LMFDB - Embedded newform 294.4.e.b.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.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:	$17.3465615417$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.4.e.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(9.00000 - 15.5885i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(9.00000 - 15.5885i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(18.0000 + 31.1769i) q^{10} +(36.0000 + 62.3538i) q^{11} +(-6.00000 + 10.3923i) q^{12} +34.0000 q^{13} -54.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(46.0000 - 79.6743i) q^{19} -72.0000 q^{20} -144.000 q^{22} +(90.0000 - 155.885i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-99.5000 - 172.339i) q^{25} +(-34.0000 + 58.8897i) q^{26} +27.0000 q^{27} -114.000 q^{29} +(54.0000 - 93.5307i) q^{30} +(28.0000 + 48.4974i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(108.000 - 187.061i) q^{33} -12.0000 q^{34} +36.0000 q^{36} +(17.0000 - 29.4449i) q^{37} +(92.0000 + 159.349i) q^{38} +(-51.0000 - 88.3346i) q^{39} +(72.0000 - 124.708i) q^{40} -6.00000 q^{41} +164.000 q^{43} +(144.000 - 249.415i) q^{44} +(81.0000 + 140.296i) q^{45} +(180.000 + 311.769i) q^{46} +(84.0000 - 145.492i) q^{47} +48.0000 q^{48} +398.000 q^{50} +(9.00000 - 15.5885i) q^{51} +(-68.0000 - 117.779i) q^{52} +(-327.000 - 566.381i) q^{53} +(-27.0000 + 46.7654i) q^{54} +1296.00 q^{55} -276.000 q^{57} +(114.000 - 197.454i) q^{58} +(-246.000 - 426.084i) q^{59} +(108.000 + 187.061i) q^{60} +(-125.000 + 216.506i) q^{61} -112.000 q^{62} +64.0000 q^{64} +(306.000 - 530.008i) q^{65} +(216.000 + 374.123i) q^{66} +(62.0000 + 107.387i) q^{67} +(12.0000 - 20.7846i) q^{68} -540.000 q^{69} +36.0000 q^{71} +(-36.0000 + 62.3538i) q^{72} +(505.000 + 874.686i) q^{73} +(34.0000 + 58.8897i) q^{74} +(-298.500 + 517.017i) q^{75} -368.000 q^{76} +204.000 q^{78} +(-28.0000 + 48.4974i) q^{79} +(144.000 + 249.415i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(6.00000 - 10.3923i) q^{82} -228.000 q^{83} +108.000 q^{85} +(-164.000 + 284.056i) q^{86} +(171.000 + 296.181i) q^{87} +(288.000 + 498.831i) q^{88} +(195.000 - 337.750i) q^{89} -324.000 q^{90} -720.000 q^{92} +(84.0000 - 145.492i) q^{93} +(168.000 + 290.985i) q^{94} +(-828.000 - 1434.14i) q^{95} +(-48.0000 + 83.1384i) q^{96} +70.0000 q^{97} -648.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} - 4 q^{4} + 18 q^{5} + 12 q^{6} + 16 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 + 18 * q^5 + 12 * q^6 + 16 * q^8 - 9 * q^9	\( 2 q - 2 q^{2} - 3 q^{3} - 4 q^{4} + 18 q^{5} + 12 q^{6} + 16 q^{8} - 9 q^{9} + 36 q^{10} + 72 q^{11} - 12 q^{12} + 68 q^{13} - 108 q^{15} - 16 q^{16} + 6 q^{17} - 18 q^{18} + 92 q^{19} - 144 q^{20} - 288 q^{22} + 180 q^{23} - 24 q^{24} - 199 q^{25} - 68 q^{26} + 54 q^{27} - 228 q^{29} + 108 q^{30} + 56 q^{31} - 32 q^{32} + 216 q^{33} - 24 q^{34} + 72 q^{36} + 34 q^{37} + 184 q^{38} - 102 q^{39} + 144 q^{40} - 12 q^{41} + 328 q^{43} + 288 q^{44} + 162 q^{45} + 360 q^{46} + 