LMFDB - Embedded newform 147.4.e.k.79.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [147,4,Mod(67,147)] 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("147.67"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(147, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,6,10,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.k.67.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.207107 - 0.358719i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.91421 + 6.77962i) q^{4} +(-0.0502525 + 0.0870399i) q^{5} +1.24264 q^{6} +6.55635 q^{8} +(-4.50000 + 7.79423i) q^{9} +(0.0208153 + 0.0360531i) q^{10} +(21.9706 + 38.0541i) q^{11} +(-11.7426 + 20.3389i) q^{12} +16.6447 q^{13} -0.301515 q^{15} +(-29.9558 + 51.8850i) q^{16} +(-60.8198 - 105.343i) q^{17} +(1.86396 + 3.22848i) q^{18} +(-63.5563 + 110.083i) q^{19} -0.786797 q^{20} +18.2010 q^{22} +(-26.7990 + 46.4172i) q^{23} +(9.83452 + 17.0339i) q^{24} +(62.4949 + 108.244i) q^{25} +(3.44722 - 5.97076i) q^{26} -27.0000 q^{27} +235.681 q^{29} +(-0.0624458 + 0.108159i) q^{30} +(-9.35534 - 16.2039i) q^{31} +(38.6335 + 66.9152i) q^{32} +(-65.9117 + 114.162i) q^{33} -50.3848 q^{34} -70.4558 q^{36} +(95.9411 - 166.175i) q^{37} +(26.3259 + 45.5978i) q^{38} +(24.9670 + 43.2441i) q^{39} +(-0.329473 + 0.570664i) q^{40} +319.713 q^{41} -218.579 q^{43} +(-171.995 + 297.904i) q^{44} +(-0.452273 - 0.783359i) q^{45} +(11.1005 + 19.2266i) q^{46} +(200.777 - 347.755i) q^{47} -179.735 q^{48} +51.7725 q^{50} +(182.459 - 316.029i) q^{51} +(65.1508 + 112.844i) q^{52} +(-321.558 - 556.956i) q^{53} +(-5.59188 + 9.68543i) q^{54} -4.41631 q^{55} -381.338 q^{57} +(48.8112 - 84.5434i) q^{58} +(-5.80613 - 10.0565i) q^{59} +(-1.18019 - 2.04416i) q^{60} +(-6.12132 + 10.6024i) q^{61} -7.75022 q^{62} -447.288 q^{64} +(-0.836436 + 1.44875i) q^{65} +(27.3015 + 47.2876i) q^{66} +(-334.524 - 579.412i) q^{67} +(476.123 - 824.670i) q^{68} -160.794 q^{69} +822.098 q^{71} +(-29.5036 + 51.1017i) q^{72} +(257.550 + 446.089i) q^{73} +(-39.7401 - 68.8319i) q^{74} +(-187.485 + 324.733i) q^{75} -995.092 q^{76} +20.6833 q^{78} +(402.877 - 697.804i) q^{79} +(-3.01071 - 5.21471i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(66.2147 - 114.687i) q^{82} +394.863 q^{83} +12.2254 q^{85} +(-45.2691 + 78.4084i) q^{86} +(353.522 + 612.318i) q^{87} +(144.047 + 249.496i) q^{88} +(336.709 - 583.197i) q^{89} -0.374675 q^{90} -419.588 q^{92} +(28.0660 - 48.6118i) q^{93} +(-83.1644 - 144.045i) q^{94} +(-6.38773 - 11.0639i) q^{95} +(-115.901 + 200.746i) q^{96} +1091.11 q^{97} -395.470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{3} + 10 q^{4} - 20 q^{5} - 12 q^{6} - 36 q^{8} - 18 q^{9} - 48 q^{10} + 20 q^{11} - 30 q^{12} + 208 q^{13} - 120 q^{15} - 18 q^{16} - 116 q^{17} - 18 q^{18} - 192 q^{19} - 88 q^{20}+ \cdots - 360 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^3 + 10 * q^4 - 20 * q^5 - 12 * q^6 - 36 * q^8 - 18 * q^9 - 48 * q^10 + 20 * q^11 - 30 * q^12 + 208 * q^13 - 120 * q^15 - 18 * q^16 - 116 * q^17 - 18 * q^18 - 192 * q^19 - 88 * q^20 + 152 * q^22 - 28 * q^23 - 54 * q^24 - 146 * q^25 - 204 * q^26 - 108 * q^27 + 592 * q^29 + 144 * q^30 + 104 * q^31 - 18 * q^32 - 60 * q^33 - 128 * q^34 - 180 * q^36 + 248 * q^37 - 104 * q^38 + 312 * q^39 + 488 * q^40 + 40 * q^41 - 1440 * q^43 - 292 * q^44 - 180 * q^45 + 84 * q^46 + 96 * q^47 - 108 * q^48 + 1412 * q^50 + 348 * q^51 + 320 * q^52 - 268 * q^53 + 54 * q^54 + 944 * q^55 - 1152 * q^57 - 48 * q^58 + 616 * q^59 - 132 * q^60 - 16 * q^61 - 608 * q^62 + 236 * q^64 - 1740 * q^65 + 228 * q^66 + 144 * q^67 + 940 * q^68 - 168 * q^69 + 1976 * q^71 + 162 * q^72 - 104 * q^73 + 56 * q^74 + 438 * q^75 - 2272 * q^76 - 1224 * q^78 + 944 * q^79 + 828 * q^80 - 162 * q^81 + 856 * q^82 + 2032 * q^83 - 200 * q^85 + 1120 * q^86 + 888 * q^87 + 876 * q^88 + 388 * q^89 + 864 * q^90 - 728 * q^92 - 312 * q^93 - 904 * q^94 - 1304 * q^95 + 54 * q^96 + 976 * q^97 - 360 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.207107	−	0.358719i	0.0732233	−	0.126826i	−0.827089	−	0.562071i	$-0.810005\pi$
$2$	0.207107	−	0.358719i	0.0732233	−	0.126826i	0.900312	+	0.435245i	$0.143338\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	3.91421	+	6.77962i	0.489277	+	0.847452i
$5$	−0.0502525	+	0.0870399i	−0.00449472	+	0.00778509i	−0.868264	−	0.496102i	$-0.834764\pi$
$5$	−0.0502525	+	0.0870399i	−0.00449472	+	0.00778509i	0.863769	+	0.503887i	$0.168097\pi$
$6$	1.24264			0.0845510
$7$		0			0
$7$		0			0
$8$	6.55635			0.289752
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	0.0208153	+	0.0360531i	0.000658237	+	0.00114010i
$11$	21.9706	+	38.0541i	0.602216	+	1.04307i	0.992485	+	0.122368i	$0.0390487\pi$
$11$	21.9706	+	38.0541i	0.602216	+	1.04307i	−0.390269	+	0.920701i	$0.627618\pi$
$12$	−11.7426	+	20.3389i	−0.282484	+	0.489277i
$13$	16.6447			0.355108			0.177554	−	0.984111i	$-0.443182\pi$
$13$	16.6447			0.355108			0.177554	+	0.984111i	$0.443182\pi$
$14$		0			0
$15$	−0.301515			−0.00519006
$16$	−29.9558	+	51.8850i	−0.468060	+	0.810704i
$17$	−60.8198	−	105.343i	−0.867704	−	1.50291i	−0.864337	−	0.502913i	$-0.832262\pi$
$17$	−60.8198	−	105.343i	−0.867704	−	1.50291i	−0.00336718	−	0.999994i	$-0.501072\pi$
$18$	1.86396	+	3.22848i	0.0244078	+	0.0422755i
$19$	−63.5563	+	110.083i	−0.767412	+	1.32920i	0.171550	+	0.985175i	$0.445122\pi$
$19$	−63.5563	+	110.083i	−0.767412	+	1.32920i	−0.938962	+	0.344021i	$0.888211\pi$
$20$	−0.786797			−0.00879665
$21$		0			0
$22$	18.2010			0.176385
$23$	−26.7990	+	46.4172i	−0.242955	+	0.420811i	−0.961555	−	0.274613i	$-0.911450\pi$
$23$	−26.7990	+	46.4172i	−0.242955	+	0.420811i	0.718599	+	0.695424i	$0.244784\pi$
$24$	9.83452	+	17.0339i	0.0836443	+	0.144876i
$25$	62.4949	+	108.244i	0.499960	+	0.865955i
$26$	3.44722	−	5.97076i	0.0260021	−	0.0450370i
$27$	−27.0000			−0.192450
$28$		0			0
$29$	235.681			1.50913			0.754567	−	0.656223i	$-0.227847\pi$
$29$	235.681			1.50913			0.754567	+	0.656223i	$0.227847\pi$
$30$	−0.0624458	+	0.108159i	−0.000380033	+	0.000658237i
$31$	−9.35534	−	16.2039i	−0.0542022	−	0.0938810i	0.837651	−	0.546205i	$-0.183928\pi$
$31$	−9.35534	−	16.2039i	−0.0542022	−	0.0938810i	−0.891853	+	0.452324i	$0.850595\pi$
$32$	38.6335	+	66.9152i	0.213422	+	0.369658i
$33$	−65.9117	+	114.162i	−0.347689	+	0.602216i
$34$	−50.3848			−0.254145
$35$		0			0
$36$	−70.4558			−0.326184
$37$	95.9411	−	166.175i	0.426287	−	0.738351i	−0.570253	−	0.821469i	$-0.693155\pi$
$37$	95.9411	−	166.175i	0.426287	−	0.738351i	0.996540	+	0.0831185i	$0.0264880\pi$
$38$	26.3259	+	45.5978i	0.112385	+	0.194656i
$39$	24.9670	+	43.2441i	0.102511	+	0.177554i
$40$	−0.329473	+	0.570664i	−0.00130236	+	0.00225575i
$41$	319.713			1.21782			0.608912	−	0.793238i	$-0.291606\pi$
$41$	319.713			1.21782			0.608912	+	0.793238i	$0.291606\pi$
$42$		0			0
$43$	−218.579			−0.775184			−0.387592	−	0.921831i	$-0.626693\pi$
$43$	−218.579			−0.775184			−0.387592	+	0.921831i	$0.626693\pi$
$44$	−171.995	+	297.904i	−0.589300	+	1.02070i
$45$	−0.452273	−	0.783359i	−0.00149824	−	0.00259503i
$46$	11.1005	+	19.2266i	0.0355800	+	0.0616264i
$47$	200.777	−	347.755i	0.623113	−	1.07926i	−0.365790	−	0.930697i	$-0.619201\pi$
$47$	200.777	−	347.755i	0.623113	−	1.07926i	0.988903	−	0.148565i	$-0.0474655\pi$
$48$	−179.735			−0.540469
$49$		0			0
$50$	51.7725			0.146435
$51$	182.459	−	316.029i	0.500969	−	0.867704i
$52$	65.1508	+	112.844i	0.173746	+	0.300937i
$53$	−321.558	−	556.956i	−0.833386	−	1.44347i	−0.895338	−	0.445387i	$-0.853066\pi$
$53$	−321.558	−	556.956i	−0.833386	−	1.44347i	0.0619521	−	0.998079i	$-0.480267\pi$
$54$	−5.59188	+	9.68543i	−0.0140918	+	0.0244078i
$55$	−4.41631			−0.0108272
$56$		0			0
$57$	−381.338			−0.886131
$58$	48.8112	−	84.5434i	0.110504	−	0.191398i
$59$	−5.80613	−	10.0565i	−0.0128118	−	0.0221906i	0.859548	−	0.511054i	$-0.170745\pi$
$59$	−5.80613	−	10.0565i	−0.0128118	−	0.0221906i	−0.872360	+	0.488864i	$0.837412\pi$
$60$	−1.18019	−	2.04416i	−0.00253937	−	0.00439833i
$61$	−6.12132	+	10.6024i	−0.0128484	+	0.0222541i	−0.872378	−	0.488832i	$-0.837423\pi$
$61$	−6.12132	+	10.6024i	−0.0128484	+	0.0222541i	0.859530	+	0.511086i	$0.170757\pi$
$62$	−7.75022			−0.0158755
