LMFDB - Embedded newform 147.4.e.f.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(67,147)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.f.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-6.00000 + 10.3923i) q^{5} +3.00000 q^{6} +15.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-6.00000 + 10.3923i) q^{5} +3.00000 q^{6} +15.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(6.00000 + 10.3923i) q^{10} +(-10.0000 - 17.3205i) q^{11} +(-10.5000 + 18.1865i) q^{12} -84.0000 q^{13} -36.0000 q^{15} +(-20.5000 + 35.5070i) q^{16} +(48.0000 + 83.1384i) q^{17} +(4.50000 + 7.79423i) q^{18} +(-6.00000 + 10.3923i) q^{19} -84.0000 q^{20} -20.0000 q^{22} +(88.0000 - 152.420i) q^{23} +(22.5000 + 38.9711i) q^{24} +(-9.50000 - 16.4545i) q^{25} +(-42.0000 + 72.7461i) q^{26} -27.0000 q^{27} +58.0000 q^{29} +(-18.0000 + 31.1769i) q^{30} +(132.000 + 228.631i) q^{31} +(80.5000 + 139.430i) q^{32} +(30.0000 - 51.9615i) q^{33} +96.0000 q^{34} -63.0000 q^{36} +(-129.000 + 223.435i) q^{37} +(6.00000 + 10.3923i) q^{38} +(-126.000 - 218.238i) q^{39} +(-90.0000 + 155.885i) q^{40} +156.000 q^{43} +(70.0000 - 121.244i) q^{44} +(-54.0000 - 93.5307i) q^{45} +(-88.0000 - 152.420i) q^{46} +(204.000 - 353.338i) q^{47} -123.000 q^{48} -19.0000 q^{50} +(-144.000 + 249.415i) q^{51} +(-294.000 - 509.223i) q^{52} +(361.000 + 625.270i) q^{53} +(-13.5000 + 23.3827i) q^{54} +240.000 q^{55} -36.0000 q^{57} +(29.0000 - 50.2295i) q^{58} +(-246.000 - 426.084i) q^{59} +(-126.000 - 218.238i) q^{60} +(246.000 - 426.084i) q^{61} +264.000 q^{62} -167.000 q^{64} +(504.000 - 872.954i) q^{65} +(-30.0000 - 51.9615i) q^{66} +(-206.000 - 356.802i) q^{67} +(-336.000 + 581.969i) q^{68} +528.000 q^{69} +296.000 q^{71} +(-67.5000 + 116.913i) q^{72} +(-120.000 - 207.846i) q^{73} +(129.000 + 223.435i) q^{74} +(28.5000 - 49.3634i) q^{75} -84.0000 q^{76} -252.000 q^{78} +(-388.000 + 672.036i) q^{79} +(-246.000 - 426.084i) q^{80} +(-40.5000 - 70.1481i) q^{81} +924.000 q^{83} -1152.00 q^{85} +(78.0000 - 135.100i) q^{86} +(87.0000 + 150.688i) q^{87} +(-150.000 - 259.808i) q^{88} +(372.000 - 644.323i) q^{89} -108.000 q^{90} +1232.00 q^{92} +(-396.000 + 685.892i) q^{93} +(-204.000 - 353.338i) q^{94} +(-72.0000 - 124.708i) q^{95} +(-241.500 + 418.290i) q^{96} -168.000 q^{97} +180.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} + 7 q^{4} - 12 q^{5} + 6 q^{6} + 30 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 + 7 * q^4 - 12 * q^5 + 6 * q^6 + 30 * q^8 - 9 * q^9	\( 2 q + q^{2} + 3 q^{3} + 7 q^{4} - 12 q^{5} + 6 q^{6} + 30 q^{8} - 9 q^{9} + 12 q^{10} - 20 q^{11} - 21 q^{12} - 168 q^{13} - 72 q^{15} - 41 q^{16} + 96 q^{17} + 9 q^{18} - 12 q^{19} - 168 q^{20} - 40 q^{22} + 176 q^{23} + 45 q^{24} - 19 q^{25} - 84 q^{26} - 54 q^{27} + 116 q^{29} - 36 q^{30} + 264 q^{31} + 161 q^{32} + 60 q^{33} + 192 q^{34} - 126 q^{36} - 258 q^{37} + 12 q^{38} - 252 q^{39} - 180 q^{40} + 312 q^{43} + 140 q^{44} - 108 q^{45} - 176 q^{46} + 408 q^{47} - 246 q^{48} - 38 q^{50} - 288 q^{51} - 588 q^{52} + 722 q^{53} - 27 q^{54} + 480 q^{55} - 72 q^{57} + 58 q^{58} - 492 q^{59} - 252 q^{60} + 492 q^{61} + 528 q^{62} - 334 q^{64} + 1008 q^{65} - 60 q^{66} - 412 q^{67} - 672 q^{68} + 1056 q^{69} + 592 q^{71} - 135 q^{72} - 240 q^{73} + 258 q^{74} + 57 q^{75} - 168 q^{76} - 504 q^{78} - 776 q^{79} - 492 q^{80} - 81 q^{81} + 1848 q^{83} - 2304 q^{85} + 156 q^{86} + 174 q^{87} - 300 q^{88} + 744 q^{89} - 216 q^{90} + 2464 q^{92} - 792 q^{93} - 408 q^{94} - 144 q^{95} - 483 q^{96} - 336 q^{97} + 360 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 + 7 * q^4 - 12 * q^5 + 6 * q^6 + 30 * q^8 - 9 * q^9 + 12 * q^10 - 20 * q^11 - 21 * q^12 - 168 * q^13 - 72 * q^15 - 41 * q^16 + 96 * q^17 + 9 * q^18 - 12 * q^19 - 168 * q^20 - 40 * q^22 + 176 * q^23 + 45 * q^24 - 19 * q^25 - 84 * q^26 - 54 * q^27 + 116 * q^29 - 36 * q^30 + 264 * q^31 + 161 * q^32 + 60 * q^33 + 192 * q^34 - 126 * q^36 - 258 * q^37 + 12 * q^38 - 252 * q^39 - 180 * q^40 + 312 * q^43 + 140 * q^44 - 108 * q^45 - 176 * q^46 + 408 * q^47 - 246 * q^48 - 38 * q^50 - 288 * q^51 - 588 * q^52 + 722 * q^53 - 27 * q^54 + 480 * q^55 - 72 * q^57 + 58 * q^58 - 492 * q^59 - 252 * q^60 + 492 * q^61 + 528 * q^62 - 334 * q^64 + 1008 * q^65 - 60 * q^66 - 412 * q^67 - 672 * q^68 + 1056 * q^69 + 592 * q^71 - 135 * q^72 - 240 * q^73 + 258 * q^74 + 57 * q^75 - 168 * q^76 - 504 * q^78 - 776 * q^79 - 492 * q^80 - 81 * q^81 + 1848 * q^83 - 2304 * q^85 + 156 * q^86 + 174 * q^87 - 300 * q^88 + 744 * q^89 - 216 * q^90 + 2464 * q^92 - 792 * q^93 - 408 * q^94 - 144 * q^95 - 483 * q^96 - 336 * q^97 + 360 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	0.500000	−	0.866025i	0.176777	−	0.306186i	−0.763998	−	0.645219i	$-0.776766\pi$
$2$	0.500000	−	0.866025i	0.176777	−	0.306186i	0.940775	+	0.339032i	$0.110100\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	3.50000	+	6.06218i	0.437500	+	0.757772i
$5$	−6.00000	+	10.3923i	−0.536656	+	0.929516i	0.462425	+	0.886658i	$0.346979\pi$
$5$	−6.00000	+	10.3923i	−0.536656	+	0.929516i	−0.999081	+	0.0428575i	$0.986354\pi$
$6$	3.00000			0.204124
$7$		0			0
$7$		0			0
$8$	15.0000			0.662913
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	6.00000	+	10.3923i	0.189737	+	0.328634i
$11$	−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	$0.921714\pi$
$12$	−10.5000	+	18.1865i	−0.252591	+	0.437500i
$13$	−84.0000			−1.79211			−0.896054	−	0.443945i	$-0.853579\pi$
$13$	−84.0000			−1.79211			−0.896054	+	0.443945i	$0.853579\pi$
$14$		0			0
$15$	−36.0000			−0.619677
$16$	−20.5000	+	35.5070i	−0.320312	+	0.554798i
$17$	48.0000	+	83.1384i	0.684806	+	1.18612i	0.973498	+	0.228697i	$0.0734466\pi$
$17$	48.0000	+	83.1384i	0.684806	+	1.18612i	−0.288691	+	0.957422i	$0.593220\pi$
$18$	4.50000	+	7.79423i	0.0589256	+	0.102062i
$19$	−6.00000	+	10.3923i	−0.0724471	+	0.125482i	−0.899973	−	0.435945i	$-0.856414\pi$
$19$	−6.00000	+	10.3923i	−0.0724471	+	0.125482i	0.827526	+	0.561427i	$0.189748\pi$
$20$	−84.0000			−0.939149
$21$		0			0
$22$	−20.0000			−0.193819
$23$	88.0000	−	152.420i	0.797794	−	1.38182i	−0.123255	−	0.992375i	$-0.539333\pi$
$23$	88.0000	−	152.420i	0.797794	−	1.38182i	0.921050	−	0.389445i	$-0.127333\pi$
$24$	22.5000	+	38.9711i	0.191366	+	0.331456i
$25$	−9.50000	−	16.4545i	−0.0760000	−	0.131636i
$26$	−42.0000	+	72.7461i	−0.316803	+	0.548719i
$27$	−27.0000			−0.192450
$28$		0			0
$29$	58.0000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	58.0000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	−18.0000	+	31.1769i	−0.109545	+	0.189737i
