	8.48007	−	2.02200i	0.972730	−	0.231939i
$77$	−1.28819			−0.146803
$78$	0.0273012	−	0.121045i	0.00309125	−	0.0137056i
$79$	6.33459			0.712697			0.356348	−	0.934353i	$-0.384022\pi$
$79$	6.33459			0.712697			0.356348	+	0.934353i	$0.384022\pi$
$80$	2.52592	+	3.10157i	0.282406	+	0.346766i
$81$	1.00000			0.111111
$82$	−2.51564	+	11.1535i	−0.277806	+	1.23170i
$83$			4.89317i			0.537096i	0.963266	+	0.268548i	$0.0865437\pi$
$83$			4.89317i			0.537096i	−0.963266	+	0.268548i	$0.913456\pi$
$84$	−0.349746	+	0.735890i	−0.0381604	+	0.0802921i
$85$	3.73926			0.405580
$86$	−2.14711	+	9.51959i	−0.231528	+	1.02652i
$87$		−	8.67924i		−	0.930512i
$88$	5.52233	−	7.03518i	0.588682	−	0.749953i
$89$		−	1.37139i		−	0.145367i	−0.997355	−	0.0726835i	$-0.976844\pi$
$89$		−	1.37139i		−	0.145367i	0.997355	−	0.0726835i	$-0.0231563\pi$
$90$	1.37956	+	0.311154i	0.145418	+	0.0327985i
$91$	0.0357448			0.00374708
$92$	1.69365	−	3.56357i	0.176576	−	0.371528i
$93$	0.689183			0.0714649
$94$	2.24504	−	9.95380i	0.231558	−	1.02666i
$95$	3.39555	−	2.73317i	0.348376	−	0.280418i
$96$	−2.51959	−	5.06475i	−0.257154	−	0.516919i
$97$			6.41554i			0.651399i	0.945473	+	0.325700i	$0.105600\pi$
$97$			6.41554i			0.651399i	−0.945473	+	0.325700i	$0.894400\pi$
$98$	9.42796	+	2.12644i	0.952367	+	0.214803i
$99$		−	3.16208i		−	0.317801i
$100$	1.80637	+	0.858511i	0.180637	+	0.0858511i
$101$	0.114595			0.0114026			0.00570129	−	0.999984i	$-0.498185\pi$
$101$	0.114595			0.0114026			0.00570129	+	0.999984i	$0.498185\pi$
$102$	−5.15853	−	1.16349i	−0.510771	−	0.115202i
$103$	5.44996			0.537001			0.268500	−	0.963280i	$-0.413472\pi$
$103$	5.44996			0.537001			0.268500	+	0.963280i	$0.413472\pi$
$104$	−0.153234	+	0.195213i	−0.0150259	+	0.0191422i
$105$			0.407387i			0.0397569i
$106$	3.24643	−	14.3936i	0.315321	−	1.39803i
$107$	−17.3925			−1.68140			−0.840700	−	0.541501i	$-0.817856\pi$
$107$	−17.3925			−1.68140			−0.840700	+	0.541501i	$0.817856\pi$
$108$	−1.80637	−	0.858511i	−0.173818	−	0.0826103i
$109$			3.30988i			0.317029i	0.987357	+	0.158514i	$0.0506704\pi$
$109$			3.30988i			0.317029i	−0.987357	+	0.158514i	$0.949330\pi$
$110$	0.983893	−	4.36227i	0.0938106	−	0.415926i
$111$			3.46642i			0.329018i
$112$	1.26354	−	1.02903i	0.119393	−	0.0972338i
$113$			0.646488i			0.0608165i	0.999538	+	0.0304082i	$0.00968074\pi$
$113$			0.646488i			0.0608165i	−0.999538	+	0.0304082i	$0.990319\pi$
$114$	−5.53480	+	2.71404i	−0.518381	+	0.254193i
$115$		−	1.97278i		−	0.183963i
$116$	−7.45122	+	15.6779i	−0.691828	+	1.45565i
$117$			0.0877418i			0.00811173i
$118$	−1.27658	−	0.287928i	−0.117519	−	0.0265059i
$119$		−	1.52332i		−	0.139643i
$120$	−2.22486	−	1.74642i	−0.203101	−	0.159426i
$121$	1.00126			0.0910241
$122$	0.531767	+	0.119938i	0.0481440	+	0.0108587i
$123$		−	8.08486i		−	0.728987i
$124$	−1.24492	−	0.591671i	−0.111797	−	0.0531336i
$125$	1.00000			0.0894427
$126$	0.126760	−	0.562014i	0.0112927	−	0.0500682i
$127$	−18.2339			−1.61800			−0.808999	−	0.587810i	$-0.799990\pi$
$127$	−18.2339			−1.61800			−0.808999	+	0.587810i	$0.799990\pi$
$128$	0.203154	+	11.3119i	0.0179564	+	0.999839i
$129$		−	6.90046i		−	0.607552i
$130$	−0.0273012	+	0.121045i	−0.00239447	+	0.0106163i
$131$		−	17.9304i		−	1.56658i	−0.621654	−	0.783292i	$-0.713539\pi$
$131$		−	17.9304i		−	1.56658i	0.621654	−	0.783292i	$-0.286461\pi$
$132$	−2.71468	+	5.71187i	−0.236282	+	0.497154i
$133$	−1.11346	−	1.38330i	−0.0965491	−	0.119947i
$134$	−7.40802	−	1.67085i	−0.639956	−	0.144339i
$135$	−1.00000			−0.0860663
$136$	8.31933	+	6.53034i	0.713377	+	0.559972i
$137$	−15.2737			−1.30492			−0.652462	−	0.757821i	$-0.726264\pi$
$137$	−15.2737			−1.30492			−0.652462	+	0.757821i	$0.726264\pi$
$138$	−0.613839	+	2.72157i	−0.0522535	+	0.231675i
$139$		−	2.85097i		−	0.241816i	−0.992664	−	0.120908i	$-0.961419\pi$
$139$		−	2.85097i		−	0.241816i	0.992664	−	0.120908i	$-0.0385806\pi$
$140$	0.349746	−	0.735890i	0.0295589	−	0.0621940i
$141$			7.21521i			0.607630i
$142$	−8.46424	−	1.90908i	−0.710303	−	0.160206i
$143$	0.277446			0.0232012
$144$	2.52592	+	3.10157i	0.210493	+	0.258464i
$145$			8.67924i			0.720771i
$146$	−3.94941	−	0.890775i	−0.326856	−	0.0737210i
$147$	−6.83404			−0.563662
$148$	2.97596	−	6.26162i	0.244622	−	0.514702i
$149$	−10.6479			−0.872313			−0.436157	−	0.899871i	$-0.643661\pi$
$149$	−10.6479			−0.872313			−0.436157	+	0.899871i	$0.643661\pi$
$150$	−1.37956	−	0.311154i	−0.112641	−	0.0254056i
$151$	0.916363			0.0745726			0.0372863	−	0.999305i	$-0.488129\pi$
$151$	0.916363			0.0745726			0.0372863	+	0.999305i	$0.488129\pi$
$152$	12.3279	−	0.150857i	0.999925	−	0.0122361i
$153$	3.73926			0.302301
$154$	−1.77713	−	0.400825i	−0.143205	−	0.0322994i
$155$	−0.689183			−0.0553565
$156$	0.0753273	−	0.158494i	0.00603101	−	0.0126897i
$157$	−15.1879			−1.21212			−0.606062	−	0.795418i	$-0.707252\pi$
$157$	−15.1879			−1.21212			−0.606062	+	0.795418i	$0.707252\pi$
$158$	8.73894	+	1.97103i	0.695233	+	0.156807i
$159$			10.4335i			0.827430i
$160$	2.51959	+	5.06475i	0.199191	+	0.400404i
$161$	−0.803685			−0.0633393
$162$	1.37956	+	0.311154i	0.108388	+	0.0244466i
$163$			7.62126i			0.596943i	0.954419	+	0.298471i	$0.0964768\pi$
$163$			7.62126i			0.596943i	−0.954419	+	0.298471i	$0.903523\pi$
$164$	−6.94094	+	14.6042i	−0.541996	+	1.14040i
$165$			3.16208i			0.246167i
$166$	−1.52253	+	6.75042i	−0.118171	+	0.523934i
$167$	−4.27454			−0.330774			−0.165387	−	0.986229i	$-0.552887\pi$
$167$	−4.27454			−0.330774			−0.165387	+	0.986229i	$0.552887\pi$
$168$	−0.711470	+	0.906378i	−0.0548911	+	0.0699286i
$169$	12.9923			0.999408
$170$	5.15853	+	1.16349i	0.395641	+	0.0892353i
$171$	3.39555	−	2.73317i	0.259664	−	0.209011i
$172$	−5.92412	+	12.4648i	−0.451710	+	0.950429i
$173$			0.430737i			0.0327483i	0.999866	+	0.0163742i	$0.00521229\pi$
$173$			0.430737i			0.0327483i	−0.999866	+	0.0163742i	$0.994788\pi$
$174$	2.70058	−	11.9735i	0.204730	−	0.907710i
$175$		−	0.407387i		−	0.0307955i
$176$	9.80741	−	7.98715i	0.739261	−	0.602054i
$177$	0.925355			0.0695540
$178$	0.426713	−	1.89191i	0.0319835	−	0.141805i
$179$	−8.62395			−0.644584			−0.322292	−	0.946640i	$-0.604453\pi$
$179$	−8.62395			−0.644584			−0.322292	+	0.946640i	$0.604453\pi$
$180$	1.80637	+	0.858511i	0.134639	+	0.0639896i
$181$		−	11.3890i		−	0.846535i	−0.906005	−	0.423268i	$-0.860883\pi$
$181$		−	11.3890i		−	0.846535i	0.906005	−	0.423268i	$-0.139117\pi$
$182$	0.0493121	+	0.0111221i	0.00365526	+	0.000824429i
$183$	−0.385462			−0.0284942
$184$	3.44532	−	4.38916i	0.253992	−	0.323573i
$185$		−	3.46642i		−	0.254856i
$186$	0.950768	+	0.214442i	0.0697137	+	0.0157237i
$187$		−	11.8238i		−	0.864644i
$188$	6.19433	−	13.0333i	0.451768	−	0.950552i
$189$			0.407387i			0.0296330i
$190$	5.53480	−	2.71404i	0.401537	−	0.196897i
$191$		−	22.5660i		−	1.63282i	−0.577475	−	0.816408i	$-0.695962\pi$
$191$		−	22.5660i		−	1.63282i	0.577475	−	0.816408i	$-0.304038\pi$
$192$	−1.90000	−	7.77110i	−0.137121	−	0.560831i
$193$		−	20.6444i		−	1.48602i	−0.669281	−	0.743009i	$-0.733398\pi$