$63$		0			0
$64$	−447.288			−0.873610
$65$	−0.836436	+	1.44875i	−0.00159611	+	0.00276454i
$66$	27.3015	+	47.2876i	0.0509179	+	0.0881925i
$67$	−334.524	−	579.412i	−0.609979	−	1.05651i	−0.991243	−	0.132049i	$-0.957844\pi$
$67$	−334.524	−	579.412i	−0.609979	−	1.05651i	0.381264	−	0.924466i	$-0.375489\pi$
$68$	476.123	−	824.670i	0.849095	−	1.47068i
$69$	−160.794			−0.280541
$70$		0			0
$71$	822.098			1.37416			0.687078	−	0.726584i	$-0.258893\pi$
$71$	822.098			1.37416			0.687078	+	0.726584i	$0.258893\pi$
$72$	−29.5036	+	51.1017i	−0.0482921	+	0.0836443i
$73$	257.550	+	446.089i	0.412930	+	0.715217i	0.995209	−	0.0977730i	$-0.0311719\pi$
$73$	257.550	+	446.089i	0.412930	+	0.715217i	−0.582278	+	0.812990i	$0.697839\pi$
$74$	−39.7401	−	68.8319i	−0.0624283	−	0.108129i
$75$	−187.485	+	324.733i	−0.288652	+	0.499960i
$76$	−995.092			−1.50191
$77$		0			0
$78$	20.6833			0.0300247
$79$	402.877	−	697.804i	0.573762	−	0.993786i	−0.422413	−	0.906404i	$-0.638817\pi$
$79$	402.877	−	697.804i	0.573762	−	0.993786i	0.996175	−	0.0873819i	$-0.0278500\pi$
$80$	−3.01071	−	5.21471i	−0.00420760	−	0.00728778i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	66.2147	−	114.687i	0.0891730	−	0.154452i
$83$	394.863			0.522191			0.261095	−	0.965313i	$-0.415916\pi$
$83$	394.863			0.522191			0.261095	+	0.965313i	$0.415916\pi$
$84$		0			0
$85$	12.2254			0.0156004
$86$	−45.2691	+	78.4084i	−0.0567616	+	0.0983139i
$87$	353.522	+	612.318i	0.435650	+	0.754567i
$88$	144.047	+	249.496i	0.174493	+	0.302232i
$89$	336.709	−	583.197i	0.401024	−	0.694593i	−0.592826	−	0.805331i	$-0.701988\pi$
$89$	336.709	−	583.197i	0.401024	−	0.694593i	0.993850	+	0.110737i	$0.0353212\pi$
$90$	−0.374675			−0.000438825
$91$		0			0
$92$	−419.588			−0.475490
$93$	28.0660	−	48.6118i	0.0312937	−	0.0542022i
$94$	−83.1644	−	144.045i	−0.0912527	−	0.158054i
$95$	−6.38773	−	11.0639i	−0.00689861	−	0.0119487i
$96$	−115.901	+	200.746i	−0.123219	+	0.213422i
$97$	1091.11			1.14212			0.571061	−	0.820908i	$-0.306532\pi$
$97$	1091.11			1.14212			0.571061	+	0.820908i	$0.306532\pi$
$98$		0			0
$99$	−395.470			−0.401477
$100$	−489.237	+	847.384i	−0.489237	+	0.847384i
$101$	−685.395	−	1187.14i	−0.675242	−	1.16955i	−0.976398	−	0.215978i	$-0.930706\pi$
$101$	−685.395	−	1187.14i	−0.675242	−	1.16955i	0.301157	−	0.953575i	$-0.402627\pi$
$102$	−75.5772	−	130.903i	−0.0733652	−	0.127072i
$103$	−706.978	+	1224.52i	−0.676316	+	1.17141i	0.299766	+	0.954013i	$0.403091\pi$
$103$	−706.978	+	1224.52i	−0.676316	+	1.17141i	−0.976082	+	0.217401i	$0.930242\pi$
$104$	109.128			0.102893
$105$		0			0
$106$	−266.388			−0.244093
$107$	171.770	−	297.514i	0.155192	−	0.268801i	−0.777937	−	0.628343i	$-0.783734\pi$
$107$	171.770	−	297.514i	0.155192	−	0.268801i	0.933129	+	0.359542i	$0.117067\pi$
$108$	−105.684	−	183.050i	−0.0941613	−	0.163092i
$109$	158.828	+	275.099i	0.139569	+	0.241740i	0.927333	−	0.374236i	$-0.122095\pi$
$109$	158.828	+	275.099i	0.139569	+	0.241740i	−0.787765	+	0.615976i	$0.788762\pi$
$110$	−0.914647	+	1.58421i	−0.000792801	+	0.00137317i
$111$	575.647			0.492234
$112$		0			0
$113$	798.373			0.664643			0.332321	−	0.943166i	$-0.392168\pi$
$113$	798.373			0.664643			0.332321	+	0.943166i	$0.392168\pi$
$114$	−78.9777	+	136.793i	−0.0648854	+	0.112385i
$115$	−2.69343	−	4.66516i	−0.00218404	−	0.00378286i
$116$	922.507	+	1597.83i	0.738384	+	1.27892i
$117$	−74.9010	+	129.732i	−0.0591846	+	0.102511i
$118$	−4.80996			−0.00375248
$119$		0			0
$120$	−1.97684			−0.00150383
$121$	−299.911	+	519.462i	−0.225328	+	0.390279i
$122$	2.53553	+	4.39167i	0.00188161	+	0.00325904i
$123$	479.569	+	830.638i	0.351555	+	0.608912i
$124$	73.2376	−	126.851i	0.0530398	−	0.0918676i
$125$	−25.1253			−0.0179782
$126$		0			0
$127$	1071.40			0.748593			0.374297	−	0.927309i	$-0.377884\pi$
$127$	1071.40			0.748593			0.374297	+	0.927309i	$0.377884\pi$
$128$	−401.705	+	695.773i	−0.277391	+	0.480455i
$129$	−327.868	−	567.884i	−0.223776	−	0.387592i
$130$	0.346463	+	0.600092i	0.000233745	+	0.000404858i
$131$	−1257.51	+	2178.07i	−0.838695	+	1.45266i	0.0522910	+	0.998632i	$0.483348\pi$
$131$	−1257.51	+	2178.07i	−0.838695	+	1.45266i	−0.890986	+	0.454031i	$0.849986\pi$
$132$	−1031.97			−0.680465
$133$		0			0
$134$	−277.129			−0.178659
$135$	1.35682	−	2.35008i	0.000865010	−	0.00149824i
$136$	−398.756	−	690.665i	−0.251419	−	0.435471i
$137$	−125.532	−	217.428i	−0.0782841	−	0.135592i	0.824226	−	0.566262i	$-0.191611\pi$
$137$	−125.532	−	217.428i	−0.0782841	−	0.135592i	−0.902510	+	0.430670i	$0.858277\pi$
$138$	−33.3015	+	57.6799i	−0.0205421	+	0.0355800i
$139$	−886.067			−0.540685			−0.270343	−	0.962764i	$-0.587137\pi$
$139$	−886.067			−0.540685			−0.270343	+	0.962764i	$0.587137\pi$
$140$		0			0
$141$	1204.66			0.719508
$142$	170.262	−	294.902i	0.100620	−	0.174279i
$143$	365.693	+	633.398i	0.213851	+	0.370401i
$144$	−269.603	−	466.965i	−0.156020	−	0.270235i
$145$	−11.8436	+	20.5137i	−0.00678314	+	0.0117487i
$146$	213.361			0.120945
$147$		0			0
$148$	1502.14			0.834289
$149$	−291.313	+	504.569i	−0.160170	+	0.277422i	−0.934929	−	0.354834i	$-0.884537\pi$
$149$	−291.313	+	504.569i	−0.160170	+	0.277422i	0.774760	+	0.632256i	$0.217871\pi$
$150$	77.6588	+	134.509i	0.0422721	+	0.0732174i
$151$	1405.88	+	2435.06i	0.757676	+	1.31233i	0.944033	+	0.329851i	$0.106999\pi$
$151$	1405.88	+	2435.06i	0.757676	+	1.31233i	−0.186357	+	0.982482i	$0.559668\pi$
$152$	−416.698	+	721.741i	−0.222359	+	0.385138i
$153$	1094.76			0.578469
$154$		0			0
$155$	1.88052			0.000974496
$156$	−195.452	+	338.533i	−0.100312	+	0.173746i
$157$	−845.672	−	1464.75i	−0.429885	−	0.744583i	0.566978	−	0.823733i	$-0.308113\pi$
$157$	−845.672	−	1464.75i	−0.429885	−	0.744583i	−0.996863	+	0.0791504i	$0.974779\pi$
$158$	−166.877	−	289.040i	−0.0840256	−	0.145537i
$159$	964.675	−	1670.87i	0.481156	−	0.833386i
$160$	−7.76573			−0.00383709
$161$		0			0
$162$	−33.5513			−0.0162718
$163$	20.3616	−	35.2674i	0.00978432	−	0.0169469i	−0.861092	−	0.508450i	$-0.830219\pi$
$163$	20.3616	−	35.2674i	0.00978432	−	0.0169469i	0.870876	+	0.491503i	$0.163552\pi$
$164$	1251.42	+	2167.53i	0.595852	+	1.03205i
$165$	−6.62446	−	11.4739i	−0.00312554	−	0.00541359i
$166$	81.7788	−	141.645i	0.0382365	−	0.0662276i
$167$	−2900.47			−1.34398			−0.671990	−	0.740560i	$-0.734560\pi$
$167$	−2900.47			−1.34398			−0.671990	+	0.740560i	$0.734560\pi$
$168$		0			0
$169$	−1919.96			−0.873899
$170$	2.53196	−	4.38549i	0.00114231	−	0.00197854i
$171$	−572.007	−	990.745i	−0.255804	−	0.443065i
$172$	−855.563	−	1481.88i	−0.379280	−	0.656932i
$173$	−1073.07	+	1858.62i	−0.471585	+	0.816810i	−0.999472	−	0.0325052i	$-0.989651\pi$
$173$	−1073.07	+	1858.62i	−0.471585	+	0.816810i	0.527886	+	0.849315i	$0.322985\pi$
$174$	292.867			0.127599
$175$		0			0
$176$	−2632.59			−1.12749
$177$	17.4184	−	30.1695i	0.00739688	−	0.0128118i
$178$	−139.470	−	241.568i	−0.0587286	−	0.101721i
$179$	−601.770	−	1042.30i	−0.251276	−	0.435222i	0.712602	−	0.701569i	$-0.247517\pi$
$179$	−601.770	−	1042.30i	−0.251276	−	0.435222i	−0.963877	+	0.266347i	$0.914183\pi$
$180$	3.54058	−	6.13247i	0.00146611	−	0.00253937i
$181$	2990.47			1.22807			0.614033	−	0.789280i	$-0.289546\pi$
$181$	2990.47			1.22807			0.614033	+	0.789280i	$0.289546\pi$
$182$		0			0
$183$	−36.7279			−0.0148361
$184$	−175.704	+	304.327i	−0.0703969	+	0.121931i
$185$	9.64257	+	16.7014i	0.00383209	+	0.00663737i
$186$	−11.6253	−	20.1357i	−0.00458285	−	0.00793773i
$187$	2672.49	−	4628.89i	1.04509	−	1.81015i
$188$	3143.53			1.21950
$189$		0			0
$190$	−5.29177			−0.00202056
$191$	1403.70	−	2431.29i	0.531772	−	0.921057i	−0.467540	−	0.883972i	$-0.654860\pi$
$191$	1403.70	−	2431.29i	0.531772	−	0.921057i	0.999312	−	0.0370847i	$-0.0118071\pi$
$192$	−670.933	−	1162.09i	−0.252190	−	0.436805i
$193$	−1668.18	−	2889.38i	−0.622169	−	1.07763i	−0.989081	−	0.147372i	$-0.952919\pi$
$193$	−1668.18	−	2889.38i	−0.622169	−	1.07763i	0.366913	−	0.930255i	$-0.380415\pi$
$194$	225.977	−	391.404i	0.0836299	−	0.144851i
$195$	−5.01862			−0.00184303
$196$		0			0
$197$	−4226.65			−1.52861			−0.764305	−	0.644855i	$-0.776918\pi$
$197$	−4226.65			−1.52861			−0.764305	+	0.644855i	$0.776918\pi$
$198$	−81.9045	+	141.863i	−0.0293975	+	0.0509179i