$31$	132.000	+	228.631i	0.764771	+	1.32462i	0.940368	+	0.340160i	$0.110481\pi$
$31$	132.000	+	228.631i	0.764771	+	1.32462i	−0.175597	+	0.984462i	$0.556185\pi$
$32$	80.5000	+	139.430i	0.444704	+	0.770250i
$33$	30.0000	−	51.9615i	0.158252	−	0.274101i
$34$	96.0000			0.484231
$35$		0			0
$36$	−63.0000			−0.291667
$37$	−129.000	+	223.435i	−0.573175	+	0.992768i	0.423062	+	0.906101i	$0.360955\pi$
$37$	−129.000	+	223.435i	−0.573175	+	0.992768i	−0.996237	+	0.0866674i	$0.972378\pi$
$38$	6.00000	+	10.3923i	0.0256139	+	0.0443646i
$39$	−126.000	−	218.238i	−0.517337	−	0.896054i
$40$	−90.0000	+	155.885i	−0.355756	+	0.616188i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	156.000			0.553251			0.276625	−	0.960978i	$-0.410784\pi$
$43$	156.000			0.553251			0.276625	+	0.960978i	$0.410784\pi$
$44$	70.0000	−	121.244i	0.239839	−	0.415413i
$45$	−54.0000	−	93.5307i	−0.178885	−	0.309839i
$46$	−88.0000	−	152.420i	−0.282063	−	0.488547i
$47$	204.000	−	353.338i	0.633116	−	1.09659i	−0.353795	−	0.935323i	$-0.615109\pi$
$47$	204.000	−	353.338i	0.633116	−	1.09659i	0.986911	−	0.161266i	$-0.0515578\pi$
$48$	−123.000			−0.369865
$49$		0			0
$50$	−19.0000			−0.0537401
$51$	−144.000	+	249.415i	−0.395373	+	0.684806i
$52$	−294.000	−	509.223i	−0.784047	−	1.35801i
$53$	361.000	+	625.270i	0.935607	+	1.62052i	0.773548	+	0.633737i	$0.218480\pi$
$53$	361.000	+	625.270i	0.935607	+	1.62052i	0.162059	+	0.986781i	$0.448187\pi$
$54$	−13.5000	+	23.3827i	−0.0340207	+	0.0589256i
$55$	240.000			0.588393
$56$		0			0
$57$	−36.0000			−0.0836547
$58$	29.0000	−	50.2295i	0.0656532	−	0.113715i
$59$	−246.000	−	426.084i	−0.542822	−	0.940195i	−0.998741	−	0.0501732i	$-0.984023\pi$
$59$	−246.000	−	426.084i	−0.542822	−	0.940195i	0.455919	−	0.890021i	$-0.349311\pi$
$60$	−126.000	−	218.238i	−0.271109	−	0.469574i
$61$	246.000	−	426.084i	0.516345	−	0.894337i	−0.483474	−	0.875358i	$-0.660625\pi$
$61$	246.000	−	426.084i	0.516345	−	0.894337i	0.999820	−	0.0189781i	$-0.00604127\pi$
$62$	264.000			0.540775
$63$		0			0
$64$	−167.000			−0.326172
$65$	504.000	−	872.954i	0.961746	−	1.66579i
$66$	−30.0000	−	51.9615i	−0.0559507	−	0.0969094i
$67$	−206.000	−	356.802i	−0.375625	−	0.650602i	0.614795	−	0.788687i	$-0.289239\pi$
$67$	−206.000	−	356.802i	−0.375625	−	0.650602i	−0.990420	+	0.138085i	$0.955905\pi$
$68$	−336.000	+	581.969i	−0.599206	+	1.03785i
$69$	528.000			0.921213
$70$		0			0
$71$	296.000			0.494771			0.247385	−	0.968917i	$-0.420429\pi$
$71$	296.000			0.494771			0.247385	+	0.968917i	$0.420429\pi$
$72$	−67.5000	+	116.913i	−0.110485	+	0.191366i
$73$	−120.000	−	207.846i	−0.192396	−	0.333240i	0.753647	−	0.657279i	$-0.228293\pi$
$73$	−120.000	−	207.846i	−0.192396	−	0.333240i	−0.946044	+	0.324038i	$0.894959\pi$
$74$	129.000	+	223.435i	0.202648	+	0.350996i
$75$	28.5000	−	49.3634i	0.0438786	−	0.0760000i
$76$	−84.0000			−0.126782
$77$		0			0
$78$	−252.000			−0.365813
$79$	−388.000	+	672.036i	−0.552575	+	0.957088i	0.445513	+	0.895275i	$0.353021\pi$
$79$	−388.000	+	672.036i	−0.552575	+	0.957088i	−0.998088	+	0.0618122i	$0.980312\pi$
$80$	−246.000	−	426.084i	−0.343795	−	0.595471i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	924.000			1.22195			0.610977	−	0.791648i	$-0.290777\pi$
$83$	924.000			1.22195			0.610977	+	0.791648i	$0.290777\pi$
$84$		0			0
$85$	−1152.00			−1.47002
$86$	78.0000	−	135.100i	0.0978018	−	0.169398i
$87$	87.0000	+	150.688i	0.107211	+	0.185695i
$88$	−150.000	−	259.808i	−0.181705	−	0.314723i
$89$	372.000	−	644.323i	0.443055	−	0.767394i	−0.554859	−	0.831944i	$-0.687228\pi$
$89$	372.000	−	644.323i	0.443055	−	0.767394i	0.997914	+	0.0645500i	$0.0205612\pi$
$90$	−108.000			−0.126491
$91$		0			0
$92$	1232.00			1.39614
$93$	−396.000	+	685.892i	−0.441541	+	0.764771i
$94$	−204.000	−	353.338i	−0.223840	−	0.387703i
$95$	−72.0000	−	124.708i	−0.0777584	−	0.134681i
$96$	−241.500	+	418.290i	−0.256750	+	0.444704i
$97$	−168.000			−0.175854			−0.0879269	−	0.996127i	$-0.528024\pi$
$97$	−168.000			−0.175854			−0.0879269	+	0.996127i	$0.528024\pi$
$98$		0			0
$99$	180.000			0.182734
$100$	66.5000	−	115.181i	0.0665000	−	0.115181i
$101$	762.000	+	1319.82i	0.750711	+	1.30027i	0.947478	+	0.319820i	$0.103622\pi$
$101$	762.000	+	1319.82i	0.750711	+	1.30027i	−0.196767	+	0.980450i	$0.563044\pi$
$102$	144.000	+	249.415i	0.139786	+	0.242116i
$103$	204.000	−	353.338i	0.195153	−	0.338014i	−0.751798	−	0.659394i	$-0.770813\pi$
$103$	204.000	−	353.338i	0.195153	−	0.338014i	0.946951	+	0.321379i	$0.104146\pi$
$104$	−1260.00			−1.18801
$105$		0			0
$106$	722.000			0.661574
$107$	410.000	−	710.141i	0.370432	−	0.641607i	−0.619200	−	0.785233i	$-0.712543\pi$
$107$	410.000	−	710.141i	0.370432	−	0.641607i	0.989632	+	0.143627i	$0.0458764\pi$
$108$	−94.5000	−	163.679i	−0.0841969	−	0.145833i
$109$	459.000	+	795.011i	0.403342	+	0.698608i	0.994127	−	0.108221i	$-0.0345153\pi$
$109$	459.000	+	795.011i	0.403342	+	0.698608i	−0.590785	+	0.806829i	$0.701182\pi$
$110$	120.000	−	207.846i	0.104014	−	0.180158i
$111$	−774.000			−0.661845
$112$		0			0
$113$	−110.000			−0.0915746			−0.0457873	−	0.998951i	$-0.514580\pi$
$113$	−110.000			−0.0915746			−0.0457873	+	0.998951i	$0.514580\pi$
$114$	−18.0000	+	31.1769i	−0.0147882	+	0.0256139i
$115$	1056.00	+	1829.05i	0.856283	+	1.48313i
$116$	203.000	+	351.606i	0.162483	+	0.281430i
$117$	378.000	−	654.715i	0.298685	−	0.517337i
$118$	−492.000			−0.383833
$119$		0			0
$120$	−540.000			−0.410792
$121$	465.500	−	806.270i	0.349737	−	0.605762i
$122$	−246.000	−	426.084i	−0.182556	−	0.316196i
$123$		0			0
$124$	−924.000	+	1600.41i	−0.669175	+	1.15904i
$125$	−1272.00			−0.910169
$126$		0			0
$127$	16.0000			0.0111793			0.00558965	−	0.999984i	$-0.498221\pi$
$127$	16.0000			0.0111793			0.00558965	+	0.999984i	$0.498221\pi$
$128$	−727.500	+	1260.07i	−0.502363	+	0.870119i
$129$	234.000	+	405.300i	0.159710	+	0.276625i
$130$	−504.000	−	872.954i	−0.340029	−	0.588947i
$131$	−846.000	+	1465.31i	−0.564239	+	0.977291i	0.432881	+	0.901451i	$0.357497\pi$
$131$	−846.000	+	1465.31i	−0.564239	+	0.977291i	−0.997120	+	0.0758401i	$0.975836\pi$
$132$	420.000			0.276942
$133$		0			0
$134$	−412.000			−0.265607
$135$	162.000	−	280.592i	0.103280	−	0.178885i
$136$	720.000	+	1247.08i	0.453967	+	0.786294i
$137$	−563.000	−	975.145i	−0.351097	−	0.608118i	0.635345	−	0.772229i	$-0.280858\pi$
$137$	−563.000	−	975.145i	−0.351097	−	0.608118i	−0.986442	+	0.164110i	$0.947525\pi$
$138$	264.000	−	457.261i	0.162849	−	0.282063i
$139$	1092.00			0.666347			0.333173	−	0.942866i	$-0.391881\pi$
$139$	1092.00			0.666347			0.333173	+	0.942866i	$0.391881\pi$