$193$		−	20.6444i		−	1.48602i	0.669281	−	0.743009i	$-0.266602\pi$
$194$	−1.99622	+	8.85061i	−0.143320	+	0.635437i
$195$		−	0.0877418i		−	0.00628332i
$196$	12.3448	+	5.86709i	0.881769	+	0.419078i
$197$	−21.1531			−1.50709			−0.753547	−	0.657394i	$-0.771659\pi$
$197$	−21.1531			−1.50709			−0.753547	+	0.657394i	$0.771659\pi$
$198$	0.983893	−	4.36227i	0.0699223	−	0.310013i
$199$			14.3465i			1.01700i	0.861063	+	0.508498i	$0.169799\pi$
$199$			14.3465i			1.01700i	−0.861063	+	0.508498i	$0.830201\pi$
$200$	2.22486	+	1.74642i	0.157321	+	0.123491i
$201$	5.36985			0.378760
$202$	0.158090	+	0.0356566i	0.0111232	+	0.00250879i
$203$	3.53581			0.248165
$204$	−6.75447	−	3.21020i	−0.472908	−	0.224759i
$205$			8.08486i			0.564671i
$206$	7.51855	+	1.69578i	0.523842	+	0.118150i
$207$		−	1.97278i		−	0.137118i
$208$	−0.272137	+	0.221628i	−0.0188693	+	0.0153672i
$209$	−8.64251	−	10.7370i	−0.597815	−	0.742693i
$210$	−0.126760	+	0.562014i	−0.00874727	+	0.0387827i
$211$	−0.0399114			−0.00274762			−0.00137381	−	0.999999i	$-0.500437\pi$
$211$	−0.0399114			−0.00274762			−0.00137381	+	0.999999i	$0.500437\pi$
$212$	8.95727	−	18.8467i	0.615188	−	1.29440i
$213$	6.13547			0.420395
$214$	−23.9940	−	5.41176i	−1.64020	−	0.369940i
$215$			6.90046i			0.470608i
$216$	−2.22486	−	1.74642i	−0.151383	−	0.118829i
$217$			0.280764i			0.0190595i
$218$	−1.02988	+	4.56617i	−0.0697524	+	0.309260i
$219$	2.86281			0.193451
$220$	2.71468	−	5.71187i	0.183024	−	0.385094i
$221$			0.328089i			0.0220697i
$222$	−1.07859	+	4.78213i	−0.0723902	+	0.320955i
$223$	2.20126			0.147407			0.0737037	−	0.997280i	$-0.476518\pi$
$223$	2.20126			0.147407			0.0737037	+	0.997280i	$0.476518\pi$
$224$	2.06331	−	1.02645i	0.137861	−	0.0685823i
$225$	1.00000			0.0666667
$226$	−0.201157	+	0.891869i	−0.0133808	+	0.0593262i
$227$	−18.5260			−1.22961			−0.614807	−	0.788677i	$-0.710766\pi$
$227$	−18.5260			−1.22961			−0.614807	+	0.788677i	$0.710766\pi$
$228$	−8.48007	+	2.02200i	−0.561606	+	0.133910i
$229$	0.00178692			0.000118083			5.90414e−5	−	1.00000i	$-0.499981\pi$
$229$	0.00178692			0.000118083			5.90414e−5		1.00000i	$0.499981\pi$
$230$	0.613839	−	2.72157i	0.0404754	−	0.179455i
$231$	1.28819			0.0847566
$232$	−15.1576	+	19.3101i	−0.995147	+	1.26777i
$233$	−19.7774			−1.29566			−0.647830	−	0.761785i	$-0.724323\pi$
$233$	−19.7774			−1.29566			−0.647830	+	0.761785i	$0.724323\pi$
$234$	−0.0273012	+	0.121045i	−0.00178474	+	0.00791295i
$235$		−	7.21521i		−	0.470668i
$236$	−1.67153	−	0.794428i	−0.108807	−	0.0517128i
$237$	−6.33459			−0.411476
$238$	0.473989	−	2.10152i	0.0307241	−	0.136221i
$239$			14.2664i			0.922816i	0.887188	+	0.461408i	$0.152656\pi$
$239$			14.2664i			0.922816i	−0.887188	+	0.461408i	$0.847344\pi$
$240$	−2.52592	−	3.10157i	−0.163047	−	0.200206i
$241$			23.6486i			1.52334i	0.647966	+	0.761669i	$0.275620\pi$
$241$			23.6486i			1.52334i	−0.647966	+	0.761669i	$0.724380\pi$
$242$	1.38130	+	0.311548i	0.0887936	+	0.0200270i
$243$	−1.00000			−0.0641500
$244$	0.696285	+	0.330923i	0.0445751	+	0.0211852i
$245$	6.83404			0.436611
$246$	2.51564	−	11.1535i	0.160391	−	0.711124i
$247$	0.239814	+	0.297931i	0.0152590	+	0.0189569i
$248$	−1.53333	−	1.20361i	−0.0973668	−	0.0764290i
$249$		−	4.89317i		−	0.310092i
$250$	1.37956	+	0.311154i	0.0872510	+	0.0196791i
$251$			10.9092i			0.688582i	0.938863	+	0.344291i	$0.111881\pi$
$251$			10.9092i			0.688582i	−0.938863	+	0.344291i	$0.888119\pi$
$252$	0.349746	−	0.735890i	0.0220319	−	0.0463567i
$253$	−6.23809			−0.392185
$254$	−25.1547	−	5.67355i	−1.57835	−	0.355990i
$255$	−3.73926			−0.234162
$256$	−3.23948	+	15.6686i	−0.202467	+	0.979289i
$257$		−	18.8150i		−	1.17365i	−0.809715	−	0.586823i	$-0.800378\pi$
$257$		−	18.8150i		−	1.17365i	0.809715	−	0.586823i	$-0.199622\pi$
$258$	2.14711	−	9.51959i	0.133673	−	0.592664i
$259$	−1.41217			−0.0877481
$260$	−0.0753273	+	0.158494i	−0.00467160	+	0.00982936i
$261$			8.67924i			0.537231i
$262$	5.57911	−	24.7360i	0.344679	−	1.52820i
$263$			27.6061i			1.70226i	0.524952	+	0.851132i	$0.324083\pi$
$263$			27.6061i			1.70226i	−0.524952	+	0.851132i	$0.675917\pi$
$264$	−5.52233	+	7.03518i	−0.339876	+	0.432985i
$265$		−	10.4335i		−	0.640925i
$266$	−1.10566	−	2.25480i	−0.0677925	−	0.138251i
$267$			1.37139i			0.0839276i
$268$	−9.69991	−	4.61007i	−0.592516	−	0.281605i
$269$		−	30.6681i		−	1.86986i	−0.354826	−	0.934932i	$-0.615460\pi$
$269$		−	30.6681i		−	1.86986i	0.354826	−	0.934932i	$-0.384540\pi$
$270$	−1.37956	−	0.311154i	−0.0839573	−	0.0189362i
$271$			15.3633i			0.933256i	0.884454	+	0.466628i	$0.154531\pi$
$271$			15.3633i			0.933256i	−0.884454	+	0.466628i	$0.845469\pi$
$272$	9.44506	+	11.5976i	0.572691	+	0.703206i
$273$	−0.0357448			−0.00216338
$274$	−21.0710	−	4.75249i	−1.27295	−	0.287108i
$275$		−	3.16208i		−	0.190680i
$276$	−1.69365	+	3.56357i	−0.101946	+	0.214502i
$277$	−4.80900			−0.288945			−0.144473	−	0.989509i	$-0.546149\pi$
$277$	−4.80900			−0.288945			−0.144473	+	0.989509i	$0.546149\pi$
$278$	0.887091	−	3.93308i	0.0532042	−	0.235891i
$279$	−0.689183			−0.0412603
$280$	0.711470	−	0.906378i	0.0425185	−	0.0541665i
$281$			8.94204i			0.533437i	0.963774	+	0.266719i	$0.0859395\pi$
$281$			8.94204i			0.533437i	−0.963774	+	0.266719i	$0.914061\pi$
$282$	−2.24504	+	9.95380i	−0.133690	+	0.592740i
$283$			9.11343i			0.541737i	0.962616	+	0.270868i	$0.0873108\pi$
$283$			9.11343i			0.541737i	−0.962616	+	0.270868i	$0.912689\pi$
$284$	−11.0829	−	5.26737i	−0.657649	−	0.312561i
$285$	−3.39555	+	2.73317i	−0.201135	+	0.161899i
$286$	0.382753	+	0.0863285i	0.0226327	+	0.00510471i
$287$	3.29366			0.194419
$288$	2.51959	+	5.06475i	0.148468	+	0.298443i
$289$	−3.01793			−0.177525
$290$	−2.70058	+	11.9735i	−0.158584	+	0.703109i
$291$		−	6.41554i		−	0.376085i
$292$	−5.17128	−	2.45775i	−0.302626	−	0.143829i
$293$		−	12.8243i		−	0.749206i	−0.927185	−	0.374603i	$-0.877779\pi$
$293$		−	12.8243i		−	0.749206i	0.927185	−	0.374603i	$-0.122221\pi$
$294$	−9.42796	−	2.12644i	−0.549850	−	0.124016i
$295$	−0.925355			−0.0538763
$296$	6.05384	−	7.71229i	0.351872	−	0.448268i
$297$			3.16208i			0.183482i
$298$	−14.6895	−	3.31315i	−0.850938	−	0.191926i
$299$	0.173095			0.0100104
$300$	−1.80637	−	0.858511i	−0.104291	−	0.0495662i
$301$	2.81116			0.162032
$302$	1.26418	+	0.285130i	0.0727452	+	0.0164074i
$303$	−0.114595			−0.00658329
$304$	17.0540	+	3.62776i	0.978115	+	0.208066i
$305$	0.385462			0.0220715
$306$	5.15853	+	1.16349i	0.294894	+	0.0665121i
$307$	18.2952			1.04416			0.522081	−	0.852896i	$-0.325156\pi$
$307$	18.2952			1.04416			0.522081	+	0.852896i	$0.325156\pi$
$308$	−2.32694	−	1.10592i	−0.132590	−	0.0630159i
$309$	−5.44996			−0.310038
$310$	−0.950768	−	0.214442i	−0.0540000	−	0.0121795i
$311$			18.6603i			1.05813i	0.848582	+	0.529064i	$0.177457\pi$
$311$			18.6603i			1.05813i	−0.848582	+	0.529064i	$0.822543\pi$
$312$	0.153234	−	0.195213i	0.00867519	−	0.0110518i
$313$	15.8179			0.894083			0.447041	−	0.894513i	$-0.352478\pi$
$313$	15.8179			0.894083			0.447041	+	0.894513i	$0.352478\pi$