$199$	2192.85	+	3798.12i	0.781140	+	1.35297i	0.931278	+	0.364309i	$0.118695\pi$
$199$	2192.85	+	3798.12i	0.781140	+	1.35297i	−0.150139	+	0.988665i	$0.547972\pi$
$200$	409.739	+	709.688i	0.144865	+	0.250913i
$201$	1003.57	−	1738.24i	0.352172	−	0.609979i
$202$	−567.800			−0.197774
$203$		0			0
$204$	2856.74			0.980450
$205$	−16.0664	+	27.8278i	−0.00547378	+	0.00948086i
$206$	292.840	+	507.213i	0.0990442	+	0.171550i
$207$	−241.191	−	417.755i	−0.0809852	−	0.140270i
$208$	−498.605	+	863.609i	−0.166212	+	0.287887i
$209$	−5585.48			−1.84859
$210$		0			0
$211$	2291.56			0.747665			0.373833	−	0.927496i	$-0.378043\pi$
$211$	2291.56			0.747665			0.373833	+	0.927496i	$0.378043\pi$
$212$	2517.30	−	4360.09i	0.815513	−	1.41251i
$213$	1233.15	+	2135.87i	0.396684	+	0.687078i
$214$	−71.1493	−	123.234i	−0.0227274	−	0.0393650i
$215$	10.9841	−	19.0251i	0.00348424	−	0.00603488i
$216$	−177.021			−0.0557629
$217$		0			0
$218$	131.578			0.0408788
$219$	−772.649	+	1338.27i	−0.238406	+	0.412930i
$220$	−17.2864	−	29.9409i	−0.00529748	−	0.00917551i
$221$	−1012.33	−	1753.40i	−0.308128	−	0.533694i
$222$	119.220	−	206.496i	0.0360430	−	0.0624283i
$223$	217.970			0.0654544			0.0327272	−	0.999464i	$-0.489581\pi$
$223$	217.970			0.0654544			0.0327272	+	0.999464i	$0.489581\pi$
$224$		0			0
$225$	−1124.91			−0.333306
$226$	165.349	−	286.392i	0.0486674	−	0.0842943i
$227$	917.680	+	1589.47i	0.268320	+	0.464743i	0.968428	−	0.249293i	$-0.0801983\pi$
$227$	917.680	+	1589.47i	0.268320	+	0.464743i	−0.700108	+	0.714037i	$0.746865\pi$
$228$	−1492.64	−	2585.33i	−0.433563	−	0.750954i
$229$	1387.00	−	2402.36i	0.400244	−	0.693243i	−0.593511	−	0.804826i	$-0.702259\pi$
$229$	1387.00	−	2402.36i	0.400244	−	0.693243i	0.993755	+	0.111583i	$0.0355921\pi$
$230$	−2.23131			−0.000639689
$231$		0			0
$232$	1545.21			0.437275
$233$	494.356	−	856.250i	0.138997	−	0.240750i	−0.788120	−	0.615522i	$-0.788945\pi$
$233$	494.356	−	856.250i	0.138997	−	0.240750i	0.927117	+	0.374771i	$0.122279\pi$
$234$	31.0250	+	53.7369i	0.00866738	+	0.0150123i
$235$	20.1791	+	34.9512i	0.00560144	+	0.00970197i
$236$	45.4529	−	78.7267i	0.0125370	−	0.0217147i
$237$	2417.26			0.662524
$238$		0			0
$239$	−837.928			−0.226783			−0.113391	−	0.993550i	$-0.536171\pi$
$239$	−837.928			−0.226783			−0.113391	+	0.993550i	$0.536171\pi$
$240$	9.03214	−	15.6441i	0.00242926	−	0.00420760i
$241$	−1727.49	−	2992.11i	−0.461733	−	0.799745i	0.537315	−	0.843382i	$-0.319439\pi$
$241$	−1727.49	−	2992.11i	−0.461733	−	0.799745i	−0.999047	+	0.0436371i	$0.986105\pi$
$242$	124.227	+	215.168i	0.0329985	+	0.0571551i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−95.8406			−0.0251458
$245$		0			0
$246$	397.288			0.102968
$247$	−1057.87	+	1832.29i	−0.272514	+	0.472008i
$248$	−61.3369	−	106.239i	−0.0157052	−	0.0272022i
$249$	592.294	+	1025.88i	0.150743	+	0.261095i
$250$	−5.20361	+	9.01292i	−0.00131642	+	0.00228011i
$251$	−5635.01			−1.41705			−0.708523	−	0.705688i	$-0.750638\pi$
$251$	−5635.01			−1.41705			−0.708523	+	0.705688i	$0.750638\pi$
$252$		0			0
$253$	−2355.16			−0.585246
$254$	221.894	−	384.332i	0.0548145	−	0.0949414i
$255$	18.3381	+	31.7625i	0.00450344	+	0.00780018i
$256$	−1622.76	−	2810.71i	−0.396182	−	0.686208i
$257$	−1135.58	+	1966.88i	−0.275624	+	0.477395i	−0.970292	−	0.241935i	$-0.922218\pi$
$257$	−1135.58	+	1966.88i	−0.275624	+	0.477395i	0.694668	+	0.719330i	$0.255551\pi$
$258$	−271.615			−0.0655426
$259$		0			0
$260$	−13.0960			−0.00312376
$261$	−1060.57	+	1836.95i	−0.251522	+	0.435650i
$262$	520.877	+	902.186i	0.122824	+	0.212737i
$263$	−81.9336	−	141.913i	−0.0192101	−	0.0332728i	0.856261	−	0.516544i	$-0.172782\pi$
$263$	−81.9336	−	141.913i	−0.0192101	−	0.0332728i	−0.875471	+	0.483271i	$0.839448\pi$
$264$	−432.140	+	748.489i	−0.100744	+	0.174493i
$265$	64.6365			0.0149834
$266$		0			0
$267$	2020.26			0.463062
$268$	2618.80	−	4535.89i	0.596897	−	1.03386i
$269$	−2583.55	−	4474.84i	−0.585582	−	1.01426i	−0.994803	−	0.101823i	$-0.967533\pi$
$269$	−2583.55	−	4474.84i	−0.585582	−	1.01426i	0.409220	−	0.912436i	$-0.365801\pi$
$270$	−0.562013	−	0.973434i	−0.000126678	−	0.000219412i
$271$	−811.136	+	1404.93i	−0.181819	+	0.314920i	−0.942500	−	0.334206i	$-0.891532\pi$
$271$	−811.136	+	1404.93i	−0.181819	+	0.314920i	0.760681	+	0.649126i	$0.224865\pi$
$272$	7287.63			1.62455
$273$		0			0
$274$	−103.994			−0.0229289
$275$	−2746.10	+	4756.38i	−0.602167	+	1.04298i
$276$	−629.382	−	1090.12i	−0.137262	−	0.237745i
$277$	2306.18	+	3994.43i	0.500235	+	0.866433i	1.00000		0.000271708i	$8.64874e-5\pi$
$277$	2306.18	+	3994.43i	0.500235	+	0.866433i	−0.499765	+	0.866161i	$0.666580\pi$
$278$	−183.511	+	317.850i	−0.0395908	+	0.0685732i
$279$	168.396			0.0361348
$280$		0			0
$281$	−2125.22			−0.451174			−0.225587	−	0.974223i	$-0.572430\pi$
$281$	−2125.22			−0.451174			−0.225587	+	0.974223i	$0.572430\pi$
$282$	249.493	−	432.135i	0.0526848	−	0.0912527i
$283$	1285.77	+	2227.02i	0.270075	+	0.467783i	0.968881	−	0.247528i	$-0.0796183\pi$
$283$	1285.77	+	2227.02i	0.270075	+	0.467783i	−0.698806	+	0.715311i	$0.746285\pi$
$284$	3217.87	+	5573.51i	0.672342	+	1.16453i
$285$	19.1632	−	33.1916i	0.00398291	−	0.00689861i
$286$	302.950			0.0626356
$287$		0			0
$288$	−695.403			−0.142281
$289$	−4941.60	+	8559.10i	−1.00582	+	1.74213i
$290$	4.90577	+	8.49704i	0.000993368	+	0.00172056i
$291$	1636.67	+	2834.80i	0.329702	+	0.571061i
$292$	−2016.21	+	3492.18i	−0.404075	+	0.699878i
$293$	3324.96			0.662957			0.331478	−	0.943463i	$-0.392453\pi$
$293$	3324.96			0.662957			0.331478	+	0.943463i	$0.392453\pi$
$294$		0			0
$295$	1.16709			0.000230341
$296$	629.024	−	1089.50i	0.123518	−	0.213939i
$297$	−593.205	−	1027.46i	−0.115896	−	0.200739i
$298$	120.666	+	208.999i	0.0234563	+	0.0406275i
$299$	−446.060	+	772.599i	−0.0862753	+	0.149433i
$300$	−2935.42			−0.564922
$301$		0			0
$302$	1164.67			0.221918
$303$	2056.19	−	3561.42i	0.389851	−	0.675242i
$304$	−3807.77	−	6595.25i	−0.718390	−	1.24429i
$305$	−0.615224	−	1.06560i	−0.000115500	−	0.000200052i
$306$	226.731	−	392.710i	0.0423574	−	0.0733652i
$307$	−887.096			−0.164916			−0.0824580	−	0.996595i	$-0.526277\pi$
$307$	−887.096			−0.164916			−0.0824580	+	0.996595i	$0.526277\pi$
$308$		0			0
$309$	−4241.87			−0.780943
$310$	0.389468	−	0.674578i	7.13558e−5	−	0.000123592i
$311$	2255.41	+	3906.48i	0.411230	+	0.712271i	0.995025	−	0.0996300i	$-0.0317659\pi$
$311$	2255.41	+	3906.48i	0.411230	+	0.712271i	−0.583794	+	0.811902i	$0.698433\pi$
$312$	163.692	+	283.523i	0.0297027	+	0.0514466i
$313$	−1857.89	+	3217.96i	−0.335509	+	0.581118i	−0.983582	−	0.180459i	$-0.942242\pi$
$313$	−1857.89	+	3217.96i	−0.335509	+	0.581118i	0.648074	+	0.761578i	$0.275575\pi$
$314$	−700.577			−0.125910
$315$		0			0
$316$	6307.79			1.12291
$317$	−3477.26	+	6022.79i	−0.616096	+	1.06711i	0.374095	+	0.927390i	$0.377953\pi$
$317$	−3477.26	+	6022.79i	−0.616096	+	1.06711i	−0.990191	+	0.139719i	$0.955380\pi$
$318$	−399.582	−	692.096i	−0.0704636	−	0.122047i
$319$	5178.05	+	8968.64i	0.908825	+	1.57413i
$320$	22.4774	−	38.9320i	0.00392664	−	0.00680113i
$321$	1030.62			0.179201
$322$		0			0
$323$	15461.9			2.66355
$324$	317.051	−	549.149i	0.0543641	−	0.0941613i
$325$	1040.21	+	1801.69i	0.177539	+	0.307507i
$326$	−8.43406	−	14.6082i	−0.00143288	−	0.00248182i
$327$	−476.485	+	825.297i	−0.0805801	+	0.139569i
$328$	2096.15			0.352867
$329$		0			0
$330$	−5.48788			−0.000915448
$331$	4931.59	−	8541.76i	0.818926	−	1.41842i	−0.0875478	−	0.996160i	$-0.527903\pi$
$331$	4931.59	−	8541.76i	0.818926	−	1.41842i	0.906474	−	0.422262i	$-0.138764\pi$
$332$	1545.58	+	2677.02i	0.255496	+	0.442532i
$333$	863.470	+	1495.57i	0.142096	+	0.246117i
$334$	−600.706	+	1040.45i	−0.0984107	+	0.170452i
$335$	67.2427			0.0109668
$336$		0			0
$337$	−5945.06			−0.960974			−0.480487	−	0.877002i	$-0.659540\pi$
$337$	−5945.06			−0.960974			−0.480487	+	0.877002i	$0.659540\pi$
$338$	−397.636	+	688.725i	−0.0639897	+	0.110833i
$339$	1197.56	+	2074.24i	0.191866	+	0.332321i
$340$	47.8528	+	82.8835i	0.00763289	+	0.0132206i
$341$	411.084	−	712.019i	0.0652829	−	0.113073i
$342$	−473.866			−0.0749232
$343$		0			0
$344$	−1433.08			−0.224612