$140$		0			0
$141$	1224.00			0.731060
$142$	148.000	−	256.344i	0.0874640	−	0.151492i
$143$	840.000	+	1454.92i	0.491219	+	0.850816i
$144$	−184.500	−	319.563i	−0.106771	−	0.184933i
$145$	−348.000	+	602.754i	−0.199309	+	0.345214i
$146$	−240.000			−0.136045
$147$		0			0
$148$	−1806.00			−1.00306
$149$	−535.000	+	926.647i	−0.294154	+	0.509489i	−0.974788	−	0.223134i	$-0.928371\pi$
$149$	−535.000	+	926.647i	−0.294154	+	0.509489i	0.680634	+	0.732624i	$0.261704\pi$
$150$	−28.5000	−	49.3634i	−0.0155134	−	0.0268701i
$151$	60.0000	+	103.923i	0.0323360	+	0.0560075i	0.881741	−	0.471735i	$-0.156372\pi$
$151$	60.0000	+	103.923i	0.0323360	+	0.0560075i	−0.849405	+	0.527742i	$0.823039\pi$
$152$	−90.0000	+	155.885i	−0.0480261	+	0.0831836i
$153$	−864.000			−0.456538
$154$		0			0
$155$	−3168.00			−1.64168
$156$	882.000	−	1527.67i	0.452670	−	0.784047i
$157$	−918.000	−	1590.02i	−0.466652	−	0.808265i	0.532622	−	0.846353i	$-0.321207\pi$
$157$	−918.000	−	1590.02i	−0.466652	−	0.808265i	−0.999274	+	0.0380879i	$0.987873\pi$
$158$	388.000	+	672.036i	0.195365	+	0.338382i
$159$	−1083.00	+	1875.81i	−0.540173	+	0.935607i
$160$	−1932.00			−0.954613
$161$		0			0
$162$	−81.0000			−0.0392837
$163$	−458.000	+	793.279i	−0.220082	+	0.381193i	−0.954833	−	0.297144i	$-0.903966\pi$
$163$	−458.000	+	793.279i	−0.220082	+	0.381193i	0.734751	+	0.678337i	$0.237299\pi$
$164$		0			0
$165$	360.000	+	623.538i	0.169854	+	0.294196i
$166$	462.000	−	800.207i	0.216013	−	0.374145i
$167$	504.000			0.233537			0.116769	−	0.993159i	$-0.462746\pi$
$167$	504.000			0.233537			0.116769	+	0.993159i	$0.462746\pi$
$168$		0			0
$169$	4859.00			2.21165
$170$	−576.000	+	997.661i	−0.259866	+	0.450101i
$171$	−54.0000	−	93.5307i	−0.0241490	−	0.0418273i
$172$	546.000	+	945.700i	0.242047	+	0.419238i
$173$	918.000	−	1590.02i	0.403435	−	0.698770i	−0.590703	−	0.806889i	$-0.701149\pi$
$173$	918.000	−	1590.02i	0.403435	−	0.698770i	0.994138	+	0.108119i	$0.0344828\pi$
$174$	174.000			0.0758098
$175$		0			0
$176$	820.000			0.351192
$177$	738.000	−	1278.25i	0.313398	−	0.542822i
$178$	−372.000	−	644.323i	−0.156644	−	0.271315i
$179$	−1186.00	−	2054.21i	−0.495228	−	0.857760i	0.504757	−	0.863262i	$-0.331582\pi$
$179$	−1186.00	−	2054.21i	−0.495228	−	0.857760i	−0.999985	+	0.00550156i	$0.998249\pi$
$180$	378.000	−	654.715i	0.156525	−	0.271109i
$181$	−1092.00			−0.448440			−0.224220	−	0.974539i	$-0.571983\pi$
$181$	−1092.00			−0.448440			−0.224220	+	0.974539i	$0.571983\pi$
$182$		0			0
$183$	1476.00			0.596224
$184$	1320.00	−	2286.31i	0.528868	−	0.916026i
$185$	−1548.00	−	2681.21i	−0.615196	−	1.06555i
$186$	396.000	+	685.892i	0.156108	+	0.270387i
$187$	960.000	−	1662.77i	0.375413	−	0.650234i
$188$	2856.00			1.10795
$189$		0			0
$190$	−144.000			−0.0549835
$191$	−1256.00	+	2175.46i	−0.475817	+	0.824139i	−0.999616	−	0.0277030i	$-0.991181\pi$
$191$	−1256.00	+	2175.46i	−0.475817	+	0.824139i	0.523800	+	0.851842i	$0.324514\pi$
$192$	−250.500	−	433.879i	−0.0941577	−	0.163086i
$193$	1215.00	+	2104.44i	0.453148	+	0.784876i	0.998580	−	0.0532797i	$-0.0169675\pi$
$193$	1215.00	+	2104.44i	0.453148	+	0.784876i	−0.545431	+	0.838155i	$0.683634\pi$
$194$	−84.0000	+	145.492i	−0.0310868	+	0.0538440i
$195$	3024.00			1.11053
$196$		0			0
$197$	−1762.00			−0.637245			−0.318623	−	0.947882i	$-0.603220\pi$
$197$	−1762.00			−0.637245			−0.318623	+	0.947882i	$0.603220\pi$
$198$	90.0000	−	155.885i	0.0323031	−	0.0559507i
$199$	−1548.00	−	2681.21i	−0.551431	−	0.955107i	−0.998172	−	0.0604433i	$-0.980749\pi$
$199$	−1548.00	−	2681.21i	−0.551431	−	0.955107i	0.446740	−	0.894664i	$-0.352585\pi$
$200$	−142.500	−	246.817i	−0.0503814	−	0.0872631i
$201$	618.000	−	1070.41i	0.216867	−	0.375625i
$202$	1524.00			0.530833
$203$		0			0
$204$	−2016.00			−0.691903
$205$		0			0
$206$	−204.000	−	353.338i	−0.0689969	−	0.119506i
$207$	792.000	+	1371.78i	0.265931	+	0.460607i
$208$	1722.00	−	2982.59i	0.574035	−	0.994257i
$209$	240.000			0.0794313
$210$		0			0
$211$	156.000			0.0508980			0.0254490	−	0.999676i	$-0.491898\pi$
$211$	156.000			0.0508980			0.0254490	+	0.999676i	$0.491898\pi$
$212$	−2527.00	+	4376.89i	−0.818656	+	1.41795i
$213$	444.000	+	769.031i	0.142828	+	0.247385i
$214$	−410.000	−	710.141i	−0.130967	−	0.226842i
$215$	−936.000	+	1621.20i	−0.296905	+	0.514255i
$216$	−405.000			−0.127578
$217$		0			0
$218$	918.000			0.285206
$219$	360.000	−	623.538i	0.111080	−	0.192396i
$220$	840.000	+	1454.92i	0.257422	+	0.445868i
$221$	−4032.00	−	6983.63i	−1.22725	−	2.12565i
$222$	−387.000	+	670.304i	−0.116999	+	0.202648i
$223$	5040.00			1.51347			0.756734	−	0.653723i	$-0.226794\pi$
$223$	5040.00			1.51347			0.756734	+	0.653723i	$0.226794\pi$
$224$		0			0
$225$	171.000			0.0506667
$226$	−55.0000	+	95.2628i	−0.0161883	+	0.0280389i
$227$	−1086.00	−	1881.01i	−0.317535	−	0.549986i	0.662438	−	0.749116i	$-0.269522\pi$
$227$	−1086.00	−	1881.01i	−0.317535	−	0.549986i	−0.979973	+	0.199130i	$0.936188\pi$
$228$	−126.000	−	218.238i	−0.0365989	−	0.0633912i
$229$	−1350.00	+	2338.27i	−0.389566	+	0.674747i	−0.992391	−	0.123126i	$-0.960708\pi$
$229$	−1350.00	+	2338.27i	−0.389566	+	0.674747i	0.602826	+	0.797873i	$0.294041\pi$
$230$	2112.00			0.605483
$231$		0			0
$232$	870.000			0.246200
$233$	1901.00	−	3292.63i	0.534501	−	0.925782i	−0.464687	−	0.885475i	$-0.653833\pi$
$233$	1901.00	−	3292.63i	0.534501	−	0.925782i	0.999187	−	0.0403071i	$-0.0128336\pi$
$234$	−378.000	−	654.715i	−0.105601	−	0.182906i
$235$	2448.00	+	4240.06i	0.679532	+	1.17698i
$236$	1722.00	−	2982.59i	0.474969	−	0.822670i
$237$	−2328.00			−0.638058
$238$		0			0
$239$	−4408.00			−1.19301			−0.596506	−	0.802609i	$-0.703445\pi$
$239$	−4408.00			−1.19301			−0.596506	+	0.802609i	$0.703445\pi$
$240$	738.000	−	1278.25i	0.198490	−	0.343795i
$241$	−1548.00	−	2681.21i	−0.413757	−	0.716648i	0.581540	−	0.813518i	$-0.302450\pi$
$241$	−1548.00	−	2681.21i	−0.413757	−	0.716648i	−0.995297	+	0.0968696i	$0.969117\pi$
$242$	−465.500	−	806.270i	−0.123651	−	0.214169i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	3444.00			0.903605
$245$		0			0
$246$		0			0
$247$	504.000	−	872.954i	0.129833	−	0.224877i
$248$	1980.00	+	3429.46i	0.506976	+	0.878109i
$249$	1386.00	+	2400.62i	0.352748	+	0.610977i
$250$	−636.000	+	1101.58i	−0.160897	+	0.278681i
$251$	−924.000			−0.232360			−0.116180	−	0.993228i	$-0.537065\pi$
$251$	−924.000			−0.232360			−0.116180	+	0.993228i	$0.537065\pi$
$252$		0			0
$253$	−3520.00			−0.874706
$254$	8.00000	−	13.8564i	0.00197624	−	0.00342295i
$255$	−1728.00	−	2992.98i	−0.424359	−	0.735011i
$256$	59.5000	+	103.057i	0.0145264	+	0.0251604i