168 q^{47} + 96 q^{48} + 796 q^{50} + 18 q^{51} - 136 q^{52} - 654 q^{53} - 54 q^{54} + 2592 q^{55} - 552 q^{57} + 228 q^{58} - 492 q^{59} + 216 q^{60} - 250 q^{61} - 224 q^{62} + 128 q^{64} + 612 q^{65} + 432 q^{66} + 124 q^{67} + 24 q^{68} - 1080 q^{69} + 72 q^{71} - 72 q^{72} + 1010 q^{73} + 68 q^{74} - 597 q^{75} - 736 q^{76} + 408 q^{78} - 56 q^{79} + 288 q^{80} - 81 q^{81} + 12 q^{82} - 456 q^{83} + 216 q^{85} - 328 q^{86} + 342 q^{87} + 576 q^{88} + 390 q^{89} - 648 q^{90} - 1440 q^{92} + 168 q^{93} + 336 q^{94} - 1656 q^{95} - 96 q^{96} + 140 q^{97} - 1296 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 + 18 * q^5 + 12 * q^6 + 16 * q^8 - 9 * q^9 + 36 * q^10 + 72 * q^11 - 12 * q^12 + 68 * q^13 - 108 * q^15 - 16 * q^16 + 6 * q^17 - 18 * q^18 + 92 * q^19 - 144 * q^20 - 288 * q^22 + 180 * q^23 - 24 * q^24 - 199 * q^25 - 68 * q^26 + 54 * q^27 - 228 * q^29 + 108 * q^30 + 56 * q^31 - 32 * q^32 + 216 * q^33 - 24 * q^34 + 72 * q^36 + 34 * q^37 + 184 * q^38 - 102 * q^39 + 144 * q^40 - 12 * q^41 + 328 * q^43 + 288 * q^44 + 162 * q^45 + 360 * q^46 + 168 * q^47 + 96 * q^48 + 796 * q^50 + 18 * q^51 - 136 * q^52 - 654 * q^53 - 54 * q^54 + 2592 * q^55 - 552 * q^57 + 228 * q^58 - 492 * q^59 + 216 * q^60 - 250 * q^61 - 224 * q^62 + 128 * q^64 + 612 * q^65 + 432 * q^66 + 124 * q^67 + 24 * q^68 - 1080 * q^69 + 72 * q^71 - 72 * q^72 + 1010 * q^73 + 68 * q^74 - 597 * q^75 - 736 * q^76 + 408 * q^78 - 56 * q^79 + 288 * q^80 - 81 * q^81 + 12 * q^82 - 456 * q^83 + 216 * q^85 - 328 * q^86 + 342 * q^87 + 576 * q^88 + 390 * q^89 - 648 * q^90 - 1440 * q^92 + 168 * q^93 + 336 * q^94 - 1656 * q^95 - 96 * q^96 + 140 * q^97 - 1296 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	9.00000	−	15.5885i	0.804984	−	1.39427i	−0.111317	−	0.993785i	$-0.535507\pi$
$5$	9.00000	−	15.5885i	0.804984	−	1.39427i	0.916302	−	0.400489i	$-0.131160\pi$
$6$	6.00000			0.408248
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	18.0000	+	31.1769i	0.569210	+	0.985901i
$11$	36.0000	+	62.3538i	0.986764	+	1.70913i	0.633817	+	0.773483i	$0.281487\pi$
$11$	36.0000	+	62.3538i	0.986764	+	1.70913i	0.352947	+	0.935643i	$0.385180\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	34.0000			0.725377			0.362689	−	0.931910i	$-0.381859\pi$
$13$	34.0000			0.725377			0.362689	+	0.931910i	$0.381859\pi$
$14$		0			0
$15$	−54.0000			−0.929516
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	3.00000	+	5.19615i	0.0428004	+	0.0741325i	0.886632	−	0.462476i	$-0.153039\pi$
$17$	3.00000	+	5.19615i	0.0428004	+	0.0741325i	−0.843832	+	0.536608i	$0.819705\pi$
$18$	−9.00000	−	15.5885i	−0.117851	−	0.204124i
$19$	46.0000	−	79.6743i	0.555428	−	0.962029i	−0.442443	−	0.896797i	$-0.645888\pi$
$19$	46.0000	−	79.6743i	0.555428	−	0.962029i	0.997870	−	0.0652319i	$-0.0207787\pi$
$20$	−72.0000			−0.804984
$21$		0			0
$22$	−144.000			−1.39550
$23$	90.0000	−	155.885i	0.815926	−	1.41323i	−0.0927351	−	0.995691i	$-0.529561\pi$
