LMFDB - Embedded newform 147.4.e.f.67.1

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			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.4.e.f.79.1

$q$-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 $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	0.940775	−	0.339032i	$-0.110100\pi$
$2$	0.500000	+	0.866025i	0.176777	+	0.306186i	−0.763998	+	0.645219i	$0.776766\pi$
$3$	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	−0.999081	−	0.0428575i	$-0.986354\pi$
$5$	−6.00000	−	10.3923i	−0.536656	−	0.929516i	0.462425	−	0.886658i	$-0.346979\pi$
$6$	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	−0.969908	−	0.243472i	$-0.921714\pi$
$11$	−10.0000	+	17.3205i	−0.274101	+	0.474757i	0.695807	+	0.718229i	$0.255047\pi$
$12$	−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	−0.288691	−	0.957422i	$-0.593220\pi$
$17$	48.0000	−	83.1384i	0.684806	−	1.18612i	0.973498	−	0.228697i	$-0.0734466\pi$
$18$	4.50000	−	7.79423i	0.0589256	−	0.102062i
$19$	−6.00000	−	10.3923i	−0.0724471	−	0.125482i	0.827526	−	0.561427i	$-0.189748\pi$
$19$	−6.00000	−	10.3923i	−0.0724471	−	0.125482i	−0.899973	+	0.435945i	$0.856414\pi$
$20$	−84.0000			−0.939149
$21$		0			0
$22$	−20.0000			−0.193819
$23$	88.0000	+	152.420i	0.797794	+	1.38182i	0.921050	+	0.389445i	$0.127333\pi$
$23$	88.0000	+	152.420i	0.797794	+	1.38182i	−0.123255	+	0.992375i	$0.539333\pi$
$24$	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	−0.175597	−	0.984462i	$-0.556185\pi$
$31$	132.000	−	228.631i	0.764771	−	1.32462i	0.940368	−	0.340160i	$-0.110481\pi$
$32$	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	−0.996237	−	0.0866674i	$-0.972378\pi$
$37$	−129.000	−	223.435i	−0.573175	−	0.992768i	0.423062	−	0.906101i	$-0.360955\pi$
$38$	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	0.986911	+	0.161266i	$0.0515578\pi$
$47$	204.000	+	353.338i	0.633116	+	1.09659i	−0.353795	+	0.935323i	$0.615109\pi$
$48$	−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	0.162059	−	0.986781i	$-0.448187\pi$
$53$	361.000	−	625.270i	0.935607	−	1.62052i	0.773548	−	0.633737i	$-0.218480\pi$
$54$	−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	0.455919	+	0.890021i	$0.349311\pi$
$59$	−246.000	+	426.084i	−0.542822	+	0.940195i	−0.998741	+	0.0501732i	$0.984023\pi$
$60$	−126.000	+	218.238i	−0.271109	+	0.469574i
$61$	246.000	+	426.084i	0.516345	+	0.894337i	0.999820	+	0.0189781i	$0.00604127\pi$
$61$	246.000	+	426.084i	0.516345	+	0.894337i	−0.483474	+	0.875358i	$0.660625\pi$
$62$	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	−0.990420	−	0.138085i	$-0.955905\pi$
$67$	−206.000	+	356.802i	−0.375625	+	0.650602i	0.614795	+	0.788687i	$0.289239\pi$
$68$	−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	−0.946044	−	0.324038i	$-0.894959\pi$
$73$	−120.000	+	207.846i	−0.192396	+	0.333240i	0.753647	+	0.657279i	$0.228293\pi$
$74$	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	−0.998088	−	0.0618122i	$-0.980312\pi$
$79$	−388.000	−	672.036i	−0.552575	−	0.957088i	0.445513	−	0.895275i	$-0.353021\pi$
$80$	−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	0.997914	−	0.0645500i	$-0.0205612\pi$
$89$	372.000	+	644.323i	0.443055	+	0.767394i	−0.554859	+	0.831944i	$0.687228\pi$
$90$	−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	−0.196767	−	0.980450i	$-0.563044\pi$
$101$	762.000	−	1319.82i	0.750711	−	1.30027i	0.947478	−	0.319820i	$-0.103622\pi$
$102$	144.000	−	249.415i	0.139786	−	0.242116i
$103$	204.000	+	353.338i	0.195153	+	0.338014i	0.946951	−	0.321379i	$-0.104146\pi$
$103$	204.000	+	353.338i	0.195153	+	0.338014i	−0.751798	+	0.659394i	$0.770813\pi$
$104$	−1260.00			−1.18801
$105$		0			0
$106$	722.000			0.661574
$107$	410.000	+	710.141i	0.370432	+	0.641607i	0.989632	−	0.143627i	$-0.0458764\pi$
