LMFDB - Embedded newform 98.4.c.g.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,4,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.78218718056$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 22x^{2} + 484 $ x^4 + 22*x^2 + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$-2.34521 + 4.06202i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.4.c.g.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(4.69042 + 8.12404i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.69042 + 8.12404i) q^{5} -18.7617 q^{6} +8.00000 q^{8} +(-30.5000 + 52.8275i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(4.69042 + 8.12404i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.69042 + 8.12404i) q^{5} -18.7617 q^{6} +8.00000 q^{8} +(-30.5000 + 52.8275i) q^{9} +(-9.38083 - 16.2481i) q^{10} +(-10.0000 - 17.3205i) q^{11} +(18.7617 - 32.4962i) q^{12} +65.6658 q^{13} -88.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-28.1425 - 48.7442i) q^{17} +(-61.0000 - 105.655i) q^{18} +(-4.69042 + 8.12404i) q^{19} +37.5233 q^{20} +40.0000 q^{22} +(-24.0000 + 41.5692i) q^{23} +(37.5233 + 64.9923i) q^{24} +(18.5000 + 32.0429i) q^{25} +(-65.6658 + 113.737i) q^{26} -318.948 q^{27} -166.000 q^{29} +(88.0000 - 152.420i) q^{30} +(103.189 + 178.729i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(93.8083 - 162.481i) q^{33} +112.570 q^{34} +244.000 q^{36} +(39.0000 - 67.5500i) q^{37} +(-9.38083 - 16.2481i) q^{38} +(308.000 + 533.472i) q^{39} +(-37.5233 + 64.9923i) q^{40} +393.995 q^{41} +436.000 q^{43} +(-40.0000 + 69.2820i) q^{44} +(-286.115 - 495.566i) q^{45} +(-48.0000 - 83.1384i) q^{46} +(-103.189 + 178.729i) q^{47} -150.093 q^{48} -74.0000 q^{50} +(264.000 - 457.261i) q^{51} +(-131.332 - 227.473i) q^{52} +(-31.0000 - 53.6936i) q^{53} +(318.948 - 552.435i) q^{54} +187.617 q^{55} -88.0000 q^{57} +(166.000 - 287.520i) q^{58} +(333.020 + 576.807i) q^{59} +(176.000 + 304.841i) q^{60} +(-136.022 + 235.597i) q^{61} -412.757 q^{62} +64.0000 q^{64} +(-308.000 + 533.472i) q^{65} +(187.617 + 324.962i) q^{66} +(-290.000 - 502.295i) q^{67} +(-112.570 + 194.977i) q^{68} -450.280 q^{69} -544.000 q^{71} +(-244.000 + 422.620i) q^{72} +(300.187 + 519.938i) q^{73} +(78.0000 + 135.100i) q^{74} +(-173.545 + 300.589i) q^{75} +37.5233 q^{76} -1232.00 q^{78} +(340.000 - 588.897i) q^{79} +(-75.0467 - 129.985i) q^{80} +(-672.500 - 1164.80i) q^{81} +(-393.995 + 682.419i) q^{82} +196.997 q^{83} +528.000 q^{85} +(-436.000 + 755.174i) q^{86} +(-778.609 - 1348.59i) q^{87} +(-80.0000 - 138.564i) q^{88} +(750.467 - 1299.85i) q^{89} +1144.46 q^{90} +192.000 q^{92} +(-968.000 + 1676.63i) q^{93} +(-206.378 - 357.458i) q^{94} +(-44.0000 - 76.2102i) q^{95} +(150.093 - 259.969i) q^{96} -656.658 q^{97} +1220.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} - 122 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 - 122 * q^9	$ 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} - 122 q^{9} - 40 q^{11} - 352 q^{15} - 32 q^{16} - 244 q^{18} + 160 q^{22} - 96 q^{23} + 74 q^{25} - 664 q^{29} + 352 q^{30} - 64 q^{32} + 976 q^{36} + 156 q^{37} + 1232 q^{39} + 1744 q^{43} - 160 q^{44} - 192 q^{46} - 296 q^{50} + 1056 q^{51} - 124 q^{53} - 352 q^{57} + 664 q^{58} + 704 q^{60} + 256 q^{64} - 1232 q^{65} - 1160 q^{67} - 2176 q^{71} - 976 q^{72} + 312 q^{74} - 4928 q^{78} + 1360 q^{79} - 2690 q^{81} + 2112 q^{85} - 1744 q^{86} - 320 q^{88} + 768 q^{92} - 3872 q^{93} - 176 q^{95} + 4880 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 - 122 * q^9 - 40 * q^11 - 352 * q^15 - 32 * q^16 - 244 * q^18 + 160 * q^22 - 96 * q^23 + 74 * q^25 - 664 * q^29 + 352 * q^30 - 64 * q^32 + 976 * q^36 + 156 * q^37 + 1232 * q^39 + 1744 * q^43 - 160 * q^44 - 192 * q^46 - 296 * q^50 + 1056 * q^51 - 124 * q^53 - 352 * q^57 + 664 * q^58 + 704 * q^60 + 256 * q^64 - 1232 * q^65 - 1160 * q^67 - 2176 * q^71 - 976 * q^72 + 312 * q^74 - 4928 * q^78 + 1360 * q^79 - 2690 * q^81 + 2112 * q^85 - 1744 * q^86 - 320 * q^88 + 768 * q^92 - 3872 * q^93 - 176 * q^95 + 4880 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	4.69042	+	8.12404i	0.902671	+	1.56347i	0.824013	+	0.566570i	$0.191730\pi$
$3$	4.69042	+	8.12404i	0.902671	+	1.56347i	0.0786575	+	0.996902i	$0.474937\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−4.69042	+	8.12404i	−0.419524	+	0.726636i	−0.995892	−	0.0905542i	$-0.971136\pi$
$5$	−4.69042	+	8.12404i	−0.419524	+	0.726636i	0.576368	+	0.817190i	$0.304470\pi$
$6$	−18.7617			−1.27657
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$	−30.5000	+	52.8275i	−1.12963	+	1.95658i
$10$	−9.38083	−	16.2481i	−0.296648	−	0.513809i
$11$	−10.0000	−	17.3205i	−0.274101	−	0.474757i	0.695807	−	0.718229i	$-0.255047\pi$
$11$	−10.0000	−	17.3205i	−0.274101	−	0.474757i	−0.969908	+	0.243472i	$0.921714\pi$
$12$	18.7617	−	32.4962i	0.451335	−	0.781736i
$13$	65.6658			1.40096			0.700478	−	0.713674i	$-0.252970\pi$
$13$	65.6658			1.40096			0.700478	+	0.713674i	$0.252970\pi$
$14$		0			0
$15$	−88.0000			−1.51477
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−28.1425	−	48.7442i	−0.401503	−	0.695424i	0.592404	−	0.805641i	$-0.298179\pi$
$17$	−28.1425	−	48.7442i	−0.401503	−	0.695424i	−0.993908	+	0.110217i	$0.964846\pi$
$18$	−61.0000	−	105.655i	−0.798769	−	1.38351i
$19$	−4.69042	+	8.12404i	−0.0566345	+	0.0980938i	−0.892953	−	0.450151i	$-0.851370\pi$
$19$	−4.69042	+	8.12404i	−0.0566345	+	0.0980938i	0.836318	+	0.548244i	$0.184704\pi$
$20$	37.5233			0.419524
$21$		0			0
$22$	40.0000			0.387638
$23$	−24.0000	+	41.5692i	−0.217580	+	0.376860i	−0.954068	−	0.299591i	$-0.903150\pi$
$23$	−24.0000	+	41.5692i	−0.217580	+	0.376860i	0.736487	+	0.676451i	$0.236483\pi$
$24$	37.5233	+	64.9923i	0.319142	+	0.552771i
$25$	18.5000	+	32.0429i	0.148000	+	0.256344i
$26$	−65.6658	+	113.737i	−0.495313	+	0.857907i
$27$	−318.948			−2.27339
$28$		0			0
$29$	−166.000			−1.06295			−0.531473	−	0.847075i	$-0.678361\pi$
$29$	−166.000			−1.06295			−0.531473	+	0.847075i	$0.678361\pi$
$30$	88.0000	−	152.420i	0.535551	−	0.927601i
$31$	103.189	+	178.729i	0.597849	+	1.03550i	0.993138	+	0.116948i	$0.0373111\pi$
$31$	103.189	+	178.729i	0.597849	+	1.03550i	−0.395289	+	0.918557i	$0.629356\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	93.8083	−	162.481i	0.494846	−	0.857099i
$34$	112.570			0.567812
$35$		0			0
$36$	244.000			1.12963
$37$	39.0000	−	67.5500i	0.173285	−	0.300139i	−0.766281	−	0.642505i	$-0.777895\pi$
$37$	39.0000	−	67.5500i	0.173285	−	0.300139i	0.939567	+	0.342366i	$0.111228\pi$
$38$	−9.38083	−	16.2481i	−0.0400466	−	0.0693628i
$39$	308.000	+	533.472i	1.26460	+	2.19035i
$40$	−37.5233	+	64.9923i	−0.148324	+	0.256905i
$41$	393.995			1.50077			0.750386	−	0.661000i	$-0.229868\pi$
$41$	393.995			1.50077			0.750386	+	0.661000i	$0.229868\pi$
$42$		0			0
$43$	436.000			1.54626			0.773132	−	0.634245i	$-0.218689\pi$
$43$	436.000			1.54626			0.773132	+	0.634245i	$0.218689\pi$
$44$	−40.0000	+	69.2820i	−0.137051	+	0.237379i
$45$	−286.115	−	495.566i	−0.947812	−	1.64166i
$46$	−48.0000	−	83.1384i	−0.153852	−	0.266480i
$47$	−103.189	+	178.729i	−0.320249	+	0.554687i	−0.980539	−	0.196323i	$-0.937100\pi$
$47$	−103.189	+	178.729i	−0.320249	+	0.554687i	0.660291	+	0.751010i	$0.270433\pi$
$48$	−150.093			−0.451335
$49$		0			0
$50$	−74.0000			−0.209304
$51$	264.000	−	457.261i	0.724851	−	1.25548i
$52$	−131.332	−	227.473i	−0.350239	−	0.606632i
$53$	−31.0000	−	53.6936i	−0.0803430	−	0.139158i	0.823054	−	0.567963i	$-0.192268\pi$
$53$	−31.0000	−	53.6936i	−0.0803430	−	0.139158i	−0.903397	+	0.428805i	$0.858935\pi$
$54$	318.948	−	552.435i	0.803766	−	1.39216i
$55$	187.617			0.459968
$56$		0			0
$57$	−88.0000			−0.204489
$58$	166.000	−	287.520i	0.375808	−	0.650919i
$59$	333.020	+	576.807i	0.734838	+	1.27278i	0.954794	+	0.297267i	$0.0960752\pi$
$59$	333.020	+	576.807i	0.734838	+	1.27278i	−0.219956	+	0.975510i	$0.570591\pi$
$60$	176.000	+	304.841i	0.378692	+	0.655913i
$61$	−136.022	+	235.597i	−0.285506	+	0.494510i	−0.972732	−	0.231933i	$-0.925495\pi$
$61$	−136.022	+	235.597i	−0.285506	+	0.494510i	0.687226	+	0.726444i	$0.258828\pi$