$257$	1380.00	−	2390.23i	0.334950	−	0.580150i	−0.648526	−	0.761193i	$-0.724614\pi$
$257$	1380.00	−	2390.23i	0.334950	−	0.580150i	0.983475	+	0.181043i	$0.0579474\pi$
$258$	468.000			0.112932
$259$		0			0
$260$	7056.00			1.68306
$261$	−261.000	+	452.065i	−0.0618984	+	0.107211i
$262$	846.000	+	1465.31i	0.199489	+	0.345525i
$263$	1180.00	+	2043.82i	0.276661	+	0.479191i	0.970553	−	0.240888i	$-0.0774387\pi$
$263$	1180.00	+	2043.82i	0.276661	+	0.479191i	−0.693892	+	0.720079i	$0.744105\pi$
$264$	450.000	−	779.423i	0.104908	−	0.181705i
$265$	−8664.00			−2.00840
$266$		0			0
$267$	2232.00			0.511596
$268$	1442.00	−	2497.62i	0.328672	−	0.569277i
$269$	−2010.00	−	3481.42i	−0.455583	−	0.789093i	0.543138	−	0.839643i	$-0.317236\pi$
$269$	−2010.00	−	3481.42i	−0.455583	−	0.789093i	−0.998722	+	0.0505501i	$0.983903\pi$
$270$	−162.000	−	280.592i	−0.0365148	−	0.0632456i
$271$	−2400.00	+	4156.92i	−0.537969	+	0.931790i	0.461044	+	0.887377i	$0.347475\pi$
$271$	−2400.00	+	4156.92i	−0.537969	+	0.931790i	−0.999013	+	0.0444126i	$0.985858\pi$
$272$	−3936.00			−0.877408
$273$		0			0
$274$	−1126.00			−0.248263
$275$	−190.000	+	329.090i	−0.0416634	+	0.0721631i
$276$	1848.00	+	3200.83i	0.403031	+	0.698070i
$277$	−3223.00	−	5582.40i	−0.699102	−	1.21088i	−0.968778	−	0.247929i	$-0.920250\pi$
$277$	−3223.00	−	5582.40i	−0.699102	−	1.21088i	0.269676	−	0.962951i	$-0.413083\pi$
$278$	546.000	−	945.700i	0.117795	−	0.204026i
$279$	−2376.00			−0.509847
$280$		0			0
$281$	−2602.00			−0.552393			−0.276196	−	0.961101i	$-0.589074\pi$
$281$	−2602.00			−0.552393			−0.276196	+	0.961101i	$0.589074\pi$
$282$	612.000	−	1060.02i	0.129234	−	0.223840i
$283$	3450.00	+	5975.58i	0.724669	+	1.25516i	0.959110	+	0.283033i	$0.0913405\pi$
$283$	3450.00	+	5975.58i	0.724669	+	1.25516i	−0.234442	+	0.972130i	$0.575326\pi$
$284$	1036.00	+	1794.40i	0.216462	+	0.374924i
$285$	216.000	−	374.123i	0.0448938	−	0.0777584i
$286$	1680.00			0.347344
$287$		0			0
$288$	−1449.00			−0.296469
$289$	−2151.50	+	3726.51i	−0.437920	+	0.758499i
$290$	348.000	+	602.754i	0.0704664	+	0.122051i
$291$	−252.000	−	436.477i	−0.0507646	−	0.0879269i
$292$	840.000	−	1454.92i	0.168347	−	0.291585i
$293$	−4452.00			−0.887674			−0.443837	−	0.896107i	$-0.646383\pi$
$293$	−4452.00			−0.887674			−0.443837	+	0.896107i	$0.646383\pi$
$294$		0			0
$295$	5904.00			1.16523
$296$	−1935.00	+	3351.52i	−0.379965	+	0.658118i
$297$	270.000	+	467.654i	0.0527508	+	0.0913671i
$298$	535.000	+	926.647i	0.103999	+	0.180132i
$299$	−7392.00	+	12803.3i	−1.42973	+	2.47637i
$300$	399.000			0.0767876
$301$		0			0
$302$	120.000			0.0228650
$303$	−2286.00	+	3959.47i	−0.433423	+	0.750711i
$304$	−246.000	−	426.084i	−0.0464114	−	0.0803869i
$305$	2952.00	+	5113.01i	0.554200	+	0.959903i
$306$	−432.000	+	748.246i	−0.0807052	+	0.139786i
$307$	−2436.00			−0.452866			−0.226433	−	0.974027i	$-0.572706\pi$
$307$	−2436.00			−0.452866			−0.226433	+	0.974027i	$0.572706\pi$
$308$		0			0
$309$	1224.00			0.225343
$310$	−1584.00	+	2743.57i	−0.290210	+	0.502659i
$311$	3744.00	+	6484.80i	0.682646	+	1.18238i	0.974171	+	0.225814i	$0.0725040\pi$
$311$	3744.00	+	6484.80i	0.682646	+	1.18238i	−0.291525	+	0.956563i	$0.594163\pi$
$312$	−1890.00	−	3273.58i	−0.342949	−	0.594006i
$313$	876.000	−	1517.28i	0.158193	−	0.273999i	−0.776024	−	0.630703i	$-0.782766\pi$
$313$	876.000	−	1517.28i	0.158193	−	0.273999i	0.934217	+	0.356705i	$0.116100\pi$
$314$	−1836.00			−0.329973
$315$		0			0
$316$	−5432.00			−0.967006
$317$	781.000	−	1352.73i	0.138376	−	0.239675i	−0.788506	−	0.615027i	$-0.789145\pi$
$317$	781.000	−	1352.73i	0.138376	−	0.239675i	0.926882	+	0.375352i	$0.122478\pi$
$318$	1083.00	+	1875.81i	0.190980	+	0.330787i
$319$	−580.000	−	1004.59i	−0.101799	−	0.176320i
$320$	1002.00	−	1735.51i	0.175042	−	0.303182i
$321$	2460.00			0.427738
$322$		0			0
$323$	−1152.00			−0.198449
$324$	283.500	−	491.036i	0.0486111	−	0.0841969i
$325$	798.000	+	1382.18i	0.136200	+	0.235906i
$326$	458.000	+	793.279i	0.0778107	+	0.134772i
$327$	−1377.00	+	2385.03i	−0.232869	+	0.403342i
$328$		0			0
$329$		0			0
$330$	720.000			0.120105
$331$	3546.00	−	6141.85i	0.588839	−	1.01990i	−0.405546	−	0.914075i	$-0.632918\pi$
$331$	3546.00	−	6141.85i	0.588839	−	1.01990i	0.994385	−	0.105825i	$-0.0337482\pi$
$332$	3234.00	+	5601.45i	0.534605	+	0.925963i
$333$	−1161.00	−	2010.91i	−0.191058	−	0.330923i
$334$	252.000	−	436.477i	0.0412839	−	0.0715058i
$335$	4944.00			0.806327
$336$		0			0
$337$	366.000			0.0591611			0.0295805	−	0.999562i	$-0.490583\pi$
$337$	366.000			0.0591611			0.0295805	+	0.999562i	$0.490583\pi$
$338$	2429.50	−	4208.02i	0.390969	−	0.677177i
$339$	−165.000	−	285.788i	−0.0264353	−	0.0457873i
$340$	−4032.00	−	6983.63i	−0.643135	−	1.11394i
$341$	2640.00	−	4572.61i	0.419249	−	0.726161i
$342$	−108.000			−0.0170759
$343$		0			0
$344$	2340.00			0.366757
$345$	−3168.00	+	5487.14i	−0.494375	+	0.856283i
$346$	−918.000	−	1590.02i	−0.142636	−	0.247052i
$347$	3182.00	+	5511.39i	0.492273	+	0.852642i	0.999960	−	0.00889958i	$-0.00283286\pi$
$347$	3182.00	+	5511.39i	0.492273	+	0.852642i	−0.507687	+	0.861541i	$0.669500\pi$
$348$	−609.000	+	1054.82i	−0.0938098	+	0.162483i
$349$	−10500.0			−1.61046			−0.805232	−	0.592960i	$-0.797959\pi$
$349$	−10500.0			−1.61046			−0.805232	+	0.592960i	$0.797959\pi$
$350$		0			0
$351$	2268.00			0.344891
$352$	1610.00	−	2788.60i	0.243788	−	0.422253i
$353$	−204.000	−	353.338i	−0.0307587	−	0.0532756i	0.850236	−	0.526401i	$-0.176459\pi$
$353$	−204.000	−	353.338i	−0.0307587	−	0.0532756i	−0.880995	+	0.473126i	$0.843126\pi$
$354$	−738.000	−	1278.25i	−0.110803	−	0.191916i
$355$	−1776.00	+	3076.12i	−0.265522	+	0.459898i
$356$	5208.00			0.775347
$357$		0			0
$358$	−2372.00			−0.350179
$359$	5968.00	−	10336.9i	0.877379	−	1.51966i	0.0231719	−	0.999731i	$-0.492624\pi$
$359$	5968.00	−	10336.9i	0.877379	−	1.51966i	0.854207	−	0.519933i	$-0.174043\pi$
$360$	−810.000	−	1402.96i	−0.118585	−	0.205396i
$361$	3357.50	+	5815.36i	0.489503	+	0.847844i
$362$	−546.000	+	945.700i	−0.0792738	+	0.137306i
$363$	2793.00			0.403842
$364$		0			0
$365$	2880.00			0.413003
$366$	738.000	−	1278.25i	0.105399	−	0.182556i
$367$	1224.00	+	2120.03i	0.174093	+	0.301539i	0.939847	−	0.341595i	$-0.110967\pi$
$367$	1224.00	+	2120.03i	0.174093	+	0.301539i	−0.765754	+	0.643134i	$0.777634\pi$
$368$	3608.00	+	6249.24i	0.511087	+	0.885229i
$369$		0			0
$370$	−3096.00			−0.435009
$371$		0			0
$372$	−5544.00			−0.772696
$373$	−5687.00	+	9850.17i	−0.789442	+	1.36735i	0.136868	+	0.990589i	$0.456296\pi$
$373$	−5687.00	+	9850.17i	−0.789442	+	1.36735i	−0.926309	+	0.376764i	$0.877037\pi$