$107$	410.000	+	710.141i	0.370432	+	0.641607i	−0.619200	+	0.785233i	$0.712543\pi$
$108$	−94.5000	+	163.679i	−0.0841969	+	0.145833i
$109$	459.000	−	795.011i	0.403342	−	0.698608i	−0.590785	−	0.806829i	$-0.701182\pi$
$109$	459.000	−	795.011i	0.403342	−	0.698608i	0.994127	+	0.108221i	$0.0345153\pi$
$110$	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	−0.997120	−	0.0758401i	$-0.975836\pi$
$131$	−846.000	−	1465.31i	−0.564239	−	0.977291i	0.432881	−	0.901451i	$-0.357497\pi$
$132$	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	−0.986442	−	0.164110i	$-0.947525\pi$
$137$	−563.000	+	975.145i	−0.351097	+	0.608118i	0.635345	+	0.772229i	$0.280858\pi$
$138$	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	0.680634	−	0.732624i	$-0.261704\pi$
$149$	−535.000	−	926.647i	−0.294154	−	0.509489i	−0.974788	+	0.223134i	$0.928371\pi$
$150$	−28.5000	+	49.3634i	−0.0155134	+	0.0268701i
$151$	60.0000	−	103.923i	0.0323360	−	0.0560075i	−0.849405	−	0.527742i	$-0.823039\pi$
$151$	60.0000	−	103.923i	0.0323360	−	0.0560075i	0.881741	+	0.471735i	$0.156372\pi$
$152$	−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	−0.999274	−	0.0380879i	$-0.987873\pi$
$157$	−918.000	+	1590.02i	−0.466652	+	0.808265i	0.532622	+	0.846353i	$0.321207\pi$
$158$	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	0.734751	−	0.678337i	$-0.237299\pi$
$163$	−458.000	−	793.279i	−0.220082	−	0.381193i	−0.954833	+	0.297144i	$0.903966\pi$
$164$		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	0.994138	−	0.108119i	$-0.0344828\pi$
$173$	918.000	+	1590.02i	0.403435	+	0.698770i	−0.590703	+	0.806889i	$0.701149\pi$
$174$	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	−0.999985	−	0.00550156i	$-0.998249\pi$
$179$	−1186.00	+	2054.21i	−0.495228	+	0.857760i	0.504757	+	0.863262i	$0.331582\pi$
$180$	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	0.523800	−	0.851842i	$-0.324514\pi$
$191$	−1256.00	−	2175.46i	−0.475817	−	0.824139i	−0.999616	+	0.0277030i	$0.991181\pi$
$192$	−250.500	+	433.879i	−0.0941577	+	0.163086i
$193$	1215.00	−	2104.44i	0.453148	−	0.784876i	−0.545431	−	0.838155i	$-0.683634\pi$
$193$	1215.00	−	2104.44i	0.453148	−	0.784876i	0.998580	+	0.0532797i	$0.0169675\pi$
$194$	−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	0.446740	+	0.894664i	$0.352585\pi$
$199$	−1548.00	+	2681.21i	−0.551431	+	0.955107i	−0.998172	+	0.0604433i	$0.980749\pi$
$200$	−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	−0.979973	−	0.199130i	$-0.936188\pi$
$227$	−1086.00	+	1881.01i	−0.317535	+	0.549986i	0.662438	+	0.749116i	$0.269522\pi$
$228$	−126.000	+	218.238i	−0.0365989	+	0.0633912i
$229$	−1350.00	−	2338.27i	−0.389566	−	0.674747i	0.602826	−	0.797873i	$-0.294041\pi$
$229$	−1350.00	−	2338.27i	−0.389566	−	0.674747i	−0.992391	+	0.123126i	$0.960708\pi$
$230$	2112.00			0.605483
$231$		0			0
$232$	870.000			0.246200
$233$	1901.00	+	3292.63i	0.534501	+	0.925782i	0.999187	+	0.0403071i	$0.0128336\pi$
$233$	1901.00	+	3292.63i	0.534501	+	0.925782i	−0.464687	+	0.885475i	$0.653833\pi$
$234$	−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	−0.995297	−	0.0968696i	$-0.969117\pi$
$241$	−1548.00	+	2681.21i	−0.413757	+	0.716648i	0.581540	+	0.813518i	$0.302450\pi$
$242$	−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	0.983475	−	0.181043i	$-0.0579474\pi$
$257$	1380.00	+	2390.23i	0.334950	+	0.580150i	−0.648526	+	0.761193i	$0.724614\pi$
$258$	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	−0.693892	−	0.720079i	$-0.744105\pi$
$263$	1180.00	−	2043.82i	0.276661	−	0.479191i	0.970553	+	0.240888i	$0.0774387\pi$
$264$	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	−0.998722	−	0.0505501i	$-0.983903\pi$
$269$	−2010.00	+	3481.42i	−0.455583	+	0.789093i	0.543138	+	0.839643i	$0.317236\pi$
$270$	−162.000	+	280.592i	−0.0365148	+	0.0632456i