$62$	−412.757			−0.845486
$63$		0			0
$64$	64.0000			0.125000
$65$	−308.000	+	533.472i	−0.587734	+	1.01798i
$66$	187.617	+	324.962i	0.349909	+	0.606061i
$67$	−290.000	−	502.295i	−0.528793	−	0.915897i	−0.999436	−	0.0335729i	$-0.989311\pi$
$67$	−290.000	−	502.295i	−0.528793	−	0.915897i	0.470643	−	0.882324i	$-0.344022\pi$
$68$	−112.570	+	194.977i	−0.200752	+	0.347712i
$69$	−450.280			−0.785613
$70$		0			0
$71$	−544.000			−0.909309			−0.454654	−	0.890668i	$-0.650237\pi$
$71$	−544.000			−0.909309			−0.454654	+	0.890668i	$0.650237\pi$
$72$	−244.000	+	422.620i	−0.399384	+	0.691754i
$73$	300.187	+	519.938i	0.481290	+	0.833619i	0.999769	−	0.0214711i	$-0.00683499\pi$
$73$	300.187	+	519.938i	0.481290	+	0.833619i	−0.518479	+	0.855090i	$0.673502\pi$
$74$	78.0000	+	135.100i	0.122531	+	0.212230i
$75$	−173.545	+	300.589i	−0.267191	+	0.462788i
$76$	37.5233			0.0566345
$77$		0			0
$78$	−1232.00			−1.78842
$79$	340.000	−	588.897i	0.484215	−	0.838685i	−0.515621	−	0.856817i	$-0.672439\pi$
$79$	340.000	−	588.897i	0.484215	−	0.838685i	0.999836	+	0.0181320i	$0.00577190\pi$
$80$	−75.0467	−	129.985i	−0.104881	−	0.181659i
$81$	−672.500	−	1164.80i	−0.922497	−	1.59781i
$82$	−393.995	+	682.419i	−0.530603	+	0.919032i
$83$	196.997			0.260521			0.130261	−	0.991480i	$-0.458419\pi$
$83$	196.997			0.260521			0.130261	+	0.991480i	$0.458419\pi$
$84$		0			0
$85$	528.000			0.673760
$86$	−436.000	+	755.174i	−0.546687	+	0.946890i
$87$	−778.609	−	1348.59i	−0.959490	−	1.66189i
$88$	−80.0000	−	138.564i	−0.0969094	−	0.167852i
$89$	750.467	−	1299.85i	0.893812	−	1.54813i	0.0585446	−	0.998285i	$-0.481354\pi$
$89$	750.467	−	1299.85i	0.893812	−	1.54813i	0.835268	−	0.549843i	$-0.185313\pi$
$90$	1144.46			1.34041
$91$		0			0
$92$	192.000			0.217580
$93$	−968.000	+	1676.63i	−1.07932	+	1.86944i
$94$	−206.378	−	357.458i	−0.226450	−	0.392223i
$95$	−44.0000	−	76.2102i	−0.0475190	−	0.0823053i
$96$	150.093	−	259.969i	0.159571	−	0.276385i
$97$	−656.658			−0.687356			−0.343678	−	0.939088i	$-0.611673\pi$
$97$	−656.658			−0.687356			−0.343678	+	0.939088i	$0.611673\pi$
$98$		0			0
$99$	1220.00			1.23853
$100$	74.0000	−	128.172i	0.0740000	−	0.128172i
$101$	−60.9754	−	105.612i	−0.0600721	−	0.104048i	0.834425	−	0.551121i	$-0.185800\pi$
$101$	−60.9754	−	105.612i	−0.0600721	−	0.104048i	−0.894497	+	0.447073i	$0.852466\pi$
$102$	528.000	+	914.523i	0.512547	+	0.887757i
$103$	684.801	−	1186.11i	0.655101	−	1.13467i	−0.326767	−	0.945105i	$-0.605959\pi$
$103$	684.801	−	1186.11i	0.655101	−	1.13467i	0.981868	−	0.189564i	$-0.0607073\pi$
$104$	525.327			0.495313
$105$		0			0
$106$	124.000			0.113622
$107$	130.000	−	225.167i	0.117454	−	0.203436i	−0.801304	−	0.598257i	$-0.795860\pi$
$107$	130.000	−	225.167i	0.117454	−	0.203436i	0.918758	+	0.394821i	$0.129193\pi$
$108$	637.897	+	1104.87i	0.568348	+	0.984408i
$109$	−941.000	−	1629.86i	−0.826894	−	1.43222i	−0.900463	−	0.434932i	$-0.856772\pi$
$109$	−941.000	−	1629.86i	−0.826894	−	1.43222i	0.0735690	−	0.997290i	$-0.476561\pi$
$110$	−187.617	+	324.962i	−0.162623	+	0.281672i
$111$	731.705			0.625679
$112$		0			0
$113$	−1286.00			−1.07059			−0.535295	−	0.844665i	$-0.679800\pi$
$113$	−1286.00			−1.07059			−0.535295	+	0.844665i	$0.679800\pi$
$114$	88.0000	−	152.420i	0.0722979	−	0.125224i
$115$	−225.140	−	389.954i	−0.182560	−	0.316203i
$116$	332.000	+	575.041i	0.265736	+	0.460269i
$117$	−2002.81	+	3468.96i	−1.58256	+	2.74108i
$118$	−1332.08			−1.03922
$119$		0			0
$120$	−704.000			−0.535551
$121$	465.500	−	806.270i	0.349737	−	0.605762i
$122$	−272.044	−	471.194i	−0.201883	−	0.349671i
$123$	1848.00	+	3200.83i	1.35470	+	2.34642i
$124$	412.757	−	714.915i	0.298924	−	0.517752i
$125$	−1519.69			−1.08741
$126$		0			0
$127$	2312.00			1.61541			0.807704	−	0.589588i	$-0.200710\pi$
$127$	2312.00			1.61541			0.807704	+	0.589588i	$0.200710\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	2045.02	+	3542.08i	1.39577	+	2.41754i
$130$	−616.000	−	1066.94i	−0.415591	−	0.719824i
$131$	126.641	−	219.349i	0.0844633	−	0.146295i	−0.820699	−	0.571361i	$-0.806416\pi$
$131$	126.641	−	219.349i	0.0844633	−	0.146295i	0.905162	+	0.425066i	$0.139749\pi$
$132$	−750.467			−0.494846
$133$		0			0
$134$	1160.00			0.747826
$135$	1496.00	−	2591.15i	0.953742	−	1.65193i
$136$	−225.140	−	389.954i	−0.141953	−	0.245870i
$137$	557.000	+	964.752i	0.347356	+	0.601638i	0.985779	−	0.168048i	$-0.0537463\pi$
$137$	557.000	+	964.752i	0.347356	+	0.601638i	−0.638423	+	0.769686i	$0.720413\pi$
$138$	450.280	−	779.908i	0.277756	−	0.481088i
$139$	1378.98			0.841466			0.420733	−	0.907185i	$-0.361773\pi$
$139$	1378.98			0.841466			0.420733	+	0.907185i	$0.361773\pi$
$140$		0			0
$141$	−1936.00			−1.15632
$142$	544.000	−	942.236i	0.321489	−	0.556836i
$143$	−656.658	−	1137.37i	−0.384004	−	0.665114i
$144$	−488.000	−	845.241i	−0.282407	−	0.489144i
$145$	778.609	−	1348.59i	0.445931	−	0.772375i
$146$	−1200.75			−0.680647
$147$		0			0
$148$	−312.000			−0.173285
$149$	473.000	−	819.260i	0.260065	−	0.450446i	−0.706194	−	0.708018i	$-0.749589\pi$
$149$	473.000	−	819.260i	0.260065	−	0.450446i	0.966259	+	0.257573i	$0.0829227\pi$
$150$	−347.091	−	601.179i	−0.188932	−	0.327240i
$151$	−416.000	−	720.533i	−0.224196	−	0.388319i	0.731882	−	0.681431i	$-0.238642\pi$
$151$	−416.000	−	720.533i	−0.224196	−	0.388319i	−0.956078	+	0.293113i	$0.905309\pi$
$152$	−37.5233	+	64.9923i	−0.0200233	+	0.0346814i
$153$	3433.38			1.81420
$154$		0			0
$155$	−1936.00			−1.00325
$156$	1232.00	−	2133.89i	0.632301	−	1.09518i
$157$	−1439.96	−	2494.08i	−0.731982	−	1.26783i	−0.956035	−	0.293253i	$-0.905262\pi$
$157$	−1439.96	−	2494.08i	−0.731982	−	1.26783i	0.224053	−	0.974577i	$-0.428071\pi$
$158$	680.000	+	1177.79i	0.342392	+	0.593040i
$159$	290.806	−	503.690i	0.145047	−	0.251228i
$160$	300.187			0.148324
$161$		0			0
$162$	2690.00			1.30461
$163$	−318.000	+	550.792i	−0.152808	+	0.264671i	−0.932259	−	0.361792i	$-0.882165\pi$
$163$	−318.000	+	550.792i	−0.152808	+	0.264671i	0.779451	+	0.626463i	$0.215498\pi$
$164$	−787.990	−	1364.84i	−0.375193	−	0.649854i
$165$	880.000	+	1524.20i	0.415199	+	0.719147i
$166$	−196.997	+	341.210i	−0.0921082	+	0.159536i
$167$	−656.658			−0.304274			−0.152137	−	0.988359i	$-0.548615\pi$
$167$	−656.658			−0.304274			−0.152137	+	0.988359i	$0.548615\pi$
$168$		0			0
$169$	2115.00			0.962676
$170$	−528.000	+	914.523i	−0.238210	+	0.412592i
$171$	−286.115	−	495.566i	−0.127952	−	0.221619i
$172$	−872.000	−	1510.35i	−0.386566	−	0.669552i
$173$	−333.020	+	576.807i	−0.146353	+	0.253490i	−0.929877	−	0.367871i	$-0.880087\pi$
$173$	−333.020	+	576.807i	−0.146353	+	0.253490i	0.783524	+	0.621361i	$0.213420\pi$
$174$	3114.44			1.35692
$175$		0			0
$176$	320.000			0.137051
$177$	−3124.00	+	5410.93i	−1.32663	+	2.29780i
$178$	1500.93	+	2599.69i	0.632021	+	1.09469i
$179$	1614.00	+	2795.53i	0.673944	+	1.16731i	0.976776	+	0.214262i	$0.0687346\pi$
$179$	1614.00	+	2795.53i	0.673944	+	1.16731i	−0.302832	+	0.953044i	$0.597932\pi$
$180$	−1144.46	+	1982.27i	−0.473906	+	0.820830i
$181$	−2823.63			−1.15955			−0.579776	−	0.814776i	$-0.696860\pi$
$181$	−2823.63			−1.15955			−0.579776	+	0.814776i	$0.696860\pi$
$182$		0			0
$183$	−2552.00			−1.03087
$184$	−192.000	+	332.554i	−0.0769262	+	0.133240i
$185$	365.852	+	633.675i	0.145395	+	0.251831i
$186$	−1936.00	−	3353.25i	−0.763196	−	1.32189i
$187$	−562.850	+	974.885i	−0.220105	+	0.381233i
$188$	825.513			0.320249
$189$		0			0
$190$	176.000			0.0672020
$191$	1068.00	−	1849.83i	0.404596	−	0.700780i	−0.589679	−	0.807638i	$-0.700746\pi$
$191$	1068.00	−	1849.83i	0.404596	−	0.700780i	0.994274	+	0.106858i	$0.0340789\pi$
$192$	300.187	+	519.938i	0.112834	+	0.195434i
$193$	−829.000	−	1435.87i	−0.309185	−	0.535524i	0.668999	−	0.743263i	$-0.266723\pi$
$193$	−829.000	−	1435.87i	−0.309185	−	0.535524i	−0.978184	+	0.207739i	$0.933390\pi$
$194$	656.658	−	1137.37i	0.243017	−	0.420918i
$195$	−5778.59			−2.12212
$196$		0			0
$197$	−978.000			−0.353704			−0.176852	−	0.984237i	$-0.556591\pi$
$197$	−978.000			−0.353704			−0.176852	+	0.984237i	$0.556591\pi$
$198$	−1220.00	+	2113.10i	−0.437887	+	0.758443i