$374$	−960.000	−	1662.77i	−0.132728	−	0.229892i
$375$	−1908.00	−	3304.75i	−0.262743	−	0.455085i
$376$	3060.00	−	5300.08i	0.419701	−	0.726943i
$377$	−4872.00			−0.665572
$378$		0			0
$379$	−5892.00			−0.798553			−0.399277	−	0.916830i	$-0.630739\pi$
$379$	−5892.00			−0.798553			−0.399277	+	0.916830i	$0.630739\pi$
$380$	504.000	−	872.954i	0.0680386	−	0.117846i
$381$	24.0000	+	41.5692i	0.00322718	+	0.00558965i
$382$	1256.00	+	2175.46i	0.168227	+	0.291377i
$383$	5244.00	−	9082.87i	0.699624	−	1.21178i	−0.268973	−	0.963148i	$-0.586684\pi$
$383$	5244.00	−	9082.87i	0.699624	−	1.21178i	0.968597	−	0.248636i	$-0.0799823\pi$
$384$	−4365.00			−0.580079
$385$		0			0
$386$	2430.00			0.320424
$387$	−702.000	+	1215.90i	−0.0922084	+	0.159710i
$388$	−588.000	−	1018.45i	−0.0769360	−	0.133257i
$389$	−2257.00	−	3909.24i	−0.294176	−	0.509528i	0.680617	−	0.732639i	$-0.261712\pi$
$389$	−2257.00	−	3909.24i	−0.294176	−	0.509528i	−0.974793	+	0.223112i	$0.928379\pi$
$390$	1512.00	−	2618.86i	0.196316	−	0.340029i
$391$	16896.0			2.18534
$392$		0			0
$393$	−5076.00			−0.651528
$394$	−881.000	+	1525.94i	−0.112650	+	0.195116i
$395$	−4656.00	−	8064.43i	−0.593086	−	1.02725i
$396$	630.000	+	1091.19i	0.0799462	+	0.138471i
$397$	3018.00	−	5227.33i	0.381534	−	0.660837i	−0.609748	−	0.792596i	$-0.708729\pi$
$397$	3018.00	−	5227.33i	0.381534	−	0.660837i	0.991282	+	0.131759i	$0.0420625\pi$
$398$	−3096.00			−0.389921
$399$		0			0
$400$	779.000			0.0973750
$401$	3385.00	−	5862.99i	0.421543	−	0.730134i	−0.574547	−	0.818471i	$-0.694822\pi$
$401$	3385.00	−	5862.99i	0.421543	−	0.730134i	0.996091	+	0.0883370i	$0.0281552\pi$
$402$	−618.000	−	1070.41i	−0.0766742	−	0.132804i
$403$	−11088.0	−	19205.0i	−1.37055	−	2.37387i
$404$	−5334.00	+	9238.76i	−0.656872	+	1.13774i
$405$	972.000			0.119257
$406$		0			0
$407$	5160.00			0.628432
$408$	−2160.00	+	3741.23i	−0.262098	+	0.453967i
$409$	−6252.00	−	10828.8i	−0.755847	−	1.30917i	−0.944952	−	0.327209i	$-0.893892\pi$
$409$	−6252.00	−	10828.8i	−0.755847	−	1.30917i	0.189105	−	0.981957i	$-0.439441\pi$
$410$		0			0
$411$	1689.00	−	2925.43i	0.202706	−	0.351097i
$412$	2856.00			0.341517
$413$		0			0
$414$	1584.00			0.188042
$415$	−5544.00	+	9602.49i	−0.655769	+	1.13583i
$416$	−6762.00	−	11712.1i	−0.796958	−	1.38037i
$417$	1638.00	+	2837.10i	0.192358	+	0.333173i
$418$	120.000	−	207.846i	0.0140416	−	0.0243208i
$419$	9492.00			1.10672			0.553359	−	0.832943i	$-0.313346\pi$
$419$	9492.00			1.10672			0.553359	+	0.832943i	$0.313346\pi$
$420$		0			0
$421$	5182.00			0.599894			0.299947	−	0.953956i	$-0.403031\pi$
$421$	5182.00			0.599894			0.299947	+	0.953956i	$0.403031\pi$
$422$	78.0000	−	135.100i	0.00899758	−	0.0155843i
$423$	1836.00	+	3180.05i	0.211039	+	0.365530i
$424$	5415.00	+	9379.06i	0.620226	+	1.07426i
$425$	912.000	−	1579.63i	0.104091	−	0.180290i
$426$	888.000			0.100995
$427$		0			0
$428$	5740.00			0.648256
$429$	−2520.00	+	4364.77i	−0.283605	+	0.491219i
$430$	936.000	+	1621.20i	0.104972	+	0.181817i
$431$	2860.00	+	4953.67i	0.319632	+	0.553619i	0.980411	−	0.196962i	$-0.0631074\pi$
$431$	2860.00	+	4953.67i	0.319632	+	0.553619i	−0.660779	+	0.750580i	$0.729774\pi$
$432$	553.500	−	958.690i	0.0616442	−	0.106771i
$433$	13608.0			1.51030			0.755149	−	0.655554i	$-0.227565\pi$
$433$	13608.0			1.51030			0.755149	+	0.655554i	$0.227565\pi$
$434$		0			0
$435$	−2088.00			−0.230142
$436$	−3213.00	+	5565.08i	−0.352924	+	0.611282i
$437$	1056.00	+	1829.05i	0.115596	+	0.200218i
$438$	−360.000	−	623.538i	−0.0392728	−	0.0680224i
$439$	−6432.00	+	11140.6i	−0.699277	+	1.21118i	0.269440	+	0.963017i	$0.413161\pi$
$439$	−6432.00	+	11140.6i	−0.699277	+	1.21118i	−0.968717	+	0.248166i	$0.920172\pi$
$440$	3600.00			0.390053
$441$		0			0
$442$	−8064.00			−0.867795
$443$	6626.00	−	11476.6i	0.710634	−	1.23085i	−0.253986	−	0.967208i	$-0.581742\pi$
$443$	6626.00	−	11476.6i	0.710634	−	1.23085i	0.964620	−	0.263646i	$-0.0849250\pi$
$444$	−2709.00	−	4692.13i	−0.289557	−	0.501528i
$445$	4464.00	+	7731.87i	0.475537	+	0.823654i
$446$	2520.00	−	4364.77i	0.267546	−	0.463403i
$447$	−3210.00			−0.339659
$448$		0			0
$449$	226.000			0.0237541			0.0118771	−	0.999929i	$-0.496219\pi$
$449$	226.000			0.0237541			0.0118771	+	0.999929i	$0.496219\pi$
$450$	85.5000	−	148.090i	0.00895669	−	0.0155134i
$451$		0			0
$452$	−385.000	−	666.840i	−0.0400639	−	0.0693927i
$453$	−180.000	+	311.769i	−0.0186692	+	0.0323360i
$454$	−2172.00			−0.224531
$455$		0			0
$456$	−540.000			−0.0554557
$457$	5667.00	−	9815.53i	0.580068	−	1.00471i	−0.415403	−	0.909638i	$-0.636359\pi$
$457$	5667.00	−	9815.53i	0.580068	−	1.00471i	0.995471	−	0.0950696i	$-0.0303074\pi$
$458$	1350.00	+	2338.27i	0.137732	+	0.238559i
$459$	−1296.00	−	2244.74i	−0.131791	−	0.228269i
$460$	−7392.00	+	12803.3i	−0.749247	+	1.29773i
$461$	−1596.00			−0.161243			−0.0806216	−	0.996745i	$-0.525691\pi$
$461$	−1596.00			−0.161243			−0.0806216	+	0.996745i	$0.525691\pi$
$462$		0			0
$463$	12728.0			1.27758			0.638791	−	0.769380i	$-0.279435\pi$
$463$	12728.0			1.27758			0.638791	+	0.769380i	$0.279435\pi$
$464$	−1189.00	+	2059.41i	−0.118961	+	0.206047i
$465$	−4752.00	−	8230.71i	−0.473911	−	0.820838i
$466$	−1901.00	−	3292.63i	−0.188975	−	0.327313i
$467$	1506.00	−	2608.47i	0.149228	−	0.258470i	−0.781715	−	0.623636i	$-0.785655\pi$
$467$	1506.00	−	2608.47i	0.149228	−	0.258470i	0.930942	+	0.365166i	$0.118988\pi$
$468$	5292.00			0.522698
$469$		0			0
$470$	4896.00			0.480501
$471$	2754.00	−	4770.07i	0.269422	−	0.466652i
$472$	−3690.00	−	6391.27i	−0.359843	−	0.623267i
$473$	−1560.00	−	2702.00i	−0.151647	−	0.262660i
$474$	−1164.00	+	2016.11i	−0.112794	+	0.195365i
$475$	228.000			0.0220239
$476$		0			0
$477$	−6498.00			−0.623738
$478$	−2204.00	+	3817.44i	−0.210897	+	0.365284i
$479$	2148.00	+	3720.45i	0.204895	+	0.354888i	0.950099	−	0.311948i	$-0.100981\pi$
$479$	2148.00	+	3720.45i	0.204895	+	0.354888i	−0.745204	+	0.666836i	$0.767648\pi$
$480$	−2898.00	−	5019.48i	−0.275573	−	0.477306i
$481$	10836.0	−	18768.5i	1.02719	−	1.77915i
$482$	−3096.00			−0.292570
$483$		0			0
$484$	6517.00			0.612040
$485$	1008.00	−	1745.91i	0.0943730	−	0.163459i
$486$	−121.500	−	210.444i	−0.0113402	−	0.0196419i
$487$	4092.00	+	7087.55i	0.380752	+	0.659482i	0.991170	−	0.132598i	$-0.0423318\pi$
$487$	4092.00	+	7087.55i	0.380752	+	0.659482i	−0.610418	+	0.792079i	$0.708998\pi$
$488$	3690.00	−	6391.27i	0.342292	−	0.592867i
$489$	−2748.00			−0.254129
$490$		0			0
$491$	−12164.0			−1.11803			−0.559016	−	0.829157i	$-0.688821\pi$
$491$	−12164.0			−1.11803			−0.559016	+	0.829157i	$0.688821\pi$