$271$	−2400.00	−	4156.92i	−0.537969	−	0.931790i	−0.999013	−	0.0444126i	$-0.985858\pi$
$271$	−2400.00	−	4156.92i	−0.537969	−	0.931790i	0.461044	−	0.887377i	$-0.347475\pi$
$272$	−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	0.269676	+	0.962951i	$0.413083\pi$
$277$	−3223.00	+	5582.40i	−0.699102	+	1.21088i	−0.968778	+	0.247929i	$0.920250\pi$
$278$	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	−0.234442	−	0.972130i	$-0.575326\pi$
$283$	3450.00	−	5975.58i	0.724669	−	1.25516i	0.959110	−	0.283033i	$-0.0913405\pi$
$284$	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	−0.291525	−	0.956563i	$-0.594163\pi$
$311$	3744.00	−	6484.80i	0.682646	−	1.18238i	0.974171	−	0.225814i	$-0.0725040\pi$
$312$	−1890.00	+	3273.58i	−0.342949	+	0.594006i
$313$	876.000	+	1517.28i	0.158193	+	0.273999i	0.934217	−	0.356705i	$-0.116100\pi$
$313$	876.000	+	1517.28i	0.158193	+	0.273999i	−0.776024	+	0.630703i	$0.782766\pi$
$314$	−1836.00			−0.329973
$315$		0			0
$316$	−5432.00			−0.967006
$317$	781.000	+	1352.73i	0.138376	+	0.239675i	0.926882	−	0.375352i	$-0.122478\pi$
$317$	781.000	+	1352.73i	0.138376	+	0.239675i	−0.788506	+	0.615027i	$0.789145\pi$
$318$	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	0.994385	+	0.105825i	$0.0337482\pi$
$331$	3546.00	+	6141.85i	0.588839	+	1.01990i	−0.405546	+	0.914075i	$0.632918\pi$
$332$	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	−0.507687	−	0.861541i	$-0.669500\pi$
$347$	3182.00	−	5511.39i	0.492273	−	0.852642i	0.999960	+	0.00889958i	$0.00283286\pi$
$348$	−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	−0.880995	−	0.473126i	$-0.843126\pi$
$353$	−204.000	+	353.338i	−0.0307587	+	0.0532756i	0.850236	+	0.526401i	$0.176459\pi$
$354$	−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	0.854207	+	0.519933i	$0.174043\pi$
$359$	5968.00	+	10336.9i	0.877379	+	1.51966i	0.0231719	+	0.999731i	$0.492624\pi$
$360$	−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	−0.765754	−	0.643134i	$-0.777634\pi$
$367$	1224.00	−	2120.03i	0.174093	−	0.301539i	0.939847	+	0.341595i	$0.110967\pi$
$368$	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	−0.926309	−	0.376764i	$-0.877037\pi$
$373$	−5687.00	−	9850.17i	−0.789442	−	1.36735i	0.136868	−	0.990589i	$-0.456296\pi$
$374$	−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	0.968597	+	0.248636i	$0.0799823\pi$
$383$	5244.00	+	9082.87i	0.699624	+	1.21178i	−0.268973	+	0.963148i	$0.586684\pi$
$384$	−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	−0.974793	−	0.223112i	$-0.928379\pi$
$389$	−2257.00	+	3909.24i	−0.294176	+	0.509528i	0.680617	+	0.732639i	$0.261712\pi$
$390$	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	0.991282	−	0.131759i	$-0.0420625\pi$
$397$	3018.00	+	5227.33i	0.381534	+	0.660837i	−0.609748	+	0.792596i	$0.708729\pi$
$398$	−3096.00			−0.389921
$399$		0			0
$400$	779.000			0.0973750
$401$	3385.00	+	5862.99i	0.421543	+	0.730134i	0.996091	−	0.0883370i	$-0.0281552\pi$
$401$	3385.00	+	5862.99i	0.421543	+	0.730134i	−0.574547	+	0.818471i	$0.694822\pi$
$402$	−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	0.189105	+	0.981957i	$0.439441\pi$
$409$	−6252.00	+	10828.8i	−0.755847	+	1.30917i	−0.944952	+	0.327209i	$0.893892\pi$
$410$		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	−0.660779	−	0.750580i	$-0.729774\pi$
$431$	2860.00	−	4953.67i	0.319632	−	0.553619i	0.980411	+	0.196962i	$0.0631074\pi$
$432$	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	−0.968717	−	0.248166i	$-0.920172\pi$
$439$	−6432.00	−	11140.6i	−0.699277	−	1.21118i	0.269440	−	0.963017i	$-0.413161\pi$
$440$	3600.00			0.390053
$441$		0			0
$442$	−8064.00			−0.867795
$443$	6626.00	+	11476.6i	0.710634	+	1.23085i	0.964620	+	0.263646i	$0.0849250\pi$
$443$	6626.00	+	11476.6i	0.710634	+	1.23085i	−0.253986	+	0.967208i	$0.581742\pi$