$314$	−20.9526	−	4.72577i	−1.18242	−	0.266690i
$315$		−	0.407387i		−	0.0229536i
$316$	11.4426	+	5.43831i	0.643696	+	0.305929i
$317$		−	24.2196i		−	1.36031i	−0.733069	−	0.680155i	$-0.761913\pi$
$317$		−	24.2196i		−	1.36031i	0.733069	−	0.680155i	$-0.238087\pi$
$318$	−3.24643	+	14.3936i	−0.182051	+	0.807155i
$319$	27.4444			1.53659
$320$	1.90000	+	7.77110i	0.106213	+	0.434418i
$321$	17.3925			0.970757
$322$	−1.10873	−	0.250070i	−0.0617872	−	0.0139359i
$323$	12.6968	−	10.2200i	0.706471	−	0.568659i
$324$	1.80637	+	0.858511i	0.100354	+	0.0476951i
$325$			0.0877418i			0.00486704i
$326$	−2.37139	+	10.5140i	−0.131339	+	0.582315i
$327$		−	3.30988i		−	0.183037i
$328$	−14.1196	+	17.9877i	−0.779624	+	0.993203i
$329$	−2.93938			−0.162053
$330$	−0.983893	+	4.36227i	−0.0541616	+	0.240135i
$331$	7.35910			0.404493			0.202246	−	0.979335i	$-0.435176\pi$
$331$	7.35910			0.404493			0.202246	+	0.979335i	$0.435176\pi$
$332$	−4.20084	+	8.83887i	−0.230551	+	0.485096i
$333$		−	3.46642i		−	0.189958i
$334$	−5.89698	−	1.33004i	−0.322668	−	0.0727766i
$335$	−5.36985			−0.293386
$336$	−1.26354	+	1.02903i	−0.0689317	+	0.0561379i
$337$			15.1844i			0.827145i	0.910471	+	0.413572i	$0.135719\pi$
$337$			15.1844i			0.827145i	−0.910471	+	0.413572i	$0.864281\pi$
$338$	17.9236	+	4.04261i	0.974918	+	0.219889i
$339$		−	0.646488i		−	0.0351124i
$340$	6.75447	+	3.21020i	0.366313	+	0.174097i
$341$			2.17925i			0.118013i
$342$	5.53480	−	2.71404i	0.299288	−	0.146758i
$343$		−	5.63580i		−	0.304305i
$344$	−12.0511	+	15.3526i	−0.649754	+	0.827754i
$345$			1.97278i			0.106211i
$346$	−0.134026	+	0.594227i	−0.00720526	+	0.0319458i
$347$			18.3659i			0.985934i	0.870048	+	0.492967i	$0.164088\pi$
$347$			18.3659i			0.985934i	−0.870048	+	0.492967i	$0.835912\pi$
$348$	7.45122	−	15.6779i	0.399427	−	0.840423i
$349$	30.0198			1.60692			0.803461	−	0.595357i	$-0.202989\pi$
$349$	30.0198			1.60692			0.803461	+	0.595357i	$0.202989\pi$
$350$	0.126760	−	0.562014i	0.00677561	−	0.0300409i
$351$		−	0.0877418i		−	0.00468331i
$352$	16.0151	−	7.96713i	0.853609	−	0.424649i
$353$	−7.16788			−0.381508			−0.190754	−	0.981638i	$-0.561093\pi$
$353$	−7.16788			−0.381508			−0.190754	+	0.981638i	$0.561093\pi$
$354$	1.27658	+	0.287928i	0.0678496	+	0.0153032i
$355$	−6.13547			−0.325637
$356$	1.17735	−	2.47723i	0.0623996	−	0.131293i
$357$			1.52332i			0.0806229i
$358$	−11.8973	−	2.68338i	−0.628789	−	0.141821i
$359$			9.44053i			0.498252i	0.968471	+	0.249126i	$0.0801434\pi$
$359$			9.44053i			0.498252i	−0.968471	+	0.249126i	$0.919857\pi$
$360$	2.22486	+	1.74642i	0.117260	+	0.0920447i
$361$	4.05952	−	18.5613i	0.213659	−	0.976908i
$362$	3.54372	−	15.7118i	0.186254	−	0.825791i
$363$	−1.00126			−0.0525528
$364$	0.0645682	+	0.0306873i	0.00338430	+	0.00160845i
$365$	−2.86281			−0.149846
$366$	−0.531767	−	0.119938i	−0.0277959	−	0.00626926i
$367$		−	6.59918i		−	0.344474i	−0.985056	−	0.172237i	$-0.944900\pi$
$367$		−	6.59918i		−	0.344474i	0.985056	−	0.172237i	$-0.0550996\pi$
$368$	6.11872	−	4.98309i	0.318960	−	0.259761i
$369$			8.08486i			0.420881i
$370$	1.07859	−	4.78213i	0.0560732	−	0.248611i
$371$	−4.25047			−0.220673
$372$	1.24492	+	0.591671i	0.0645459	+	0.0306767i
$373$		−	10.9994i		−	0.569528i	−0.958598	−	0.284764i	$-0.908085\pi$
$373$		−	10.9994i		−	0.569528i	0.958598	−	0.284764i	$-0.0919152\pi$
$374$	3.67903	−	16.3117i	0.190238	−	0.843457i
$375$	−1.00000			−0.0516398
$376$	12.6008	−	16.0528i	0.649837	−	0.827861i
$377$	−0.761531			−0.0392209
$378$	−0.126760	+	0.562014i	−0.00651983	+	0.0289069i
$379$	8.53800			0.438568			0.219284	−	0.975661i	$-0.429628\pi$
$379$	8.53800			0.438568			0.219284	+	0.975661i	$0.429628\pi$
$380$	8.48007	−	2.02200i	0.435018	−	0.103726i
$381$	18.2339			0.934151
$382$	7.02149	−	31.1311i	0.359251	−	1.59281i
$383$	35.1407			1.79561			0.897804	−	0.440395i	$-0.145162\pi$
$383$	35.1407			1.79561			0.897804	+	0.440395i	$0.145162\pi$
$384$	−0.203154	−	11.3119i	−0.0103671	−	0.577257i
$385$	−1.28819			−0.0656522
$386$	6.42360	−	28.4802i	0.326952	−	1.44960i
$387$			6.90046i			0.350770i
$388$	−5.50781	+	11.5888i	−0.279617	+	0.588333i
$389$	−32.2594			−1.63562			−0.817808	−	0.575492i	$-0.804811\pi$
$389$	−32.2594			−1.63562			−0.817808	+	0.575492i	$0.804811\pi$
$390$	0.0273012	−	0.121045i	0.00138245	−	0.00612935i
$391$		−	7.37675i		−	0.373058i
$392$	15.2048	+	11.9351i	0.767957	+	0.602815i
$393$			17.9304i			0.904468i
$394$	−29.1819	−	6.58187i	−1.47016	−	0.331590i
$395$	6.33459			0.318728
$396$	2.71468	−	5.71187i	0.136418	−	0.287032i
$397$	35.3600			1.77467			0.887333	−	0.461130i	$-0.152556\pi$
$397$	35.3600			1.77467			0.887333	+	0.461130i	$0.152556\pi$
$398$	−4.46397	+	19.7918i	−0.223759	+	0.992075i
$399$	1.11346	+	1.38330i	0.0557427	+	0.0692517i
$400$	2.52592	+	3.10157i	0.126296	+	0.155079i
$401$		−	5.25982i		−	0.262663i	−0.991339	−	0.131331i	$-0.958075\pi$
$401$		−	5.25982i		−	0.262663i	0.991339	−	0.131331i	$-0.0419252\pi$
$402$	7.40802	+	1.67085i	0.369479	+	0.0833344i
$403$		−	0.0604701i		−	0.00301223i
$404$	0.207000	+	0.0983807i	0.0102986	+	0.00489462i
$405$	1.00000			0.0496904
$406$	4.87785	+	1.10018i	0.242084	+	0.0546010i
$407$	−10.9611			−0.543321
$408$	−8.31933	−	6.53034i	−0.411868	−	0.323300i
$409$			24.5542i			1.21413i	0.794653	+	0.607063i	$0.207653\pi$
$409$			24.5542i			1.21413i	−0.794653	+	0.607063i	$0.792347\pi$
$410$	−2.51564	+	11.1535i	−0.124238	+	0.550834i
$411$	15.2737			0.753398
$412$	9.84463	+	4.67885i	0.485010	+	0.230511i
$413$			0.376978i			0.0185499i
$414$	0.613839	−	2.72157i	0.0301686	−	0.133758i
$415$			4.89317i			0.240196i
$416$	−0.444390	+	0.221073i	−0.0217880	+	0.0108390i
$417$			2.85097i			0.139613i
$418$	−8.58199	−	17.5015i	−0.419759	−	0.856025i
$419$			27.0716i			1.32253i	0.750150	+	0.661267i	$0.229981\pi$
$419$			27.0716i			1.32253i	−0.750150	+	0.661267i	$0.770019\pi$
$420$	−0.349746	+	0.735890i	−0.0170659	+	0.0359077i
$421$			6.21223i			0.302766i	0.988475	+	0.151383i	$0.0483726\pi$
$421$			6.21223i			0.302766i	−0.988475	+	0.151383i	$0.951627\pi$
$422$	−0.0550602	−	0.0124186i	−0.00268029	−	0.000604528i
$423$		−	7.21521i		−	0.350815i
$424$	18.2213	−	23.2131i	0.884906	−	1.12733i
$425$	3.73926			0.181381
$426$	8.46424	+	1.90908i	0.410094	+	0.0924951i
$427$		−	0.157032i		−	0.00759931i
$428$	−31.4173	−	14.9317i	−1.51861	−	0.721750i
$429$	−0.277446			−0.0133952
$430$	−2.14711	+	9.51959i	−0.103543	+	0.459076i
$431$	−10.2808			−0.495208			−0.247604	−	0.968861i	$-0.579643\pi$
$431$	−10.2808			−0.495208			−0.247604	+	0.968861i	$0.579643\pi$
$432$	−2.52592	−	3.10157i	−0.121528	−	0.149224i
$433$			10.1372i			0.487162i	0.969881	+	0.243581i	$0.0783222\pi$
$433$			10.1372i			0.487162i	−0.969881	+	0.243581i	$0.921678\pi$
$434$	−0.0873608	+	0.387330i	−0.00419345	+	0.0185924i
$435$		−	8.67924i		−	0.416138i
$436$	−2.84156	+	5.97885i	−0.136086	+	0.286335i
$437$	−5.39196	−	6.69868i	−0.257932	−	0.320441i
$438$	3.94941	+	0.890775i	0.188710	+	0.0425629i