$345$	8.08030	−	13.9955i	0.00126095	−	0.00218404i
$346$	444.482	+	769.865i	0.0690621	+	0.119619i
$347$	−584.786	−	1012.88i	−0.0904697	−	0.156698i	0.817239	−	0.576299i	$-0.195503\pi$
$347$	−584.786	−	1012.88i	−0.0904697	−	0.156698i	−0.907709	+	0.419601i	$0.862170\pi$
$348$	−2767.52	+	4793.49i	−0.426306	+	0.738384i
$349$	−9176.66			−1.40749			−0.703747	−	0.710451i	$-0.748491\pi$
$349$	−9176.66			−1.40749			−0.703747	+	0.710451i	$0.748491\pi$
$350$		0			0
$351$	−449.406			−0.0683405
$352$	−1697.60	+	2940.33i	−0.257052	+	0.445228i
$353$	−5293.60	−	9168.78i	−0.798158	−	1.38245i	−0.920814	−	0.390001i	$-0.872474\pi$
$353$	−5293.60	−	9168.78i	−0.798158	−	1.38245i	0.122656	−	0.992449i	$-0.460859\pi$
$354$	−7.21494	−	12.4966i	−0.00108325	−	0.00187624i
$355$	−41.3125	+	71.5553i	−0.00617645	+	0.0106979i
$356$	5271.81			0.784846
$357$		0			0
$358$	−498.522			−0.0735970
$359$	−4307.61	+	7460.99i	−0.633278	+	1.09687i	0.353599	+	0.935397i	$0.384958\pi$
$359$	−4307.61	+	7460.99i	−0.633278	+	1.09687i	−0.986877	+	0.161472i	$0.948376\pi$
$360$	−2.96526	−	5.13598i	−0.000434119	−	0.000751916i
$361$	−4649.32	−	8052.86i	−0.677842	−	1.17406i
$362$	619.347	−	1072.74i	0.0899230	−	0.155751i
$363$	−1799.47			−0.260186
$364$		0			0
$365$	−51.7701			−0.00742403
$366$	−7.60660	+	13.1750i	−0.00108635	+	0.00188161i
$367$	−4148.89	−	7186.10i	−0.590110	−	1.02210i	−0.994217	−	0.107389i	$-0.965751\pi$
$367$	−4148.89	−	7186.10i	−0.590110	−	1.02210i	0.404107	−	0.914712i	$-0.367582\pi$
$368$	−1605.57	−	2780.93i	−0.227436	−	0.393930i
$369$	−1438.71	+	2491.91i	−0.202971	+	0.351555i
$370$	7.98817			0.00112239
$371$		0			0
$372$	439.426			0.0612450
$373$	2561.93	−	4437.39i	0.355634	−	0.615977i	−0.631592	−	0.775301i	$-0.717598\pi$
$373$	2561.93	−	4437.39i	0.355634	−	0.615977i	0.987226	+	0.159324i	$0.0509315\pi$
$374$	−1106.98	−	1917.35i	−0.153050	−	0.265090i
$375$	−37.6879	−	65.2773i	−0.00518985	−	0.00898908i
$376$	1316.36	−	2280.01i	0.180548	−	0.312719i
$377$	3922.83			0.535905
$378$		0			0
$379$	−1502.49			−0.203635			−0.101817	−	0.994803i	$-0.532466\pi$
$379$	−1502.49			−0.203635			−0.101817	+	0.994803i	$0.532466\pi$
$380$	50.0059	−	86.6128i	0.00675066	−	0.0116925i
$381$	1607.10	+	2783.58i	0.216100	+	0.374297i
$382$	−581.434	−	1007.07i	−0.0778763	−	0.134886i
$383$	5436.47	−	9416.24i	0.725301	−	1.25626i	−0.233548	−	0.972345i	$-0.575034\pi$
$383$	5436.47	−	9416.24i	0.725301	−	1.25626i	0.958850	−	0.283914i	$-0.0916330\pi$
$384$	−2410.23			−0.320303
$385$		0			0
$386$	−1381.97			−0.182229
$387$	983.604	−	1703.65i	0.129197	−	0.223776i
$388$	4270.85	+	7397.33i	0.558814	+	0.967894i
$389$	−2309.50	−	4000.16i	−0.301018	−	0.521379i	0.675349	−	0.737499i	$-0.263993\pi$
$389$	−2309.50	−	4000.16i	−0.301018	−	0.521379i	−0.976367	+	0.216120i	$0.930660\pi$
$390$	−1.03939	+	1.80028i	−0.000134953	+	0.000233745i
$391$	6519.64			0.843254
$392$		0			0
$393$	−7545.05			−0.968442
$394$	−875.367	+	1516.18i	−0.111930	+	0.193868i
$395$	40.4912	+	70.1328i	0.00515781	+	0.00893358i
$396$	−1547.95	−	2681.14i	−0.196433	−	0.340233i
$397$	−4803.48	+	8319.86i	−0.607253	+	1.05179i	0.384438	+	0.923151i	$0.374395\pi$
$397$	−4803.48	+	8319.86i	−0.607253	+	1.05179i	−0.991691	+	0.128642i	$0.958938\pi$
$398$	1816.61			0.228791
$399$		0			0
$400$	−7488.36			−0.936044
$401$	5250.52	−	9094.17i	0.653862	−	1.13252i	−0.328316	−	0.944568i	$-0.606481\pi$
$401$	5250.52	−	9094.17i	0.653862	−	1.13252i	0.982178	−	0.187954i	$-0.0601857\pi$
$402$	−415.693	−	720.002i	−0.0515743	−	0.0893294i
$403$	−155.716	−	269.709i	−0.0192476	−	0.0333378i
$404$	5365.57	−	9293.44i	0.660760	−	1.14447i
$405$	8.14091			0.000998827
$406$		0			0
$407$	8431.52			1.02687
$408$	1196.27	−	2072.00i	0.145157	−	0.251419i
$409$	6033.47	+	10450.3i	0.729427	+	1.26340i	0.957126	+	0.289673i	$0.0935466\pi$
$409$	6033.47	+	10450.3i	0.729427	+	1.26340i	−0.227699	+	0.973732i	$0.573120\pi$
$410$	6.65491	+	11.5266i	0.000801616	+	0.00138844i
$411$	376.596	−	652.283i	0.0451973	−	0.0782841i
$412$	−11069.0			−1.32362
$413$		0			0
$414$	−199.809			−0.0237200
$415$	−19.8429	+	34.3688i	−0.00234710	+	0.00406530i
$416$	643.042	+	1113.78i	0.0757878	+	0.131268i
$417$	−1329.10	−	2302.07i	−0.156082	−	0.270343i
$418$	−1156.79	+	2003.62i	−0.135360	+	0.234450i
$419$	−6366.31			−0.742278			−0.371139	−	0.928577i	$-0.621033\pi$
$419$	−6366.31			−0.742278			−0.371139	+	0.928577i	$0.621033\pi$
$420$		0			0
$421$	−4731.84			−0.547781			−0.273890	−	0.961761i	$-0.588311\pi$
$421$	−4731.84			−0.547781			−0.273890	+	0.961761i	$0.588311\pi$
$422$	474.597	−	822.026i	0.0547465	−	0.0948237i
$423$	1806.99	+	3129.80i	0.207704	+	0.359754i
$424$	−2108.25	−	3651.60i	−0.241476	−	0.418248i
$425$	7601.86	−	13166.8i	0.867634	−	1.50279i
$426$	1021.57			0.116186
$427$		0			0
$428$	2689.37			0.303728
$429$	−1097.08	+	1900.19i	−0.123467	+	0.213851i
$430$	−4.54978	−	7.88044i	−0.000510255	−	0.000883788i
$431$	−1876.39	−	3250.01i	−0.209704	−	0.363219i	0.741917	−	0.670492i	$-0.233917\pi$
$431$	−1876.39	−	3250.01i	−0.209704	−	0.363219i	−0.951621	+	0.307273i	$0.900584\pi$
$432$	808.808	−	1400.90i	0.0900782	−	0.156020i
$433$	11709.2			1.29956			0.649780	−	0.760122i	$-0.274861\pi$
$433$	11709.2			1.29956			0.649780	+	0.760122i	$0.274861\pi$
$434$		0			0
$435$	−71.0615			−0.00783250
$436$	−1243.38	+	2153.59i	−0.136576	+	0.236556i
$437$	−3406.49	−	5900.22i	−0.372894	−	0.645871i
$438$	320.042	+	554.329i	0.0349137	+	0.0604723i
$439$	7462.36	−	12925.2i	0.811296	−	1.40521i	−0.100661	−	0.994921i	$-0.532096\pi$
$439$	7462.36	−	12925.2i	0.811296	−	1.40521i	0.911957	−	0.410285i	$-0.134571\pi$
$440$	−28.9548			−0.00313720
$441$		0			0
$442$	−838.638			−0.0902487
$443$	4258.83	−	7376.51i	0.456756	−	0.791125i	−0.542031	−	0.840359i	$-0.682344\pi$
$443$	4258.83	−	7376.51i	0.456756	−	0.791125i	0.998787	+	0.0492333i	$0.0156778\pi$
$444$	2253.20	+	3902.66i	0.240839	+	0.417145i
$445$	33.8410	+	58.6143i	0.00360498	+	0.00624401i
$446$	45.1430	−	78.1900i	0.00479279	−	0.00830135i
$447$	−1747.88			−0.184948
$448$		0			0
$449$	−5965.73			−0.627038			−0.313519	−	0.949582i	$-0.601508\pi$
$449$	−5965.73			−0.627038			−0.313519	+	0.949582i	$0.601508\pi$
$450$	−232.976	+	403.527i	−0.0244058	+	0.0422721i
$451$	7024.27	+	12166.4i	0.733392	+	1.27027i
$452$	3125.00	+	5412.67i	0.325194	+	0.563253i
$453$	−4217.65	+	7305.18i	−0.437444	+	0.757676i
$454$	760.231			0.0785890
$455$		0			0
$456$	−2500.19			−0.256759
$457$	6930.28	−	12003.6i	0.709376	−	1.22868i	−0.255712	−	0.966753i	$-0.582310\pi$
$457$	6930.28	−	12003.6i	0.709376	−	1.22868i	0.965089	−	0.261923i	$-0.0843567\pi$
$458$	−574.516	−	995.091i	−0.0586143	−	0.101523i
$459$	1642.13	+	2844.26i	0.166990	+	0.289235i
$460$	21.0854	−	36.5209i	0.00213719	−	0.00370173i
$461$	−149.312			−0.0150850			−0.00754249	−	0.999972i	$-0.502401\pi$
$461$	−149.312			−0.0150850			−0.00754249	+	0.999972i	$0.502401\pi$
$462$		0			0
$463$	5403.95			0.542425			0.271213	−	0.962519i	$-0.412575\pi$
$463$	5403.95			0.542425			0.271213	+	0.962519i	$0.412575\pi$
$464$	−7060.03	+	12228.3i	−0.706366	+	1.22346i
$465$	2.82078	+	4.88573i	0.000281313	+	0.000487248i
$466$	−204.769	−	354.670i	−0.0203557	−	0.0352571i
$467$	−1852.33	+	3208.33i	−0.183545	+	0.317909i	−0.943085	−	0.332551i	$-0.892091\pi$
$467$	−1852.33	+	3208.33i	−0.183545	+	0.317909i	0.759540	+	0.650460i	$0.225424\pi$
$468$	−1172.71			−0.115831
$469$		0			0
$470$	16.7169			0.00164062
$471$	2537.02	−	4394.24i	0.248194	−	0.429885i
$472$	−38.0670	−	65.9340i	−0.00371224	−	0.00642979i
$473$	−4802.30	−	8317.82i	−0.466828	−	0.808570i
$474$	500.632	−	867.119i	0.0485122	−	0.0840256i
$475$	−15887.8			−1.53470
$476$		0			0
$477$	5788.05			0.555591
$478$	−173.540	+	300.581i	−0.0166058	+	0.0287620i
$479$	5335.88	+	9242.02i	0.508982	+	0.881583i	0.999946	+	0.0104033i	$0.00331152\pi$
$479$	5335.88	+	9242.02i	0.508982	+	0.881583i	−0.490963	+	0.871180i	$0.663355\pi$
$480$	−11.6486	−	20.1760i	−0.00110767	−	0.00191855i
$481$	1596.91	−	2765.92i	0.151378	−	0.262194i
$482$	−1431.10			−0.135238
$483$		0			0
$484$	−4695.67			−0.440990
$485$	−54.8312	+	94.9705i	−0.00513352	+	0.00889152i
$486$	−50.3269	−	87.1688i	−0.00469728	−	0.00813592i