$444$	−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	0.995471	+	0.0950696i	$0.0303074\pi$
$457$	5667.00	+	9815.53i	0.580068	+	1.00471i	−0.415403	+	0.909638i	$0.636359\pi$
$458$	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	0.930942	−	0.365166i	$-0.118988\pi$
$467$	1506.00	+	2608.47i	0.149228	+	0.258470i	−0.781715	+	0.623636i	$0.785655\pi$
$468$	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	−0.745204	−	0.666836i	$-0.767648\pi$
$479$	2148.00	−	3720.45i	0.204895	−	0.354888i	0.950099	+	0.311948i	$0.100981\pi$
$480$	−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	−0.610418	−	0.792079i	$-0.708998\pi$
$487$	4092.00	−	7087.55i	0.380752	−	0.659482i	0.991170	+	0.132598i	$0.0423318\pi$
$488$	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	0.843402	−	0.537283i	$-0.180549\pi$
$499$	−486.000	−	841.777i	−0.0435999	−	0.0755172i	−0.887002	+	0.461766i	$0.847216\pi$
$500$	−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	−0.999982	−	0.00606572i	$-0.998069\pi$
$509$	−5802.00	−	10049.4i	−0.505244	−	0.875108i	0.494738	−	0.869042i	$-0.335264\pi$
$510$	−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	−0.542648	−	0.839960i	$-0.682578\pi$
$521$	5424.00	−	9394.64i	0.456103	−	0.789994i	0.998751	+	0.0499665i	$0.0159115\pi$
$522$	261.000	−	452.065i	0.0218844	−	0.0379049i
$523$	9066.00	+	15702.8i	0.757989	+	1.31288i	0.943874	+	0.330305i	$0.107152\pi$
$523$	9066.00	+	15702.8i	0.757989	+	1.31288i	−0.185885	+	0.982572i	$0.559515\pi$
$524$	−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	0.694268	−	0.719717i	$-0.255728\pi$
$541$	−3475.00	−	6018.88i	−0.276159	−	0.478321i	−0.970427	+	0.241395i	$0.922395\pi$
$542$	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	−0.930979	−	0.365073i	$-0.881044\pi$
$557$	−1963.00	+	3400.02i	−0.149327	+	0.258641i	0.781652	+	0.623715i	$0.214377\pi$
$558$	−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	−0.262084	−	0.965045i	$-0.584410\pi$
$563$	9414.00	−	16305.5i	0.704712	−	1.22060i	0.966795	−	0.255552i	$-0.0822571\pi$
$564$	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	0.556122	−	0.831101i	$-0.312289\pi$
$569$	−5995.00	−	10383.6i	−0.441693	−	0.765035i	−0.997815	+	0.0660655i	$0.978955\pi$
$570$	−216.000	+	374.123i	−0.0158724	+	0.0274917i
$571$	7858.00	−	13610.5i	0.575914	−	0.997513i	−0.420027	−	0.907511i	$-0.637980\pi$
$571$	7858.00	−	13610.5i	0.575914	−	0.997513i	0.995942	−	0.0900014i	$-0.0286871\pi$
$572$	−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	−0.499568	−	0.866275i	$-0.666508\pi$
$577$	6936.00	−	12013.5i	0.500432	−	0.866774i	1.00000		0.000499291i	$-0.000158929\pi$
$578$	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	0.994976	+	0.100116i	$0.0319213\pi$
$593$	8436.00	+	14611.6i	0.584191	+	1.01185i	−0.410785	+	0.911732i	$0.634745\pi$
$594$	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	−0.744079	−	0.668092i	$-0.767111\pi$
$599$	3028.00	−	5244.65i	0.206545	−	0.357747i	0.950624	+	0.310345i	$0.100445\pi$
$600$	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	−0.975810	−	0.218622i	$-0.929844\pi$
$607$	−10128.0	−	17542.2i	−0.677237	−	1.17301i	0.298573	−	0.954387i	$-0.403489\pi$
$608$	−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	0.143194	−	0.989695i	$-0.454263\pi$
$613$	14095.0	−	24413.3i	0.928698	−	1.60855i	0.785504	−	0.618857i	$-0.212404\pi$
$614$	−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	0.135171	+	0.990822i	$0.456842\pi$
$619$	−12174.0	+	21086.0i	−0.790492	+	1.36917i	−0.925663	+	0.378350i	$0.876492\pi$
$620$	−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	−0.417600	+	0.908631i	$0.637129\pi$
$641$	−16159.0	+	27988.2i	−0.995698	+	1.72460i	−0.578097	+	0.815968i	$0.696205\pi$
$642$	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	−0.996011	−	0.0892331i	$-0.971558\pi$