$23$	90.0000	−	155.885i	0.815926	−	1.41323i	0.908661	−	0.417534i	$-0.137106\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	−99.5000	−	172.339i	−0.796000	−	1.37871i
$26$	−34.0000	+	58.8897i	−0.256460	+	0.444201i
$27$	27.0000			0.192450
$28$		0			0
$29$	−114.000			−0.729975			−0.364987	−	0.931012i	$-0.618927\pi$
$29$	−114.000			−0.729975			−0.364987	+	0.931012i	$0.618927\pi$
$30$	54.0000	−	93.5307i	0.328634	−	0.569210i
$31$	28.0000	+	48.4974i	0.162224	+	0.280980i	0.935666	−	0.352887i	$-0.114800\pi$
$31$	28.0000	+	48.4974i	0.162224	+	0.280980i	−0.773442	+	0.633867i	$0.781467\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	108.000	−	187.061i	0.569709	−	0.986764i
$34$	−12.0000			−0.0605289
$35$		0			0
$36$	36.0000			0.166667
$37$	17.0000	−	29.4449i	0.0755347	−	0.130830i	−0.825784	−	0.563987i	$-0.809267\pi$
$37$	17.0000	−	29.4449i	0.0755347	−	0.130830i	0.901319	+	0.433157i	$0.142600\pi$
$38$	92.0000	+	159.349i	0.392747	+	0.680257i
$39$	−51.0000	−	88.3346i	−0.209398	−	0.362689i
$40$	72.0000	−	124.708i	0.284605	−	0.492950i
$41$	−6.00000			−0.0228547			−0.0114273	−	0.999935i	$-0.503638\pi$
$41$	−6.00000			−0.0228547			−0.0114273	+	0.999935i	$0.503638\pi$
$42$		0			0
$43$	164.000			0.581622			0.290811	−	0.956780i	$-0.406075\pi$
$43$	164.000			0.581622			0.290811	+	0.956780i	$0.406075\pi$
$44$	144.000	−	249.415i	0.493382	−	0.854563i
$45$	81.0000	+	140.296i	0.268328	+	0.464758i
$46$	180.000	+	311.769i	0.576947	+	0.999301i
$47$	84.0000	−	145.492i	0.260695	−	0.451537i	−0.705732	−	0.708479i	$-0.749382\pi$
$47$	84.0000	−	145.492i	0.260695	−	0.451537i	0.966427	+	0.256942i	$0.0827150\pi$
$48$	48.0000			0.144338
$49$		0			0
$50$	398.000			1.12571
$51$	9.00000	−	15.5885i	0.0247108	−	0.0428004i
$52$	−68.0000	−	117.779i	−0.181344	−	0.314098i
$53$	−327.000	−	566.381i	−0.847489	−	1.46789i	−0.883442	−	0.468540i	$-0.844780\pi$
$53$	−327.000	−	566.381i	−0.847489	−	1.46789i	0.0359535	−	0.999353i	$-0.488553\pi$
$54$	−27.0000	+	46.7654i	−0.0680414	+	0.117851i
$55$	1296.00			3.17732
$56$		0			0
$57$	−276.000			−0.641353
$58$	114.000	−	197.454i	0.258085	−	0.447016i
$59$	−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	$-0.349311\pi$
$60$	108.000	+	187.061i	0.232379	+	0.402492i
$61$	−125.000	+	216.506i	−0.262371	+	0.454439i	−0.966871	−	0.255264i	$-0.917838\pi$
$61$	−125.000	+	216.506i	−0.262371	+	0.454439i	0.704501	+	0.709703i	$0.251171\pi$
$62$	−112.000			−0.229420
$63$		0			0
$64$	64.0000			0.125000
$65$	306.000	−	530.008i	0.583917	−	1.01137i
$66$	216.000	+	374.123i	0.402845	+	0.697748i
$67$	62.0000	+	107.387i	0.113052	+	0.195812i	0.917000	−	0.398888i	$-0.130604\pi$
$67$	62.0000	+	107.387i	0.113052	+	0.195812i	−0.803947	+	0.594701i	$0.797271\pi$
$68$	12.0000	−	20.7846i	0.0214002	−	0.0370662i
$69$	−540.000			−0.942150
$70$		0			0
$71$	36.0000			0.0601748			0.0300874	−	0.999547i	$-0.490421\pi$
$71$	36.0000			0.0601748			0.0300874	+	0.999547i	$0.490421\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	505.000	+	874.686i	0.809668	+	1.40239i	0.913094	+	0.407749i	$0.133686\pi$