$199$	2467.16	+	4273.24i	0.878855	+	1.52222i	0.852598	+	0.522567i	$0.175026\pi$
$199$	2467.16	+	4273.24i	0.878855	+	1.52222i	0.0262574	+	0.999655i	$0.491641\pi$
$200$	148.000	+	256.344i	0.0523259	+	0.0906311i
$201$	2720.44	−	4711.94i	0.954652	−	1.65351i
$202$	243.902			0.0849547
$203$		0			0
$204$	−2112.00			−0.724851
$205$	−1848.00	+	3200.83i	−0.629609	+	1.09052i
$206$	1369.60	+	2372.22i	0.463226	+	0.802332i
$207$	−1464.00	−	2535.72i	−0.491570	−	0.851425i
$208$	−525.327	+	909.892i	−0.175119	+	0.303316i
$209$	187.617			0.0620943
$210$		0			0
$211$	1556.00			0.507675			0.253838	−	0.967247i	$-0.418307\pi$
$211$	1556.00			0.507675			0.253838	+	0.967247i	$0.418307\pi$
$212$	−124.000	+	214.774i	−0.0401715	+	0.0695791i
$213$	−2551.59	−	4419.48i	−0.820807	−	1.42168i
$214$	260.000	+	450.333i	0.0830525	+	0.143851i
$215$	−2045.02	+	3542.08i	−0.648694	+	1.12357i
$216$	−2551.59			−0.803766
$217$		0			0
$218$	3764.00			1.16940
$219$	−2816.00	+	4877.46i	−0.868893	+	1.50497i
$220$	−375.233	−	649.923i	−0.114992	−	0.199172i
$221$	−1848.00	−	3200.83i	−0.562488	−	0.974258i
$222$	−731.705	+	1267.35i	−0.221211	+	0.383148i
$223$	2889.30			0.867630			0.433815	−	0.901002i	$-0.357167\pi$
$223$	2889.30			0.867630			0.433815	+	0.901002i	$0.357167\pi$
$224$		0			0
$225$	−2257.00			−0.668741
$226$	1286.00	−	2227.42i	0.378511	−	0.655600i
$227$	989.678	+	1714.17i	0.289371	+	0.501205i	0.973660	−	0.228006i	$-0.0732205\pi$
$227$	989.678	+	1714.17i	0.289371	+	0.501205i	−0.684289	+	0.729211i	$0.739887\pi$
$228$	176.000	+	304.841i	0.0511223	+	0.0885464i
$229$	−1383.67	+	2396.59i	−0.399282	+	0.691577i	−0.993638	−	0.112625i	$-0.964074\pi$
$229$	−1383.67	+	2396.59i	−0.399282	+	0.691577i	0.594355	+	0.804203i	$0.297407\pi$
$230$	900.560			0.258179
$231$		0			0
$232$	−1328.00			−0.375808
$233$	3245.00	−	5620.50i	0.912391	−	1.58031i	0.101713	−	0.994814i	$-0.467568\pi$
$233$	3245.00	−	5620.50i	0.912391	−	1.58031i	0.810677	−	0.585493i	$-0.199099\pi$
$234$	−4005.62	−	6937.93i	−1.11904	−	1.93823i
$235$	−968.000	−	1676.63i	−0.268704	−	0.465408i
$236$	1332.08	−	2307.23i	0.367419	−	0.636388i
$237$	6378.97			1.74835
$238$		0			0
$239$	−4296.00			−1.16270			−0.581350	−	0.813654i	$-0.697475\pi$
$239$	−4296.00			−1.16270			−0.581350	+	0.813654i	$0.697475\pi$
$240$	704.000	−	1219.36i	0.189346	−	0.327957i
$241$	−2260.78	−	3915.79i	−0.604272	−	1.04663i	−0.992166	−	0.124926i	$-0.960131\pi$
$241$	−2260.78	−	3915.79i	−0.604272	−	1.04663i	0.387894	−	0.921704i	$-0.373203\pi$
$242$	931.000	+	1612.54i	0.247301	+	0.428339i
$243$	2002.81	−	3468.96i	0.528725	−	0.915778i
$244$	1088.18			0.285506
$245$		0			0
$246$	−7392.00			−1.91584
$247$	−308.000	+	533.472i	−0.0793424	+	0.137425i
$248$	825.513	+	1429.83i	0.211372	+	0.366106i
$249$	924.000	+	1600.41i	0.235165	+	0.407318i
$250$	1519.69	−	2632.19i	0.384456	−	0.665897i
$251$	5581.59			1.40361			0.701807	−	0.712367i	$-0.252377\pi$
$251$	5581.59			1.40361			0.701807	+	0.712367i	$0.252377\pi$
$252$		0			0
$253$	960.000			0.238556
$254$	−2312.00	+	4004.50i	−0.571133	+	0.989231i
$255$	2476.54	+	4289.49i	0.608184	+	1.05341i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	750.467	−	1299.85i	0.182151	−	0.315495i	−0.760462	−	0.649383i	$-0.775027\pi$
$257$	750.467	−	1299.85i	0.182151	−	0.315495i	0.942613	+	0.333888i	$0.108361\pi$
$258$	−8180.09			−1.97391
$259$		0			0
$260$	2464.00			0.587734
$261$	5063.00	−	8769.37i	1.20073	−	2.07973i
$262$	253.282	+	438.698i	0.0597246	+	0.103446i
$263$	200.000	+	346.410i	0.0468917	+	0.0812189i	0.888519	−	0.458841i	$-0.151735\pi$
$263$	200.000	+	346.410i	0.0468917	+	0.0812189i	−0.841627	+	0.540059i	$0.818402\pi$
$264$	750.467	−	1299.85i	0.174955	−	0.303030i
$265$	581.612			0.134823
$266$		0			0
$267$	14080.0			3.22727
$268$	−1160.00	+	2009.18i	−0.264397	+	0.457948i
$269$	136.022	+	235.597i	0.0308305	+	0.0534000i	0.881029	−	0.473062i	$-0.156851\pi$
$269$	136.022	+	235.597i	0.0308305	+	0.0534000i	−0.850198	+	0.526462i	$0.823518\pi$
$270$	2992.00	+	5182.30i	0.674397	+	1.16809i
$271$	−3452.15	+	5979.29i	−0.773812	+	1.34028i	0.161648	+	0.986848i	$0.448319\pi$
$271$	−3452.15	+	5979.29i	−0.773812	+	1.34028i	−0.935460	+	0.353433i	$0.885014\pi$
$272$	900.560			0.200752
$273$		0			0
$274$	−2228.00			−0.491235
$275$	370.000	−	640.859i	0.0811340	−	0.140528i
$276$	900.560	+	1559.82i	0.196403	+	0.340181i
$277$	3385.00	+	5862.99i	0.734242	+	1.27174i	0.955055	+	0.296428i	$0.0957954\pi$
$277$	3385.00	+	5862.99i	0.734242	+	1.27174i	−0.220814	+	0.975316i	$0.570871\pi$
$278$	−1378.98	+	2388.47i	−0.297503	+	0.515290i
$279$	−12589.1			−2.70139
$280$		0			0
$281$	1878.00			0.398691			0.199345	−	0.979929i	$-0.436118\pi$
$281$	1878.00			0.398691			0.199345	+	0.979929i	$0.436118\pi$
$282$	1936.00	−	3353.25i	0.408820	−	0.708096i
$283$	−192.307	−	333.086i	−0.0403939	−	0.0699642i	0.845122	−	0.534574i	$-0.179528\pi$
$283$	−192.307	−	333.086i	−0.0403939	−	0.0699642i	−0.885516	+	0.464610i	$0.846195\pi$
$284$	1088.00	+	1884.47i	0.227327	+	0.393742i
$285$	412.757	−	714.915i	0.0857880	−	0.148589i
$286$	2626.63			0.543063
$287$		0			0
$288$	1952.00			0.399384
$289$	872.500	−	1511.21i	0.177590	−	0.307595i
$290$	1557.22	+	2697.18i	0.315321	+	0.546151i
$291$	−3080.00	−	5334.72i	−0.620456	−	1.07466i
$292$	1200.75	−	2079.75i	0.240645	−	0.416810i
$293$	−3742.95			−0.746299			−0.373149	−	0.927771i	$-0.621722\pi$
$293$	−3742.95			−0.746299			−0.373149	+	0.927771i	$0.621722\pi$
$294$		0			0
$295$	−6248.00			−1.23313
$296$	312.000	−	540.400i	0.0612656	−	0.106115i
$297$	3189.48	+	5524.35i	0.623140	+	1.07931i
$298$	946.000	+	1638.52i	0.183894	+	0.318513i
$299$	−1575.98	+	2729.68i	−0.304820	+	0.527964i
$300$	1388.36			0.267191
$301$		0			0
$302$	1664.00			0.317061
$303$	572.000	−	990.733i	0.108451	−	0.187842i
$304$	−75.0467	−	129.985i	−0.0141586	−	0.0245235i
$305$	−1276.00	−	2210.10i	−0.239553	−	0.414917i
$306$	−3433.38	+	5946.80i	−0.641417	+	1.11097i
$307$	722.324			0.134284			0.0671420	−	0.997743i	$-0.478612\pi$
$307$	722.324			0.134284			0.0671420	+	0.997743i	$0.478612\pi$
$308$		0			0
$309$	12848.0			2.36536
$310$	1936.00	−	3353.25i	0.354701	−	0.614361i
$311$	−3639.76	−	6304.25i	−0.663640	−	1.14946i	−0.979652	−	0.200703i	$-0.935677\pi$
$311$	−3639.76	−	6304.25i	−0.663640	−	1.14946i	0.316012	−	0.948755i	$-0.397656\pi$
$312$	2464.00	+	4267.77i	0.447104	+	0.774407i
$313$	−759.847	+	1316.09i	−0.137218	+	0.237668i	−0.926442	−	0.376437i	$-0.877149\pi$
$313$	−759.847	+	1316.09i	−0.137218	+	0.237668i	0.789225	+	0.614104i	$0.210483\pi$
$314$	5759.83			1.03518
$315$		0			0
$316$	−2720.00			−0.484215
$317$	−1179.00	+	2042.09i	−0.208893	+	0.361814i	−0.951366	−	0.308062i	$-0.900320\pi$
$317$	−1179.00	+	2042.09i	−0.208893	+	0.361814i	0.742473	+	0.669876i	$0.233653\pi$
$318$	581.612	+	1007.38i	0.102563	+	0.177645i
$319$	1660.00	+	2875.20i	0.291355	+	0.504641i
$320$	−300.187	+	519.938i	−0.0524404	+	0.0908295i
$321$	2439.02			0.424089
$322$		0			0
$323$	528.000			0.0909557
$324$	−2690.00	+	4659.22i	−0.461248	+	0.798905i
$325$	1214.82	+	2104.13i	0.207341	+	0.359126i
$326$	−636.000	−	1101.58i	−0.108051	−	0.187151i
$327$	8827.36	−	15289.4i	1.49283	−	2.58565i
$328$	3151.96			0.530603
$329$		0			0
$330$	−3520.00			−0.587181
$331$	−1186.00	+	2054.21i	−0.196944	+	0.341117i	−0.947536	−	0.319649i	$-0.896435\pi$
$331$	−1186.00	+	2054.21i	−0.196944	+	0.341117i	0.750592	+	0.660766i	$0.229768\pi$
$332$	−393.995	−	682.419i	−0.0651304	−	0.112809i
$333$	2379.00	+	4120.55i	0.391497	+	0.678092i
$334$	656.658	−	1137.37i	0.107577	−	0.186329i
$335$	5440.88			0.887365
$336$		0			0
$337$	−250.000			−0.0404106			−0.0202053	−	0.999796i	$-0.506432\pi$
$337$	−250.000			−0.0404106			−0.0202053	+	0.999796i	$0.506432\pi$
$338$	−2115.00	+	3663.29i	−0.340357	+	0.589516i
$339$	−6031.87	−	10447.5i	−0.966391	−	1.67384i
$340$	−1056.00	−	1829.05i	−0.168440	−	0.291747i
$341$	2063.78	−	3574.58i	0.327742	−	0.567666i
$342$	1144.46			0.180951
$343$		0			0
$344$	3488.00			0.546687
$345$	2112.00	−	3658.09i	0.329583	−	0.570855i
$346$	−666.039	−	1153.61i	−0.103487	−	0.179245i