$492$		0			0
$493$	2784.00	+	4822.03i	0.254331	+	0.440514i
$494$	−504.000	−	872.954i	−0.0459029	−	0.0795062i
$495$	−1080.00	+	1870.61i	−0.0980654	+	0.169854i
$496$	−10824.0			−0.979863
$497$		0			0
$498$	2772.00			0.249430
$499$	−486.000	+	841.777i	−0.0435999	+	0.0755172i	−0.887002	−	0.461766i	$-0.847216\pi$
$499$	−486.000	+	841.777i	−0.0435999	+	0.0755172i	0.843402	+	0.537283i	$0.180549\pi$
$500$	−4452.00	−	7711.09i	−0.398199	−	0.689701i
$501$	756.000	+	1309.43i	0.0674163	+	0.116769i
$502$	−462.000	+	800.207i	−0.0410758	+	0.0711454i
$503$	7728.00			0.685039			0.342519	−	0.939511i	$-0.388720\pi$
$503$	7728.00			0.685039			0.342519	+	0.939511i	$0.388720\pi$
$504$		0			0
$505$	−18288.0			−1.61150
$506$	−1760.00	+	3048.41i	−0.154628	+	0.267823i
$507$	7288.50	+	12624.1i	0.638449	+	1.10583i
$508$	56.0000	+	96.9948i	0.00489094	+	0.00847136i
$509$	−5802.00	+	10049.4i	−0.505244	+	0.875108i	0.494738	+	0.869042i	$0.335264\pi$
$509$	−5802.00	+	10049.4i	−0.505244	+	0.875108i	−0.999982	+	0.00606572i	$0.998069\pi$
$510$	−3456.00			−0.300067
$511$		0			0
$512$	−11521.0			−0.994455
$513$	162.000	−	280.592i	0.0139424	−	0.0241490i
$514$	−1380.00	−	2390.23i	−0.118423	−	0.205114i
$515$	2448.00	+	4240.06i	0.209460	+	0.362795i
$516$	−1638.00	+	2837.10i	−0.139746	+	0.242047i
$517$	−8160.00			−0.694152
$518$		0			0
$519$	5508.00			0.465847
$520$	7560.00	−	13094.3i	0.637554	−	1.10428i
$521$	5424.00	+	9394.64i	0.456103	+	0.789994i	0.998751	−	0.0499665i	$-0.0159115\pi$
$521$	5424.00	+	9394.64i	0.456103	+	0.789994i	−0.542648	+	0.839960i	$0.682578\pi$
$522$	261.000	+	452.065i	0.0218844	+	0.0379049i
$523$	9066.00	−	15702.8i	0.757989	−	1.31288i	−0.185885	−	0.982572i	$-0.559515\pi$
$523$	9066.00	−	15702.8i	0.757989	−	1.31288i	0.943874	−	0.330305i	$-0.107152\pi$
$524$	−11844.0			−0.987419
$525$		0			0
$526$	2360.00			0.195629
$527$	−12672.0	+	21948.5i	−1.04744	+	1.81422i
$528$	1230.00	+	2130.42i	0.101380	+	0.175596i
$529$	−9404.50	−	16289.1i	−0.772951	−	1.33879i
$530$	−4332.00	+	7503.24i	−0.355038	+	0.614944i
$531$	4428.00			0.361881
$532$		0			0
$533$		0			0
$534$	1116.00	−	1932.97i	0.0904383	−	0.156644i
$535$	4920.00	+	8521.69i	0.397589	+	0.688644i
$536$	−3090.00	−	5352.04i	−0.249007	−	0.431293i
$537$	3558.00	−	6162.64i	0.285920	−	0.495228i
$538$	−4020.00			−0.322146
$539$		0			0
$540$	2268.00			0.180739
$541$	−3475.00	+	6018.88i	−0.276159	+	0.478321i	−0.970427	−	0.241395i	$-0.922395\pi$
$541$	−3475.00	+	6018.88i	−0.276159	+	0.478321i	0.694268	+	0.719717i	$0.255728\pi$
$542$	2400.00	+	4156.92i	0.190201	+	0.329437i
$543$	−1638.00	−	2837.10i	−0.129454	−	0.224220i
$544$	−7728.00	+	13385.3i	−0.609072	+	1.05494i
$545$	−11016.0			−0.865823
$546$		0			0
$547$	17012.0			1.32976			0.664882	−	0.746949i	$-0.268482\pi$
$547$	17012.0			1.32976			0.664882	+	0.746949i	$0.268482\pi$
$548$	3941.00	−	6826.01i	0.307210	−	0.532104i
$549$	2214.00	+	3834.76i	0.172115	+	0.298112i
$550$	190.000	+	329.090i	0.0147302	+	0.0255135i
$551$	−348.000	+	602.754i	−0.0269062	+	0.0466028i
$552$	7920.00			0.610684
$553$		0			0
$554$	−6446.00			−0.494340
$555$	4644.00	−	8043.64i	0.355183	−	0.615196i
$556$	3822.00	+	6619.90i	0.291527	+	0.504939i
$557$	−1963.00	−	3400.02i	−0.149327	−	0.258641i	0.781652	−	0.623715i	$-0.214377\pi$
$557$	−1963.00	−	3400.02i	−0.149327	−	0.258641i	−0.930979	+	0.365073i	$0.881044\pi$
$558$	−1188.00	+	2057.68i	−0.0901291	+	0.156108i
$559$	−13104.0			−0.991485
$560$		0			0
$561$	5760.00			0.433489
$562$	−1301.00	+	2253.40i	−0.0976501	+	0.169135i
$563$	9414.00	+	16305.5i	0.704712	+	1.22060i	0.966795	+	0.255552i	$0.0822571\pi$
$563$	9414.00	+	16305.5i	0.704712	+	1.22060i	−0.262084	+	0.965045i	$0.584410\pi$
$564$	4284.00	+	7420.11i	0.319839	+	0.553977i
$565$	660.000	−	1143.15i	0.0491441	−	0.0851201i
$566$	6900.00			0.512418
$567$		0			0
$568$	4440.00			0.327990
$569$	−5995.00	+	10383.6i	−0.441693	+	0.765035i	−0.997815	−	0.0660655i	$-0.978955\pi$
$569$	−5995.00	+	10383.6i	−0.441693	+	0.765035i	0.556122	+	0.831101i	$0.312289\pi$
$570$	−216.000	−	374.123i	−0.0158724	−	0.0274917i
$571$	7858.00	+	13610.5i	0.575914	+	0.997513i	0.995942	+	0.0900014i	$0.0286871\pi$
$571$	7858.00	+	13610.5i	0.575914	+	0.997513i	−0.420027	+	0.907511i	$0.637980\pi$
$572$	−5880.00	+	10184.5i	−0.429817	+	0.744464i
$573$	−7536.00			−0.549426
$574$		0			0
$575$	−3344.00			−0.242529
$576$	751.500	−	1301.64i	0.0543620	−	0.0941577i
$577$	6936.00	+	12013.5i	0.500432	+	0.866774i	1.00000		0.000499291i	$0.000158929\pi$
$577$	6936.00	+	12013.5i	0.500432	+	0.866774i	−0.499568	+	0.866275i	$0.666508\pi$
$578$	2151.50	+	3726.51i	0.154828	+	0.268170i
$579$	−3645.00	+	6313.33i	−0.261625	+	0.453148i
$580$	−4872.00			−0.348791
$581$		0			0
$582$	−504.000			−0.0358960
$583$	7220.00	−	12505.4i	0.512902	−	0.888372i
$584$	−1800.00	−	3117.69i	−0.127542	−	0.220909i
$585$	4536.00	+	7856.58i	0.320582	+	0.555264i
$586$	−2226.00	+	3855.55i	−0.156920	+	0.271794i
$587$	8820.00			0.620171			0.310085	−	0.950709i	$-0.399642\pi$
$587$	8820.00			0.620171			0.310085	+	0.950709i	$0.399642\pi$
$588$		0			0
$589$	−3168.00			−0.221622
$590$	2952.00	−	5113.01i	0.205986	−	0.356779i
$591$	−2643.00	−	4577.81i	−0.183957	−	0.318623i
$592$	−5289.00	−	9160.82i	−0.367190	−	0.635992i
$593$	8436.00	−	14611.6i	0.584191	−	1.01185i	−0.410785	−	0.911732i	$-0.634745\pi$
$593$	8436.00	−	14611.6i	0.584191	−	1.01185i	0.994976	−	0.100116i	$-0.0319213\pi$
$594$	540.000			0.0373005
$595$		0			0
$596$	−7490.00			−0.514769
$597$	4644.00	−	8043.64i	0.318369	−	0.551431i
$598$	7392.00	+	12803.3i	0.505487	+	0.875530i
$599$	3028.00	+	5244.65i	0.206545	+	0.357747i	0.950624	−	0.310345i	$-0.100445\pi$
$599$	3028.00	+	5244.65i	0.206545	+	0.357747i	−0.744079	+	0.668092i	$0.767111\pi$
$600$	427.500	−	740.452i	0.0290877	−	0.0503814i
$601$	10752.0			0.729756			0.364878	−	0.931055i	$-0.381111\pi$
$601$	10752.0			0.729756			0.364878	+	0.931055i	$0.381111\pi$
$602$		0			0
$603$	3708.00			0.250417
$604$	−420.000	+	727.461i	−0.0282940	+	0.0490066i
$605$	5586.00	+	9675.24i	0.375377	+	0.650172i
$606$	2286.00	+	3959.47i	0.153238	+	0.265416i
$607$	−10128.0	+	17542.2i	−0.677237	+	1.17301i	0.298573	+	0.954387i	$0.403489\pi$
$607$	−10128.0	+	17542.2i	−0.677237	+	1.17301i	−0.975810	+	0.218622i	$0.929844\pi$
$608$	−1932.00			−0.128870
$609$		0			0
$610$	5904.00			0.391879
$611$	−17136.0	+	29680.4i	−1.13461	+	1.96521i
$612$	−3024.00	−	5237.72i	−0.199735	−	0.345952i
$613$	14095.0	+	24413.3i	0.928698	+	1.60855i	0.785504	+	0.618857i	$0.212404\pi$