$487$	−2926.96	−	5069.65i	−0.272348	−	0.471720i	0.697115	−	0.716959i	$-0.254467\pi$
$487$	−2926.96	−	5069.65i	−0.272348	−	0.471720i	−0.969463	+	0.245239i	$0.921133\pi$
$488$	−40.1335	+	69.5133i	−0.00372287	+	0.00644819i
$489$	122.170			0.0112980
$490$		0			0
$491$	4065.31			0.373656			0.186828	−	0.982393i	$-0.440179\pi$
$491$	4065.31			0.373656			0.186828	+	0.982393i	$0.440179\pi$
$492$	−3754.27	+	6502.59i	−0.344016	+	0.595852i
$493$	−14334.1	−	24827.4i	−1.30948	−	2.26809i
$494$	438.186	+	758.960i	0.0399087	+	0.0691239i
$495$	19.8734	−	34.4217i	0.00180453	−	0.00312554i
$496$	1120.99			0.101480
$497$		0			0
$498$	490.673			0.0441517
$499$	−2405.59	+	4166.61i	−0.215810	+	0.373794i	−0.953523	−	0.301321i	$-0.902572\pi$
$499$	−2405.59	+	4166.61i	−0.215810	+	0.373794i	0.737713	+	0.675115i	$0.235906\pi$
$500$	−98.3456	−	170.340i	−0.00879630	−	0.0152356i
$501$	−4350.70	−	7535.63i	−0.387974	−	0.671990i
$502$	−1167.05	+	2021.39i	−0.103761	+	0.179719i
$503$	17001.2			1.50705			0.753526	−	0.657418i	$-0.228351\pi$
$503$	17001.2			1.50705			0.753526	+	0.657418i	$0.228351\pi$
$504$		0			0
$505$	137.771			0.0121401
$506$	−487.769	+	844.840i	−0.0428537	+	0.0742248i
$507$	−2879.93	−	4988.19i	−0.252273	−	0.436949i
$508$	4193.69	+	7263.68i	0.366269	+	0.634397i
$509$	−6898.61	+	11948.7i	−0.600738	+	1.04051i	0.391972	+	0.919977i	$0.371793\pi$
$509$	−6898.61	+	11948.7i	−0.600738	+	1.04051i	−0.992710	+	0.120531i	$0.961540\pi$
$510$	15.1918			0.00131903
$511$		0			0
$512$	−7771.61			−0.670820
$513$	1716.02	−	2972.24i	0.147688	−	0.255804i
$514$	470.372	+	814.708i	0.0403642	+	0.0699129i
$515$	−71.0548	−	123.071i	−0.00607971	−	0.0105304i
$516$	2566.69	−	4445.64i	0.218977	−	0.379280i
$517$	17644.7			1.50099
$518$		0			0
$519$	−6438.44			−0.544540
$520$	−5.48397	+	9.49851i	−0.000462477	+	0.000801033i
$521$	−1968.31	−	3409.21i	−0.165515	−	0.286680i	0.771323	−	0.636443i	$-0.219595\pi$
$521$	−1968.31	−	3409.21i	−0.165515	−	0.286680i	−0.936838	+	0.349764i	$0.886262\pi$
$522$	439.301	+	760.891i	0.0368346	+	0.0637994i
$523$	−8729.63	+	15120.2i	−0.729866	+	1.26417i	0.227073	+	0.973878i	$0.427084\pi$
$523$	−8729.63	+	15120.2i	−0.729866	+	1.26417i	−0.956939	+	0.290288i	$0.906249\pi$
$524$	−19688.6			−1.64142
$525$		0			0
$526$	−67.8760			−0.00562649
$527$	−1137.98	+	1971.04i	−0.0940630	+	0.162922i
$528$	−3948.88	−	6839.66i	−0.325479	−	0.563746i
$529$	4647.13	+	8049.06i	0.381945	+	0.661549i
$530$	13.3867	−	23.1864i	0.00109713	−	0.00190029i
$531$	104.510			0.00854118
$532$		0			0
$533$	5321.51			0.432458
$534$	418.409	−	724.705i	0.0339069	−	0.0587286i
$535$	17.2637	+	29.9016i	0.00139509	+	0.00241637i
$536$	−2193.26	−	3798.83i	−0.176743	−	0.306128i
$537$	1805.31	−	3126.89i	0.145074	−	0.251276i
$538$	−2140.28			−0.171513
$539$		0			0
$540$	21.2435			0.00169292
$541$	−9550.66	+	16542.2i	−0.758992	+	1.31461i	0.184373	+	0.982856i	$0.440975\pi$
$541$	−9550.66	+	16542.2i	−0.758992	+	1.31461i	−0.943365	+	0.331757i	$0.892359\pi$
$542$	335.983	+	581.940i	0.0266268	+	0.0461190i
$543$	4485.71	+	7769.47i	0.354512	+	0.614033i
$544$	4699.37	−	8139.54i	0.370374	−	0.641507i
$545$	−31.9261			−0.00250929
$546$		0			0
$547$	15413.5			1.20481			0.602407	−	0.798189i	$-0.294208\pi$
$547$	15413.5			1.20481			0.602407	+	0.798189i	$0.294208\pi$
$548$	982.718	−	1702.12i	0.0766052	−	0.132684i
$549$	−55.0919	−	95.4219i	−0.00428281	−	0.00741805i
$550$	1137.47	+	1970.16i	0.0881853	+	0.152741i
$551$	−14979.0	+	25944.5i	−1.15813	+	2.00594i
$552$	−1054.22			−0.0812874
$553$		0			0
$554$	1910.51			0.146516
$555$	−28.9277	+	50.1043i	−0.00221246	+	0.00383209i
$556$	−3468.26	−	6007.20i	−0.264545	−	0.458205i
$557$	10246.4	+	17747.3i	0.779453	+	1.35005i	0.932257	+	0.361796i	$0.117836\pi$
$557$	10246.4	+	17747.3i	0.779453	+	1.35005i	−0.152804	+	0.988257i	$0.548830\pi$
$558$	34.8760	−	60.4070i	0.00264591	−	0.00458285i
$559$	−3638.17			−0.275274
$560$		0			0
$561$	16034.9			1.20677
$562$	−440.147	+	762.357i	−0.0330364	+	0.0572208i
$563$	3571.24	+	6185.57i	0.267336	+	0.463039i	0.968173	−	0.250282i	$-0.0805234\pi$
$563$	3571.24	+	6185.57i	0.267336	+	0.463039i	−0.700837	+	0.713321i	$0.747190\pi$
$564$	4715.30	+	8167.13i	0.352039	+	0.609749i
$565$	−40.1203	+	69.4904i	−0.00298739	+	0.00517430i
$566$	1065.17			0.0791030
$567$		0			0
$568$	5389.96			0.398165
$569$	−2048.96	+	3548.90i	−0.150961	+	0.261472i	−0.931581	−	0.363534i	$-0.881570\pi$
$569$	−2048.96	+	3548.90i	−0.150961	+	0.261472i	0.780620	+	0.625006i	$0.214903\pi$
$570$	−7.93766	−	13.7484i	−0.000583284	−	0.00101028i
$571$	1419.24	+	2458.20i	0.104016	+	0.180162i	0.913336	−	0.407207i	$-0.133497\pi$
$571$	1419.24	+	2458.20i	0.104016	+	0.180162i	−0.809320	+	0.587369i	$0.800164\pi$
$572$	−2862.80	+	4958.51i	−0.209265	+	0.362458i
$573$	8422.23			0.614038
$574$		0			0
$575$	−6699.21			−0.485872
$576$	2012.80	−	3486.27i	0.145602	−	0.252190i
$577$	7732.23	+	13392.6i	0.557881	+	0.966277i	0.997673	+	0.0681781i	$0.0217186\pi$
$577$	7732.23	+	13392.6i	0.557881	+	0.966277i	−0.439793	+	0.898099i	$0.644948\pi$
$578$	2046.88	+	3545.29i	0.147299	+	0.255129i
$579$	5004.55	−	8668.14i	0.359209	−	0.622169i
$580$	−185.433			−0.0132753
$581$		0			0
$582$	1355.86			0.0965675
$583$	14129.6	−	24473.3i	1.00376	−	1.73856i
$584$	1688.59	+	2924.72i	0.119648	+	0.207236i
$585$	−7.52793	−	13.0388i	−0.000532037	−	0.000921515i
$586$	688.622	−	1192.73i	0.0485439	−	0.0840805i
$587$	14003.6			0.984652			0.492326	−	0.870411i	$-0.336147\pi$
$587$	14003.6			0.984652			0.492326	+	0.870411i	$0.336147\pi$
$588$		0			0
$589$	2378.36			0.166382
$590$	0.241713	−	0.418658i	1.68664e−5	−	2.92134e-5i
$591$	−6339.97	−	10981.1i	−0.441272	−	0.764305i
$592$	5747.99	+	9955.82i	0.399056	+	0.691185i
$593$	−3252.25	+	5633.06i	−0.225217	+	0.390088i	−0.956385	−	0.292110i	$-0.905643\pi$
$593$	−3252.25	+	5633.06i	−0.225217	+	0.390088i	0.731167	+	0.682198i	$0.238976\pi$
$594$	−491.427			−0.0339453
$595$		0			0
$596$	−4561.04			−0.313469
$597$	−6578.54	+	11394.4i	−0.450991	+	0.781140i
$598$	184.764	+	320.021i	0.0126347	+	0.0218840i
$599$	6308.05	+	10925.9i	0.430284	+	0.745273i	0.996898	−	0.0787104i	$-0.0250802\pi$
$599$	6308.05	+	10925.9i	0.430284	+	0.745273i	−0.566614	+	0.823983i	$0.691747\pi$
$600$	−1229.22	+	2129.06i	−0.0836376	+	0.144865i
$601$	8270.87			0.561358			0.280679	−	0.959802i	$-0.409440\pi$
$601$	8270.87			0.561358			0.280679	+	0.959802i	$0.409440\pi$
$602$		0			0
$603$	6021.43			0.406653
$604$	−11005.8	+	19062.7i	−0.741426	+	1.28419i
$605$	−30.1426	−	52.2085i	−0.00202557	−	0.00350839i
$606$	−851.700	−	1475.19i	−0.0570923	−	0.0988868i
$607$	−1905.92	+	3301.15i	−0.127445	+	0.220740i	−0.922686	−	0.385553i	$-0.874011\pi$
$607$	−1905.92	+	3301.15i	−0.127445	+	0.220740i	0.795241	+	0.606293i	$0.207344\pi$
$608$	−9821.62			−0.655130
$609$		0			0
$610$	−0.509668			−3.38293e−5
$611$	3341.86	−	5788.27i	0.221272	−	0.383254i
$612$	4285.11	+	7422.03i	0.283032	+	0.490225i
$613$	−5679.63	−	9837.42i	−0.374222	−	0.648172i	0.615988	−	0.787756i	$-0.288757\pi$
$613$	−5679.63	−	9837.42i	−0.374222	−	0.648172i	−0.990210	+	0.139583i	$0.955424\pi$
$614$	−183.724	+	318.219i	−0.0120757	+	0.0209157i
$615$	−96.3983			−0.00632057
$616$		0			0
$617$	−18272.2			−1.19224			−0.596118	−	0.802896i	$-0.703291\pi$
$617$	−18272.2			−1.19224			−0.596118	+	0.802896i	$0.703291\pi$
$618$	−878.519	+	1521.64i	−0.0571832	+	0.0990442i
$619$	−14800.1	−	25634.6i	−0.961013	−	1.66452i	−0.719965	−	0.694010i	$-0.755842\pi$
$619$	−14800.1	−	25634.6i	−0.961013	−	1.66452i	−0.241048	−	0.970513i	$-0.577491\pi$
$620$	7.36075	+	12.7492i	0.000476798	+	0.000825838i
$621$	723.573	−	1253.26i	0.0467568	−	0.0809852i
$622$	1868.44			0.120447
$623$		0			0
$624$	−2991.63			−0.191925
$625$	−7810.61	+	13528.4i	−0.499879	+	0.865815i
$626$	769.564	+	1332.92i	0.0491341	+	0.0851028i
$627$	−8378.21	−	14511.5i	−0.533642	−	0.924295i
$628$	6620.28	−	11466.7i	0.420665	−	0.728614i
$629$	−23340.5			−1.47956
$630$		0			0
$631$	7185.41			0.453322			0.226661	−	0.973974i	$-0.427219\pi$
$631$	7185.41			0.453322			0.226661	+	0.973974i	$0.427219\pi$
$632$	2641.40	−	4575.05i	0.166249	−	0.287952i
$633$	3437.34	+	5953.64i	0.215832	+	0.373833i