$647$	−6924.00	+	11992.7i	−0.420727	+	0.728721i	0.575284	+	0.817954i	$0.304892\pi$
$648$	−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	0.909453	−	0.415808i	$-0.136501\pi$
$653$	1579.00	+	2734.91i	0.0946264	+	0.163898i	−0.814826	+	0.579705i	$0.803168\pi$
$654$	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	−0.543599	−	0.839345i	$-0.682939\pi$
$661$	7734.00	−	13395.7i	0.455095	−	0.788248i	0.998694	+	0.0510977i	$0.0162720\pi$
$662$	−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	0.969239	−	0.246121i	$-0.0791559\pi$
$677$	4782.00	+	8282.67i	0.271473	+	0.470205i	−0.697766	+	0.716326i	$0.745823\pi$
$678$	−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	−0.992183	−	0.124793i	$-0.960173\pi$
$683$	−6926.00	+	11996.2i	−0.388018	+	0.672066i	0.604165	+	0.796859i	$0.293507\pi$
$684$	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	0.870450	−	0.492256i	$-0.163828\pi$
$691$	162.000	+	280.592i	0.00891863	+	0.0154475i	−0.861532	+	0.507704i	$0.830494\pi$
$692$	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	0.999547	−	0.0300939i	$-0.00958064\pi$
$709$	8943.00	+	15489.7i	0.473711	+	0.820492i	−0.525836	+	0.850586i	$0.676247\pi$
$710$	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	0.940557	−	0.339635i	$-0.110303\pi$
$719$	3396.00	+	5882.04i	0.176147	+	0.305095i	−0.764411	+	0.644729i	$0.776970\pi$
$720$	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	0.972194	−	0.234178i	$-0.0752400\pi$
$733$	5622.00	+	9737.59i	0.283292	+	0.490677i	−0.688901	+	0.724855i	$0.741907\pi$
$734$	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	−0.840117	−	0.542405i	$-0.817514\pi$
$739$	998.000	−	1728.59i	0.0496780	−	0.0860448i	0.889795	+	0.456360i	$0.150847\pi$
$740$	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	0.852913	−	0.522053i	$-0.174834\pi$
$751$	−528.000	−	914.523i	−0.0256551	−	0.0444360i	−0.878568	+	0.477617i	$0.841501\pi$
$752$	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	0.570127	−	0.821557i	$-0.306894\pi$
$761$	−8952.00	−	15505.3i	−0.426425	−	0.738590i	−0.996552	+	0.0829661i	$0.973561\pi$
$762$	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	0.332502	−	0.575910i	−0.650500	−	0.759506i	$-0.725441\pi$
$773$	7146.00	−	12377.2i	0.332502	−	0.575910i	0.983002	+	0.183596i	$0.0587740\pi$
$774$	702.000	−	1215.90i	0.0326006	−	0.0564659i
$775$	2508.00	+	4343.98i	0.116245	+	0.201343i
$776$	−2520.00			−0.116576
$777$		0			0
$778$	−4514.00			−0.208014
$779$		0			0
$780$	10584.0	−	18332.0i	0.485856	−	0.841528i
$781$	−2960.00	+	5126.87i	−0.135617	+	0.234896i
$782$	8448.00	+	14632.4i	0.386317	+	0.669121i
$783$	−1566.00			−0.0714742
$784$		0			0
$785$	22032.0			1.00173
$786$	−2538.00	−	4395.94i	−0.115175	−	0.199489i
$787$	−13182.0	+	22831.9i	−0.597062	+	1.03414i	0.396191	+	0.918168i	$0.370332\pi$
$787$	−13182.0	+	22831.9i	−0.597062	+	1.03414i	−0.993252	+	0.115973i	$0.963001\pi$
$788$	−6167.00	+	10681.6i	−0.278795	+	0.482887i
$789$	−3540.00	−	6131.46i	−0.159730	−	0.276661i
$790$	−9312.00			−0.419375
$791$		0			0
$792$	2700.00			0.121137
$793$	−20664.0	−	35791.1i	−0.925347	−	1.60275i
$794$	−3018.00	+	5227.33i	−0.134893	+	0.233641i
$795$	−12996.0	+	22509.7i	−0.579774	+	1.00420i
$796$	10836.0	+	18768.5i	0.482502	+	0.835719i
$797$	17220.0			0.765325			0.382662	−	0.923888i	$-0.375007\pi$
$797$	17220.0			0.765325			0.382662	+	0.923888i	$0.375007\pi$
$798$		0			0
$799$	39168.0			1.73425
$800$	1529.50	+	2649.17i	0.0675950	+	0.117078i
$801$	3348.00	−	5798.91i	0.147685	−	0.255798i
$802$	−3385.00	+	5862.99i	−0.149038	+	0.258141i
$803$	−2400.00	−	4156.92i	−0.105472	−	0.182683i
$804$	8652.00			0.379518
$805$		0			0
$806$	−22176.0			−0.969127
$807$	6030.00	+	10444.3i	0.263031	+	0.455583i
$808$	11430.0	−	19797.3i	0.497656	−	0.861965i