$613$	14095.0	+	24413.3i	0.928698	+	1.60855i	0.143194	+	0.989695i	$0.454263\pi$
$614$	−1218.00	+	2109.64i	−0.0800562	+	0.138661i
$615$		0			0
$616$		0			0
$617$	29318.0			1.91296			0.956482	−	0.291793i	$-0.0942518\pi$
$617$	29318.0			1.91296			0.956482	+	0.291793i	$0.0942518\pi$
$618$	612.000	−	1060.02i	0.0398354	−	0.0689969i
$619$	−12174.0	−	21086.0i	−0.790492	−	1.36917i	−0.925663	−	0.378350i	$-0.876492\pi$
$619$	−12174.0	−	21086.0i	−0.790492	−	1.36917i	0.135171	−	0.990822i	$-0.456842\pi$
$620$	−11088.0	−	19205.0i	−0.718234	−	1.24402i
$621$	−2376.00	+	4115.35i	−0.153536	+	0.265931i
$622$	7488.00			0.482703
$623$		0			0
$624$	10332.0			0.662838
$625$	8819.50	−	15275.8i	0.564448	−	0.977653i
$626$	−876.000	−	1517.28i	−0.0559297	−	0.0968731i
$627$	360.000	+	623.538i	0.0229298	+	0.0397157i
$628$	6426.00	−	11130.2i	0.408321	−	0.707232i
$629$	−24768.0			−1.57006
$630$		0			0
$631$	−25184.0			−1.58884			−0.794421	−	0.607368i	$-0.792226\pi$
$631$	−25184.0			−1.58884			−0.794421	+	0.607368i	$0.792226\pi$
$632$	−5820.00	+	10080.5i	−0.366309	+	0.634465i
$633$	234.000	+	405.300i	0.0146930	+	0.0254490i
$634$	−781.000	−	1352.73i	−0.0489235	−	0.0847379i
$635$	−96.0000	+	166.277i	−0.00599944	+	0.0103913i
$636$	−15162.0			−0.945303
$637$		0			0
$638$	−1160.00			−0.0719825
$639$	−1332.00	+	2307.09i	−0.0824618	+	0.142828i
$640$	−8730.00	−	15120.8i	−0.539193	−	0.933910i
$641$	−16159.0	−	27988.2i	−0.995698	−	1.72460i	−0.578097	−	0.815968i	$-0.696205\pi$
$641$	−16159.0	−	27988.2i	−0.995698	−	1.72460i	−0.417600	−	0.908631i	$-0.637129\pi$
$642$	1230.00	−	2130.42i	0.0756141	−	0.130967i
$643$	−3948.00			−0.242137			−0.121068	−	0.992644i	$-0.538632\pi$
$643$	−3948.00			−0.242137			−0.121068	+	0.992644i	$0.538632\pi$
$644$		0			0
$645$	−5616.00			−0.342837
$646$	−576.000	+	997.661i	−0.0350811	+	0.0607623i
$647$	−6924.00	−	11992.7i	−0.420727	−	0.728721i	0.575284	−	0.817954i	$-0.304892\pi$
$647$	−6924.00	−	11992.7i	−0.420727	−	0.728721i	−0.996011	+	0.0892331i	$0.971558\pi$
$648$	−607.500	−	1052.22i	−0.0368285	−	0.0637888i
$649$	−4920.00	+	8521.69i	−0.297576	+	0.515417i
$650$	1596.00			0.0963081
$651$		0			0
$652$	−6412.00			−0.385143
$653$	1579.00	−	2734.91i	0.0946264	−	0.163898i	−0.814826	−	0.579705i	$-0.803168\pi$
$653$	1579.00	−	2734.91i	0.0946264	−	0.163898i	0.909453	+	0.415808i	$0.136501\pi$
$654$	1377.00	+	2385.03i	0.0823317	+	0.142603i
$655$	−10152.0	−	17583.8i	−0.605605	−	1.04894i
$656$		0			0
$657$	2160.00			0.128264
$658$		0			0
$659$	−24596.0			−1.45391			−0.726953	−	0.686687i	$-0.759064\pi$
$659$	−24596.0			−1.45391			−0.726953	+	0.686687i	$0.759064\pi$
$660$	−2520.00	+	4364.77i	−0.148623	+	0.257422i
$661$	7734.00	+	13395.7i	0.455095	+	0.788248i	0.998694	−	0.0510977i	$-0.0162720\pi$
$661$	7734.00	+	13395.7i	0.455095	+	0.788248i	−0.543599	+	0.839345i	$0.682939\pi$
$662$	−3546.00	−	6141.85i	−0.208186	−	0.360589i
$663$	12096.0	−	20950.9i	0.708552	−	1.22725i
$664$	13860.0			0.810049
$665$		0			0
$666$	−2322.00			−0.135099
$667$	5104.00	−	8840.39i	0.296293	−	0.513195i
$668$	1764.00	+	3055.34i	0.102172	+	0.176968i
$669$	7560.00	+	13094.3i	0.436901	+	0.756734i
$670$	2472.00	−	4281.63i	0.142540	−	0.246886i
$671$	−9840.00			−0.566124
$672$		0			0
$673$	13470.0			0.771516			0.385758	−	0.922600i	$-0.373940\pi$
$673$	13470.0			0.771516			0.385758	+	0.922600i	$0.373940\pi$
$674$	183.000	−	316.965i	0.0104583	−	0.0181143i
$675$	256.500	+	444.271i	0.0146262	+	0.0253333i
$676$	17006.5	+	29456.1i	0.967598	+	1.67593i
$677$	4782.00	−	8282.67i	0.271473	−	0.470205i	−0.697766	−	0.716326i	$-0.745823\pi$
$677$	4782.00	−	8282.67i	0.271473	−	0.470205i	0.969239	+	0.246121i	$0.0791559\pi$
$678$	−330.000			−0.0186926
$679$		0			0
$680$	−17280.0			−0.974497
$681$	3258.00	−	5643.02i	0.183329	−	0.317535i
$682$	−2640.00	−	4572.61i	−0.148227	−	0.256737i
$683$	−6926.00	−	11996.2i	−0.388018	−	0.672066i	0.604165	−	0.796859i	$-0.293507\pi$
$683$	−6926.00	−	11996.2i	−0.388018	−	0.672066i	−0.992183	+	0.124793i	$0.960173\pi$
$684$	378.000	−	654.715i	0.0211304	−	0.0365989i
$685$	13512.0			0.753674
$686$		0			0
$687$	−8100.00			−0.449832
$688$	−3198.00	+	5539.10i	−0.177213	+	0.306942i
$689$	−30324.0	−	52522.7i	−1.67671	−	2.90414i
$690$	3168.00	+	5487.14i	0.174788	+	0.302742i
$691$	162.000	−	280.592i	0.00891863	−	0.0154475i	−0.861532	−	0.507704i	$-0.830494\pi$
$691$	162.000	−	280.592i	0.00891863	−	0.0154475i	0.870450	+	0.492256i	$0.163828\pi$
$692$	12852.0			0.706011
$693$		0			0
$694$	6364.00			0.348090
$695$	−6552.00	+	11348.4i	−0.357599	+	0.619380i
$696$	1305.00	+	2260.33i	0.0710717	+	0.123100i
$697$		0			0
$698$	−5250.00	+	9093.27i	−0.284693	+	0.493102i
$699$	11406.0			0.617188
$700$		0			0
$701$	24922.0			1.34278			0.671392	−	0.741103i	$-0.265697\pi$
$701$	24922.0			1.34278			0.671392	+	0.741103i	$0.265697\pi$
$702$	1134.00	−	1964.15i	0.0609688	−	0.105601i
$703$	−1548.00	−	2681.21i	−0.0830497	−	0.143846i
$704$	1670.00	+	2892.52i	0.0894041	+	0.154852i
$705$	−7344.00	+	12720.2i	−0.392328	+	0.679532i
$706$	−408.000			−0.0217497
$707$		0			0
$708$	10332.0			0.548447
$709$	8943.00	−	15489.7i	0.473711	−	0.820492i	−0.525836	−	0.850586i	$-0.676247\pi$
$709$	8943.00	−	15489.7i	0.473711	−	0.820492i	0.999547	+	0.0300939i	$0.00958064\pi$
$710$	1776.00	+	3076.12i	0.0938762	+	0.162598i
$711$	−3492.00	−	6048.32i	−0.184192	−	0.319029i
$712$	5580.00	−	9664.84i	0.293707	−	0.508715i
$713$	46464.0			2.44052
$714$		0			0
$715$	−20160.0			−1.05446
$716$	8302.00	−	14379.5i	0.433324	−	0.750540i
$717$	−6612.00	−	11452.3i	−0.344393	−	0.596506i
$718$	−5968.00	−	10336.9i	−0.310200	−	0.537283i
$719$	3396.00	−	5882.04i	0.176147	−	0.305095i	−0.764411	−	0.644729i	$-0.776970\pi$
$719$	3396.00	−	5882.04i	0.176147	−	0.305095i	0.940557	+	0.339635i	$0.110303\pi$
$720$	4428.00			0.229197
$721$		0			0
$722$	6715.00			0.346131
$723$	4644.00	−	8043.64i	0.238883	−	0.413757i
$724$	−3822.00	−	6619.90i	−0.196193	−	0.339816i
$725$	−551.000	−	954.360i	−0.0282257	−	0.0488883i
$726$	1396.50	−	2418.81i	0.0713898	−	0.123651i
$727$	1512.00			0.0771348			0.0385674	−	0.999256i	$-0.487721\pi$
$727$	1512.00			0.0771348			0.0385674	+	0.999256i	$0.487721\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	1440.00	−	2494.15i	0.0730093	−	0.126456i
$731$	7488.00	+	12969.6i	0.378870	+	0.656221i
$732$	5166.00	+	8947.77i	0.260848	+	0.451802i
$733$	5622.00	−	9737.59i	0.283292	−	0.490677i	−0.688901	−	0.724855i	$-0.741907\pi$
$733$	5622.00	−	9737.59i	0.283292	−	0.490677i	0.972194	+	0.234178i	$0.0752400\pi$
$734$	2448.00			0.123103
$735$		0			0
$736$	28336.0			1.41913