$634$	1440.33	+	2494.72i	0.0902252	+	0.156275i
$635$	−53.8405	+	93.2545i	−0.00336472	+	0.00582786i
$636$	15103.8			0.941673
$637$		0			0
$638$	4289.64			0.266189
$639$	−3699.44	+	6407.62i	−0.229026	+	0.396684i
$640$	−40.3733	−	69.9287i	−0.00249359	−	0.00431902i
$641$	116.491	+	201.768i	0.00717803	+	0.0124327i	0.869592	−	0.493771i	$-0.164382\pi$
$641$	116.491	+	201.768i	0.00717803	+	0.0124327i	−0.862414	+	0.506203i	$0.831048\pi$
$642$	213.448	−	369.702i	0.0131217	−	0.0227274i
$643$	−1837.96			−0.112725			−0.0563624	−	0.998410i	$-0.517950\pi$
$643$	−1837.96			−0.112725			−0.0563624	+	0.998410i	$0.517950\pi$
$644$		0			0
$645$	65.9048			0.00402325
$646$	3202.27	−	5546.50i	0.195034	−	0.337808i
$647$	9297.35	+	16103.5i	0.564941	+	0.978506i	0.997055	+	0.0766874i	$0.0244343\pi$
$647$	9297.35	+	16103.5i	0.564941	+	0.978506i	−0.432114	+	0.901819i	$0.642232\pi$
$648$	−265.532	−	459.915i	−0.0160974	−	0.0278814i
$649$	255.128	−	441.895i	0.0154309	−	0.0267271i
$650$	861.736			0.0520001
$651$		0			0
$652$	318.799			0.0191490
$653$	14432.3	−	24997.6i	0.864902	−	1.49805i	−0.00224162	−	0.999997i	$-0.500714\pi$
$653$	14432.3	−	24997.6i	0.864902	−	1.49805i	0.867144	−	0.498057i	$-0.165953\pi$
$654$	197.367	+	341.849i	0.0118007	+	0.0204394i
$655$	−126.386	−	218.907i	−0.00753940	−	0.0130586i
$656$	−9577.27	+	16588.3i	−0.570014	+	0.987294i
$657$	−4635.90			−0.275287
$658$		0			0
$659$	−29066.3			−1.71815			−0.859076	−	0.511847i	$-0.828961\pi$
$659$	−29066.3			−1.71815			−0.859076	+	0.511847i	$0.828961\pi$
$660$	51.8591	−	89.8226i	0.00305850	−	0.00529748i
$661$	1989.75	+	3446.36i	0.117084	+	0.202795i	0.918611	−	0.395163i	$-0.129312\pi$
$661$	1989.75	+	3446.36i	0.117084	+	0.202795i	−0.801527	+	0.597959i	$0.795979\pi$
$662$	−2042.73	−	3538.11i	−0.119929	−	0.207723i
$663$	3036.98	−	5260.20i	0.177898	−	0.308128i
$664$	2588.86			0.151306
$665$		0			0
$666$	715.322			0.0416189
$667$	−6316.02	+	10939.7i	−0.366653	+	0.635061i
$668$	−11353.0	−	19664.0i	−0.657578	−	1.13896i
$669$	326.955	+	566.302i	0.0188951	+	0.0327272i
$670$	13.9264	−	24.1213i	0.000803022	−	0.00139087i
$671$	−537.955			−0.0309501
$672$		0			0
$673$	−184.229			−0.0105520			−0.00527601	−	0.999986i	$-0.501679\pi$
$673$	−184.229			−0.0105520			−0.00527601	+	0.999986i	$0.501679\pi$
$674$	−1231.26	+	2132.61i	−0.0703657	+	0.121877i
$675$	−1687.36	−	2922.60i	−0.0962173	−	0.166653i
$676$	−7515.11	−	13016.6i	−0.427578	−	0.740587i
$677$	8341.73	−	14448.3i	0.473558	−	0.820227i	−0.525984	−	0.850495i	$-0.676303\pi$
$677$	8341.73	−	14448.3i	0.473558	−	0.820227i	0.999542	+	0.0302680i	$0.00963607\pi$
$678$	992.091			0.0561962
$679$		0			0
$680$	80.1540			0.00452024
$681$	−2753.04	+	4768.41i	−0.154914	+	0.268320i
$682$	−170.277	−	294.928i	−0.00956045	−	0.0165592i
$683$	−8904.11	−	15422.4i	−0.498838	−	0.864013i	0.501161	−	0.865354i	$-0.332906\pi$
$683$	−8904.11	−	15422.4i	−0.498838	−	0.864013i	−0.999999	+	0.00134107i	$0.999573\pi$
$684$	4477.92	−	7755.98i	0.250318	−	0.433563i
$685$	25.2332			0.00140746
$686$		0			0
$687$	8322.03			0.462162
$688$	6547.71	−	11341.0i	0.362833	−	0.628445i
$689$	−5352.23	−	9270.34i	−0.295942	−	0.512586i
$690$	−3.34697	−	5.79712i	−0.000184662	−	0.000319845i
$691$	10072.8	−	17446.7i	0.554542	−	0.960495i	−0.443397	−	0.896325i	$-0.646227\pi$
$691$	10072.8	−	17446.7i	0.554542	−	0.960495i	0.997939	−	0.0641695i	$-0.0204398\pi$
$692$	−16801.0			−0.922943
$693$		0			0
$694$	−484.453			−0.0264980
$695$	44.5271	−	77.1232i	0.00243023	−	0.00420928i
$696$	2317.81	+	4014.57i	0.126231	+	0.218638i
$697$	−19444.9	−	33679.5i	−1.05671	−	1.83028i
$698$	−1900.55	+	3291.85i	−0.103061	+	0.178507i
$699$	2966.14			0.160500
$700$		0			0
$701$	−2719.67			−0.146534			−0.0732672	−	0.997312i	$-0.523343\pi$
$701$	−2719.67			−0.146534			−0.0732672	+	0.997312i	$0.523343\pi$
$702$	−93.0750	+	161.211i	−0.00500412	+	0.00866738i
$703$	12195.3	+	21122.9i	0.654276	+	1.13324i
$704$	−9827.18	−	17021.2i	−0.526102	−	0.911235i
$705$	−60.5372	+	104.854i	−0.00323399	+	0.00560144i
$706$	−4385.36			−0.233775
$707$		0			0
$708$	272.717			0.0144765
$709$	312.854	−	541.879i	0.0165719	−	0.0287034i	−0.857621	−	0.514283i	$-0.828058\pi$
$709$	312.854	−	541.879i	0.0165719	−	0.0287034i	0.874192	+	0.485580i	$0.161391\pi$
$710$	17.1122	+	29.6392i	0.000904520	+	0.00156667i
$711$	3625.89	+	6280.23i	0.191254	+	0.331262i
$712$	2207.58	−	3823.65i	0.116198	−	0.201260i
$713$	1002.85			0.0526749
$714$		0			0
$715$	−73.5079			−0.00384481
$716$	4710.91	−	8159.53i	0.245887	−	0.425888i
$717$	−1256.89	−	2177.00i	−0.0654665	−	0.113391i
$718$	1784.27	+	3090.44i	0.0927414	+	0.160633i
$719$	4788.77	−	8294.39i	0.248388	−	0.430221i	−0.714691	−	0.699441i	$-0.753433\pi$
$719$	4788.77	−	8294.39i	0.248388	−	0.430221i	0.963079	+	0.269220i	$0.0867659\pi$
$720$	54.1929			0.00280507
$721$		0			0
$722$	−3851.62			−0.198535
$723$	5182.48	−	8976.32i	0.266582	−	0.461733i
$724$	11705.3	+	20274.2i	0.600864	+	1.04073i
$725$	14728.9	+	25511.2i	0.754506	+	1.30684i
$726$	−372.682	+	645.504i	−0.0190517	+	0.0329985i
$727$	−16741.2			−0.854053			−0.427027	−	0.904239i	$-0.640439\pi$
$727$	−16741.2			−0.854053			−0.427027	+	0.904239i	$0.640439\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−10.7219	+	18.5710i	−0.000543612	+	0.000941564i
$731$	13293.9	+	23025.7i	0.672631	+	1.16503i
$732$	−143.761	−	249.001i	−0.00725896	−	0.0125729i
$733$	3248.02	−	5625.74i	0.163668	−	0.283481i	−0.772514	−	0.634998i	$-0.781001\pi$
$733$	3248.02	−	5625.74i	0.163668	−	0.283481i	0.936181	+	0.351517i	$0.114334\pi$
$734$	−3437.06			−0.172839
$735$		0			0
$736$	−4141.36			−0.207408
$737$	14699.4	−	25460.0i	0.734678	−	1.27250i
$738$	595.932	+	1032.18i	0.0297243	+	0.0514841i
$739$	−249.640	−	432.389i	−0.0124265	−	0.0215233i	0.859745	−	0.510723i	$-0.170622\pi$
$739$	−249.640	−	432.389i	−0.0124265	−	0.0215233i	−0.872172	+	0.489200i	$0.837289\pi$
$740$	−75.4861	+	130.746i	−0.00374990	+	0.00649502i
$741$	−6347.24			−0.314672
$742$		0			0
$743$	−6367.30			−0.314393			−0.157196	−	0.987567i	$-0.550246\pi$
$743$	−6367.30			−0.314393			−0.157196	+	0.987567i	$0.550246\pi$
$744$	184.011	−	318.716i	0.00906741	−	0.0157052i
$745$	−29.2784	−	50.7117i	−0.00143984	−	0.00249387i
$746$	−1061.19	−	1838.03i	−0.0520814	−	0.0902077i
$747$	−1776.88	+	3077.65i	−0.0870318	+	0.150743i
$748$	41842.8			2.04535
$749$		0			0
$750$	−31.2217			−0.00152007
$751$	−248.049	+	429.634i	−0.0120525	+	0.0208756i	−0.871989	−	0.489526i	$-0.837170\pi$
$751$	−248.049	+	429.634i	−0.0120525	+	0.0208756i	0.859936	+	0.510401i	$0.170503\pi$
$752$	12028.9	+	20834.6i	0.583308	+	1.01032i
$753$	−8452.51	−	14640.2i	−0.409066	−	0.708523i
$754$	812.446	−	1407.20i	0.0392407	−	0.0679670i
$755$	−282.597			−0.0136222
$756$		0			0
$757$	13025.9			0.625408			0.312704	−	0.949851i	$-0.398765\pi$
$757$	13025.9			0.625408			0.312704	+	0.949851i	$0.398765\pi$
$758$	−311.175	+	538.971i	−0.0149108	+	0.0258263i
$759$	−3532.73	−	6118.87i	−0.168946	−	0.292623i
$760$	−41.8802	−	72.5387i	−0.00199889	−	0.00346218i
$761$	12737.3	−	22061.6i	0.606736	−	1.05090i	−0.385039	−	0.922900i	$-0.625812\pi$
$761$	12737.3	−	22061.6i	0.606736	−	1.05090i	0.991775	−	0.127997i	$-0.0408548\pi$
$762$	1331.36			0.0632943
$763$		0			0
$764$	21977.6			1.04074
$765$	−55.0143	+	95.2875i	−0.00260006	+	0.00450344i
$766$	−2251.86	−	3900.33i	−0.106218	−	0.183975i
$767$	−96.6411	−	167.387i	−0.00454955	−	0.00788006i
$768$	4868.29	−	8432.12i	0.228736	−	0.396182i
$769$	−29054.0			−1.36244			−0.681218	−	0.732080i	$-0.738550\pi$
$769$	−29054.0			−1.36244			−0.681218	+	0.732080i	$0.738550\pi$
$770$		0			0
$771$	−6813.47			−0.318263
$772$	13059.3	−	22619.3i	0.608825	−	1.05452i
$773$	−948.677	−	1643.16i	−0.0441417	−	0.0764557i	0.843110	−	0.537740i	$-0.180722\pi$
$773$	−948.677	−	1643.16i	−0.0441417	−	0.0764557i	−0.887252	+	0.461285i	$0.847389\pi$
$774$	−407.422	−	705.676i	−0.0189205	−	0.0327713i
$775$	1169.32	−	2025.33i	0.0541978	−	0.0938734i
$776$	7153.72			0.330933
$777$		0			0
$778$	−1913.25			−0.0881662
$779$	−20319.8	+	35194.9i	−0.934572	+	1.61873i
$780$	−19.6439	−	34.0243i	−0.000901751	−	0.00156188i
$781$	18061.9	+	31284.2i	0.827538	+	1.43334i