$439$	28.4759			1.35908			0.679540	−	0.733639i	$-0.262179\pi$
$439$	28.4759			1.35908			0.679540	+	0.733639i	$0.262179\pi$
$440$	5.52233	−	7.03518i	0.263267	−	0.335389i
$441$	6.83404			0.325430
$442$	−0.102086	+	0.452618i	−0.00485575	+	0.0215289i
$443$			3.83437i			0.182176i	0.995843	+	0.0910882i	$0.0290345\pi$
$443$			3.83437i			0.182176i	−0.995843	+	0.0910882i	$0.970965\pi$
$444$	−2.97596	+	6.26162i	−0.141233	+	0.297163i
$445$		−	1.37139i		−	0.0650101i
$446$	3.03677	+	0.684932i	0.143795	+	0.0324325i
$447$	10.6479			0.503630
$448$	3.16584	−	0.774035i	0.149572	−	0.0365697i
$449$			27.2932i			1.28805i	0.765006	+	0.644023i	$0.222736\pi$
$449$			27.2932i			1.28805i	−0.765006	+	0.644023i	$0.777264\pi$
$450$	1.37956	+	0.311154i	0.0650330	+	0.0146679i
$451$	25.5649			1.20381
$452$	−0.555017	+	1.16779i	−0.0261058	+	0.0549284i
$453$	−0.916363			−0.0430545
$454$	−25.5577	−	5.76444i	−1.19948	−	0.270539i
$455$	0.0357448			0.00167574
$456$	−12.3279	+	0.150857i	−0.577307	+	0.00706452i
$457$	25.8551			1.20945			0.604726	−	0.796434i	$-0.293283\pi$
$457$	25.8551			1.20945			0.604726	+	0.796434i	$0.293283\pi$
$458$	0.00246516		0.000556006i	0.000115189		2.59805e-5i
$459$	−3.73926			−0.174534
$460$	1.69365	−	3.56357i	0.0789671	−	0.166152i
$461$	−8.50560			−0.396145			−0.198073	−	0.980187i	$-0.563468\pi$
$461$	−8.50560			−0.396145			−0.198073	+	0.980187i	$0.563468\pi$
$462$	1.77713	+	0.400825i	0.0826797	+	0.0186481i
$463$		−	34.9447i		−	1.62402i	−0.583644	−	0.812010i	$-0.698374\pi$
$463$		−	34.9447i		−	1.62402i	0.583644	−	0.812010i	$-0.301626\pi$
$464$	−26.9193	+	21.9230i	−1.24970	+	1.01775i
$465$	0.689183			0.0319601
$466$	−27.2841	−	6.15382i	−1.26391	−	0.285070i
$467$		−	0.114556i		−	0.00530104i	−0.999996	−	0.00265052i	$-0.999156\pi$
$467$		−	0.114556i		−	0.00530104i	0.999996	−	0.00265052i	$-0.000843688\pi$
$468$	−0.0753273	+	0.158494i	−0.00348200	+	0.00732638i
$469$			2.18760i			0.101014i
$470$	2.24504	−	9.95380i	0.103556	−	0.459135i
$471$	15.1879			0.699820
$472$	−2.05879	−	1.61606i	−0.0947633	−	0.0743854i
$473$	21.8198			1.00328
$474$	−8.73894	−	1.97103i	−0.401393	−	0.0905326i
$475$	3.39555	−	2.73317i	0.155799	−	0.125407i
$476$	1.30779	−	2.75168i	0.0599425	−	0.126123i
$477$		−	10.4335i		−	0.477717i
$478$	−4.43905	+	19.6813i	−0.203037	+	0.900203i
$479$			5.51606i			0.252035i	0.992028	+	0.126018i	$0.0402196\pi$
$479$			5.51606i			0.252035i	−0.992028	+	0.126018i	$0.959780\pi$
$480$	−2.51959	−	5.06475i	−0.115003	−	0.231173i
$481$	0.304149			0.0138680
$482$	−7.35835	+	32.6246i	−0.335164	+	1.48601i
$483$	0.803685			0.0365689
$484$	1.80865	+	0.859597i	0.0822114	+	0.0390726i
$485$			6.41554i			0.291315i
$486$	−1.37956	−	0.311154i	−0.0625781	−	0.0141142i
$487$	−8.21666			−0.372332			−0.186166	−	0.982518i	$-0.559606\pi$
$487$	−8.21666			−0.372332			−0.186166	+	0.982518i	$0.559606\pi$
$488$	0.857599	+	0.673180i	0.0388217	+	0.0304734i
$489$		−	7.62126i		−	0.344645i
$490$	9.42796	+	2.12644i	0.425912	+	0.0960627i
$491$		−	39.5385i		−	1.78435i	−0.451694	−	0.892173i	$-0.649180\pi$
$491$		−	39.5385i		−	1.78435i	0.451694	−	0.892173i	$-0.350820\pi$
$492$	6.94094	−	14.6042i	0.312922	−	0.658409i
$493$			32.4539i			1.46165i
$494$	0.238134	+	0.485633i	0.0107142	+	0.0218497i
$495$		−	3.16208i		−	0.142125i
$496$	−1.74082	−	2.13755i	−0.0781651	−	0.0959788i
$497$			2.49951i			0.112118i
$498$	1.52253	−	6.75042i	0.0682263	−	0.302494i
$499$			36.2793i			1.62408i	0.583599	+	0.812042i	$0.301644\pi$
$499$			36.2793i			1.62408i	−0.583599	+	0.812042i	$0.698356\pi$
$500$	1.80637	+	0.858511i	0.0807832	+	0.0383938i
$501$	4.27454			0.190972
$502$	−3.39444	+	15.0499i	−0.151501	+	0.671709i
$503$			28.8353i			1.28570i	0.765990	+	0.642852i	$0.222249\pi$
$503$			28.8353i			1.28570i	−0.765990	+	0.642852i	$0.777751\pi$
$504$	0.711470	−	0.906378i	0.0316914	−	0.0403733i
$505$	0.114595			0.00509939
$506$	−8.60581	−	1.94101i	−0.382575	−	0.0862883i
$507$	−12.9923			−0.577008
$508$	−32.9371	−	15.6540i	−1.46135	−	0.694534i
$509$		−	34.7482i		−	1.54019i	−0.637931	−	0.770094i	$-0.720209\pi$
$509$		−	34.7482i		−	1.54019i	0.637931	−	0.770094i	$-0.279791\pi$
$510$	−5.15853	−	1.16349i	−0.228424	−	0.0515200i
$511$			1.16627i			0.0515927i
$512$	−9.34441	+	20.6078i	−0.412968	+	0.910745i
$513$	−3.39555	+	2.73317i	−0.149917	+	0.120673i
$514$	5.85436	−	25.9564i	0.258225	−	1.14489i
$515$	5.44996			0.240154
$516$	5.92412	−	12.4648i	0.260795	−	0.548730i
$517$	−22.8150			−1.00340
$518$	−1.94817	−	0.439403i	−0.0855979	−	0.0193063i
$519$		−	0.430737i		−	0.0189073i
$520$	−0.153234	+	0.195213i	−0.00671977	+	0.00856066i
$521$			19.0231i			0.833415i	0.909041	+	0.416708i	$0.136816\pi$
$521$			19.0231i			0.833415i	−0.909041	+	0.416708i	$0.863184\pi$
$522$	−2.70058	+	11.9735i	−0.118201	+	0.524067i
$523$	−7.81447			−0.341703			−0.170852	−	0.985297i	$-0.554652\pi$
$523$	−7.81447			−0.341703			−0.170852	+	0.985297i	$0.554652\pi$
$524$	15.3934	−	32.3888i	0.672465	−	1.41491i
$525$			0.407387i			0.0177798i
$526$	−8.58974	+	38.0842i	−0.374531	+	1.66055i
$527$	−2.57703			−0.112257
$528$	−9.80741	+	7.98715i	−0.426813	+	0.347596i
$529$	19.1081			0.830788
$530$	3.24643	−	14.3936i	0.141016	−	0.625219i
$531$	−0.925355			−0.0401570
$532$	−0.823735	−	3.45467i	−0.0357134	−	0.149779i
$533$	−0.709380			−0.0307266
$534$	−0.426713	+	1.89191i	−0.0184657	+	0.0818710i
$535$	−17.3925			−0.751945
$536$	−11.9472	−	9.37804i	−0.516039	−	0.405069i
$537$	8.62395			0.372151
$538$	9.54249	−	42.3084i	0.411406	−	1.82404i
$539$		−	21.6098i		−	0.930798i
$540$	−1.80637	−	0.858511i	−0.0777336	−	0.0369444i
$541$	−27.4606			−1.18062			−0.590312	−	0.807175i	$-0.700995\pi$
$541$	−27.4606			−1.18062			−0.590312	+	0.807175i	$0.700995\pi$
$542$	−4.78037	+	21.1946i	−0.205334	+	0.910387i
$543$			11.3890i			0.488747i
$544$	9.42139	+	18.9384i	0.403939	+	0.811978i
$545$			3.30988i			0.141780i
$546$	−0.0493121	−	0.0111221i	−0.00211036	−	0.000475984i
$547$	−0.883328			−0.0377684			−0.0188842	−	0.999822i	$-0.506011\pi$
$547$	−0.883328			−0.0377684			−0.0188842	+	0.999822i	$0.506011\pi$
$548$	−27.5900	−	13.1127i	−1.17859	−	0.560146i
$549$	0.385462			0.0164511
$550$	0.983893	−	4.36227i	0.0419534	−	0.186008i
$551$	23.7219	+	29.4708i	1.01059	+	1.25550i
$552$	−3.44532	+	4.38916i	−0.146642	+	0.186815i
$553$		−	2.58063i		−	0.109739i
$554$	−6.63430	−	1.49634i	−0.281865	−	0.0635734i
$555$			3.46642i			0.147141i
$556$	2.44759	−	5.14990i	0.103801	−	0.218404i
$557$	−33.9642			−1.43911			−0.719554	−	0.694437i	$-0.755654\pi$
$557$	−33.9642			−1.43911			−0.719554	+	0.694437i	$0.755654\pi$
$558$	−0.950768	−	0.214442i	−0.0402492	−	0.00907805i
$559$	−0.605459			−0.0256082
$560$	1.26354	−	1.02903i	0.0533942	−	0.0434843i
$561$			11.8238i			0.499203i
$562$	−2.78235	+	12.3361i	−0.117366	+	0.520366i
$563$	14.7527			0.621751			0.310876	−	0.950451i	$-0.399378\pi$
$563$	14.7527			0.621751			0.310876	+	0.950451i	$0.399378\pi$
$564$	−6.19433	+	13.0333i	−0.260829	+	0.548801i
$565$			0.646488i			0.0271980i
$566$	−2.83568	+	12.5725i	−0.119193	+	0.528462i