$73$	505.000	+	874.686i	0.809668	+	1.40239i	−0.103426	+	0.994637i	$0.532980\pi$
$74$	34.0000	+	58.8897i	0.0534111	+	0.0925107i
$75$	−298.500	+	517.017i	−0.459571	+	0.796000i
$76$	−368.000			−0.555428
$77$		0			0
$78$	204.000			0.296134
$79$	−28.0000	+	48.4974i	−0.0398765	+	0.0690682i	−0.885275	−	0.465068i	$-0.846030\pi$
$79$	−28.0000	+	48.4974i	−0.0398765	+	0.0690682i	0.845398	+	0.534136i	$0.179363\pi$
$80$	144.000	+	249.415i	0.201246	+	0.348569i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	6.00000	−	10.3923i	0.00808036	−	0.0139956i
$83$	−228.000			−0.301521			−0.150761	−	0.988570i	$-0.548172\pi$
$83$	−228.000			−0.301521			−0.150761	+	0.988570i	$0.548172\pi$
$84$		0			0
$85$	108.000			0.137815
$86$	−164.000	+	284.056i	−0.205635	+	0.356170i
$87$	171.000	+	296.181i	0.210726	+	0.364987i
$88$	288.000	+	498.831i	0.348874	+	0.604267i
$89$	195.000	−	337.750i	0.232247	−	0.402263i	−0.726222	−	0.687460i	$-0.758726\pi$
$89$	195.000	−	337.750i	0.232247	−	0.402263i	0.958469	+	0.285197i	$0.0920590\pi$
$90$	−324.000			−0.379473
$91$		0			0
$92$	−720.000			−0.815926
$93$	84.0000	−	145.492i	0.0936602	−	0.162224i
$94$	168.000	+	290.985i	0.184339	+	0.319285i
$95$	−828.000	−	1434.14i	−0.894221	−	1.54884i
$96$	−48.0000	+	83.1384i	−0.0510310	+	0.0883883i
$97$	70.0000			0.0732724			0.0366362	−	0.999329i	$-0.488336\pi$
$97$	70.0000			0.0732724			0.0366362	+	0.999329i	$0.488336\pi$
$98$		0			0
$99$	−648.000			−0.657843
$100$	−398.000	+	689.356i	−0.398000	+	0.689356i
$101$	−675.000	−	1169.13i	−0.665000	−	1.15181i	−0.979285	−	0.202485i	$-0.935098\pi$
$101$	−675.000	−	1169.13i	−0.665000	−	1.15181i	0.314285	−	0.949329i	$-0.398235\pi$
$102$	18.0000	+	31.1769i	0.0174732	+	0.0302645i
$103$	1000.00	−	1732.05i	0.956630	−	1.65693i	0.226038	−	0.974118i	$-0.427423\pi$
$103$	1000.00	−	1732.05i	0.956630	−	1.65693i	0.730592	−	0.682814i	$-0.239244\pi$
$104$	272.000			0.256460
$105$		0			0
$106$	1308.00			1.19853
$107$	−348.000	+	602.754i	−0.314415	+	0.544583i	−0.979313	−	0.202351i	$-0.935142\pi$
$107$	−348.000	+	602.754i	−0.314415	+	0.544583i	0.664898	+	0.746934i	$0.268475\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$	557.000	+	964.752i	0.489458	+	0.847766i	0.999926	−	0.0121304i	$-0.00386131\pi$
$109$	557.000	+	964.752i	0.489458	+	0.847766i	−0.510468	+	0.859897i	$0.670528\pi$
$110$	−1296.00	+	2244.74i	−1.12335	+	1.94570i
$111$	−102.000			−0.0872199
$112$		0			0
$113$	−462.000			−0.384613			−0.192307	−	0.981335i	$-0.561597\pi$
$113$	−462.000			−0.384613			−0.192307	+	0.981335i	$0.561597\pi$
$114$	276.000	−	478.046i	0.226752	−	0.392747i
$115$	−1620.00	−	2805.92i	−1.31362	−	2.27525i
$116$	228.000	+	394.908i	0.182494	+	0.316088i
$117$	−153.000	+	265.004i	−0.120896	+	0.209398i
$118$	984.000			0.767666
$119$		0			0
$120$	−432.000			−0.328634
$121$	−1926.50	+	3336.80i	−1.44741	+	2.50698i
$122$	−250.000	−	433.013i	−0.185524	−	0.321337i
$123$	9.00000	+	15.5885i	0.00659758	+	0.0114273i
$124$	112.000	−	193.990i	0.0811121	−	0.140490i
$125$	−1332.00			−0.953102
$126$		0			0