$782$	1350.26	−	2338.72i	0.0617458	−	0.106947i
$783$	−6363.39			−0.290433
$784$		0			0
$785$	169.989			0.00772886
$786$	−1562.63	+	2706.56i	−0.0709125	+	0.122824i
$787$	−21325.1	−	36936.2i	−0.965895	−	1.67298i	−0.707192	−	0.707021i	$-0.750039\pi$
$787$	−21325.1	−	36936.2i	−0.965895	−	1.67298i	−0.258702	−	0.965957i	$-0.583295\pi$
$788$	−16544.0	−	28655.0i	−0.747913	−	1.29542i
$789$	245.801	−	425.740i	0.0110909	−	0.0192101i
$790$	33.5440			0.00151069
$791$		0			0
$792$	−2592.84			−0.116329
$793$	−101.887	+	176.474i	−0.00456258	+	0.00790262i
$794$	1989.66	+	3446.20i	0.0889302	+	0.154032i
$795$	96.9548	+	167.931i	0.00432532	+	0.00749168i
$796$	−17166.5	+	29733.3i	−0.764387	+	1.32396i
$797$	36822.8			1.63655			0.818275	−	0.574828i	$-0.194931\pi$
$797$	36822.8			1.63655			0.818275	+	0.574828i	$0.194931\pi$
$798$		0			0
$799$	−48844.8			−2.16271
$800$	−4828.80	+	8363.73i	−0.213405	+	0.369628i
$801$	3030.38	+	5248.78i	0.133675	+	0.231531i
$802$	−2174.84	−	3766.93i	−0.0957559	−	0.165854i
$803$	−11317.0	+	19601.7i	−0.497347	+	0.861429i
$804$	15712.8			0.689238
$805$		0			0
$806$	−129.000			−0.00563750
$807$	7750.64	−	13424.5i	0.338086	−	0.585582i
$808$	−4493.69	−	7783.30i	−0.195653	−	0.338881i
$809$	−2540.97	−	4401.09i	−0.110427	−	0.191266i	0.805515	−	0.592575i	$-0.201889\pi$
$809$	−2540.97	−	4401.09i	−0.110427	−	0.191266i	−0.915943	+	0.401309i	$0.868555\pi$
$810$	1.68604	−	2.92030i	7.31374e−5	−	0.000126678i
$811$	11873.4			0.514097			0.257048	−	0.966399i	$-0.417250\pi$
$811$	11873.4			0.514097			0.257048	+	0.966399i	$0.417250\pi$
$812$		0			0
$813$	−4866.82			−0.209947
$814$	1746.23	−	3024.55i	0.0751906	−	0.130234i
$815$	2.04645	+	3.54455i	8.79557e−5	+	0.000152344i
$816$	10931.5	+	18933.8i	0.468967	+	0.812275i
$817$	13892.1	−	24061.8i	0.594886	−	1.03037i
$818$	4998.29			0.213644
$819$		0			0
$820$	−251.549			−0.0107128
$821$	−8484.72	+	14696.0i	−0.360681	+	0.624717i	−0.988073	−	0.153986i	$-0.950789\pi$
$821$	−8484.72	+	14696.0i	−0.360681	+	0.624717i	0.627392	+	0.778703i	$0.284122\pi$
$822$	−155.991	−	270.185i	−0.00661900	−	0.0114644i
$823$	−1997.97	−	3460.58i	−0.0846231	−	0.146572i	0.820607	−	0.571492i	$-0.193635\pi$
$823$	−1997.97	−	3460.58i	−0.0846231	−	0.146572i	−0.905231	+	0.424921i	$0.860302\pi$
$824$	−4635.19	+	8028.39i	−0.195964	+	0.339420i
$825$	−16476.6			−0.695323
$826$		0			0
$827$	−13589.7			−0.571417			−0.285708	−	0.958317i	$-0.592229\pi$
$827$	−13589.7			−0.571417			−0.285708	+	0.958317i	$0.592229\pi$
$828$	1888.15	−	3270.36i	0.0792483	−	0.137262i
$829$	15323.0	+	26540.2i	0.641966	+	1.11192i	0.984993	+	0.172592i	$0.0552141\pi$
$829$	15323.0	+	26540.2i	0.641966	+	1.11192i	−0.343028	+	0.939325i	$0.611453\pi$
$830$	8.21918	+	14.2360i	0.000343725	+	0.000595350i
$831$	−6918.55	+	11983.3i	−0.288811	+	0.500235i
$832$	−7444.96			−0.310226
$833$		0			0
$834$	−1101.06			−0.0457155
$835$	145.756	−	252.456i	0.00604082	−	0.0104630i
$836$	−21862.7	−	37867.4i	−0.904472	−	1.56659i
$837$	252.594	+	437.506i	0.0104312	+	0.0180674i
$838$	−1318.51	+	2283.72i	−0.0543521	+	0.0941405i
$839$	−7497.57			−0.308516			−0.154258	−	0.988031i	$-0.549299\pi$
$839$	−7497.57			−0.308516			−0.154258	+	0.988031i	$0.549299\pi$
$840$		0			0
$841$	31156.6			1.27749
$842$	−979.996	+	1697.40i	−0.0401103	+	0.0694731i
$843$	−3187.83	−	5521.48i	−0.130243	−	0.225587i
$844$	8969.65	+	15535.9i	0.365815	+	0.633610i
$845$	96.4826	−	167.113i	0.00392793	−	0.00680338i
$846$	1496.96			0.0608351
$847$		0			0
$848$	38530.2			1.56030
$849$	−3857.31	+	6681.06i	−0.155928	+	0.270075i
$850$	−3148.79	−	5453.87i	−0.127062	−	0.220078i
$851$	5142.25	+	8906.64i	0.207138	+	0.358773i
$852$	−9653.60	+	16720.5i	−0.388177	+	0.672342i
$853$	−10347.6			−0.415352			−0.207676	−	0.978198i	$-0.566590\pi$
$853$	−10347.6			−0.415352			−0.207676	+	0.978198i	$0.566590\pi$
$854$		0			0
$855$	114.979			0.00459907
$856$	1126.18	−	1950.60i	0.0449674	−	0.0778858i
$857$	−774.999	−	1342.34i	−0.0308909	−	0.0535045i	0.850167	−	0.526514i	$-0.176501\pi$
$857$	−774.999	−	1342.34i	−0.0308909	−	0.0535045i	−0.881058	+	0.473009i	$0.843168\pi$
$858$	454.424	+	787.086i	0.0180813	+	0.0313178i
$859$	−7593.76	+	13152.8i	−0.301625	+	0.522430i	−0.976504	−	0.215499i	$-0.930862\pi$
$859$	−7593.76	+	13152.8i	−0.301625	+	0.522430i	0.674879	+	0.737928i	$0.264196\pi$
$860$	171.977			0.00681903
$861$		0			0
$862$	−1554.45			−0.0614210
$863$	−20775.1	+	35983.5i	−0.819459	+	1.41934i	0.0866230	+	0.996241i	$0.472392\pi$
$863$	−20775.1	+	35983.5i	−0.819459	+	1.41934i	−0.906082	+	0.423103i	$0.860941\pi$
$864$	−1043.10	−	1806.71i	−0.0410731	−	0.0711407i
$865$	−107.849	−	186.801i	−0.00423929	−	0.00734267i
$866$	2425.06	−	4200.33i	0.0951581	−	0.164819i
$867$	−29649.6			−1.16142
$868$		0			0
$869$	35405.8			1.38212
$870$	−14.7173	+	25.4911i	−0.000573521	+	0.000993368i
$871$	−5568.04	−	9644.12i	−0.216608	−	0.375176i
$872$	1041.33	+	1803.64i	0.0404404	+	0.0700449i
$873$	−4910.01	+	8504.39i	−0.190354	+	0.329702i
$874$	−2822.03			−0.109218
$875$		0			0
$876$	−12097.3			−0.466585
$877$	−13918.7	+	24107.9i	−0.535919	+	0.928239i	0.463199	+	0.886254i	$0.346701\pi$
$877$	−13918.7	+	24107.9i	−0.535919	+	0.928239i	−0.999118	+	0.0419846i	$0.986632\pi$
$878$	−3091.01	−	5353.79i	−0.118812	−	0.205788i
$879$	4987.44	+	8638.51i	0.191379	+	0.331478i
$880$	132.294	−	229.140i	0.00506777	−	0.00877763i
$881$	−2587.85			−0.0989635			−0.0494817	−	0.998775i	$-0.515757\pi$
$881$	−2587.85			−0.0989635			−0.0494817	+	0.998775i	$0.515757\pi$
$882$		0			0
$883$	−16382.0			−0.624346			−0.312173	−	0.950025i	$-0.601057\pi$
$883$	−16382.0			−0.624346			−0.312173	+	0.950025i	$0.601057\pi$
$884$	7924.91	−	13726.4i	0.301520	−	0.522248i
$885$	1.75064	+	3.03219i	6.64938e−5	+	0.000115171i
$886$	−1764.06	−	3055.45i	−0.0668904	−	0.115858i
$887$	11490.1	−	19901.4i	0.434948	−	0.753352i	−0.562343	−	0.826904i	$-0.690100\pi$
$887$	11490.1	−	19901.4i	0.434948	−	0.753352i	0.997291	+	0.0735516i	$0.0234334\pi$
$888$	3774.14			0.142626
$889$		0			0
$890$	28.0348			0.00105587
$891$	1779.62	−	3082.38i	0.0669129	−	0.115896i
$892$	853.180	+	1477.75i	0.0320253	+	0.0554695i
$893$	25521.3	+	44204.1i	0.956368	+	1.65648i
$894$	−361.997	+	626.998i	−0.0135425	+	0.0234563i
$895$	120.962			0.00451766
$896$		0			0
$897$	−2676.36			−0.0996222
$898$	−1235.54	+	2140.02i	−0.0459138	+	0.0795251i
$899$	−2204.88	−	3818.96i	−0.0817984	−	0.141679i
$900$	−4403.13	−	7626.45i	−0.163079	−	0.282461i
$901$	−39114.2	+	67747.9i	−1.44626	+	2.50500i
$902$	5819.10			0.214806
$903$		0			0
$904$	5234.42			0.192582
$905$	−150.279	+	260.290i	−0.00551982	+	0.00956060i
$906$	1747.01	+	3025.90i	0.0640623	+	0.110959i
$907$	11357.7	+	19672.1i	0.415795	+	0.720178i	0.995512	−	0.0946400i	$-0.0301700\pi$
$907$	11357.7	+	19672.1i	0.415795	+	0.720178i	−0.579716	+	0.814818i	$0.696837\pi$
$908$	−7183.99	+	12443.0i	−0.262565	+	0.454776i
$909$	12337.1			0.450161
$910$		0			0
$911$	34922.3			1.27006			0.635031	−	0.772487i	$-0.280987\pi$
$911$	34922.3			1.27006			0.635031	+	0.772487i	$0.280987\pi$
$912$	11423.3	−	19785.7i	0.414763	−	0.718390i
$913$	8675.36	+	15026.2i	0.314472	+	0.544681i
$914$	−2870.62	−	4972.06i	−0.103886	−	0.179935i
$915$	1.84567	−	3.19680i	6.66842e−5	−	0.000115500i
$916$	21716.1			0.783320
$917$		0			0
$918$	1360.39			0.0489102
$919$	−5851.32	+	10134.8i	−0.210030	+	0.363782i	−0.951724	−	0.306956i	$-0.900689\pi$
$919$	−5851.32	+	10134.8i	−0.210030	+	0.363782i	0.741694	+	0.670739i	$0.234023\pi$
$920$	−17.6591	−	30.5864i	−0.000632829	−	0.00109609i
$921$	−1330.64	−	2304.74i	−0.0476072	−	0.0824580i
$922$	−30.9236	+	53.5613i	−0.00110457	+	0.00191317i
$923$	13683.5			0.487973
$924$		0			0
$925$	23983.3			0.852505
$926$	1119.20	−	1938.50i	0.0397182	−	0.0687939i
$927$	−6362.80	−	11020.7i	−0.225439	−	0.390471i
$928$	9105.19	+	15770.7i	0.322083	+	0.557863i
$929$	26548.2	−	45982.9i	0.937588	−	1.62395i	0.167637	−	0.985849i	$-0.446386\pi$
$929$	26548.2	−	45982.9i	0.937588	−	1.62395i	0.769952	−	0.638102i	$-0.220280\pi$
$930$	2.33681			8.23946e−5
$931$		0			0
$932$	7740.06			0.272032
$933$	−6766.23	+	11719.5i	−0.237424	+	0.411230i
$934$	767.259	+	1328.93i	0.0268795	+	0.0465567i