$737$	−4120.00	+	7136.05i	−0.205919	+	0.356662i
$738$		0			0
$739$	998.000	+	1728.59i	0.0496780	+	0.0860448i	0.889795	−	0.456360i	$-0.150847\pi$
$739$	998.000	+	1728.59i	0.0496780	+	0.0860448i	−0.840117	+	0.542405i	$0.817514\pi$
$740$	10836.0	−	18768.5i	0.538296	−	0.932357i
$741$	3024.00			0.149918
$742$		0			0
$743$	−656.000			−0.0323907			−0.0161954	−	0.999869i	$-0.505155\pi$
$743$	−656.000			−0.0323907			−0.0161954	+	0.999869i	$0.505155\pi$
$744$	−5940.00	+	10288.4i	−0.292703	+	0.506976i
$745$	−6420.00	−	11119.8i	−0.315719	−	0.546841i
$746$	5687.00	+	9850.17i	0.279110	+	0.483432i
$747$	−4158.00	+	7201.87i	−0.203659	+	0.352748i
$748$	13440.0			0.656972
$749$		0			0
$750$	−3816.00			−0.185787
$751$	−528.000	+	914.523i	−0.0256551	+	0.0444360i	−0.878568	−	0.477617i	$-0.841501\pi$
$751$	−528.000	+	914.523i	−0.0256551	+	0.0444360i	0.852913	+	0.522053i	$0.174834\pi$
$752$	8364.00	+	14486.9i	0.405590	+	0.702503i
$753$	−1386.00	−	2400.62i	−0.0670766	−	0.116180i
$754$	−2436.00	+	4219.28i	−0.117658	+	0.203789i
$755$	−1440.00			−0.0694132
$756$		0			0
$757$	−18702.0			−0.897934			−0.448967	−	0.893548i	$-0.648208\pi$
$757$	−18702.0			−0.897934			−0.448967	+	0.893548i	$0.648208\pi$
$758$	−2946.00	+	5102.62i	−0.141166	+	0.244506i
$759$	−5280.00	−	9145.23i	−0.252506	−	0.437353i
$760$	−1080.00	−	1870.61i	−0.0515470	−	0.0892820i
$761$	−8952.00	+	15505.3i	−0.426425	+	0.738590i	−0.996552	−	0.0829661i	$-0.973561\pi$
$761$	−8952.00	+	15505.3i	−0.426425	+	0.738590i	0.570127	+	0.821557i	$0.306894\pi$
$762$	48.0000			0.00228196
$763$		0			0
$764$	−17584.0			−0.832679
$765$	5184.00	−	8978.95i	0.245004	−	0.424359i
$766$	−5244.00	−	9082.87i	−0.247354	−	0.428430i
$767$	20664.0	+	35791.1i	0.972795	+	1.68493i
$768$	−178.500	+	309.171i	−0.00838680	+	0.0145264i
$769$	−7560.00			−0.354513			−0.177257	−	0.984165i	$-0.556722\pi$
$769$	−7560.00			−0.354513			−0.177257	+	0.984165i	$0.556722\pi$
$770$		0			0
$771$	8280.00			0.386766
$772$	−8505.00	+	14731.1i	−0.396505	+	0.686766i
$773$	7146.00	+	12377.2i

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-6.00000 + 10.3923i) q^{5} +3.00000 q^{6} +15.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-6.00000 + 10.3923i) q^{5} +3.00000 q^{6} +15.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(6.00000 + 10.3923i) q^{10} +(-10.0000 - 17.3205i) q^{11} +(-10.5000 + 18.1865i) q^{12} -84.0000 q^{13} -36.0000 q^{15} +(-20.5000 + 35.5070i) q^{16} +(48.0000 + 83.1384i) q^{17} +(4.50000 + 7.79423i) q^{18} +(-6.00000 + 10.3923i) q^{19} -84.0000 q^{20} -20.0000 q^{22} +(88.0000 - 152.420i) q^{23} +(22.5000 + 38.9711i) q^{24} +(-9.50000 - 16.4545i) q^{25} +(-42.0000 + 72.7461i) q^{26} -27.0000 q^{27} +58.0000 q^{29} +(-18.0000 + 31.1769i) q^{30} +(132.000 + 228.631i) q^{31} +(80.5000 + 139.430i) q^{32} +(30.0000 - 51.9615i) q^{33} +96.0000 q^{34} -63.0000 q^{36} +(-129.000 + 223.435i) q^{37} +(6.00000 + 10.3923i) q^{38} +(-126.000 - 218.238i) q^{39} +(-90.0000 + 155.885i) q^{40} +156.000 q^{43} +(70.0000 - 121.244i) q^{44} +(-54.0000 - 93.5307i) q^{45} +(-88.0000 - 152.420i) q^{46} +(204.000 - 353.338i) q^{47} -123.000 q^{48} -19.0000 q^{50} +(-144.000 + 249.415i) q^{51} +(-294.000 - 509.223i) q^{52} +(361.000 + 625.270i) q^{53} +(-13.5000 + 23.3827i) q^{54} +240.000 q^{55} -36.0000 q^{57} +(29.0000 - 50.2295i) q^{58} +(-246.000 - 426.084i) q^{59} +(-126.000 - 218.238i) q^{60} +(246.000 - 426.084i) q^{61} +264.000 q^{62} -167.000 q^{64} +(504.000 - 872.954i) q^{65} +(-30.0000 - 51.9615i) q^{66} +(-206.000 - 356.802i) q^{67} +(-336.000 + 581.969i) q^{68} +528.000 q^{69} +296.000 q^{71} +(-67.5000 + 116.913i) q^{72} +(-120.000 - 207.846i) q^{73} +(129.000 + 223.435i) q^{74} +(28.5000 - 49.3634i) q^{75} -84.0000 q^{76} -252.000 q^{78} +(-388.000 + 672.036i) q^{79} +(-246.000 - 426.084i) q^{80} +(-40.5000 - 70.1481i) q^{81} +924.000 q^{83} -1152.00 q^{85} +(78.0000 - 135.100i) q^{86} +(87.0000 + 150.688i) q^{87} +(-150.000 - 259.808i) q^{88} +(372.000 - 644.323i) q^{89} -108.000 q^{90} +1232.00 q^{92} +(-396.000 + 685.892i) q^{93} +(-204.000 - 353.338i) q^{94} +(-72.0000 - 124.708i) q^{95} +(-241.500 + 418.290i) q^{96} -168.000 q^{97} +180.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} + 7 q^{4} - 12 q^{5} + 6 q^{6} + 30 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 + 7 * q^4 - 12 * q^5 + 6 * q^6 + 30 * q^8 - 9 * q^9	\( 2 q + q^{2} + 3 q^{3} + 7 q^{4} - 12 q^{5} + 6 q^{6} + 30 q^{8} - 9 q^{9} + 12 q^{10} - 20 q^{11} - 21 q^{12} - 168 q^{13} - 72 q^{15} - 41 q^{16} + 96 q^{17} + 9 q^{18} - 12 q^{19} - 168 q^{20} - 40 q^{22} + 176 q^{23} + 45 q^{24} - 19 q^{25} - 84 q^{26} - 54 q^{27} + 116 q^{29} - 36 q^{30} + 264 q^{31} + 161 q^{32} + 60 q^{33} + 192 q^{34} - 126 q^{36} - 258 q^{37} + 12 q^{38} - 252 q^{39} - 180 q^{40} + 312 q^{43} + 140 q^{44} - 108 q^{45} - 176 q^{46} + 408 q^{47} - 246 q^{48} - 38 q^{50} - 288 q^{51} - 588 q^{52} + 722 q^{53} - 27 q^{54} + 480 q^{55} - 72 q^{57} + 58 q^{58} - 492 q^{59} - 252 q^{60} + 492 q^{61} + 528 q^{62} - 334 q^{64} + 1008 q^{65} - 60 q^{66} - 412 q^{67} - 672 q^{68} + 1056 q^{69} + 592 q^{71} - 135 q^{72} - 240 q^{73} + 258 q^{74} + 57 q^{75} - 168 q^{76} - 504 q^{78} - 776 q^{79} - 492 q^{80} - 81 q^{81} + 1848 q^{83} - 2304 q^{85} + 156 q^{86} + 174 q^{87} - 300 q^{88} + 744 q^{89} - 216 q^{90} + 2464 q^{92} - 792 q^{93} - 408 q^{94} - 144 q^{95} - 483 q^{96} - 336 q^{97} + 360 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 + 7 * q^4 - 12 * q^5 + 6 * q^6 + 30 * q^8 - 9 * q^9 + 12 * q^10 - 20 * q^11 - 21 * q^12 - 168 * q^13 - 72 * q^15 - 41 * q^16 + 96 * q^17 + 9 * q^18 - 12 * q^19 - 168 * q^20 - 40 * q^22 + 176 * q^23 + 45 * q^24 - 19 * q^25 - 84 * q^26 - 54 * q^27 + 116 * q^29 - 36 * q^30 + 264 * q^31 + 161 * q^32 + 60 * q^33 + 192 * q^34 - 126 * q^36 - 258 * q^37 + 12 * q^38 - 252 * q^39 - 180 * q^40 + 312 * q^43 + 140 * q^44 - 108 * q^45 - 176 * q^46 + 408 * q^47 - 246 * q^48 - 38 * q^50 - 288 * q^51 - 588 * q^52 + 722 * q^53 - 27 * q^54 + 480 * q^55 - 72 * q^57 + 58 * q^58 - 492 * q^59 - 252 * q^60 + 492 * q^61 + 528 * q^62 - 334 * q^64 + 1008 * q^65 - 60 * q^66 - 412 * q^67 - 672 * q^68 + 1056 * q^69 + 592 * q^71 - 135 * q^72 - 240 * q^73 + 258 * q^74 + 57 * q^75 - 168 * q^76 - 504 * q^78 - 776 * q^79 - 492 * q^80 - 81 * q^81 + 1848 * q^83 - 2304 * q^85 + 156 * q^86 + 174 * q^87 - 300 * q^88 + 744 * q^89 - 216 * q^90 + 2464 * q^92 - 792 * q^93 - 408 * q^94 - 144 * q^95 - 483 * q^96 - 336 * q^97 + 360 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more