$567$		−	0.407387i		−	0.0171086i
$568$	−13.6506	−	10.7151i	−0.572765	−	0.449597i
$569$			3.46273i			0.145165i	0.997362	+	0.0725825i	$0.0231241\pi$
$569$			3.46273i			0.145165i	−0.997362	+	0.0725825i	$0.976876\pi$
$570$	−5.53480	+	2.71404i	−0.231827	+	0.113678i
$571$			33.1866i			1.38881i	0.719582	+	0.694407i	$0.244333\pi$
$571$			33.1866i			1.38881i	−0.719582	+	0.694407i	$0.755667\pi$
$572$	0.501170	+	0.238191i	0.0209550	+	0.00995925i
$573$			22.5660i			0.942707i
$574$	4.54380	+	1.02484i	0.189655	+	0.0427759i
$575$		−	1.97278i		−	0.0822707i
$576$	1.90000	+	7.77110i	0.0791667	+	0.323796i
$577$	31.4508			1.30932			0.654658	−	0.755926i	$-0.272813\pi$
$577$	31.4508			1.30932			0.654658	+	0.755926i	$0.272813\pi$
$578$	−4.16342	−	0.939042i	−0.173175	−	0.0390590i
$579$			20.6444i			0.857953i
$580$	−7.45122	+	15.6779i	−0.309395	+	0.650989i
$581$	1.99341			0.0827008
$582$	1.99622	−	8.85061i	0.0827460	−	0.366870i
$583$	−32.9915			−1.36637
$584$	−6.36935	−	4.99968i	−0.263565	−	0.206888i
$585$			0.0877418i			0.00362768i
$586$	3.99034	−	17.6919i	0.164840	−	0.730847i
$587$		−	42.0595i		−	1.73598i	−0.496581	−	0.867990i	$-0.665411\pi$
$587$		−	42.0595i		−	1.73598i	0.496581	−	0.867990i	$-0.334589\pi$
$588$	−12.3448	−	5.86709i	−0.509090	−	0.241955i
$589$	−2.34015	+	1.88366i	−0.0964244	+	0.0776147i
$590$	−1.27658	−	0.287928i	−0.0525561	−	0.0118538i
$591$	21.1531			0.870121
$592$	10.7513	−	8.75588i	0.441877	−	0.359865i
$593$	28.5708			1.17326			0.586631	−	0.809855i	$-0.300454\pi$
$593$	28.5708			1.17326			0.586631	+	0.809855i	$0.300454\pi$
$594$	−0.983893	+	4.36227i	−0.0403696	+	0.178986i
$595$		−	1.52332i		−	0.0624502i
$596$	−19.2341	−	9.14137i	−0.787859	−	0.374445i
$597$		−	14.3465i		−	0.587163i
$598$	0.238795	+	0.0538593i	0.00976506	+	0.00220247i
$599$	18.2649			0.746285			0.373142	−	0.927774i	$-0.378280\pi$
$599$	18.2649			0.746285			0.373142	+	0.927774i	$0.378280\pi$
$600$	−2.22486	−	1.74642i	−0.0908295	−	0.0712975i
$601$		−	39.4277i		−	1.60829i	−0.594434	−	0.804144i	$-0.702624\pi$
$601$		−	39.4277i		−	1.60829i	0.594434	−	0.804144i	$-0.297376\pi$
$602$	3.87816	+	0.874703i	0.158062	+	0.0356502i
$603$	−5.36985			−0.218677
$604$	1.65529	+	0.786708i	0.0673527	+	0.0320107i
$605$	1.00126			0.0407072
$606$	−0.158090	−	0.0356566i	−0.00642197	−	0.00144845i
$607$	−37.5014			−1.52213			−0.761067	−	0.648673i	$-0.775324\pi$
$607$	−37.5014			−1.52213			−0.761067	+	0.648673i	$0.775324\pi$
$608$	22.3982	+	10.3111i	0.908368	+	0.418172i
$609$	−3.53581			−0.143278
$610$	0.531767	+	0.119938i	0.0215306	+	0.00485615i
$611$	0.633075			0.0256115
$612$	6.75447	+	3.21020i	0.273033	+	0.129764i
$613$	−37.2585			−1.50486			−0.752428	−	0.658675i	$-0.771117\pi$
$613$	−37.2585			−1.50486			−0.752428	+	0.658675i	$0.771117\pi$
$614$	25.2393	+	5.69262i	1.01857	+	0.229736i
$615$		−	8.08486i		−	0.326013i
$616$	−2.86604	−	2.24972i	−0.115476	−	0.0906440i
$617$	5.69162			0.229136			0.114568	−	0.993415i	$-0.463452\pi$
$617$	5.69162			0.229136			0.114568	+	0.993415i	$0.463452\pi$
$618$	−7.51855	−	1.69578i	−0.302440	−	0.0682142i
$619$		−	34.7660i		−	1.39736i	−0.715433	−	0.698682i	$-0.753770\pi$
$619$		−	34.7660i		−	1.39736i	0.715433	−	0.698682i	$-0.246230\pi$
$620$	−1.24492	−	0.591671i	−0.0499970	−	0.0237621i
$621$			1.97278i			0.0791650i
$622$	−5.80623	+	25.7430i	−0.232809	+	1.03220i
$623$	−0.558686			−0.0223833
$624$	0.272137	−	0.221628i	0.0108942	−	0.00887224i
$625$	1.00000			0.0400000
$626$	21.8218	+	4.92182i	0.872174	+	0.196715i
$627$	8.64251	+	10.7370i	0.345149	+	0.428794i
$628$	−27.4348	−	13.0389i	−1.09477	−	0.520311i
$629$		−	12.9618i		−	0.516822i
$630$	0.126760	−	0.562014i	0.00505024	−	0.0223912i
$631$			11.3120i			0.450322i	0.974322	+	0.225161i	$0.0722908\pi$
$631$			11.3120i			0.450322i	−0.974322	+	0.225161i	$0.927709\pi$
$632$	14.0936	+	11.0629i	0.560612	+	0.440058i
$633$	0.0399114			0.00158634
$634$	7.53603	−	33.4124i	0.299294	−	1.32698i
$635$	−18.2339			−0.723590
$636$	−8.95727	+	18.8467i	−0.355179	+	0.747321i
$637$			0.599630i			0.0237582i
$638$	37.8612	+	8.53944i	1.49894	+	0.338080i
$639$	−6.13547			−0.242715
$640$	0.203154	+	11.3119i	0.00803036	+	0.447141i
$641$		−	11.1755i		−	0.441405i	−0.975341	−	0.220702i	$-0.929165\pi$
$641$		−	11.1755i		−	0.441405i	0.975341	−	0.220702i	$-0.0708349\pi$
$642$	23.9940	+	5.41176i	0.946969	+	0.213585i
$643$			24.8699i			0.980774i	0.871505	+	0.490387i	$0.163145\pi$
$643$			24.8699i			0.980774i	−0.871505	+	0.490387i	$0.836855\pi$
$644$	−1.45175	−	0.689973i	−0.0572070	−	0.0271887i
$645$		−	6.90046i		−	0.271705i
$646$	20.6961	−	10.1485i	0.814275	−	0.399287i
$647$		−	30.6834i		−	1.20629i	−0.797632	−	0.603145i	$-0.793914\pi$
$647$		−	30.6834i		−	1.20629i	0.797632	−	0.603145i	$-0.206086\pi$
$648$	2.22486	+	1.74642i	0.0874007	+	0.0686060i
$649$			2.92605i			0.114857i
$650$	−0.0273012	+	0.121045i	−0.00107084	+	0.00474777i
$651$		−	0.280764i		−	0.0110040i
$652$	−6.54293	+	13.7668i	−0.256241	+	0.539149i
$653$	11.3227			0.443092			0.221546	−	0.975150i	$-0.428890\pi$
$653$	11.3227			0.443092			0.221546	+	0.975150i	$0.428890\pi$
$654$	1.02988	−	4.56617i	0.0402716	−	0.178551i
$655$		−	17.9304i		−	0.700598i
$656$	−25.0758	+	20.4217i	−0.979044	+	0.797333i
$657$	−2.86281			−0.111689
$658$	−4.05505	−	0.914600i	−0.158082	−	0.0356548i
$659$	24.2382			0.944184			0.472092	−	0.881549i	$-0.343499\pi$
$659$	24.2382			0.944184			0.472092	+	0.881549i	$0.343499\pi$
$660$	−2.71468	+	5.71187i	−0.105669	+	0.222334i
$661$		−	31.9083i		−	1.24109i	−0.784172	−	0.620544i	$-0.786912\pi$
$661$		−	31.9083i		−	1.24109i	0.784172	−	0.620544i	$-0.213088\pi$
$662$	10.1523	+	2.28981i	0.394581	+	0.0889961i
$663$		−	0.328089i		−	0.0127419i
$664$	−8.54556	+	10.8866i	−0.331632	+	0.422483i
$665$	−1.11346	−	1.38330i	−0.0431781	−	0.0536421i
$666$	1.07859	−	4.78213i	0.0417945	−	0.185304i
$667$	17.1222			0.662976
$668$	−7.72138	−	3.66974i	−0.298749	−	0.141986i
$669$	−2.20126			−0.0851057
$670$	−7.40802	−	1.67085i	−0.286197	−	0.0645506i
$671$		−	1.21886i		−	0.0470536i
$672$	−2.06331	+	1.02645i	−0.0795940	+	0.0395960i
$673$			24.9109i			0.960246i	0.877201	+	0.480123i	$0.159408\pi$
$673$			24.9109i			0.960246i	−0.877201	+	0.480123i	$0.840592\pi$
$674$	−4.72468	+	20.9477i	−0.181988	+	0.806876i
$675$	−1.00000			−0.0384900
$676$	23.4689	+	11.1540i	0.902648	+	0.429001i
$677$			20.9128i			0.803744i	0.915696	+	0.401872i	$0.131640\pi$
$677$			20.9128i			0.803744i	−0.915696	+	0.401872i	$0.868360\pi$
$678$	0.201157	−	0.891869i	0.00772541	−	0.0342520i
$679$	2.61360			0.100301
$680$	8.31933	+	6.53034i	0.319032	+	0.250427i
$681$	18.5260			0.709918
$682$	−0.678082	+	3.00640i	−0.0259651	+	0.115121i
$683$	−28.2110			−1.07946			−0.539732	−	0.841837i	$-0.681475\pi$
$683$	−28.2110			−1.07946			−0.539732	+	0.841837i	$0.681475\pi$
$684$	8.48007	−	2.02200i	0.324243	−	0.0773130i
$685$	−15.2737			−0.583580
$686$	1.75360	−	7.77492i	0.0669529	−	0.296848i
$687$	−0.00178692			−6.81751e−5