$127$	1064.00			0.743423			0.371712	−	0.928348i	$-0.378771\pi$
$127$	1064.00			0.743423			0.371712	+	0.928348i	$0.378771\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−246.000	−	426.084i	−0.167900	−	0.290811i
$130$	612.000	+	1060.02i	0.412892	+	0.715150i
$131$	90.0000	−	155.885i	0.0600255	−	0.103967i	−0.834451	−	0.551082i	$-0.814215\pi$
$131$	90.0000	−	155.885i	0.0600255	−	0.103967i	0.894477	+	0.447115i	$0.147548\pi$
$132$	−864.000			−0.569709
$133$		0			0
$134$	−248.000			−0.159880
$135$	243.000	−	420.888i	0.154919	−	0.268328i
$136$	24.0000	+	41.5692i	0.0151322	+	0.0262098i
$137$	1359.00	+	2353.86i	0.847498	+	1.46791i	0.883434	+	0.468555i	$0.155225\pi$
$137$	1359.00	+	2353.86i	0.847498	+	1.46791i	−0.0359363	+	0.999354i	$0.511441\pi$
$138$	540.000	−	935.307i	0.333100	−	0.576947i
$139$	1348.00			0.822560			0.411280	−	0.911509i	$-0.365082\pi$
$139$	1348.00			0.822560			0.411280	+	0.911509i	$0.365082\pi$
$140$		0			0
$141$	−504.000			−0.301025
$142$	−36.0000	+	62.3538i	−0.0212750	+	0.0368494i
$143$	1224.00	+	2120.03i	0.715776	+	1.23976i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−1026.00	+	1777.08i	−0.587618	+	1.01778i
$146$	−2020.00			−1.14504
$147$		0			0
$148$	−136.000			−0.0755347
$149$	−279.000	+	483.242i	−0.153400	+	0.265696i	−0.932475	−	0.361234i	$-0.882356\pi$
$149$	−279.000	+	483.242i	−0.153400	+	0.265696i	0.779075	+	0.626930i	$0.215689\pi$
$150$	−597.000	−	1034.03i	−0.324966	−	0.562857i
$151$	−964.000	−	1669.70i	−0.519531	−	0.899854i	−0.999742	−	0.0227014i	$-0.992773\pi$
$151$	−964.000	−	1669.70i	−0.519531	−	0.899854i	0.480211	−	0.877153i	$-0.340560\pi$
$152$	368.000	−	637.395i	0.196373	−	0.340129i
$153$	−54.0000			−0.0285336
$154$		0			0
$155$	1008.00			0.522352
$156$	−204.000	+	353.338i	−0.104699	+	0.181344i
$157$	−1205.00	−	2087.12i	−0.612544	−	1.06096i	−0.990810	−	0.135261i	$-0.956813\pi$
$157$	−1205.00	−	2087.12i	−0.612544	−	1.06096i	0.378266	−	0.925697i	$-0.376521\pi$
$158$	−56.0000	−	96.9948i	−0.0281970	−	0.0488386i
$159$	−981.000	+	1699.14i	−0.489298	+	0.847489i
$160$	−576.000			−0.284605
$161$		0			0
$162$	162.000			0.0785674
$163$	−370.000	+	640.859i	−0.177795	+	0.307951i	−0.941125	−	0.338058i	$-0.890230\pi$
$163$	−370.000	+	640.859i	−0.177795	+	0.307951i	0.763330	+	0.646009i	$0.223563\pi$
$164$	12.0000	+	20.7846i	0.00571367	+	0.00989637i
$165$	−1944.00	−	3367.11i	−0.917213	−	1.58866i
$166$	228.000	−	394.908i	0.106604	−	0.184643i
$167$	−3984.00			−1.84605			−0.923027	−	0.384734i	$-0.874293\pi$
$167$	−3984.00			−1.84605			−0.923027	+	0.384734i	$0.874293\pi$
$168$		0			0
$169$	−1041.00			−0.473828
$170$	−108.000	+	187.061i	−0.0487248	+	0.0843939i
$171$	414.000	+	717.069i	0.185143	+	0.320676i
$172$	−328.000	−	568.113i	−0.145406	−	0.251850i
$173$	−519.000	+	898.934i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−519.000	+	898.934i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	−684.000			−0.298011
$175$		0			0
$176$	−1152.00			−0.493382
$177$	−738.000	+	1278.25i	−0.313398	+	0.542822i