$347$	−4770.00	−	8261.88i	−0.737945	−	1.27816i	−0.953419	−	0.301649i	$-0.902463\pi$
$347$	−4770.00	−	8261.88i	−0.737945	−	1.27816i	0.215474	−	0.976510i	$-0.430870\pi$
$348$	−3114.44	+	5394.36i	−0.479745	+	0.830943i
$349$	−5712.93			−0.876235			−0.438117	−	0.898918i	$-0.644355\pi$
$349$	−5712.93			−0.876235			−0.438117	+	0.898918i	$0.644355\pi$
$350$		0			0
$351$	−20944.0			−3.18492
$352$	−320.000	+	554.256i	−0.0484547	+	0.0839260i
$353$	−2195.11	−	3802.05i	−0.330975	−	0.573265i	0.651728	−	0.758452i	$-0.274044\pi$
$353$	−2195.11	−	3802.05i	−0.330975	−	0.573265i	−0.982703	+	0.185187i	$0.940711\pi$
$354$	−6248.00	−	10821.9i	−0.938072	−	1.62479i
$355$	2551.59	−	4419.48i	0.381476	−	0.660737i
$356$	−6003.73			−0.893812
$357$		0			0
$358$	−6456.00			−0.953101
$359$	−920.000	+	1593.49i	−0.135253	+	0.234265i	−0.925694	−	0.378273i	$-0.876518\pi$
$359$	−920.000	+	1593.49i	−0.135253	+	0.234265i	0.790441	+	0.612538i	$0.209851\pi$
$360$	−2288.92	−	3964.53i	−0.335102	−	0.580414i
$361$	3385.50	+	5863.86i	0.493585	+	0.854914i
$362$	2823.63	−	4890.67i	0.409963	−	0.710077i
$363$	8733.55			1.26279
$364$		0			0
$365$	−5632.00			−0.807650
$366$	2552.00	−	4420.19i	0.364468	−	0.631277i
$367$	1482.17	+	2567.20i	0.210814	+	0.365140i	0.951969	−	0.306193i	$-0.0990552\pi$
$367$	1482.17	+	2567.20i	0.210814	+	0.365140i	−0.741156	+	0.671333i	$0.765722\pi$
$368$	−384.000	−	665.108i	−0.0543951	−	0.0942150i
$369$	−12016.8	+	20813.8i	−1.69532	+	2.93638i
$370$	−1463.41			−0.205619
$371$		0			0
$372$	7744.00			1.07932
$373$	−1991.00	+	3448.51i	−0.276381	+	0.478706i	−0.970483	−	0.241171i	$-0.922468\pi$
$373$	−1991.00	+	3448.51i	−0.276381	+	0.478706i	0.694102	+	0.719877i	$0.255802\pi$
$374$	−1125.70	−	1949.77i	−0.155638	−	0.269573i
$375$	−7128.00	−	12346.1i	−0.981569	−	1.70013i
$376$	−825.513	+	1429.83i	−0.113225	+	0.196111i
$377$	−10900.5			−1.48914
$378$		0			0
$379$	2676.00			0.362683			0.181342	−	0.983420i	$-0.441956\pi$
$379$	2676.00			0.362683			0.181342	+	0.983420i	$0.441956\pi$
$380$	−176.000	+	304.841i	−0.0237595	+	0.0411527i
$381$	10844.2	+	18782.8i	1.45818	+	2.52565i
$382$	2136.00	+	3699.66i	0.286092	+	0.495526i
$383$	−3517.81	+	6093.03i	−0.469326	+	0.812896i	−0.999385	−	0.0350645i	$-0.988836\pi$
$383$	−3517.81	+	6093.03i	−0.469326	+	0.812896i	0.530059	+	0.847961i	$0.322170\pi$
$384$	−1200.75			−0.159571
$385$		0			0
$386$	3316.00			0.437254
$387$	−13298.0	+	23032.8i	−1.74671	+	3.02538i
$388$	1313.32	+	2274.73i	0.171839	+	0.297634i
$389$	−4329.00	−	7498.05i	−0.564239	−	0.977291i	−0.997120	−	0.0758397i	$-0.975836\pi$
$389$	−4329.00	−	7498.05i	−0.564239	−	0.977291i	0.432881	−	0.901451i	$-0.357497\pi$
$390$	5778.59	−	10008.8i	0.750283	−	1.29953i
$391$	2701.68			0.349437
$392$		0			0
$393$	2376.00			0.304970
$394$	978.000	−	1693.95i	0.125053	−	0.216598i
$395$	3189.48	+	5524.35i	0.406279	+	0.703696i
$396$	−2440.00	−	4226.20i	−0.309633	−	0.536300i
$397$	4526.25	−	7839.70i	0.572207	−	0.991091i	−0.424132	−	0.905600i	$-0.639421\pi$
$397$	4526.25	−	7839.70i	0.572207	−	0.991091i	0.996339	−	0.0854907i	$-0.0272458\pi$
$398$	−9868.63			−1.24289
$399$		0			0
$400$	−592.000			−0.0740000
$401$	2853.00	−	4941.54i	0.355292	−	0.615383i	−0.631876	−	0.775069i	$-0.717715\pi$
$401$	2853.00	−	4941.54i	0.355292	−	0.615383i	0.987168	+	0.159686i	$0.0510482\pi$
$402$	5440.88	+	9423.88i	0.675041	+	1.16921i
$403$	6776.00	+	11736.4i	0.837560	+	1.45070i
$404$	−243.902	+	422.450i	−0.0300360	+	0.0520239i
$405$	12617.2			1.54804
$406$		0			0
$407$	−1560.00			−0.189991
$408$	2112.00	−	3658.09i	0.256273	−	0.443879i
$409$	−1210.13	−	2096.00i	−0.146301	−	0.253400i	0.783557	−	0.621320i	$-0.213403\pi$
$409$	−1210.13	−	2096.00i	−0.146301	−	0.253400i	−0.929857	+	0.367920i	$0.880070\pi$
$410$	−3696.00	−	6401.66i	−0.445201	−	0.771111i
$411$	−5225.12	+	9050.18i	−0.627096	+	1.08616i
$412$	−5478.41			−0.655101
$413$		0			0
$414$	5856.00			0.695185
$415$	−924.000	+	1600.41i	−0.109295	+	0.189304i
$416$	−1050.65	−	1819.78i	−0.123828	−	0.214477i
$417$	6468.00	+	11202.9i	0.759567	+	1.31561i
$418$	−187.617	+	324.962i	−0.0219537	+	0.0380249i
$419$	−1510.31			−0.176095			−0.0880473	−	0.996116i	$-0.528063\pi$
$419$	−1510.31			−0.176095			−0.0880473	+	0.996116i	$0.528063\pi$
$420$		0			0
$421$	−16770.0			−1.94138			−0.970689	−	0.240341i	$-0.922741\pi$
$421$	−16770.0			−1.94138			−0.970689	+	0.240341i	$0.922741\pi$
$422$	−1556.00	+	2695.07i	−0.179490	+	0.310886i
$423$	−6294.54	−	10902.5i	−0.723525	−	1.25318i
$424$	−248.000	−	429.549i	−0.0284055	−	0.0491998i
$425$	1041.27	−	1803.54i	0.118845	−	0.205846i
$426$	10206.3			1.16080
$427$		0			0
$428$	−1040.00			−0.117454
$429$	6160.00	−	10669.4i	0.693258	−	1.20076i
$430$	−4090.04	−	7084.16i	−0.458696	−	0.794485i
$431$	−668.000	−	1157.01i	−0.0746553	−	0.129307i	0.826281	−	0.563258i	$-0.190452\pi$
$431$	−668.000	−	1157.01i	−0.0746553	−	0.129307i	−0.900936	+	0.433951i	$0.857119\pi$
$432$	2551.59	−	4419.48i	0.284174	−	0.492204i
$433$	−11163.2			−1.23896			−0.619479	−	0.785013i	$-0.712656\pi$
$433$	−11163.2			−1.23896			−0.619479	+	0.785013i	$0.712656\pi$
$434$		0			0
$435$	14608.0			1.61011
$436$	−3764.00	+	6519.44i	−0.413447	+	0.716111i
$437$	−225.140	−	389.954i	−0.0246451	−	0.0426865i
$438$	−5632.00	−	9754.91i	−0.614400	−	1.06417i
$439$	1801.12	−	3119.63i	0.195815	−	0.339161i	−0.751352	−	0.659901i	$-0.770598\pi$
$439$	1801.12	−	3119.63i	0.195815	−	0.339161i	0.947167	+	0.320740i	$0.103931\pi$
$440$	1500.93			0.162623
$441$		0			0
$442$	7392.00			0.795479
$443$	−3174.00	+	5497.53i	−0.340409	+	0.589606i	−0.984509	−	0.175336i	$-0.943899\pi$
$443$	−3174.00	+	5497.53i	−0.340409	+	0.589606i	0.644099	+	0.764942i	$0.277232\pi$
$444$	−1463.41	−	2534.70i	−0.156420	−	0.270927i
$445$	7040.00	+	12193.6i	0.749951	+	1.29895i
$446$	−2889.30	+	5004.41i	−0.306754	+	0.531313i
$447$	8874.27			0.939012
$448$		0			0
$449$	7170.00			0.753615			0.376808	−	0.926292i	$-0.377022\pi$
$449$	7170.00			0.753615			0.376808	+	0.926292i	$0.377022\pi$
$450$	2257.00	−	3909.24i	0.236436	−	0.409518i
$451$	−3939.95	−	6824.19i	−0.411364	−	0.712503i
$452$	2572.00	+	4454.83i	0.267648	+	0.463579i
$453$	3902.43	−	6759.20i	0.404750	−	0.701048i
$454$	−3958.71			−0.409232
$455$		0			0
$456$	−704.000			−0.0722979
$457$	−3433.00	+	5946.13i	−0.351398	+	0.608639i	−0.986495	−	0.163793i	$-0.947627\pi$
$457$	−3433.00	+	5946.13i	−0.351398	+	0.608639i	0.635097	+	0.772433i	$0.280960\pi$
$458$	−2767.35	−	4793.18i	−0.282335	−	0.489019i
$459$	8976.00	+	15546.9i	0.912775	+	1.58097i
$460$	−900.560	+	1559.82i	−0.0912800	+	0.158102i
$461$	1378.98			0.139318			0.0696590	−	0.997571i	$-0.477809\pi$
$461$	1378.98			0.139318			0.0696590	+	0.997571i	$0.477809\pi$
$462$		0			0
$463$	2648.00			0.265795			0.132897	−	0.991130i	$-0.457572\pi$
$463$	2648.00			0.265795			0.132897	+	0.991130i	$0.457572\pi$
$464$	1328.00	−	2300.16i	0.132868	−	0.230135i
$465$	−9080.64	−	15728.1i	−0.905602	−	1.56855i
$466$	6490.00	+	11241.0i	0.645158	+	1.11745i
$467$	6167.90	−	10683.1i	0.611170	−	1.05858i	−0.379874	−	0.925038i	$-0.624033\pi$
$467$	6167.90	−	10683.1i	0.611170	−	1.05858i	0.991044	−	0.133539i	$-0.0426340\pi$
$468$	16022.5			1.58256
$469$		0			0
$470$	3872.00			0.380004
$471$	13508.0	−	23396.5i	1.32148	−	2.28887i
$472$	2664.16	+	4614.45i	0.259805	+	0.449995i
$473$	−4360.00	−	7551.74i	−0.423833	−	0.734100i
$474$	−6378.97	+	11048.7i	−0.618134	+	1.07064i
$475$	−347.091			−0.0335276
$476$		0			0
$477$	3782.00			0.363031
$478$	4296.00	−	7440.89i	0.411076	−	0.712005i
$479$	6669.77	+	11552.4i	0.636221	+	1.10197i	0.986255	+	0.165229i	$0.0528365\pi$
$479$	6669.77	+	11552.4i	0.636221	+	1.10197i	−0.350035	+	0.936737i	$0.613830\pi$
$480$	1408.00	+	2438.73i	0.133888	+	0.231900i
$481$	2560.97	−	4435.72i	0.242765	−	0.420482i
$482$	9043.12			0.854570
$483$		0			0
$484$	−3724.00			−0.349737
$485$	3080.00	−	5334.72i	0.288362	−	0.499458i
$486$	4005.62	+	6937.93i	0.373865	+	0.647553i
$487$	−6968.00	−	12068.9i	−0.648358	−	1.12299i	−0.983515	−	0.180826i	$-0.942123\pi$
$487$	−6968.00	−	12068.9i	−0.648358	−	1.12299i	0.335157	−	0.942162i	$-0.391211\pi$