$688$	−21.4023	+	17.4300i	−0.815954	+	0.664512i
$689$	0.915454			0.0348760
$690$	−0.613839	+	2.72157i	−0.0233685	+	0.103608i
$691$			9.58258i			0.364538i	0.983249	+	0.182269i	$0.0583442\pi$
$691$			9.58258i			0.364538i	−0.983249	+	0.182269i	$0.941656\pi$
$692$	−0.369792	+	0.778069i	−0.0140574	+	0.0295777i
$693$	−1.28819			−0.0489342
$694$	−5.71463	+	25.3369i	−0.216924	+	0.961774i
$695$		−	2.85097i		−	0.108143i
$696$	15.1576	−	19.3101i	0.574549	−	0.731947i
$697$			30.2314i			1.14510i
$698$	41.4141	+	9.34078i	1.56755	+	0.353554i
$699$	19.7774			0.748050
$700$	0.349746	−	0.735890i	0.0132192	−	0.0278140i
$701$	38.2872			1.44609			0.723045	−	0.690801i	$-0.242742\pi$
$701$	38.2872			1.44609			0.723045	+	0.690801i	$0.242742\pi$
$702$	0.0273012	−	0.121045i	0.00103042	−	0.00456855i
$703$	−9.47432	−	11.7704i	−0.357331	−	0.443929i
$704$	24.5728	−	6.00795i	0.926123	−	0.226433i
$705$			7.21521i			0.271740i
$706$	−9.88852	−	2.23032i	−0.372159	−	0.0839391i
$707$		−	0.0466843i		−	0.00175574i
$708$	1.67153	+	0.794428i	0.0628200	+	0.0298564i
$709$	5.66785			0.212861			0.106430	−	0.994320i	$-0.466058\pi$
$709$	5.66785			0.212861			0.106430	+	0.994320i	$0.466058\pi$
$710$	−8.46424	−	1.90908i	−0.317657	−	0.0716464i
$711$	6.33459			0.237566
$712$	2.39503	−	3.05115i	0.0897575	−	0.114347i
$713$			1.35961i			0.0509177i
$714$	−0.473989	+	2.10152i	−0.0177386	+	0.0786473i
$715$	0.277446			0.0103759
$716$	−15.5780	−	7.40376i	−0.582178	−	0.276691i
$717$		−	14.2664i		−	0.532788i
$718$	−2.93746	+	13.0238i	−0.109625	+	0.486043i
$719$			10.9084i			0.406815i	0.979094	+	0.203407i	$0.0652016\pi$
$719$			10.9084i			0.406815i	−0.979094	+	0.203407i	$0.934798\pi$
$720$	2.52592	+	3.10157i	0.0941354	+	0.115589i
$721$		−	2.22024i		−	0.0826862i
$722$	11.3758	−	24.3432i	0.423362	−	0.905961i
$723$		−	23.6486i		−	0.879500i
$724$	9.77755	−	20.5726i	0.363380	−	0.764576i
$725$			8.67924i			0.322339i
$726$	−1.38130	−	0.311548i	−0.0512650	−	0.0115626i
$727$		−	31.4132i		−	1.16505i	−0.812813	−	0.582525i	$-0.802065\pi$
$727$		−	31.4132i		−	1.16505i	0.812813	−	0.582525i	$-0.197935\pi$
$728$	0.0795272	+	0.0624256i	0.00294747	+	0.00231365i
$729$	1.00000			0.0370370
$730$	−3.94941	−	0.890775i	−0.146174	−	0.0329690i
$731$			25.8026i			0.954344i
$732$	−0.696285	−	0.330923i	−0.0257354	−	0.0122313i
$733$	−25.8916			−0.956328			−0.478164	−	0.878271i	$-0.658697\pi$
$733$	−25.8916			−0.956328			−0.478164	+	0.878271i	$0.658697\pi$
$734$	2.05336	−	9.10396i	0.0757910	−	0.336033i
$735$	−6.83404			−0.252077
$736$	9.99165	−	4.97060i	0.368297	−	0.183219i
$737$			16.9799i			0.625462i
$738$	−2.51564	+	11.1535i	−0.0926019	+	0.410567i
$739$		−	3.08005i		−	0.113301i	−0.998394	−	0.0566507i	$-0.981958\pi$
$739$		−	3.08005i		−	0.113301i	0.998394	−	0.0566507i	$-0.0180421\pi$
$740$	2.97596	−	6.26162i	0.109398	−	0.230182i
$741$	−0.239814	−	0.297931i	−0.00880977	−	0.0109448i
$742$	−5.86377	−	1.32255i	−0.215266	−	0.0485524i
$743$	39.6677			1.45527			0.727633	−	0.685966i	$-0.240620\pi$
$743$	39.6677			1.45527			0.727633	+	0.685966i	$0.240620\pi$
$744$	1.53333	+	1.20361i	0.0562148	+	0.0441263i
$745$	−10.6479			−0.390110
$746$	3.42251	−	15.1743i	0.125307	−	0.555572i
$747$			4.89317i			0.179032i
$748$	10.1509	−	21.3582i	0.371153	−	0.780932i
$749$			7.08549i			0.258898i
$750$	−1.37956	−	0.311154i	−0.0503744	−	0.0113617i
$751$	−8.36464			−0.305230			−0.152615	−	0.988286i	$-0.548769\pi$
$751$	−8.36464			−0.305230			−0.152615	+	0.988286i	$0.548769\pi$
$752$	22.3785	−	18.2250i	0.816059	−	0.664598i
$753$		−	10.9092i		−	0.397553i
$754$	−1.05058	−	0.236954i	−0.0382598	−	0.00862934i
$755$	0.916363			0.0333499
$756$	−0.349746	+	0.735890i	−0.0127201	+	0.0267640i
$757$	−14.5285			−0.528046			−0.264023	−	0.964516i	$-0.585049\pi$
$757$	−14.5285			−0.528046			−0.264023	+	0.964516i	$0.585049\pi$
$758$	11.7787	+	2.65663i	0.427821	+	0.0964933i
$759$	6.23809			0.226428
$760$	12.3279	−	0.150857i	0.447180	−	0.00547215i
$761$	47.7811			1.73206			0.866031	−	0.499990i	$-0.166663\pi$
$761$	47.7811			1.73206			0.866031	+	0.499990i	$0.166663\pi$
$762$	25.1547	+	5.67355i	0.911260	+	0.205531i
$763$	1.34840			0.0488153
$764$	19.3731	−	40.7624i	0.700895	−	1.47473i
$765$	3.73926			0.135193
$766$	48.4787	+	10.9342i	1.75161	+	0.395068i
$767$		−	0.0811923i		−	0.00293168i
$768$	3.23948	−	15.6686i	0.116895	−	0.565393i
$769$	−1.58417			−0.0571268			−0.0285634	−	0.999592i	$-0.509093\pi$
$769$	−1.58417			−0.0571268			−0.0285634	+	0.999592i	$0.509093\pi$
$770$	−1.77713	−	0.400825i	−0.0640434	−	0.0144447i
$771$			18.8150i			0.677605i
$772$	17.7235	−	37.2914i	0.637881	−	1.34215i
$773$		−	17.1218i		−	0.615829i	−0.951414	−	0.307914i	$-0.900369\pi$
$773$		−	17.1218i		−	0.615829i	0.951414	−	0.307914i	$-0.0996310\pi$
$774$	−2.14711	+	9.51959i	−0.0771762	+	0.342175i
$775$	−0.689183			−0.0247562
$776$	−11.2043	+	14.2737i	−0.402209	+	0.512395i
$777$	1.41217			0.0506614
$778$	−44.5037	−	10.0376i	−1.59554	−	0.359867i
$779$	22.0973	+	27.4525i	0.791719	+	0.983589i
$780$	0.0753273	−	0.158494i	0.00269715	−	0.00567499i
$781$			19.4008i			0.694216i
$782$	2.29530	−	10.1767i	0.0820799	−	0.363916i
$783$		−	8.67924i		−	0.310171i
$784$	17.2622	+	21.1962i	0.616508	+	0.757009i
$785$	−15.1879			−0.542078
$786$	−5.57911	+	24.7360i	−0.199000	+	0.882304i
$787$	−7.43093			−0.264884			−0.132442	−	0.991191i	$-0.542282\pi$
$787$	−7.43093			−0.264884			−0.132442	+	0.991191i	$0.542282\pi$
$788$	−38.2102	−	18.1601i	−1.36118	−	0.646928i
$789$		−	27.6061i		−	0.982802i
$790$	8.73894	+	1.97103i	0.310918	+	0.0701262i
$791$	0.263371			0.00936438
$792$	5.52233	−	7.03518i	0.196227	−	0.249984i
$793$			0.0338211i			0.00120102i
$794$	48.7811	+	11.0024i	1.73118	+	0.390460i
$795$			10.4335i			0.370038i
$796$	−12.3166	+	25.9150i	−0.436551	+	0.918534i
$797$			14.3977i			0.509993i	0.966942	+	0.254997i	$0.0820743\pi$
$797$			14.3977i			0.509993i	−0.966942	+	0.254997i	$0.917926\pi$
$798$	1.10566	+	2.25480i	0.0391400	+	0.0798192i
$799$		−	26.9795i		−	0.954467i
$800$	2.51959	+	5.06475i	0.0890808	+	0.179066i
$801$		−	1.37139i		−	0.0484557i
$802$	1.63661	−	7.25623i	0.0577909	−	0.256226i
$803$			9.05242i			0.319453i
$804$	9.69991	+	4.61007i	0.342090	+	0.162585i
$805$	−0.803685			−0.0283262
$806$	0.0188155	−	0.0834221i	0.000662748	−	0.00293842i
$807$			30.6681i			1.07957i
$808$	0.254957	+	0.200131i	0.00896935	+	0.00704058i
$809$	6.60419			0.232191			0.116095	−	0.993238i	$-0.462962\pi$
$809$	6.60419			0.232191			0.116095	+	0.993238i	$0.462962\pi$
$810$	1.37956	+	0.311154i	0.0484728	+	0.0109328i
$811$	−13.6954			−0.480909			−0.240454	−	0.970660i	$-0.577296\pi$
$811$	−13.6954			−0.480909			−0.240454	+	0.970660i	$0.577296\pi$
$812$	6.38696	+	3.03553i	0.224138	+	0.106526i
$813$		−	15.3633i		−	0.538816i
$814$	−15.1215	−	3.41058i	−0.530007	−	0.119541i
$815$			7.62126i			0.266961i
$816$	−9.44506	−	11.5976i	−0.330643	−	0.405996i
$817$	18.8602	+	23.4309i	0.659834	+	0.819742i
$818$	−7.64014	+	33.8740i	−0.267131	+	1.18438i
$819$	0.0357448			0.00124903