$809$	−8221.00	+	14239.2i	−0.357274	+	0.618817i	−0.987504	−	0.157591i	$-0.949627\pi$
$809$	−8221.00	+	14239.2i	−0.357274	+	0.618817i	0.630230	+	0.776408i	$0.282961\pi$
$810$	486.000	+	841.777i	0.0210819	+	0.0365148i
$811$	−31332.0			−1.35662			−0.678308	−	0.734778i	$-0.737286\pi$
$811$	−31332.0			−1.35662			−0.678308	+	0.734778i	$0.737286\pi$
$812$		0			0
$813$	−14400.0			−0.621193
$814$	2580.00	+	4468.69i	0.111092	+	0.192417i
$815$	−5496.00	+	9519.35i	−0.236217	+	0.409139i
$816$	−5904.00	+	10226.0i	−0.253286	+	0.438704i
$817$	−936.000	−	1621.20i	−0.0400814	−	0.0694230i
$818$	−12504.0			−0.534465
$819$		0			0
$820$		0			0
$821$	12905.0	+	22352.1i	0.548584	+	0.950176i	0.998372	+	0.0570402i	$0.0181663\pi$
$821$	12905.0	+	22352.1i	0.548584	+	0.950176i	−0.449788	+	0.893135i	$0.648500\pi$
$822$	−1689.00	+	2925.43i	−0.0716674	+	0.124132i
$823$	−6184.00	+	10711.0i	−0.261921	+	0.453660i	−0.966752	−	0.255715i	$-0.917689\pi$
$823$	−6184.00	+	10711.0i	−0.261921	+	0.453660i	0.704832	+	0.709375i	$0.251023\pi$
$824$	3060.00	+	5300.08i	0.129369	+	0.224074i
$825$	−1140.00			−0.0481087
$826$		0			0
$827$	6316.00			0.265573			0.132786	−	0.991145i	$-0.457608\pi$
$827$	6316.00			0.265573			0.132786	+	0.991145i	$0.457608\pi$
$828$	−5544.00	−	9602.49i	−0.232690	−	0.403031i
$829$	11934.0	−	20670.3i	0.499982	−	0.865994i	−0.500018	−	0.866015i	$-0.666673\pi$
$829$	11934.0	−	20670.3i	0.499982	−	0.865994i	1.00000		2.09597e-5i	$6.67166e-6\pi$
$830$	5544.00	−	9602.49i	0.231849	−	0.401575i
$831$	9669.00	+	16747.2i	0.403627	+	0.699102i
$832$	14028.0			0.584535
$833$		0			0
$834$	3276.00			0.136018
$835$	−3024.00	−	5237.72i	−0.125329	−	0.217076i
$836$	840.000	−	1454.92i	0.0347512	−	0.0601909i
$837$	−3564.00	+	6173.03i	−0.147180	+	0.254924i
$838$	4746.00	+	8220.31i	0.195642	+	0.338862i
$839$	−48216.0			−1.98403			−0.992015	−	0.126120i	$-0.959748\pi$
$839$	−48216.0			−1.98403			−0.992015	+	0.126120i	$0.959748\pi$
$840$		0			0
$841$	−21025.0			−0.862069
$842$	2591.00	+	4487.74i	0.106047	+	0.183679i
$843$	−3903.00	+	6760.19i	−0.159462	+	0.276196i
$844$	546.000	−	945.700i	0.0222679	−	0.0385691i
$845$	−29154.0	−	50496.2i	−1.18690	−	2.05577i
$846$	3672.00			0.149227
$847$		0			0
$848$	−29602.0			−1.19875
$849$	−10350.0	−	17926.7i	−0.418388	−	0.724669i
$850$	−912.000	+	1579.63i	−0.0368016	+	0.0637422i
$851$	22704.0	−	39324.5i	0.914551	−	1.58405i
$852$	−3108.00	−	5383.21i	−0.124975	−	0.216462i
$853$	−27300.0			−1.09582			−0.547910	−	0.836537i	$-0.684576\pi$
$853$	−27300.0			−1.09582			−0.547910	+	0.836537i	$0.684576\pi$
$854$		0			0
$855$	1296.00			0.0518389
$856$	6150.00	+	10652.1i	0.245564	+	0.425329i
$857$	−4320.00	+	7482.46i	−0.172192	+	0.298245i	−0.939186	−	0.343409i	$-0.888418\pi$
$857$	−4320.00	+	7482.46i	−0.172192	+	0.298245i	0.766994	+	0.641654i	$0.221752\pi$
$858$	2520.00	−	4364.77i	0.100270	−	0.173672i
$859$	−12186.0	−	21106.8i	−0.484029	−	0.838363i	0.515803	−	0.856707i	$-0.327494\pi$
$859$	−12186.0	−	21106.8i	−0.484029	−	0.838363i	−0.999832	+	0.0183445i	$0.994160\pi$
$860$	−13104.0			−0.519585
$861$		0			0
$862$	5720.00			0.226014
$863$	−1088.00	−	1884.47i	−0.0429154	−	0.0743316i	0.843770	−	0.536705i	$-0.180331\pi$
$863$	−1088.00	−	1884.47i	−0.0429154	−	0.0743316i	−0.886685	+	0.462374i	$0.846998\pi$
$864$	−2173.50	+	3764.61i	−0.0855833	+	0.148235i
$865$	11016.0	−	19080.3i	0.433012	−	0.749998i
$866$	6804.00	+	11784.9i	0.266985	+	0.462432i
$867$	−12909.0			−0.505666
$868$		0			0
$869$	15520.0			0.605846
$870$	−1044.00	−	1808.26i	−0.0406838	−	0.0704664i
$871$	17304.0	−	29971.4i	0.673162	−	1.16595i
$872$	6885.00	−	11925.2i	0.267380	−	0.463116i
$873$	756.000	+	1309.43i	0.0293090	+	0.0507646i
$874$	2112.00			0.0817385
$875$		0			0
$876$	5040.00			0.194390
$877$	13787.0	+	23879.8i	0.530848	+	0.919456i	0.999352	+	0.0359946i	$0.0114599\pi$