$488$	−1088.18	+	1884.78i	−0.100941	+	0.174836i
$489$	−5966.21			−0.551741
$490$		0			0
$491$	−12276.0			−1.12833			−0.564163	−	0.825663i	$-0.690801\pi$
$491$	−12276.0			−1.12833			−0.564163	+	0.825663i	$0.690801\pi$
$492$	7392.00	−	12803.3i	0.677352	−	1.17321i
$493$	4671.65	+	8091.54i	0.426776	+	0.739198i
$494$	−616.000	−	1066.94i	−0.0561035	−	0.0971742i
$495$	−5722.31	+	9911.33i	−0.519593	+	0.899962i
$496$	−3302.05			−0.298924
$497$		0			0
$498$	−3696.00			−0.332574
$499$	1110.00	−	1922.58i	0.0995800	−	0.172478i	−0.811931	−	0.583754i	$-0.801583\pi$
$499$	1110.00	−	1922.58i	0.0995800	−	0.172478i	0.911511	+	0.411276i	$0.134917\pi$
$500$	3039.39	+	5264.38i	0.271851	+	0.470860i
$501$	−3080.00	−	5334.72i	−0.274659	−	0.475724i
$502$	−5581.59	+	9667.61i	−0.496253	+	0.859535i
$503$	−11294.5			−1.00119			−0.500594	−	0.865682i	$-0.666885\pi$
$503$	−11294.5			−1.00119			−0.500594	+	0.865682i	$0.666885\pi$
$504$		0			0
$505$	1144.00			0.100807
$506$	−960.000	+	1662.77i	−0.0843423	+	0.146085i
$507$	9920.23	+	17182.3i	0.868980	+	1.50512i
$508$	−4624.00	−	8009.00i	−0.403852	−	0.699492i
$509$	7940.87	−	13754.0i	0.691499	−	1.19771i	−0.279848	−	0.960044i	$-0.590284\pi$
$509$	7940.87	−	13754.0i	0.691499	−	1.19771i	0.971347	−	0.237667i	$-0.0763827\pi$
$510$	−9906.16			−0.860102
$511$		0			0
$512$	512.000			0.0441942
$513$	1496.00	−	2591.15i	0.128752	−	0.223006i
$514$	1500.93	+	2599.69i	0.128800	+	0.223089i
$515$	6424.00	+	11126.7i	0.549661	+	0.952040i
$516$	8180.09	−	14168.3i	0.697884	−	1.20877i
$517$	4127.57			0.351122
$518$		0			0
$519$	−6248.00			−0.528433
$520$	−2464.00	+	4267.77i	−0.207795	+	0.359912i
$521$	−5806.73	−	10057.6i	−0.488287	−	0.845738i	0.511622	−	0.859211i	$-0.329045\pi$
$521$	−5806.73	−	10057.6i	−0.488287	−	0.845738i	−0.999909	+	0.0134723i	$0.995712\pi$
$522$	10126.0	+	17538.7i	0.849048	+	1.47059i
$523$	−6308.61	+	10926.8i	−0.527450	+	0.913570i	0.472038	+	0.881578i	$0.343518\pi$
$523$	−6308.61	+	10926.8i	−0.527450	+	0.913570i	−0.999488	+	0.0319918i	$0.989815\pi$
$524$	−1013.13			−0.0844633
$525$		0			0
$526$	−800.000			−0.0663149
$527$	5808.00	−	10059.8i	0.480077	−	0.831517i
$528$	1500.93	+	2599.69i	0.123712	+	0.214275i
$529$	4931.50	+	8541.61i	0.405318	+	0.702031i
$530$	−581.612	+	1007.38i	−0.0476672	+	0.0825619i
$531$	−40628.4			−3.32038
$532$		0			0
$533$	25872.0			2.10252
$534$	−14080.0	+	24387.3i	−1.14101	+	1.97629i
$535$	1219.51	+	2112.25i	0.0985494	+	0.170693i
$536$	−2320.00	−	4018.36i	−0.186957	−	0.323818i
$537$	−15140.7	+	26224.4i	−1.21670	+	2.10739i
$538$	−544.088			−0.0436009
$539$		0			0
$540$	−11968.0			−0.953742
$541$	−899.000	+	1557.11i	−0.0714437	+	0.123744i	−0.899534	−	0.436850i	$-0.856094\pi$
$541$	−899.000	+	1557.11i	−0.0714437	+	0.123744i	0.828091	+	0.560594i	$0.189427\pi$
$542$	−6904.29	−	11958.6i	−0.547167	−	0.947722i
$543$	−13244.0	−	22939.3i	−1.04669	−	1.81293i
$544$	−900.560	+	1559.82i	−0.0709764	+	0.122935i
$545$	17654.7			1.38761
$546$		0			0
$547$	1276.00			0.0997401			0.0498700	−	0.998756i	$-0.484119\pi$
$547$	1276.00			0.0997401			0.0498700	+	0.998756i	$0.484119\pi$
$548$	2228.00	−	3859.01i	0.173678	−	0.300819i
$549$	−8297.35	−	14371.4i	−0.645031	−	1.11723i
$550$	740.000	+	1281.72i	0.0573704	+	0.0993684i
$551$	778.609	−	1348.59i	0.0601994	−	0.104268i
$552$	−3602.24			−0.277756
$553$		0			0
$554$	−13540.0			−1.03837
$555$	−3432.00	+	5944.40i	−0.262487	+	0.454641i
$556$	−2757.96	−	4776.93i	−0.210366	−	0.364365i
$557$	−1347.00	−	2333.07i	−0.102467	−	0.177478i	0.810233	−	0.586107i	$-0.199340\pi$
$557$	−1347.00	−	2333.07i	−0.102467	−	0.177478i	−0.912701	+	0.408629i	$0.866007\pi$
$558$	12589.1	−	21804.9i	0.955086	−	1.65426i
$559$	28630.3			2.16625
$560$		0			0
$561$	−10560.0			−0.794730
$562$	−1878.00	+	3252.79i	−0.140958	+	0.244147i
$563$	7884.59	+	13656.5i	0.590223	+	1.02230i	0.994202	+	0.107529i	$0.0342937\pi$
$563$	7884.59	+	13656.5i	0.590223	+	1.02230i	−0.403979	+	0.914768i	$0.632373\pi$
$564$	3872.00	+	6706.50i	0.289079	+	0.500700i
$565$	6031.87	−	10447.5i	0.449138	−	0.777930i
$566$	769.228			0.0571256
$567$		0			0
$568$	−4352.00			−0.321489
$569$	−6303.00	+	10917.1i	−0.464386	+	0.804340i	−0.999174	−	0.0406466i	$-0.987058\pi$
$569$	−6303.00	+	10917.1i	−0.464386	+	0.804340i	0.534788	+	0.844986i	$0.320392\pi$
$570$	825.513	+	1429.83i	0.0606613	+	0.105068i
$571$	−3426.00	−	5934.01i	−0.251092	−	0.434904i	0.712735	−	0.701434i	$-0.247456\pi$
$571$	−3426.00	−	5934.01i	−0.251092	−	0.434904i	−0.963827	+	0.266529i	$0.914123\pi$
$572$	−2626.63	+	4549.46i	−0.192002	+	0.332557i
$573$	20037.5			1.46087
$574$		0			0
$575$	−1776.00			−0.128808
$576$	−1952.00	+	3380.96i	−0.141204	+	0.244572i
$577$	−7185.72	−	12446.0i	−0.518449	−	0.897981i	−0.999770	−	0.0214362i	$-0.993176\pi$
$577$	−7185.72	−	12446.0i	−0.518449	−	0.897981i	0.481321	−	0.876545i	$-0.340157\pi$
$578$	1745.00	+	3022.43i	0.125575	+	0.217503i
$579$	7776.71	−	13469.7i	0.558185	−	0.966804i
$580$	−6228.87			−0.445931
$581$		0			0
$582$	12320.0			0.877458
$583$	−620.000	+	1073.87i	−0.0440442	+	0.0762868i
$584$	2401.49	+	4159.51i	0.170162	+	0.294729i
$585$	−18788.0	−	32541.8i	−1.32784	−	2.29989i
$586$	3742.95	−	6482.98i	0.263857	−	0.457013i
$587$	18977.4			1.33438			0.667191	−	0.744887i	$-0.267497\pi$
$587$	18977.4			1.33438			0.667191	+	0.744887i	$0.267497\pi$
$588$		0			0
$589$	−1936.00			−0.135435
$590$	6248.00	−	10821.9i	0.435976	−	0.755133i
$591$	−4587.23	−	7945.31i	−0.319278	−	0.553006i
$592$	624.000	+	1080.80i	0.0433214	+	0.0750348i
$593$	−4108.80	+	7116.66i	−0.284534	+	0.492826i	−0.972496	−	0.232920i	$-0.925172\pi$
$593$	−4108.80	+	7116.66i	−0.284534	+	0.492826i	0.687962	+	0.725746i	$0.258505\pi$
$594$	−12757.9			−0.881253
$595$		0			0
$596$	−3784.00			−0.260065
$597$	−23144.0	+	40086.6i	−1.58663	+	2.74813i
$598$	−3151.96	−	5459.35i	−0.215540	−	0.373327i
$599$	9552.00	+	16544.5i	0.651559	+	1.12853i	0.982744	+	0.184968i	$0.0592182\pi$
$599$	9552.00	+	16544.5i	0.651559	+	1.12853i	−0.331185	+	0.943566i	$0.607448\pi$
$600$	−1388.36	+	2404.72i	−0.0944661	+	0.163620i
$601$	21538.4			1.46185			0.730923	−	0.682460i	$-0.239090\pi$
$601$	21538.4			1.46185			0.730923	+	0.682460i	$0.239090\pi$
$602$		0			0
$603$	35380.0			2.38936
$604$	−1664.00	+	2882.13i	−0.112098	+	0.194159i
$605$	4366.78	+	7563.48i	0.293446	+	0.508263i
$606$	1144.00	+	1981.47i	0.0766862	+	0.132824i
$607$	−6866.77	+	11893.6i	−0.459166	+	0.795298i	−0.998917	−	0.0465262i	$-0.985185\pi$
$607$	−6866.77	+	11893.6i	−0.459166	+	0.795298i	0.539751	+	0.841824i	$0.318518\pi$
$608$	300.187			0.0200233
$609$		0			0
$610$	5104.00			0.338779
$611$	−6776.00	+	11736.4i	−0.448654	+	0.777092i
$612$	−6866.77	−	11893.6i	−0.453550	−	0.785572i
$613$	−14017.0	−	24278.2i	−0.923558	−	1.59965i	−0.793863	−	0.608096i	$-0.791934\pi$
$613$	−14017.0	−	24278.2i	−0.923558	−	1.59965i	−0.129695	−	0.991554i	$-0.541400\pi$
$614$	−722.324	+	1251.10i	−0.0474766	+	0.0822319i
$615$	−34671.6			−2.27332
$616$		0			0
$617$	−8258.00			−0.538824			−0.269412	−	0.963025i	$-0.586829\pi$
$617$	−8258.00			−0.538824			−0.269412	+	0.963025i	$0.586829\pi$
$618$	−12848.0	+	22253.4i	−0.836282	+	1.44848i
$619$	2565.66	+	4443.85i	0.166595	+	0.288551i	0.937221	−	0.348737i	$-0.113389\pi$
$619$	2565.66	+	4443.85i	0.166595	+	0.288551i	−0.770625	+	0.637288i	$0.780056\pi$
$620$	3872.00	+	6706.50i	0.250812	+	0.434419i
$621$	7654.76	−	13258.4i	0.494646	−	0.856751i
$622$	14559.1			0.938529
$623$		0			0
$624$	−9856.00			−0.632301
$625$	4815.50	−	8340.69i	0.308192	−	0.533804i
$626$	−1519.69	−	2632.19i	−0.0970275	−	0.168057i
$627$	880.000	+	1524.20i	0.0560507	+	0.0970827i
$628$	−5759.83	+	9976.32i	−0.365991	+	0.633915i
$629$	−4390.23			−0.278299
$630$		0			0
$631$	912.000			0.0575375			0.0287687	−	0.999586i	$-0.490841\pi$
$631$	912.000			0.0575375			0.0287687	+	0.999586i	$0.490841\pi$
$632$	2720.00	−	4711.18i	0.171196	−	0.296520i
$633$	7298.29	+	12641.0i	0.458264	+	0.793736i
$634$	−2358.00	−	4084.18i	−0.147710	−	0.255841i
$635$	−10844.2	+	18782.8i	−0.677702	+	1.17381i
$636$	−2326.45			−0.145047
$637$		0			0
$638$	−6640.00			−0.412038