$178$	390.000	+	675.500i	0.164223	+	0.284443i
$179$	1284.00	+	2223.95i	0.536149	+	0.928637i	0.999107	+	0.0422569i	$0.0134548\pi$
$179$	1284.00	+	2223.95i	0.536149	+	0.928637i	−0.462958	+	0.886380i	$0.653212\pi$
$180$	324.000	−	561.184i	0.134164	−	0.232379i
$181$	2698.00			1.10796			0.553980	−	0.832530i	$-0.313108\pi$
$181$	2698.00			1.10796			0.553980	+	0.832530i	$0.313108\pi$
$182$		0			0
$183$	750.000			0.302960
$184$	720.000	−	1247.08i	0.288473	−	0.499651i
$185$	−306.000	−	530.008i	−0.121608	−	0.210632i
$186$	168.000	+	290.985i	0.0662277	+	0.114710i
$187$	−216.000	+	374.123i	−0.0844678	+	0.146303i
$188$	−672.000			−0.260695
$189$		0			0
$190$	3312.00			1.26462
$191$	2058.00	−	3564.56i	0.779642	−	1.35038i	−0.152506	−	0.988303i	$-0.548734\pi$
$191$	2058.00	−	3564.56i	0.779642	−	1.35038i	0.932148	−	0.362077i	$-0.117932\pi$
$192$	−96.0000	−	166.277i	−0.0360844	−	0.0625000i
$193$	1655.00	+	2866.54i	0.617251	+	1.06911i	0.989985	+	0.141172i	$0.0450872\pi$
$193$	1655.00	+	2866.54i	0.617251	+	1.06911i	−0.372734	+	0.927938i	$0.621580\pi$
$194$	−70.0000	+	121.244i	−0.0259057	+	0.0448700i
$195$	−1836.00			−0.674250
$196$		0			0
$197$	1278.00			0.462202			0.231101	−	0.972930i	$-0.425767\pi$
$197$	1278.00			0.462202			0.231101	+	0.972930i	$0.425767\pi$
$198$	648.000	−	1122.37i	0.232583	−	0.402845i
$199$	1468.00	+	2542.65i	0.522933	+	0.905747i	0.999644	+	0.0266869i	$0.00849572\pi$
$199$	1468.00	+	2542.65i	0.522933	+	0.905747i	−0.476710	+	0.879060i	$0.658171\pi$
$200$	−796.000	−	1378.71i	−0.281428	−	0.487448i
$201$	186.000	−	322.161i	0.0652708	−	0.113052i
$202$	2700.00			0.940452
$203$		0			0
$204$	−72.0000			−0.0247108
$205$	−54.0000	+	93.5307i	−0.0183977	+	0.0318657i
$206$	2000.00	+	3464.10i	0.676440	+	1.17163i
$207$	810.000	+	1402.96i	0.271975	+	0.471075i
$208$	−272.000	+	471.118i	−0.0906721	+	0.157049i
$209$	6624.00			2.19230
$210$		0			0
$211$	−3508.00			−1.14455			−0.572276	−	0.820061i	$-0.693940\pi$
$211$	−3508.00			−1.14455			−0.572276	+	0.820061i	$0.693940\pi$
$212$	−1308.00	+	2265.52i	−0.423744	+	0.733947i
$213$	−54.0000	−	93.5307i	−0.0173710	−	0.0300874i
$214$	−696.000	−	1205.51i	−0.222325	−	0.385078i
$215$	1476.00	−	2556.51i	0.468197	−	0.810941i
$216$	216.000			0.0680414
$217$		0			0
$218$	−2228.00			−0.692198
$219$	1515.00	−	2624.06i	0.467462	−	0.809668i
$220$	−2592.00	−	4489.48i	−0.794330	−	1.37582i
$221$	102.000	+	176.669i	0.0310464	+	0.0537740i
$222$	102.000	−	176.669i	0.0308369	−	0.0534111i
$223$	1888.00			0.566950			0.283475	−	0.958980i	$-0.408513\pi$
$223$	1888.00			0.566950			0.283475	+	0.958980i	$0.408513\pi$
$224$		0			0
$225$	1791.00			0.530667
$226$	462.000	−	800.207i	0.135981	−	0.235527i
$227$	1782.00	+	3086.51i	0.521037	+	0.902463i	0.999701	+	0.0244647i	$0.00778814\pi$
$227$	1782.00	+	3086.51i	0.521037	+	0.902463i	−0.478663	+	0.877999i	$0.658879\pi$
$228$	552.000	+	956.092i	0.160338	+	0.277714i
$229$	667.000	−	1155.28i	0.192474	−	0.333375i	−0.753595	−	0.657339i	$-0.771682\pi$