$935$	268.599	+	465.227i	0.00939478	+	0.0162722i
$936$	−491.077	+	850.570i	−0.0171489	+	0.0297027i
$937$	−39020.6			−1.36046			−0.680229	−	0.733000i	$-0.738120\pi$
$937$	−39020.6			−1.36046			−0.680229	+	0.733000i	$0.738120\pi$
$938$		0			0
$939$	−11147.4			−0.387412
$940$	−157.970	+	273.613i	−0.00548131	+	0.00949390i
$941$	−15371.9	−	26624.9i	−0.532528	−	0.922366i	−0.999279	−	0.0379770i	$-0.987909\pi$
$941$	−15371.9	−	26624.9i	−0.532528	−	0.922366i	0.466750	−	0.884389i	$-0.345425\pi$
$942$	−1050.87	−	1820.15i	−0.0363472	−	0.0629552i
$943$	−8567.98	+	14840.2i	−0.295877	+	0.512474i
$944$	695.710			0.0239867
$945$		0			0
$946$	−3978.35			−0.136731
$947$	−8150.14	+	14116.5i	−0.279666	+	0.484396i	−0.971302	−	0.237851i	$-0.923557\pi$
$947$	−8150.14	+	14116.5i	−0.279666	+	0.484396i	0.691636	+	0.722247i	$0.256890\pi$
$948$	9461.68	+	16388.1i	0.324157	+	0.561457i
$949$	4286.83	+	7425.01i	0.146635	+	0.253979i
$950$	−3290.47	+	5699.26i	−0.112376	+	0.194641i
$951$	−20863.6			−0.711406
$952$		0			0
$953$	−11512.7			−0.391325			−0.195663	−	0.980671i	$-0.562686\pi$
$953$	−11512.7			−0.391325			−0.195663	+	0.980671i	$0.562686\pi$
$954$	1198.74	−	2076.29i	0.0406822	−	0.0704636i
$955$	141.079	+	244.357i	0.00478034	+	0.00827979i
$956$	−3279.83	−	5680.83i	−0.110959	−	0.192187i
$957$	−15534.1	+	26905.9i	−0.524710	+	0.908825i
$958$	4420.39			0.149078
$959$		0			0
$960$	134.864			0.00453409
$961$	14720.5	−	25496.6i	0.494124	−	0.855848i
$962$	−661.461	−	1145.68i	−0.0221688	−	0.0383974i
$963$	1545.93	+	2677.62i	0.0517308	+	0.0896004i
$964$	13523.6	−	23423.5i	0.451830	−	0.782593i
$965$	335.322			0.0111859
$966$		0			0
$967$	−18178.4			−0.604528			−0.302264	−	0.953224i	$-0.597742\pi$
$967$	−18178.4			−0.604528			−0.302264	+	0.953224i	$0.597742\pi$
$968$	−1966.32	+	3405.77i	−0.0652893	+	0.113084i
$969$	23192.9	+	40171.3i	0.768899	+	1.33177i
$970$	22.7118	+	39.3381i	0.000751787	+	0.00130213i
$971$	14138.3	−	24488.3i	0.467271	−	0.809338i	−0.532029	−	0.846726i	$-0.678570\pi$
$971$	14138.3	−	24488.3i	0.467271	−	0.809338i	0.999301	+	0.0373880i	$0.0119037\pi$
$972$	1902.31			0.0627742
$973$		0			0
$974$	−2424.77			−0.0797688
$975$	−3120.62	+	5405.08i	−0.102502	+	0.177539i
$976$	−366.739	−	635.210i	−0.0120277	−	0.0208326i
$977$	6973.53	+	12078.5i	0.228355	+	0.395523i	0.957321	−	0.289028i	$-0.0933320\pi$
$977$	6973.53	+	12078.5i	0.228355	+	0.395523i	−0.728966	+	0.684550i	$0.759999\pi$
$978$	25.3022	−	43.8246i	0.000827274	−	0.00143288i
$979$	29590.8			0.966011
$980$		0			0
$981$	−2858.91			−0.0930459
$982$	841.954	−	1458.31i	0.0273603	−	0.0473894i
$983$	−13288.4	−	23016.2i	−0.431164	−	0.746797i	0.565810	−	0.824536i	$-0.308564\pi$
$983$	−13288.4	−	23016.2i	−0.431164	−	0.746797i	−0.996974	+	0.0777381i	$0.975230\pi$
$984$	3144.22	+	5445.95i	0.101864	+	0.176434i
$985$	212.400	−	367.887i	0.00687068	−	0.0119004i
$986$	−11874.7			−0.383539
$987$		0			0
$988$	−16563.0			−0.533339
$989$	5857.69	−	10145.8i	0.188335	−	0.326206i
$990$	−8.23182	−	14.2579i	−0.000264267	−	0.000457724i
$991$	−8124.96	−	14072.8i	−0.260442	−	0.451099i	0.705917	−	0.708294i	$-0.250535\pi$
$991$	−8124.96	−	14072.8i	−0.260442	−	0.451099i	−0.966359	+	0.257195i	$0.917202\pi$
$992$	722.859	−	1252.03i	0.0231359	−	0.0400725i
$993$	29589.5			0.945615
$994$		0			0
$995$	−440.784			−0.0140440
$996$	−4636.73	+	8031.06i	−0.147511	+	0.255496i
$997$	9407.05	+	16293.5i	0.298821	+	0.517573i	0.975866	−	0.218368i	$-0.0700734\pi$
$997$	9407.05	+	16293.5i	0.298821	+	0.517573i	−0.677046	+	0.735941i	$0.736740\pi$
$998$	996.429	+	1725.87i	0.0316046	+	0.0547408i
$999$	−2590.41	+	4486.72i	−0.0820390	+	0.142096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.e.k.79.2		4
3.2	odd	2		441.4.e.v.226.1		4
7.2	even	3		147.4.a.j.1.1	✓	2
7.3	odd	6		147.4.e.j.67.2		4
7.4	even	3	inner	147.4.e.k.67.2		4
7.5	odd	6		147.4.a.k.1.1	yes	2
7.6	odd	2		147.4.e.j.79.2		4
21.2	odd	6		441.4.a.n.1.2		2
21.5	even	6		441.4.a.o.1.2		2
21.11	odd	6		441.4.e.v.361.1		4
21.17	even	6		441.4.e.u.361.1		4
21.20	even	2		441.4.e.u.226.1		4
28.19	even	6		2352.4.a.bl.1.2		2
28.23	odd	6		2352.4.a.cf.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.j.1.1	✓	2	7.2	even	3
147.4.a.k.1.1	yes	2	7.5	odd	6
147.4.e.j.67.2		4	7.3	odd	6
147.4.e.j.79.2		4	7.6	odd	2
147.4.e.k.67.2		4	7.4	even	3	inner
147.4.e.k.79.2		4	1.1	even	1	trivial
441.4.a.n.1.2		2	21.2	odd	6
441.4.a.o.1.2		2	21.5	even	6
441.4.e.u.226.1		4	21.20	even	2
441.4.e.u.361.1		4	21.17	even	6
441.4.e.v.226.1		4	3.2	odd	2
441.4.e.v.361.1		4	21.11	odd	6
2352.4.a.bl.1.2		2	28.19	even	6
2352.4.a.cf.1.1		2	28.23	odd	6

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.91421 + 6.77962i) q^{4} +(-0.0502525 + 0.0870399i) q^{5} +1.24264 q^{6} +6.55635 q^{8} +(-4.50000 + 7.79423i) q^{9} +(0.0208153 + 0.0360531i) q^{10} +(21.9706 + 38.0541i) q^{11} +(-11.7426 + 20.3389i) q^{12} +16.6447 q^{13} -0.301515 q^{15} +(-29.9558 + 51.8850i) q^{16} +(-60.8198 - 105.343i) q^{17} +(1.86396 + 3.22848i) q^{18} +(-63.5563 + 110.083i) q^{19} -0.786797 q^{20} +18.2010 q^{22} +(-26.7990 + 46.4172i) q^{23} +(9.83452 + 17.0339i) q^{24} +(62.4949 + 108.244i) q^{25} +(3.44722 - 5.97076i) q^{26} -27.0000 q^{27} +235.681 q^{29} +(-0.0624458 + 0.108159i) q^{30} +(-9.35534 - 16.2039i) q^{31} +(38.6335 + 66.9152i) q^{32} +(-65.9117 + 114.162i) q^{33} -50.3848 q^{34} -70.4558 q^{36} +(95.9411 - 166.175i) q^{37} +(26.3259 + 45.5978i) q^{38} +(24.9670 + 43.2441i) q^{39} +(-0.329473 + 0.570664i) q^{40} +319.713 q^{41} -218.579 q^{43} +(-171.995 + 297.904i) q^{44} +(-0.452273 - 0.783359i) q^{45} +(11.1005 + 19.2266i) q^{46} +(200.777 - 347.755i) q^{47} -179.735 q^{48} +51.7725 q^{50} +(182.459 - 316.029i) q^{51} +(65.1508 + 112.844i) q^{52} +(-321.558 - 556.956i) q^{53} +(-5.59188 + 9.68543i) q^{54} -4.41631 q^{55} -381.338 q^{57} +(48.8112 - 84.5434i) q^{58} +(-5.80613 - 10.0565i) q^{59} +(-1.18019 - 2.04416i) q^{60} +(-6.12132 + 10.6024i) q^{61} -7.75022 q^{62} -447.288 q^{64} +(-0.836436 + 1.44875i) q^{65} +(27.3015 + 47.2876i) q^{66} +(-334.524 - 579.412i) q^{67} +(476.123 - 824.670i) q^{68} -160.794 q^{69} +822.098 q^{71} +(-29.5036 + 51.1017i) q^{72} +(257.550 + 446.089i) q^{73} +(-39.7401 - 68.8319i) q^{74} +(-187.485 + 324.733i) q^{75} -995.092 q^{76} +20.6833 q^{78} +(402.877 - 697.804i) q^{79} +(-3.01071 - 5.21471i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(66.2147 - 114.687i) q^{82} +394.863 q^{83} +12.2254 q^{85} +(-45.2691 + 78.4084i) q^{86} +(353.522 + 612.318i) q^{87} +(144.047 + 249.496i) q^{88} +(336.709 - 583.197i) q^{89} -0.374675 q^{90} -419.588 q^{92} +(28.0660 - 48.6118i) q^{93} +(-83.1644 - 144.045i) q^{94} +(-6.38773 - 11.0639i) q^{95} +(-115.901 + 200.746i) q^{96} +1091.11 q^{97} -395.470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{3} + 10 q^{4} - 20 q^{5} - 12 q^{6} - 36 q^{8} - 18 q^{9} - 48 q^{10} + 20 q^{11} - 30 q^{12} + 208 q^{13} - 120 q^{15} - 18 q^{16} - 116 q^{17} - 18 q^{18} - 192 q^{19} - 88 q^{20}+ \cdots - 360 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 + 10 * q^4 - 20 * q^5 - 12 * q^6 - 36 * q^8 - 18 * q^9 - 48 * q^10 + 20 * q^11 - 30 * q^12 + 208 * q^13 - 120 * q^15 - 18 * q^16 - 116 * q^17 - 18 * q^18 - 192 * q^19 - 88 * q^20 + 152 * q^22 - 28 * q^23 - 54 * q^24 - 146 * q^25 - 204 * q^26 - 108 * q^27 + 592 * q^29 + 144 * q^30 + 104 * q^31 - 18 * q^32 - 60 * q^33 - 128 * q^34 - 180 * q^36 + 248 * q^37 - 104 * q^38 + 312 * q^39 + 488 * q^40 + 40 * q^41 - 1440 * q^43 - 292 * q^44 - 180 * q^45 + 84 * q^46 + 96 * q^47 - 108 * q^48 + 1412 * q^50 + 348 * q^51 + 320 * q^52 - 268 * q^53 + 54 * q^54 + 944 * q^55 - 1152 * q^57 - 48 * q^58 + 616 * q^59 - 132 * q^60 - 16 * q^61 - 608 * q^62 + 236 * q^64 - 1740 * q^65 + 228 * q^66 + 144 * q^67 + 940 * q^68 - 168 * q^69 + 1976 * q^71 + 162 * q^72 - 104 * q^73 + 56 * q^74 + 438 * q^75 - 2272 * q^76 - 1224 * q^78 + 944 * q^79 + 828 * q^80 - 162 * q^81 + 856 * q^82 + 2032 * q^83 - 200 * q^85 + 1120 * q^86 + 888 * q^87 + 876 * q^88 + 388 * q^89 + 864 * q^90 - 728 * q^92 - 312 * q^93 - 904 * q^94 - 1304 * q^95 + 54 * q^96 + 976 * q^97 - 360 * q^99

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