$639$	16592.0	−	28738.2i	1.02718	−	1.77913i
$640$	−600.373	−	1039.88i	−0.0370810	−	0.0642262i
$641$	445.000	+	770.763i	0.0274203	+	0.0474934i	0.879410	−	0.476065i	$-0.157937\pi$
$641$	445.000	+	770.763i	0.0274203	+	0.0474934i	−0.851990	+	0.523559i	$0.824604\pi$
$642$	−2439.02	+	4224.50i	−0.149938	+	0.259700i
$643$	−29352.6			−1.80024			−0.900120	−	0.435642i	$-0.856521\pi$
$643$	−29352.6			−1.80024			−0.900120	+	0.435642i	$0.856521\pi$
$644$		0			0
$645$	−38368.0			−2.34223
$646$	−528.000	+	914.523i	−0.0321577	+	0.0556988i
$647$	−5938.07	−	10285.0i	−0.360818	−	0.624956i	0.627277	−	0.778796i	$-0.284169\pi$
$647$	−5938.07	−	10285.0i	−0.360818	−	0.624956i	−0.988096	+	0.153840i	$0.950836\pi$
$648$	−5380.00	−	9318.43i	−0.326152	−	0.564911i
$649$	6660.39	−	11536.1i	0.402840	−	0.697739i
$650$	−4859.27			−0.293225
$651$		0			0
$652$	2544.00			0.152808
$653$	10763.0	−	18642.1i	0.645006	−	1.11718i	−0.339294	−	0.940680i	$-0.610188\pi$
$653$	10763.0	−	18642.1i	0.645006	−	1.11718i	0.984300	−	0.176502i	$-0.0564784\pi$
$654$	17654.7	+	30578.9i	1.05559	+	1.82833i
$655$	1188.00	+	2057.68i	0.0708687	+	0.122748i
$656$	−3151.96	+	5459.35i	−0.187597	+	0.324927i
$657$	−36622.8			−2.17472
$658$		0			0
$659$	23452.0			1.38628			0.693141	−	0.720802i	$-0.256226\pi$
$659$	23452.0			1.38628			0.693141	+	0.720802i	$0.256226\pi$
$660$	3520.00	−	6096.82i	0.207600	−	0.359573i
$661$	13334.9	+	23096.6i	0.784668	+	1.35909i	0.929197	+	0.369584i	$0.120500\pi$
$661$	13334.9	+	23096.6i	0.784668	+	1.35909i	−0.144529	+	0.989501i	$0.546167\pi$
$662$	−2372.00	−	4108.42i	−0.139260	−	0.241206i
$663$	17335.8	−	30026.4i	1.01548	−	1.75887i
$664$	1575.98			0.0921082
$665$		0			0
$666$	−9516.00			−0.553660
$667$	3984.00	−	6900.49i	0.231276	−	0.400582i
$668$	1313.32	+	2274.73i	0.0760685	+	0.131754i
$669$	13552.0	+	23472.8i	0.783185	+	1.35652i
$670$	−5440.88	+	9423.88i	−0.313731	+	0.543398i
$671$	5440.88			0.313030
$672$		0			0
$673$	−13858.0			−0.793739			−0.396870	−	0.917875i	$-0.629904\pi$
$673$	−13858.0			−0.793739			−0.396870	+	0.917875i	$0.629904\pi$
$674$	250.000	−	433.013i	0.0142873	−	0.0247463i
$675$	−5900.54	−	10220.0i	−0.336462	−	0.582770i
$676$	−4230.00	−	7326.57i	−0.240669	−	0.416851i
$677$	−16224.1	+	28101.0i	−0.921041	+	1.59529i	−0.123233	+	0.992378i	$0.539326\pi$
$677$	−16224.1	+	28101.0i	−0.921041	+	1.59529i	−0.797808	+	0.602912i	$0.794007\pi$
$678$	24127.5			1.36668
$679$		0			0
$680$	4224.00			0.238210
$681$	−9284.00	+	16080.4i	−0.522414	+	0.904847i
$682$	4127.57	+	7149.15i	0.231749	+	0.401401i
$683$	13906.0	+	24085.9i	0.779060	+	1.34937i	0.932484	+	0.361212i	$0.117637\pi$
$683$	13906.0	+	24085.9i	0.779060	+	1.34937i	−0.153423	+	0.988161i	$0.549030\pi$
$684$	−1144.46	+	1982.27i	−0.0639760	+	0.110810i
$685$	−10450.2			−0.582895
$686$		0			0
$687$	−25960.0			−1.44168
$688$	−3488.00	+	6041.39i	−0.193283	+	0.334776i
$689$	−2035.64	−	3525.83i	−0.112557	−	0.194954i
$690$	4224.00	+	7316.18i	0.233051	+	0.403656i
$691$	651.968	−	1129.24i	0.0358929	−	0.0621684i	−0.847521	−	0.530762i	$-0.821906\pi$
$691$	651.968	−	1129.24i	0.0358929	−	0.0621684i	0.883414	+	0.468594i	$0.155239\pi$
$692$	2664.16			0.146353
$693$		0			0
$694$	19080.0			1.04361
$695$	−6468.00	+	11202.9i	−0.353015	+	0.611439i
$696$	−6228.87	−	10788.7i	−0.339231	−	0.587565i
$697$	−11088.0	−	19205.0i	−0.602565	−	1.04367i
$698$	5712.93	−	9895.08i	0.309796	−	0.536582i
$699$	60881.6			3.29435
$700$		0			0
$701$	22906.0			1.23416			0.617081	−	0.786900i	$-0.288315\pi$
$701$	22906.0			1.23416			0.617081	+	0.786900i	$0.288315\pi$
$702$	20944.0	−	36276.1i	1.12604	−	1.95036i
$703$	365.852	+	633.675i	0.0196279	+	0.0339965i
$704$	−640.000	−	1108.51i	−0.0342627	−	0.0593447i
$705$	9080.64	−	15728.1i	0.485102	−	0.840221i
$706$	8780.46			0.468069
$707$		0			0
$708$	24992.0			1.32663
$709$	7543.00	−	13064.9i	0.399553	−	0.692047i	−0.594117	−	0.804378i	$-0.702499\pi$
$709$	7543.00	−	13064.9i	0.399553	−	0.692047i	0.993671	+	0.112332i	$0.0358319\pi$
$710$	5103.17	+	8838.95i	0.269745	+	0.467211i
$711$	20740.0	+	35922.7i	1.09397	+	1.89481i
$712$	6003.73	−	10398.8i	0.316010	−	0.547346i
$713$	−9906.16			−0.520321
$714$		0			0
$715$	12320.0			0.644394
$716$	6456.00	−	11182.1i	0.336972	−	0.583653i
$717$	−20150.0	−	34900.9i	−1.04953	−	1.81785i
$718$	−1840.00	−	3186.97i	−0.0956381	−	0.165650i
$719$	10272.0	−	17791.6i	0.532797	−	0.922832i	−0.466469	−	0.884538i	$-0.654474\pi$
$719$	10272.0	−	17791.6i	0.532797	−	0.922832i	0.999266	−	0.0382947i	$-0.0121926\pi$
$720$	9155.69			0.473906
$721$		0			0
$722$	−13542.0			−0.698035
$723$	21208.0	−	36733.3i	1.09092	−	1.88953i
$724$	5647.26	+	9781.34i	0.289888	+	0.502100i
$725$	−3071.00	−	5319.13i	−0.157316	−	0.272479i
$726$	−8733.55	+	15127.0i	−0.446464	+	0.773298i
$727$	−7223.24			−0.368494			−0.184247	−	0.982880i	$-0.558985\pi$
$727$	−7223.24			−0.368494			−0.184247	+	0.982880i	$0.558985\pi$
$728$		0			0
$729$	1261.00			0.0640654
$730$	5632.00	−	9754.91i	0.285547	−	0.494583i
$731$	−12270.1	−	21252.5i	−0.620830	−	1.07531i
$732$	5104.00	+	8840.39i	0.257718	+	0.446380i
$733$	−14713.8	+	25485.1i	−0.741430	+	1.28419i	0.210415	+	0.977612i	$0.432519\pi$
$733$	−14713.8	+	25485.1i	−0.741430	+	1.28419i	−0.951844	+	0.306581i	$0.900815\pi$
$734$	−5928.69			−0.298136
$735$		0			0
$736$	1536.00			0.0769262
$737$	−5800.00	+	10045.9i	−0.289886	+	0.502097i
$738$	−24033.7	−	41627.6i	−1.19877	−	2.07633i
$739$	−16334.0	−	28291.3i	−0.813066	−	1.40827i	−0.910708	−	0.413050i	$-0.864463\pi$
$739$	−16334.0	−	28291.3i	−0.813066	−	1.40827i	0.0976420	−	0.995222i	$-0.468870\pi$
$740$	1463.41	−	2534.70i	0.0726973	−	0.125915i
$741$	−5778.59			−0.286480
$742$		0			0
$743$	−37056.0			−1.82968			−0.914840	−	0.403816i	$-0.867684\pi$
$743$	−37056.0			−1.82968			−0.914840	+	0.403816i	$0.867684\pi$
$744$	−7744.00	+	13413.0i	−0.381598	+	0.660947i
$745$	4437.13	+	7685.34i	0.218207	+	0.377945i
$746$	−3982.00	−	6897.03i	−0.195431	−	0.338496i
$747$	−6008.42	+	10406.9i	−0.294293	+	0.509730i
$748$	4502.80			0.220105
$749$		0			0
$750$	28512.0			1.38815
$751$	9804.00	−	16981.0i	0.476369	−	0.825095i	−0.523265	−	0.852170i	$-0.675286\pi$
$751$	9804.00	−	16981.0i	0.476369	−	0.825095i	0.999633	+	0.0270752i	$0.00861935\pi$
$752$	−1651.03	−	2859.66i	−0.0800621	−	0.138672i
$753$	26180.0	+	45345.1i	1.26700	+	2.19451i
$754$	10900.5	−	18880.3i	0.526490	−	0.911908i
$755$	7804.85			0.376222
$756$		0			0
$757$	19378.0			0.930390			0.465195	−	0.885208i	$-0.345984\pi$
$757$	19378.0			0.930390			0.465195	+	0.885208i	$0.345984\pi$
$758$	−2676.00	+	4634.97i	−0.128228	+	0.222097i
$759$	4502.80	+	7799.08i	0.215338	+	0.372976i
$760$	−352.000	−	609.682i	−0.0168005	−	0.0290993i
$761$	6988.72	−	12104.8i	0.332905	−	0.576609i	−0.650175	−	0.759785i	$-0.725304\pi$
$761$	6988.72	−	12104.8i	0.332905	−	0.576609i	0.983080	+	0.183176i	$0.0586377\pi$
$762$	−43377.0			−2.06218
$763$		0			0
$764$	−8544.00			−0.404596
$765$	−16104.0	+	27892.9i	−0.761100	+	1.31826i
$766$	−7035.62	−	12186.1i	−0.331863	−	0.574804i
$767$	21868.0	+	37876.5i	1.02948	+	1.78310i
$768$	1200.75	−	2079.75i	0.0564169	−	0.0977170i
$769$	8536.56			0.400307			0.200154	−	0.979765i	$-0.435856\pi$
$769$	8536.56			0.400307			0.200154	+	0.979765i	$0.435856\pi$
$770$		0			0
$771$	14080.0			0.657690
$772$	−3316.00	+	5743.48i	−0.154593	+	0.267762i
$773$	14648.2	+	25371.4i	0.681576	+	1.18052i	0.974500	+	0.224388i	$0.0720383\pi$
$773$	14648.2	+	25371.4i	0.681576	+	1.18052i	−0.292924	+	0.956136i	$0.594628\pi$
$774$	−26596.0	−	46065.6i	−1.23511	−	2.13927i
$775$	−3818.00	+	6612.97i	−0.176963	+	0.306509i
$776$	−5253.27			−0.243017
$777$		0			0
$778$	17316.0			0.797955
$779$	−1848.00	+	3200.83i	−0.0849955	+	0.147216i
$780$	11557.2	+	20017.6i	0.530530	+	0.918905i
$781$	5440.00	+	9422.36i	0.249243	+	0.431701i
$782$	−2701.68	+	4679.45i	−0.123545	+	0.213985i
$783$	52945.4			2.41649
$784$		0			0
$785$	27016.0			1.22833
$786$	−2376.00	+	4115.35i	−0.107823	+	0.186755i
$787$	−6890.22	−	11934.2i	−0.312084	−	0.540545i	0.666730	−	0.745300i	$-0.267694\pi$