$820$	−6.94094	+	14.6042i	−0.242388	+	0.510001i
$821$	−24.6096			−0.858882			−0.429441	−	0.903095i	$-0.641289\pi$
$821$	−24.6096			−0.858882			−0.429441	+	0.903095i	$0.641289\pi$
$822$	21.0710	+	4.75249i	0.734937	+	0.165762i
$823$			22.1324i			0.771486i	0.922606	+	0.385743i	$0.126055\pi$
$823$			22.1324i			0.771486i	−0.922606	+	0.385743i	$0.873945\pi$
$824$	12.1254	+	9.51795i	0.422408	+	0.331574i
$825$			3.16208i			0.110089i
$826$	−0.117298	+	0.520063i	−0.00408132	+	0.0180953i
$827$	−34.8197			−1.21080			−0.605399	−	0.795922i	$-0.706986\pi$
$827$	−34.8197			−1.21080			−0.605399	+	0.795922i	$0.706986\pi$
$828$	1.69365	−	3.56357i	0.0588586	−	0.123843i
$829$			4.14941i			0.144115i	0.997400	+	0.0720575i	$0.0229565\pi$
$829$			4.14941i			0.144115i	−0.997400	+	0.0720575i	$0.977043\pi$
$830$	−1.52253	+	6.75042i	−0.0528478	+	0.234311i
$831$	4.80900			0.166822
$832$	−0.681850	+	0.166709i	−0.0236389	+	0.00577961i
$833$	25.5542			0.885402
$834$	−0.887091	+	3.93308i	−0.0307175	+	0.136192i
$835$	−4.27454			−0.147927
$836$	−6.39371	−	26.8146i	−0.221131	−	0.927403i
$837$	0.689183			0.0238216
$838$	−8.42344	+	37.3469i	−0.290983	+	1.29013i
$839$	47.7103			1.64714			0.823571	−	0.567213i	$-0.191978\pi$
$839$	47.7103			1.64714			0.823571	+	0.567213i	$0.191978\pi$
$840$	−0.711470	+	0.906378i	−0.0245481	+	0.0312730i
$841$	−46.3291			−1.59756
$842$	−1.93296	+	8.57014i	−0.0666143	+	0.295347i
$843$		−	8.94204i		−	0.307980i
$844$	−0.0720947	−	0.0342644i	−0.00248160	−	0.00117943i
$845$	12.9923			0.446949
$846$	2.24504	−	9.95380i	0.0771861	−	0.342219i
$847$		−	0.407902i		−	0.0140157i
$848$	32.3602	−	26.3542i	1.11125	−	0.905006i
$849$		−	9.11343i		−	0.312772i
$850$	5.15853	+	1.16349i	0.176936	+	0.0399072i
$851$	−6.83849			−0.234420
$852$	11.0829	+	5.26737i	0.379694	+	0.180457i
$853$	−7.07722			−0.242319			−0.121160	−	0.992633i	$-0.538661\pi$
$853$	−7.07722			−0.242319			−0.121160	+	0.992633i	$0.538661\pi$
$854$	0.0488612	−	0.216635i	0.00167199	−	0.00741310i
$855$	3.39555	−	2.73317i	0.116125	−	0.0934726i
$856$	−38.6960	−	30.3748i	−1.32260	−	1.03819i
$857$		−	23.0220i		−	0.786416i	−0.919450	−	0.393208i	$-0.871365\pi$
$857$		−	23.0220i		−	0.786416i	0.919450	−	0.393208i	$-0.128635\pi$
$858$	−0.382753	−	0.0863285i	−0.0130670	−	0.00294721i
$859$			28.7687i			0.981575i	0.871279	+	0.490788i	$0.163291\pi$
$859$			28.7687i			0.981575i	−0.871279	+	0.490788i	$0.836709\pi$
$860$	−5.92412	+	12.4648i	−0.202011	+	0.425045i
$861$	−3.29366			−0.112248
$862$	−14.1829	−	3.19891i	−0.483073	−	0.108955i
$863$	20.5155			0.698354			0.349177	−	0.937057i	$-0.386461\pi$
$863$	20.5155			0.698354			0.349177	+	0.937057i	$0.386461\pi$
$864$	−2.51959	−	5.06475i	−0.0857181	−	0.172306i
$865$			0.430737i			0.0146455i
$866$	−3.15423	+	13.9848i	−0.107185	+	0.475224i
$867$	3.01793			0.102494
$868$	−0.241039	+	0.507162i	−0.00818139	+	0.0172142i
$869$		−	20.0305i		−	0.679487i
$870$	2.70058	−	11.9735i	0.0915582	−	0.405940i
$871$		−	0.471160i		−	0.0159646i
$872$	−5.78045	+	7.36401i	−0.195751	+	0.249377i
$873$			6.41554i			0.217133i
$874$	−5.35420	−	10.9190i	−0.181109	−	0.369339i
$875$		−	0.407387i		−	0.0137722i
$876$	5.17128	+	2.45775i	0.174721	+	0.0830397i
$877$		−	22.1334i		−	0.747391i	−0.927552	−	0.373695i	$-0.878091\pi$
$877$		−	22.1334i		−	0.747391i	0.927552	−	0.373695i	$-0.121909\pi$
$878$	39.2842	+	8.86039i	1.32578	+	0.299024i
$879$			12.8243i			0.432554i
$880$	9.80741	−	7.98715i	0.330608	−	0.269247i
$881$	−2.78488			−0.0938250			−0.0469125	−	0.998899i	$-0.514938\pi$
$881$	−2.78488			−0.0938250			−0.0469125	+	0.998899i	$0.514938\pi$
$882$	9.42796	+	2.12644i	0.317456	+	0.0716009i
$883$		−	18.8482i		−	0.634293i	−0.948377	−	0.317146i	$-0.897275\pi$
$883$		−	18.8482i		−	0.634293i	0.948377	−	0.317146i	$-0.102725\pi$
$884$	−0.281668	+	0.592649i	−0.00947353	+	0.0199330i
$885$	0.925355			0.0311055
$886$	−1.19308	+	5.28974i	−0.0400823	+	0.177712i
$887$	10.5756			0.355093			0.177546	−	0.984112i	$-0.443184\pi$
$887$	10.5756			0.355093			0.177546	+	0.984112i	$0.443184\pi$
$888$	−6.05384	+	7.71229i	−0.203153	+	0.258808i
$889$			7.42825i			0.249136i
$890$	0.426713	−	1.89191i	0.0143035	−	0.0634170i
$891$		−	3.16208i		−	0.105934i
$892$	3.97629	+	1.88981i	0.133136	+	0.0632754i
$893$	−19.7204	−	24.4996i	−0.659919	−	0.819848i
$894$	14.6895	+	3.31315i	0.491289	+	0.110808i
$895$	−8.62395			−0.288267
$896$	4.60831	−	0.0827621i	0.153953	−	0.00276489i
$897$	−0.173095			−0.00577949
$898$	−8.49239	+	37.6526i	−0.283395	+	1.25648i
$899$		−	5.98158i		−	0.199497i
$900$	1.80637	+	0.858511i	0.0602122	+	0.0286170i
$901$		−	39.0136i		−	1.29973i
$902$	35.2684	+	7.95464i	1.17431	+	0.264860i
$903$	−2.81116			−0.0935494
$904$	−1.12904	+	1.43835i	−0.0375514	+	0.0478387i
$905$		−	11.3890i		−	0.378582i
$906$	−1.26418	−	0.285130i	−0.0419995	−	0.00947282i
$907$	−2.02830			−0.0673485			−0.0336742	−	0.999433i	$-0.510721\pi$
$907$	−2.02830			−0.0673485			−0.0336742	+	0.999433i	$0.510721\pi$
$908$	−33.4648	−	15.9048i	−1.11057	−	0.527819i
$909$	0.114595			0.00380086
$910$	0.0493121	+	0.0111221i	0.00163468	+	0.000368696i
$911$	−32.5471			−1.07833			−0.539167	−	0.842199i	$-0.681261\pi$
$911$	−32.5471			−1.07833			−0.539167	+	0.842199i	$0.681261\pi$
$912$	−17.0540	−	3.62776i	−0.564715	−	0.120127i
$913$	15.4726			0.512068
$914$	35.6686	+	8.04492i	1.17981	+	0.266102i
$915$	−0.385462			−0.0127430
$916$	0.00322783	+	0.00153409i	0.000106650	+	5.06877e-5i
$917$	−7.30460			−0.241219
$918$	−5.15853	−	1.16349i	−0.170257	−	0.0384008i
$919$		−	18.6993i		−	0.616833i	−0.951251	−	0.308417i	$-0.900201\pi$
$919$		−	18.6993i		−	0.616833i	0.951251	−	0.308417i	$-0.0997991\pi$
$920$	3.44532	−	4.38916i	0.113589	−	0.144706i
$921$	−18.2952			−0.602847
$922$	−11.7340	−	2.64655i	−0.386438	−	0.0871596i
$923$		−	0.538337i		−	0.0177196i
$924$	2.32694	+	1.10592i	0.0765507	+	0.0363822i
$925$		−	3.46642i		−	0.113975i
$926$	10.8732	−	48.2083i	0.357315	−	1.58422i
$927$	5.44996			0.179000
$928$	−43.9582	+	21.8681i	−1.44300	+	0.717855i
$929$	37.2700			1.22279			0.611394	−	0.791327i	$-0.290609\pi$
$929$	37.2700			1.22279			0.611394	+	0.791327i	$0.290609\pi$
$930$	0.950768	+	0.214442i	0.0311769	+	0.00703183i
$931$	23.2053	−	18.6786i	0.760523	−	0.612167i
$932$	−35.7252	−	16.9791i	−1.17022	−	0.556169i
$933$		−	18.6603i		−	0.610911i
$934$	0.0356447	−	0.158037i	0.00116633	−	0.00517114i
$935$		−	11.8238i		−	0.386681i
$936$	−0.153234	+	0.195213i	−0.00500862	+	0.00638074i
$937$	−15.5805			−0.508993			−0.254497	−	0.967074i	$-0.581910\pi$
$937$	−15.5805			−0.508993			−0.254497	+	0.967074i	$0.581910\pi$
$938$	−0.680682	+	3.01793i	−0.0222251	+	0.0985389i
$939$	−15.8179			−0.516199
$940$	6.19433	−	13.0333i	0.202037	−	0.425100i
$941$			53.9167i			1.75763i	0.477159	+	0.878817i	$0.341666\pi$
$941$			53.9167i			1.75763i	−0.477159	+	0.878817i	$0.658334\pi$
$942$	20.9526	+	4.72577i	0.682671	+	0.153974i
$943$	15.9497			0.519392
$944$	−2.33737	−	2.87006i	−0.0760750	−	0.0934123i
$945$			0.407387i			0.0132523i