$229$	667.000	−	1155.28i	0.192474	−	0.333375i	0.946070	+	0.323963i	$0.105015\pi$
$230$	6480.00			1.85773
$231$		0			0
$232$	−912.000			−0.258085
$233$	−1329.00	+	2301.90i	−0.373672	+	0.647220i	−0.990127	−	0.140171i	$-0.955235\pi$
$233$	−1329.00	+	2301.90i	−0.373672	+	0.647220i	0.616455	+	0.787390i	$0.288568\pi$
$234$	−306.000	−	530.008i	−0.0854865	−	0.148067i
$235$	−1512.00	−	2618.86i	−0.419711	−	0.726960i
$236$	−984.000	+	1704.34i	−0.271411	+	0.470097i
$237$	168.000			0.0460455
$238$		0			0
$239$	−588.000			−0.159140			−0.0795702	−	0.996829i	$-0.525355\pi$
$239$	−588.000			−0.159140			−0.0795702	+	0.996829i	$0.525355\pi$
$240$	432.000	−	748.246i	0.116190	−	0.201246i
$241$	2845.00	+	4927.68i	0.760426	+	1.31710i	0.942631	+	0.333835i	$0.108343\pi$
$241$	2845.00	+	4927.68i	0.760426	+	1.31710i	−0.182206	+	0.983260i	$0.558324\pi$
$242$	−3853.00	−	6673.59i	−1.02347	−	1.77271i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	1000.00			0.262371
$245$		0			0
$246$	−36.0000			−0.00933039
$247$	1564.00	−	2708.93i	0.402894	−	0.697834i
$248$	224.000	+	387.979i	0.0573549	+	0.0993416i
$249$	342.000	+	592.361i	0.0870416	+	0.150761i
$250$	1332.00	−	2307.09i	0.336972	−	0.583653i
$251$	−180.000			−0.0452649			−0.0226325	−	0.999744i	$-0.507205\pi$
$251$	−180.000			−0.0452649			−0.0226325	+	0.999744i	$0.507205\pi$
$252$		0			0
$253$	12960.0			3.22051
$254$	−1064.00	+	1842.90i	−0.262840	+	0.455252i
$255$	−162.000	−	280.592i	−0.0397837	−	0.0689073i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	2655.00	−	4598.59i	0.644414	−	1.11616i	−0.340023	−	0.940417i	$-0.610435\pi$
$257$	2655.00	−	4598.59i	0.644414	−	1.11616i	0.984437	−	0.175740i	$-0.0562319\pi$
$258$	984.000			0.237446
$259$		0			0
$260$	−2448.00			−0.583917
$261$	513.000	−	888.542i	0.121662	−	0.210726i
$262$	180.000	+	311.769i	0.0424444	+	0.0735159i
$263$	−414.000	−	717.069i	−0.0970659	−	0.168123i	0.813403	−	0.581701i	$-0.197612\pi$
$263$	−414.000	−	717.069i	−0.0970659	−	0.168123i	−0.910469	+	0.413577i	$0.864279\pi$
$264$	864.000	−	1496.49i	0.201422	−	0.348874i
$265$	−11772.0			−2.72886
$266$		0			0
$267$	−1170.00			−0.268175
$268$	248.000	−	429.549i	0.0565262	−	0.0979062i
$269$	−2067.00	−	3580.15i	−0.468503	−	0.811470i	0.530849	−	0.847466i	$-0.321873\pi$
$269$	−2067.00	−	3580.15i	−0.468503	−	0.811470i	−0.999352	+	0.0359958i	$0.988540\pi$
$270$	486.000	+	841.777i	0.109545	+	0.189737i
$271$	−1484.00	+	2570.36i	−0.332644	+	0.576157i	−0.983029	−	0.183448i	$-0.941274\pi$
$271$	−1484.00	+	2570.36i	−0.332644	+	0.576157i	0.650385	+	0.759605i	$0.274607\pi$
$272$	−96.0000			−0.0214002
$273$		0			0
$274$	−5436.00			−1.19854
$275$	7164.00	−	12408.4i	1.57093	−	2.72093i
$276$	1080.00	+	1870.61i	0.235538	+	0.407963i
$277$	2393.00	+	4144.80i	0.519067	+	0.899050i	0.999754	+	0.0221579i	$0.00705366\pi$
$277$	2393.00	+	4144.80i	0.519067	+	0.899050i	−0.480688	+	0.876892i	$0.659613\pi$
$278$	−1348.00	+	2334.80i	−0.290819	+	0.503713i
$279$	−504.000			−0.108149
$280$		0			0
$281$	−4398.00			−0.933675			−0.466838	−	0.884343i	$-0.654607\pi$