$877$	13787.0	+	23879.8i	0.530848	+	0.919456i	−0.468504	+	0.883462i	$0.655207\pi$
$878$	6432.00	−	11140.6i	0.247232	−	0.428218i
$879$	−6678.00	+	11566.6i	−0.256250	+	0.443837i
$880$	−4920.00	−	8521.69i	−0.188470	−	0.326439i
$881$	16968.0			0.648884			0.324442	−	0.945906i	$-0.394824\pi$
$881$	16968.0			0.648884			0.324442	+	0.945906i	$0.394824\pi$
$882$		0			0
$883$	−1860.00			−0.0708879			−0.0354439	−	0.999372i	$-0.511285\pi$
$883$	−1860.00			−0.0708879			−0.0354439	+	0.999372i	$0.511285\pi$
$884$	28224.0	+	48885.4i	1.07384	+	1.85995i
$885$	8856.00	−	15339.0i	0.336374	−	0.582617i
$886$	−6626.00	+	11476.6i	−0.251247	+	0.435173i
$887$	−1140.00	−	1974.54i	−0.0431538	−	0.0747446i	0.843642	−	0.536907i	$-0.180407\pi$
$887$	−1140.00	−	1974.54i	−0.0431538	−	0.0747446i	−0.886796	+	0.462162i	$0.847074\pi$
$888$	−11610.0			−0.438746
$889$		0			0
$890$	8928.00			0.336255
$891$	−810.000	−	1402.96i	−0.0304557	−	0.0527508i
$892$	17640.0	−	30553.4i	0.662142	−	1.14686i
$893$	2448.00	−	4240.06i	0.0917348	−	0.158889i
$894$	−1605.00	−	2779.94i	−0.0600439	−	0.103999i
$895$	28464.0			1.06307
$896$		0			0
$897$	−44352.0			−1.65091
$898$	113.000	+	195.722i	0.00419917	+	0.00727318i
$899$	7656.00	−	13260.6i	0.284029	−	0.491952i
$900$	598.500	−	1036.63i	0.0221667	−	0.0383938i
$901$	−34656.0	−	60026.0i	−1.28142	−	2.21948i
$902$		0			0
$903$		0			0
$904$	−1650.00			−0.0607060
$905$	6552.00	+	11348.4i	0.240658	+	0.416833i
$906$	180.000	−	311.769i	0.00660055	−	0.0114325i
$907$	−18042.0	+	31249.7i	−0.660501	+	1.14402i	0.319983	+	0.947423i	$0.396323\pi$
$907$	−18042.0	+	31249.7i	−0.660501	+	1.14402i	−0.980484	+	0.196599i	$0.937010\pi$
$908$	7602.00	+	13167.1i	0.277843	+	0.481238i
$909$	−13716.0			−0.500474
$910$		0			0
$911$	24152.0			0.878366			0.439183	−	0.898398i	$-0.355268\pi$
$911$	24152.0			0.878366			0.439183	+	0.898398i	$0.355268\pi$
$912$	738.000	+	1278.25i	0.0267956	+	0.0464114i
$913$	−9240.00	+	16004.1i	−0.334939	+	0.580131i
$914$	−5667.00	+	9815.53i	−0.205085	+	0.355218i
$915$	−8856.00	−	15339.0i	−0.319968	−	0.554200i
$916$	−18900.0			−0.681740
$917$		0			0
$918$	−2592.00			−0.0931904
$919$	−18168.0	−	31467.9i	−0.652130	−	1.12952i	−0.982605	−	0.185707i	$-0.940542\pi$
$919$	−18168.0	−	31467.9i	−0.652130	−	1.12952i	0.330476	−	0.943815i	$-0.392791\pi$
$920$	15840.0	−	27435.7i	0.567641	−	0.983182i
$921$	−3654.00	+	6328.91i	−0.130731	+	0.226433i
$922$	−798.000	−	1382.18i	−0.0285040	−	0.0493705i
$923$	−24864.0			−0.886683
$924$		0			0
$925$	4902.00			0.174245
$926$	6364.00	+	11022.8i	0.225847	+	0.391178i
$927$	1836.00	−	3180.05i	0.0650509	−	0.112671i
$928$	4669.00	−	8086.95i	0.165159	−	0.286064i
$929$	−216.000	−	374.123i	−0.00762834	−	0.0132127i	0.862186	−	0.506592i	$-0.169095\pi$
$929$	−216.000	−	374.123i	−0.00762834	−	0.0132127i	−0.869814	+	0.493379i	$0.835762\pi$
$930$	−9504.00			−0.335106
$931$		0			0
$932$	26614.0			0.935376
$933$	−11232.0	−	19454.4i	−0.394126	−	0.682646i
$934$	−1506.00	+	2608.47i	−0.0527600	+	0.0913830i
$935$	11520.0	−	19953.2i	0.402935	−	0.697904i
$936$	5670.00	+	9820.73i	0.198002	+	0.342949i
$937$	22176.0			0.773168			0.386584	−	0.922254i	$-0.373655\pi$
$937$	22176.0			0.773168			0.386584	+	0.922254i	$0.373655\pi$
$938$		0			0
$939$	5256.00			0.182666
$940$	−17136.0	−	29680.4i	−0.594590	−	1.02986i
$941$	21762.0	−	37692.9i	0.753901	−	1.30579i	−0.192018	−	0.981391i	$-0.561503\pi$
$941$	21762.0	−	37692.9i	0.753901	−	1.30579i	0.945919	−	0.324404i	$-0.105164\pi$
$942$	−2754.00	+	4770.07i	−0.0952550	+	0.164986i
$943$		0			0
$944$	20172.0			0.695490
$945$		0			0
$946$	−3120.00			−0.107230
$947$	−934.000	−	1617.74i	−0.0320495	−	0.0555114i	0.849556	−	0.527499i	$-0.176870\pi$
$947$	−934.000	−	1617.74i	−0.0320495	−	0.0555114i	−0.881605	+	0.471987i	$0.843537\pi$