$787$	−6890.22	−	11934.2i	−0.312084	−	0.540545i	−0.978813	+	0.204755i	$0.934360\pi$
$788$	1956.00	+	3387.89i	0.0884259	+	0.153158i
$789$	−1876.17	+	3249.62i	−0.0846556	+	0.146628i
$790$	−12757.9			−0.574566
$791$		0			0
$792$	9760.00			0.437887
$793$	−8932.00	+	15470.7i	−0.399981	+	0.692787i
$794$	9052.50	+	15679.4i	0.404611	+	0.700807i
$795$	2728.00	+	4725.03i	0.121701	+	0.210792i
$796$	9868.63	−	17093.0i	0.439428	−	0.761111i
$797$	−34868.6			−1.54970			−0.774848	−	0.632148i	$-0.782174\pi$
$797$	−34868.6			−1.54970			−0.774848	+	0.632148i	$0.782174\pi$
$798$		0			0
$799$	11616.0			0.514324
$800$	592.000	−	1025.37i	0.0261630	−	0.0453156i
$801$	45778.5	+	79290.6i	2.01935	+	3.49762i
$802$	5706.00	+	9883.08i	0.251229	+	0.435142i
$803$	6003.73	−	10398.8i	0.263844	−	0.456992i
$804$	−21763.5			−0.954652
$805$		0			0
$806$	−27104.0			−1.18449
$807$	−1276.00	+	2210.10i	−0.0556596	+	0.0964053i
$808$	−487.803	−	844.900i	−0.0212387	−	0.0367865i
$809$	−7017.00	−	12153.8i	−0.304950	−	0.528189i	0.672300	−	0.740279i	$-0.265306\pi$
$809$	−7017.00	−	12153.8i	−0.304950	−	0.528189i	−0.977250	+	0.212090i	$0.931973\pi$
$810$	−12617.2	+	21853.7i	−0.547313	+	0.947975i
$811$	−6632.25			−0.287164			−0.143582	−	0.989638i	$-0.545862\pi$
$811$	−6632.25			−0.287164			−0.143582	+	0.989638i	$0.545862\pi$
$812$		0			0
$813$	−64768.0			−2.79399
$814$	1560.00	−	2702.00i	0.0671720	−	0.116345i
$815$	−2983.10	−	5166.89i	−0.128213	−	0.222071i
$816$	4224.00	+	7316.18i	0.181213	+	0.313870i
$817$	−2045.02	+	3542.08i	−0.0875719	+	0.151679i
$818$	4840.51			0.206900
$819$		0			0
$820$	14784.0			0.629609
$821$	−14311.0	+	24787.4i	−0.608352	+	1.05370i	0.383160	+	0.923682i	$0.374836\pi$
$821$	−14311.0	+	24787.4i	−0.608352	+	1.05370i	−0.991512	+	0.130015i	$0.958497\pi$
$822$	−10450.2	−	18100.4i	−0.443424	−	0.768032i
$823$	−12344.0	−	21380.4i	−0.522825	−	0.905559i	−0.999647	−	0.0265595i	$-0.991545\pi$
$823$	−12344.0	−	21380.4i	−0.522825	−	0.905559i	0.476822	−	0.879000i	$-0.341788\pi$
$824$	5478.41	−	9488.88i	0.231613	−	0.401166i
$825$	6941.82			0.292949
$826$		0			0
$827$	−30756.0			−1.29322			−0.646609	−	0.762822i	$-0.723813\pi$
$827$	−30756.0			−1.29322			−0.646609	+	0.762822i	$0.723813\pi$
$828$	−5856.00	+	10142.9i	−0.245785	+	0.425712i
$829$	−11618.2	−	20123.2i	−0.486750	−	0.843075i	0.513134	−	0.858308i	$-0.328484\pi$
$829$	−11618.2	−	20123.2i	−0.486750	−	0.843075i	−0.999884	+	0.0152333i	$0.995151\pi$
$830$	−1848.00	−	3200.83i	−0.0772832	−	0.133858i
$831$	−31754.1	+	54999.7i	−1.32556	+	2.29593i
$832$	4202.61			0.175119
$833$		0			0
$834$	−25872.0			−1.07419
$835$	3080.00	−	5334.72i	0.127650	−	0.221096i
$836$	−375.233	−	649.923i	−0.0155236	−	0.0268876i
$837$	−32912.0	−	57005.3i	−1.35915	−	2.35411i
$838$	1510.31	−	2615.94i	0.0622589	−	0.107836i
$839$	−24033.7			−0.988957			−0.494479	−	0.869190i	$-0.664641\pi$
$839$	−24033.7			−0.988957			−0.494479	+	0.869190i	$0.664641\pi$
$840$		0			0
$841$	3167.00			0.129854
$842$	16770.0	−	29046.5i	0.686380	−	1.18885i
$843$	8808.60	+	15256.9i	0.359887	+	0.623342i
$844$	−3112.00	−	5390.14i	−0.126919	−	0.219830i
$845$	−9920.23	+	17182.3i	−0.403865	+	0.699515i
$846$	25178.2			1.02322
$847$		0			0
$848$	992.000			0.0401715
$849$	1804.00	−	3124.62i	0.0729248	−	0.126309i
$850$	2082.54	+	3607.07i	0.0840361	+	0.145555i
$851$	1872.00	+	3242.40i	0.0754070	+	0.130609i
$852$	−10206.3	+	17677.9i	−0.410403	+	0.710839i
$853$	−23574.0			−0.946260			−0.473130	−	0.880993i	$-0.656876\pi$
$853$	−23574.0			−0.946260			−0.473130	+	0.880993i	$0.656876\pi$
$854$		0			0
$855$	5368.00			0.214715
$856$	1040.00	−	1801.33i	0.0415262	−	0.0719256i
$857$	−12242.0	−	21203.7i	−0.487956	−	0.845164i	0.511948	−	0.859016i	$-0.328924\pi$
$857$	−12242.0	−	21203.7i	−0.487956	−	0.845164i	−0.999904	+	0.0138519i	$0.995591\pi$
$858$	12320.0	+	21338.9i	0.490207	+	0.849064i
$859$	16477.4	−	28539.7i	0.654485	−	1.13360i	−0.327538	−	0.944838i	$-0.606219\pi$
$859$	16477.4	−	28539.7i	0.654485	−	1.13360i	0.982023	−	0.188763i	$-0.0604479\pi$
$860$	16360.2			0.648694
$861$		0			0
$862$	2672.00			0.105579
$863$	−20436.0	+	35396.2i	−0.806083	+	1.39618i	0.109475	+	0.993990i	$0.465083\pi$
$863$	−20436.0	+	35396.2i	−0.806083	+	1.39618i	−0.915558	+	0.402187i	$0.868250\pi$
$864$	5103.17	+	8838.95i	0.200941	+	0.348041i
$865$	−3124.00	−	5410.93i	−0.122797	−	0.212690i
$866$	11163.2	−	19335.2i	0.438038	−	0.758703i
$867$	16369.6			0.641222
$868$		0			0
$869$	−13600.0			−0.530896
$870$	−14608.0	+	25301.8i	−0.569262	+	0.985990i
$871$	−19043.1	−	32983.6i	−0.740816	−	1.28313i
$872$	−7528.00	−	13038.9i	−0.292351	−	0.506367i
$873$	20028.1	−	34689.6i	0.776458	−	1.34486i
$874$	900.560			0.0348534
$875$		0			0
$876$	22528.0			0.868893
$877$	6003.00	−	10397.5i	0.231137	−	0.400341i	−0.727006	−	0.686631i	$-0.759089\pi$
$877$	6003.00	−	10397.5i	0.231137	−	0.400341i	0.958143	+	0.286290i	$0.0924222\pi$
$878$	3602.24	+	6239.26i	0.138462	+	0.239823i
$879$	−17556.0	−	30407.9i	−0.673662	−	1.16682i
$880$	−1500.93	+	2599.69i	−0.0574960	+	0.0995859i
$881$	35722.2			1.36607			0.683037	−	0.730383i	$-0.260659\pi$
$881$	35722.2			1.36607			0.683037	+	0.730383i	$0.260659\pi$
$882$		0			0
$883$	19588.0			0.746533			0.373267	−	0.927724i	$-0.378238\pi$
$883$	19588.0			0.746533			0.373267	+	0.927724i	$0.378238\pi$
$884$	−7392.00	+	12803.3i	−0.281244	+	0.487129i
$885$	−29305.7	−	50759.0i	−1.11311	−	1.92796i
$886$	−6348.00	−	10995.1i	−0.240706	−	0.416914i
$887$	20121.9	−	34852.1i	0.761699	−	1.31930i	−0.180276	−	0.983616i	$-0.557699\pi$
$887$	20121.9	−	34852.1i	0.761699	−	1.31930i	0.941974	−	0.335685i	$-0.108968\pi$
$888$	5853.64			0.221211
$889$		0			0
$890$	−28160.0			−1.06059
$891$	−13450.0	+	23296.1i	−0.505715	+	0.875924i
$892$	−5778.59	−	10008.8i	−0.216908	−	0.375695i
$893$	−968.000	−	1676.63i	−0.0362742	−	0.0628288i
$894$	−8874.27	+	15370.7i	−0.331991	+	0.575025i
$895$	−30281.3			−1.13094
$896$		0			0
$897$	−29568.0			−1.10061
$898$	−7170.00	+	12418.8i	−0.266443	+	0.461493i
$899$	−17129.4	−	29669.0i	−0.635481	−	1.10069i
$900$	4514.00	+	7818.48i	0.167185	+	0.289573i
$901$	−1744.83	+	3022.14i	−0.0645159	+	0.111745i
$902$	15759.8			0.581756
$903$		0			0
$904$	−10288.0			−0.378511
$905$	13244.0	−	22939.3i	0.486459	−	0.842572i
$906$	7804.85	+	13518.4i	0.286202	+	0.495716i
$907$	−7934.00	−	13742.1i	−0.290457	−	0.503086i	0.683461	−	0.729987i	$-0.260474\pi$
$907$	−7934.00	−	13742.1i	−0.290457	−	0.503086i	−0.973918	+	0.226901i	$0.927141\pi$
$908$	3958.71	−	6856.69i	0.144686	−	0.250603i
$909$	7439.00			0.271437
$910$		0			0
$911$	39832.0			1.44862			0.724310	−	0.689474i	$-0.242158\pi$
$911$	39832.0			1.44862			0.724310	+	0.689474i	$0.242158\pi$
$912$	704.000	−	1219.36i	0.0255612	−	0.0442732i
$913$	−1969.97	−	3412.10i	−0.0714092	−	0.123684i
$914$	−6866.00	−	11892.3i	−0.248476	−	0.430373i
$915$	11969.9	−	20732.5i	0.432474	−	0.749068i
$916$	11069.4			0.399282
$917$		0			0
$918$	−35904.0			−1.29086
$919$	15264.0	−	26438.0i	0.547892	−	0.948977i	−0.450527	−	0.892763i	$-0.648764\pi$
$919$	15264.0	−	26438.0i	0.547892	−	0.948977i	0.998419	−	0.0562141i	$-0.0179029\pi$
$920$	−1801.12	−	3119.63i	−0.0645447	−	0.111795i
$921$	3388.00	+	5868.19i	0.121214	+	0.209949i
$922$	−1378.98	+	2388.47i	−0.0492564	+	0.0853145i
$923$	−35722.2			−1.27390
$924$		0			0
$925$	2886.00			0.102585
$926$	−2648.00	+	4586.47i	−0.0939727	+	0.162765i
$927$	41772.8	+	72352.7i	1.48004	+	2.56351i
$928$	2656.00	+	4600.33i	0.0939520	+	0.162730i
$929$	8302.04	−	14379.5i	0.293198	−	0.507834i	−0.681366	−	0.731943i	$-0.738614\pi$
$929$	8302.04	−	14379.5i	0.293198	−	0.507834i	0.974564	+	0.224109i	$0.0719471\pi$
$930$	36322.6			1.28071
$931$		0			0
$932$	−25960.0			−0.912391
$933$	34144.0	−	59139.1i	1.19810	−	2.07516i
$934$	12335.8	+	21366.2i	0.432162	+	0.748527i
$935$	−5280.00	−	9145.23i	−0.184679	−	0.319873i
$936$	−16022.5	+	27751.7i	−0.559520	+	0.969117i
$937$	29943.6			1.04399			0.521993	−	0.852950i	$-0.325189\pi$
$937$	29943.6			1.04399			0.521993	+	0.852950i	$0.325189\pi$
$938$		0			0
$939$	−14256.0			−0.495449
$940$	−3872.00	+	6706.50i	−0.134352	+	0.232704i