$946$	30.1017	+	6.78932i	0.978690	+	0.220740i
$947$			16.4614i			0.534925i	0.963568	+	0.267463i	$0.0861852\pi$
$947$			16.4614i			0.534925i	−0.963568	+	0.267463i	$0.913815\pi$
$948$	−11.4426	−	5.43831i	−0.371638	−	0.176628i
$949$		−	0.251188i		−	0.00815390i
$950$	5.53480	−	2.71404i	0.179573	−	0.0880550i
$951$			24.2196i			0.785375i
$952$	2.66037	−	3.38918i	0.0862232	−	0.109844i
$953$			10.1801i			0.329766i	0.986313	+	0.164883i	$0.0527247\pi$
$953$			10.1801i			0.329766i	−0.986313	+	0.164883i	$0.947275\pi$
$954$	3.24643	−	14.3936i	0.105107	−	0.466011i
$955$		−	22.5660i		−	0.730218i
$956$	−12.2479	+	25.7703i	−0.396124	+	0.833472i
$957$	−27.4444			−0.887152
$958$	−1.71634	+	7.60973i	−0.0554526	+	0.245859i
$959$			6.22232i			0.200929i
$960$	−1.90000	−	7.77110i	−0.0613223	−	0.250811i
$961$	−30.5250			−0.984678
$962$	0.419592	+	0.0946374i	0.0135282	+	0.00305123i
$963$	−17.3925			−0.560467
$964$	−20.3026	+	42.7180i	−0.653901	+	1.37585i
$965$		−	20.6444i		−	0.664567i
$966$	1.10873	+	0.250070i	0.0356728	+	0.00804587i
$967$		−	32.4276i		−	1.04280i	−0.853312	−	0.521400i	$-0.825410\pi$
$967$		−	32.4276i		−	1.04280i	0.853312	−	0.521400i	$-0.174590\pi$
$968$	2.22767	+	1.74863i	0.0716002	+	0.0562032i
$969$	−12.6968	+	10.2200i	−0.407881	+	0.328315i
$970$	−1.99622	+	8.85061i	−0.0640948	+	0.284176i
$971$	11.7341			0.376564			0.188282	−	0.982115i	$-0.439708\pi$
$971$	11.7341			0.376564			0.188282	+	0.982115i	$0.439708\pi$
$972$	−1.80637	−	0.858511i	−0.0579392	−	0.0275368i
$973$	−1.16145			−0.0372343
$974$	−11.3354	−	2.55665i	−0.363209	−	0.0819203i
$975$		−	0.0877418i		−	0.00280999i
$976$	0.973645	+	1.19554i	0.0311656	+	0.0382682i
$977$			33.5409i			1.07307i	0.843878	+	0.536535i	$0.180267\pi$
$977$			33.5409i			1.07307i	−0.843878	+	0.536535i	$0.819733\pi$
$978$	2.37139	−	10.5140i	0.0758285	−	0.336200i
$979$	−4.33644			−0.138593
$980$	12.3448	+	5.86709i	0.394339	+	0.187417i
$981$			3.30988i			0.105676i
$982$	12.3026	−	54.5456i	0.392590	−	1.74062i
$983$	24.0818			0.768091			0.384045	−	0.923314i	$-0.374531\pi$
$983$	24.0818			0.768091			0.384045	+	0.923314i	$0.374531\pi$
$984$	14.1196	−	17.9877i	0.450116	−	0.573426i
$985$	−21.1531			−0.673993
$986$	−10.0982	+	44.7721i	−0.321591	+	1.42583i
$987$	2.93938			0.0935615
$988$	0.177414	+	0.744056i	0.00564428	+	0.0236716i
$989$	13.6131			0.432872
$990$	0.983893	−	4.36227i	0.0312702	−	0.138642i
$991$	−36.1812			−1.14933			−0.574667	−	0.818387i	$-0.694868\pi$
$991$	−36.1812			−1.14933			−0.574667	+	0.818387i	$0.694868\pi$
$992$	−1.73646	−	3.49054i	−0.0551325	−	0.110825i
$993$	−7.35910			−0.233534
$994$	−0.777732	+	3.44822i	−0.0246682	+	0.109371i
$995$			14.3465i			0.454815i
$996$	4.20084	−	8.83887i	0.133109	−	0.280070i
$997$	38.9938			1.23495			0.617473	−	0.786592i	$-0.288156\pi$
$997$	38.9938			1.23495			0.617473	+	0.786592i	$0.288156\pi$
$998$	−11.2884	+	50.0494i	−0.357330	+	1.58429i
$999$			3.46642i			0.109673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1140.2.b.e.151.20	yes	20
4.3	odd	2		1140.2.b.f.151.2	yes	20
19.18	odd	2		1140.2.b.f.151.1	yes	20
76.75	even	2	inner	1140.2.b.e.151.19	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1140.2.b.e.151.19	✓	20	76.75	even	2	inner
1140.2.b.e.151.20	yes	20	1.1	even	1	trivial
1140.2.b.f.151.1	yes	20	19.18	odd	2
1140.2.b.f.151.2	yes	20	4.3	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:	\( N \)	\(=\)	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1140.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37956 + 0.311154i) q^{2} -1.00000 q^{3} +(1.80637 + 0.858511i) q^{4} +1.00000 q^{5} +(-1.37956 - 0.311154i) q^{6} -0.407387i q^{7} +(2.22486 + 1.74642i) q^{8} +1.00000 q^{9} +(1.37956 + 0.311154i) q^{10} -3.16208i q^{11} +(-1.80637 - 0.858511i) q^{12} +0.0877418i q^{13} +(0.126760 - 0.562014i) q^{14} -1.00000 q^{15} +(2.52592 + 3.10157i) q^{16} +3.73926 q^{17} +(1.37956 + 0.311154i) q^{18} +(3.39555 - 2.73317i) q^{19} +(1.80637 + 0.858511i) q^{20} +0.407387i q^{21} +(0.983893 - 4.36227i) q^{22} -1.97278i q^{23} +(-2.22486 - 1.74642i) q^{24} +1.00000 q^{25} +(-0.0273012 + 0.121045i) q^{26} -1.00000 q^{27} +(0.349746 - 0.735890i) q^{28} +8.67924i q^{29} +(-1.37956 - 0.311154i) q^{30} -0.689183 q^{31} +(2.51959 + 5.06475i) q^{32} +3.16208i q^{33} +(5.15853 + 1.16349i) q^{34} -0.407387i q^{35} +(1.80637 + 0.858511i) q^{36} -3.46642i q^{37} +(5.53480 - 2.71404i) q^{38} -0.0877418i q^{39} +(2.22486 + 1.74642i) q^{40} +8.08486i q^{41} +(-0.126760 + 0.562014i) q^{42} +6.90046i q^{43} +(2.71468 - 5.71187i) q^{44} +1.00000 q^{45} +(0.613839 - 2.72157i) q^{46} -7.21521i q^{47} +(-2.52592 - 3.10157i) q^{48} +6.83404 q^{49} +(1.37956 + 0.311154i) q^{50} -3.73926 q^{51} +(-0.0753273 + 0.158494i) q^{52} -10.4335i q^{53} +(-1.37956 - 0.311154i) q^{54} -3.16208i q^{55} +(0.711470 - 0.906378i) q^{56} +(-3.39555 + 2.73317i) q^{57} +(-2.70058 + 11.9735i) q^{58} -0.925355 q^{59} +(-1.80637 - 0.858511i) q^{60} +0.385462 q^{61} +(-0.950768 - 0.214442i) q^{62} -0.407387i q^{63} +(1.90000 + 7.77110i) q^{64} +0.0877418i q^{65} +(-0.983893 + 4.36227i) q^{66} -5.36985 q^{67} +(6.75447 + 3.21020i) q^{68} +1.97278i q^{69} +(0.126760 - 0.562014i) q^{70} -6.13547 q^{71} +(2.22486 + 1.74642i) q^{72} -2.86281 q^{73} +(1.07859 - 4.78213i) q^{74} -1.00000 q^{75} +(8.48007 - 2.02200i) q^{76} -1.28819 q^{77} +(0.0273012 - 0.121045i) q^{78} +6.33459 q^{79} +(2.52592 + 3.10157i) q^{80} +1.00000 q^{81} +(-2.51564 + 11.1535i) q^{82} +4.89317i q^{83} +(-0.349746 + 0.735890i) q^{84} +3.73926 q^{85} +(-2.14711 + 9.51959i) q^{86} -8.67924i q^{87} +(5.52233 - 7.03518i) q^{88} -1.37139i q^{89} +(1.37956 + 0.311154i) q^{90} +0.0357448 q^{91} +(1.69365 - 3.56357i) q^{92} +0.689183 q^{93} +(2.24504 - 9.95380i) q^{94} +(3.39555 - 2.73317i) q^{95} +(-2.51959 - 5.06475i) q^{96} +6.41554i q^{97} +(9.42796 + 2.12644i) q^{98} -3.16208i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} - 20 q^{3} - q^{4} + 20 q^{5} + q^{6} - 7 q^{8} + 20 q^{9} - q^{10} + q^{12} - 20 q^{15} - 9 q^{16} + 8 q^{17} - q^{18} - 2 q^{19} - q^{20} + 7 q^{24} + 20 q^{25} + 2 q^{26} - 20 q^{27}+ \cdots - 3 q^{98}+O(q^{100}) \) 20 * q - q^2 - 20 * q^3 - q^4 + 20 * q^5 + q^6 - 7 * q^8 + 20 * q^9 - q^10 + q^12 - 20 * q^15 - 9 * q^16 + 8 * q^17 - q^18 - 2 * q^19 - q^20 + 7 * q^24 + 20 * q^25 + 2 * q^26 - 20 * q^27 + 24 * q^28 + q^30 - 20 * q^31 + 9 * q^32 + 6 * q^34 - q^36 - 5 * q^38 - 7 * q^40 + 4 * q^44 + 20 * q^45 + 6 * q^46 + 9 * q^48 - 28 * q^49 - q^50 - 8 * q^51 + 22 * q^52 + q^54 - 24 * q^56 + 2 * q^57 + 10 * q^58 + 8 * q^59 + q^60 + 28 * q^61 - q^64 - 28 * q^67 - 6 * q^68 + 8 * q^71 - 7 * q^72 + 12 * q^73 + 14 * q^74 - 20 * q^75 + 11 * q^76 - 32 * q^77 - 2 * q^78 + 32 * q^79 - 9 * q^80 + 20 * q^81 - 22 * q^82 - 24 * q^84 + 8 * q^85 - 24 * q^86 + 16 * q^88 - q^90 - 24 * q^91 - 6 * q^92 + 20 * q^93 + 30 * q^94 - 2 * q^95 - 9 * q^96 - 3 * q^98

Introduction

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