$948$	−8148.00	+	14112.7i	−0.279151	+	0.483503i
$949$	10080.0	−	17459.1i	0.344795	−	0.597203i
$950$	114.000	+	197.454i	0.00389331	+	0.00674342i
$951$	4686.00			0.159783
$952$		0			0
$953$	−9238.00			−0.314006			−0.157003	−	0.987598i	$-0.550183\pi$
$953$	−9238.00			−0.314006			−0.157003	+	0.987598i	$0.550183\pi$
$954$	−3249.00	−	5627.43i	−0.110262	−	0.190980i
$955$	−15072.0	+	26105.5i	−0.510700	+	0.884558i
$956$	−15428.0	+	26722.1i	−0.521943	+	0.904031i
$957$	1740.00	+	3013.77i	0.0587735	+	0.101799i
$958$	4296.00			0.144883
$959$		0			0
$960$	6012.00			0.202121
$961$	−19952.5	−	34558.7i	−0.669749	−	1.16004i
$962$	−10836.0	+	18768.5i	−0.363167	+	0.629024i
$963$	3690.00	−	6391.27i	0.123477	−	0.213869i
$964$	10836.0	+	18768.5i	0.362037	+	0.627067i
$965$	−29160.0			−0.972739
$966$		0			0
$967$	−30616.0			−1.01814			−0.509071	−	0.860724i	$-0.670011\pi$
$967$	−30616.0			−1.01814			−0.509071	+	0.860724i	$0.670011\pi$
$968$	6982.50	+	12094.0i	0.231845	+	0.401567i
$969$	−1728.00	+	2992.98i	−0.0572873	+	0.0992244i
$970$	−1008.00	+	1745.91i	−0.0333659	+	0.0577914i
$971$	13770.0	+	23850.3i	0.455098	+	0.788253i	0.998694	−	0.0510941i	$-0.0162708\pi$
$971$	13770.0	+	23850.3i	0.455098	+	0.788253i	−0.543596	+	0.839347i	$0.682937\pi$
$972$	1701.00			0.0561313
$973$		0			0
$974$	8184.00			0.269232
$975$	−2394.00	−	4146.53i	−0.0786352	−	0.136200i
$976$	10086.0	−	17469.5i	0.330784	−	0.572934i
$977$	8201.00	−	14204.5i	0.268550	−	0.465142i	−0.699938	−	0.714204i	$-0.746789\pi$
$977$	8201.00	−	14204.5i	0.268550	−	0.465142i	0.968488	+	0.249062i	$0.0801223\pi$
$978$	−1374.00	−	2379.84i	−0.0449240	−	0.0778107i
$979$	−14880.0			−0.485768
$980$		0			0
$981$	−8262.00			−0.268894
$982$	−6082.00	−	10534.3i	−0.197642	−	0.342326i
$983$	−27588.0	+	47783.8i	−0.895138	+	1.55042i	−0.0615040	+	0.998107i	$0.519590\pi$
$983$	−27588.0	+	47783.8i	−0.895138	+	1.55042i	−0.833634	+	0.552317i	$0.813744\pi$
$984$		0			0
$985$	10572.0	+	18311.2i	0.341982	+	0.592330i
$986$	5568.00			0.179839
$987$		0			0
$988$	7056.00			0.227208
$989$	13728.0	+	23777.6i	0.441380	+	0.764493i
$990$	1080.00	−	1870.61i	0.0346714	−	0.0600526i
$991$	−13548.0	+	23465.8i	−0.434275	+	0.752186i	−0.997236	−	0.0742971i	$-0.976329\pi$
$991$	−13548.0	+	23465.8i	−0.434275	+	0.752186i	0.562961	+	0.826483i	$0.309662\pi$
$992$	−21252.0	−	36809.5i	−0.680193	−	1.17813i
$993$	21276.0			0.679933
$994$		0			0
$995$	37152.0			1.18372
$996$	−9702.00	−	16804.4i	−0.308654	−	0.534605i
$997$	8406.00	−	14559.6i	0.267022	−	0.462495i	−0.701070	−	0.713093i	$-0.747294\pi$
$997$	8406.00	−	14559.6i	0.267022	−	0.462495i	0.968091	+	0.250598i	$0.0806271\pi$
$998$	486.000	−	841.777i	0.0154149	−	0.0266994i
$999$	3483.00	+	6032.73i	0.110308	+	0.191058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.e.f.67.1		2
3.2	odd	2		441.4.e.g.361.1		2
7.2	even	3	inner	147.4.e.f.79.1		2
7.3	odd	6		147.4.a.e.1.1	yes	1
7.4	even	3		147.4.a.d.1.1	✓	1
7.5	odd	6		147.4.e.e.79.1		2
7.6	odd	2		147.4.e.e.67.1		2
21.2	odd	6		441.4.e.g.226.1		2
21.5	even	6		441.4.e.f.226.1		2
21.11	odd	6		441.4.a.g.1.1		1
21.17	even	6		441.4.a.h.1.1		1
21.20	even	2		441.4.e.f.361.1		2
28.3	even	6		2352.4.a.b.1.1		1
28.11	odd	6		2352.4.a.bi.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.d.1.1	✓	1	7.4	even	3
147.4.a.e.1.1	yes	1	7.3	odd	6
147.4.e.e.67.1		2	7.6	odd	2
147.4.e.e.79.1		2	7.5	odd	6
147.4.e.f.67.1		2	1.1	even	1	trivial
147.4.e.f.79.1		2	7.2	even	3	inner
441.4.a.g.1.1		1	21.11	odd	6
441.4.a.h.1.1		1	21.17	even	6
441.4.e.f.226.1		2	21.5	even	6
441.4.e.f.361.1		2	21.20	even	2
441.4.e.g.226.1		2	21.2	odd	6
441.4.e.g.361.1		2	3.2	odd	2
2352.4.a.b.1.1		1	28.3	even	6
2352.4.a.bi.1.1		1	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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