$941$	−2687.61	−	4655.07i	−0.0931068	−	0.161266i	0.815710	−	0.578461i	$-0.196346\pi$
$941$	−2687.61	−	4655.07i	−0.0931068	−	0.161266i	−0.908817	+	0.417195i	$0.863013\pi$
$942$	27016.0	+	46793.1i	0.934426	+	1.61847i
$943$	−9455.88	+	16378.1i	−0.326538	+	0.565581i
$944$	−10656.6			−0.367419
$945$		0			0
$946$	17440.0			0.599390
$947$	−22606.0	+	39154.7i	−0.775709	+	1.34357i	0.158686	+	0.987329i	$0.449274\pi$
$947$	−22606.0	+	39154.7i	−0.775709	+	1.34357i	−0.934395	+	0.356238i	$0.884059\pi$
$948$	−12757.9	−	22097.4i	−0.437087	−	0.757057i
$949$	19712.0	+	34142.2i	0.674266	+	1.16786i
$950$	347.091	−	601.179i	0.0118538	−	0.0205314i
$951$	−22120.0			−0.754248
$952$		0			0
$953$	34218.0			1.16310			0.581548	−	0.813512i	$-0.302447\pi$
$953$	34218.0			1.16310			0.581548	+	0.813512i	$0.302447\pi$
$954$	−3782.00	+	6550.62i	−0.128351	+	0.222310i
$955$	10018.7	+	17352.9i	0.339475	+	0.587988i
$956$	8592.00	+	14881.8i	0.290675	+	0.503464i
$957$	−15572.2	+	26971.8i	−0.525995	+	0.911050i
$958$	−26679.1			−0.899752
$959$		0			0
$960$	−5632.00			−0.189346
$961$	−6400.50	+	11086.0i	−0.214847	+	0.372126i
$962$	5121.93	+	8871.45i	0.171661	+	0.297325i
$963$	7930.00	+	13735.2i	0.265359	+	0.459615i
$964$	−9043.12	+	15663.1i	−0.302136	+	0.523315i
$965$	15553.4			0.518842
$966$		0			0
$967$	14464.0			0.481004			0.240502	−	0.970649i	$-0.422688\pi$
$967$	14464.0			0.481004			0.240502	+	0.970649i	$0.422688\pi$
$968$	3724.00	−	6450.16i	0.123651	−	0.214169i
$969$	2476.54	+	4289.49i	0.0821031	+	0.142207i
$970$	6160.00	+	10669.4i	0.203903	+	0.353170i
$971$	−18916.4	+	32764.2i	−0.625188	+	1.08286i	0.363316	+	0.931666i	$0.381644\pi$
$971$	−18916.4	+	32764.2i	−0.625188	+	1.08286i	−0.988504	+	0.151192i	$0.951689\pi$
$972$	−16022.5			−0.528725
$973$		0			0
$974$	27872.0			0.916916
$975$	−11396.0	+	19738.5i	−0.374322	+	0.648345i
$976$	−2176.35	−	3769.55i	−0.0713764	−	0.123628i
$977$	−21031.0	−	36426.8i	−0.688681	−	1.19283i	−0.972265	−	0.233883i	$-0.924857\pi$
$977$	−21031.0	−	36426.8i	−0.688681	−	1.19283i	0.283584	−	0.958947i	$-0.408477\pi$
$978$	5966.21	−	10333.8i	0.195070	−	0.337871i
$979$	−30018.7			−0.979980
$980$		0			0
$981$	114802.			3.73634
$982$	12276.0	−	21262.7i	0.398924	−	0.690956i
$983$	21510.2	+	37256.8i	0.697935	+	1.20886i	0.969181	+	0.246349i	$0.0792310\pi$
$983$	21510.2	+	37256.8i	0.697935	+	1.20886i	−0.271246	+	0.962510i	$0.587436\pi$
$984$	14784.0	+	25606.6i	0.478960	+	0.829583i
$985$	4587.23	−	7945.31i	0.148387	−	0.257014i
$986$	−18686.6			−0.603553
$987$		0			0
$988$	2464.00			0.0793424
$989$	−10464.0	+	18124.2i	−0.336437	+	0.582725i
$990$	−11444.6	−	19822.7i	−0.367408	−	0.636369i
$991$	−10636.0	−	18422.1i	−0.340932	−	0.590512i	0.643674	−	0.765300i	$-0.277409\pi$
$991$	−10636.0	−	18422.1i	−0.340932	−	0.590512i	−0.984606	+	0.174788i	$0.944076\pi$
$992$	3302.05	−	5719.32i	0.105686	−	0.183053i
$993$	−22251.3			−0.711102
$994$		0			0
$995$	−46288.0			−1.47480
$996$	3696.00	−	6401.66i	0.117583	−	0.203659i
$997$	−60.9754	−	105.612i	−0.00193692	−	0.00335485i	0.865055	−	0.501676i	$-0.167283\pi$
$997$	−60.9754	−	105.612i	−0.00193692	−	0.00335485i	−0.866992	+	0.498322i	$0.833950\pi$
$998$	2220.00	+	3845.15i	0.0704137	+	0.121960i
$999$	−12439.0	+	21544.9i	−0.393946	+	0.682334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.4.c.g.79.2		4
3.2	odd	2		882.4.g.bi.667.2		4
7.2	even	3		98.4.a.h.1.1	✓	2
7.3	odd	6	inner	98.4.c.g.67.1		4
7.4	even	3	inner	98.4.c.g.67.2		4
7.5	odd	6		98.4.a.h.1.2	yes	2
7.6	odd	2	inner	98.4.c.g.79.1		4
21.2	odd	6		882.4.a.w.1.1		2
21.5	even	6		882.4.a.w.1.2		2
21.11	odd	6		882.4.g.bi.361.2		4
21.17	even	6		882.4.g.bi.361.1		4
21.20	even	2		882.4.g.bi.667.1		4
28.19	even	6		784.4.a.z.1.1		2
28.23	odd	6		784.4.a.z.1.2		2
35.9	even	6		2450.4.a.bs.1.2		2
35.19	odd	6		2450.4.a.bs.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.4.a.h.1.1	✓	2	7.2	even	3
98.4.a.h.1.2	yes	2	7.5	odd	6
98.4.c.g.67.1		4	7.3	odd	6	inner
98.4.c.g.67.2		4	7.4	even	3	inner
98.4.c.g.79.1		4	7.6	odd	2	inner
98.4.c.g.79.2		4	1.1	even	1	trivial
784.4.a.z.1.1		2	28.19	even	6
784.4.a.z.1.2		2	28.23	odd	6
882.4.a.w.1.1		2	21.2	odd	6
882.4.a.w.1.2		2	21.5	even	6
882.4.g.bi.361.1		4	21.17	even	6
882.4.g.bi.361.2		4	21.11	odd	6
882.4.g.bi.667.1		4	21.20	even	2
882.4.g.bi.667.2		4	3.2	odd	2
2450.4.a.bs.1.1		2	35.19	odd	6
2450.4.a.bs.1.2		2	35.9	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(4.69042 + 8.12404i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.69042 + 8.12404i) q^{5} -18.7617 q^{6} +8.00000 q^{8} +(-30.5000 + 52.8275i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(4.69042 + 8.12404i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.69042 + 8.12404i) q^{5} -18.7617 q^{6} +8.00000 q^{8} +(-30.5000 + 52.8275i) q^{9} +(-9.38083 - 16.2481i) q^{10} +(-10.0000 - 17.3205i) q^{11} +(18.7617 - 32.4962i) q^{12} +65.6658 q^{13} -88.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-28.1425 - 48.7442i) q^{17} +(-61.0000 - 105.655i) q^{18} +(-4.69042 + 8.12404i) q^{19} +37.5233 q^{20} +40.0000 q^{22} +(-24.0000 + 41.5692i) q^{23} +(37.5233 + 64.9923i) q^{24} +(18.5000 + 32.0429i) q^{25} +(-65.6658 + 113.737i) q^{26} -318.948 q^{27} -166.000 q^{29} +(88.0000 - 152.420i) q^{30} +(103.189 + 178.729i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(93.8083 - 162.481i) q^{33} +112.570 q^{34} +244.000 q^{36} +(39.0000 - 67.5500i) q^{37} +(-9.38083 - 16.2481i) q^{38} +(308.000 + 533.472i) q^{39} +(-37.5233 + 64.9923i) q^{40} +393.995 q^{41} +436.000 q^{43} +(-40.0000 + 69.2820i) q^{44} +(-286.115 - 495.566i) q^{45} +(-48.0000 - 83.1384i) q^{46} +(-103.189 + 178.729i) q^{47} -150.093 q^{48} -74.0000 q^{50} +(264.000 - 457.261i) q^{51} +(-131.332 - 227.473i) q^{52} +(-31.0000 - 53.6936i) q^{53} +(318.948 - 552.435i) q^{54} +187.617 q^{55} -88.0000 q^{57} +(166.000 - 287.520i) q^{58} +(333.020 + 576.807i) q^{59} +(176.000 + 304.841i) q^{60} +(-136.022 + 235.597i) q^{61} -412.757 q^{62} +64.0000 q^{64} +(-308.000 + 533.472i) q^{65} +(187.617 + 324.962i) q^{66} +(-290.000 - 502.295i) q^{67} +(-112.570 + 194.977i) q^{68} -450.280 q^{69} -544.000 q^{71} +(-244.000 + 422.620i) q^{72} +(300.187 + 519.938i) q^{73} +(78.0000 + 135.100i) q^{74} +(-173.545 + 300.589i) q^{75} +37.5233 q^{76} -1232.00 q^{78} +(340.000 - 588.897i) q^{79} +(-75.0467 - 129.985i) q^{80} +(-672.500 - 1164.80i) q^{81} +(-393.995 + 682.419i) q^{82} +196.997 q^{83} +528.000 q^{85} +(-436.000 + 755.174i) q^{86} +(-778.609 - 1348.59i) q^{87} +(-80.0000 - 138.564i) q^{88} +(750.467 - 1299.85i) q^{89} +1144.46 q^{90} +192.000 q^{92} +(-968.000 + 1676.63i) q^{93} +(-206.378 - 357.458i) q^{94} +(-44.0000 - 76.2102i) q^{95} +(150.093 - 259.969i) q^{96} -656.658 q^{97} +1220.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} - 122 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 - 122 * q^9	\( 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} - 122 q^{9} - 40 q^{11} - 352 q^{15} - 32 q^{16} - 244 q^{18} + 160 q^{22} - 96 q^{23} + 74 q^{25} - 664 q^{29} + 352 q^{30} - 64 q^{32} + 976 q^{36} + 156 q^{37} + 1232 q^{39} + 1744 q^{43} - 160 q^{44} - 192 q^{46} - 296 q^{50} + 1056 q^{51} - 124 q^{53} - 352 q^{57} + 664 q^{58} + 704 q^{60} + 256 q^{64} - 1232 q^{65} - 1160 q^{67} - 2176 q^{71} - 976 q^{72} + 312 q^{74} - 4928 q^{78} + 1360 q^{79} - 2690 q^{81} + 2112 q^{85} - 1744 q^{86} - 320 q^{88} + 768 q^{92} - 3872 q^{93} - 176 q^{95} + 4880 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 - 122 * q^9 - 40 * q^11 - 352 * q^15 - 32 * q^16 - 244 * q^18 + 160 * q^22 - 96 * q^23 + 74 * q^25 - 664 * q^29 + 352 * q^30 - 64 * q^32 + 976 * q^36 + 156 * q^37 + 1232 * q^39 + 1744 * q^43 - 160 * q^44 - 192 * q^46 - 296 * q^50 + 1056 * q^51 - 124 * q^53 - 352 * q^57 + 664 * q^58 + 704 * q^60 + 256 * q^64 - 1232 * q^65 - 1160 * q^67 - 2176 * q^71 - 976 * q^72 + 312 * q^74 - 4928 * q^78 + 1360 * q^79 - 2690 * q^81 + 2112 * q^85 - 1744 * q^86 - 320 * q^88 + 768 * q^92 - 3872 * q^93 - 176 * q^95 + 4880 * q^99

Introduction

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