$281$	−4398.00			−0.933675			−0.466838	+	0.884343i	$0.654607\pi$
$282$	504.000	−	872.954i	0.106428	−	0.184339i
$283$	2386.00	+	4132.67i	0.501177	+	0.868063i	0.999999	+	0.00135915i	$0.000432632\pi$
$283$	2386.00	+	4132.67i	0.501177	+	0.868063i	−0.498822	+	0.866704i	$0.666234\pi$
$284$	−72.0000	−	124.708i	−0.0150437	−	0.0260565i
$285$	−2484.00	+	4302.41i	−0.516279	+	0.894221i
$286$	−4896.00			−1.01226
$287$		0			0
$288$	288.000			0.0589256
$289$	2438.50	−	4223.61i	0.496336	−	0.859680i
$290$	−2052.00	−	3554.17i	−0.415509	−	0.719683i
$291$	−105.000	−	181.865i	−0.0211519	−	0.0366362i
$292$	2020.00	−	3498.74i	0.404834	−	0.701193i
$293$	−6522.00			−1.30041			−0.650204	−	0.759760i	$-0.725316\pi$
$293$	−6522.00			−1.30041			−0.650204	+	0.759760i	$0.725316\pi$
$294$		0			0
$295$	−8856.00			−1.74785
$296$	136.000	−	235.559i	0.0267055	−	0.0462553i
$297$	972.000	+	1683.55i	0.189903	+	0.328921i
$298$	−558.000	−	966.484i	−0.108470	−	0.187876i
$299$	3060.00	−	5300.08i	0.591854	−	1.02512i
$300$	2388.00			0.459571
$301$		0			0
$302$	3856.00			0.734728
$303$	−2025.00	+	3507.40i	−0.383938	+	0.665000i
$304$	736.000	+	1274.79i	0.138857	+	0.240507i
$305$	2250.00	+	3897.11i	0.422409	+	0.731633i
$306$	54.0000	−	93.5307i	0.0100882	−	0.0174732i
$307$	6244.00			1.16079			0.580397	−	0.814333i	$-0.302897\pi$
$307$	6244.00			1.16079			0.580397	+	0.814333i	$0.302897\pi$
$308$		0			0
$309$	−6000.00			−1.10462
$310$	−1008.00	+	1745.91i	−0.184679	+	0.319874i
$311$	−264.000	−	457.261i	−0.0481353	−	0.0833727i	0.840954	−	0.541107i	$-0.181995\pi$
$311$	−264.000	−	457.261i	−0.0481353	−	0.0833727i	−0.889089	+	0.457734i	$0.848661\pi$
$312$	−408.000	−	706.677i	−0.0740335	−	0.128230i
$313$	−2915.00	+	5048.93i	−0.526407	+	0.911765i	0.473119	+	0.880998i	$0.343128\pi$
$313$	−2915.00	+	5048.93i	−0.526407	+	0.911765i	−0.999527	+	0.0307660i	$0.990205\pi$
$314$	4820.00			0.866269
$315$		0			0
$316$	224.000			0.0398765
$317$	−2523.00	+	4369.96i	−0.447021	+	0.774264i	−0.998191	−	0.0601297i	$-0.980849\pi$
$317$	−2523.00	+	4369.96i	−0.447021	+	0.774264i	0.551169	+	0.834394i	$0.314182\pi$
$318$	−1962.00	−	3398.28i	−0.345986	−	0.599265i
$319$	−4104.00	−	7108.34i	−0.720313	−	1.24762i
$320$	576.000	−	997.661i	0.100623	−	0.174284i
$321$	2088.00			0.363055
$322$		0			0
$323$	552.000			0.0950901
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	−3383.00	−	5859.53i	−0.577400	−	1.00009i
$326$	−740.000	−	1281.72i	−0.125720	−	0.217754i
$327$	1671.00	−	2894.26i	0.282589	−	0.489458i
$328$	−48.0000			−0.00808036
$329$		0			0
$330$	7776.00			1.29714
$331$	2510.00	−	4347.45i	0.416804	−	0.721925i	−0.578812	−	0.815461i	$-0.696484\pi$
$331$	2510.00	−	4347.45i	0.416804	−	0.721925i	0.995616	+	0.0935355i	$0.0298169\pi$
$332$	456.000	+	789.815i	0.0753803	+	0.130562i
$333$	153.000	+	265.004i	0.0251782	+	0.0436100i
$334$	3984.00	−	6900.49i	0.652679	−	1.13047i
$335$	2232.00			0.364021
$336$		0			0
$337$	−7486.00			−1.21005			−0.605027	−	0.796205i	$-0.706838\pi$
$337$	−7486.00			−1.21005			−0.605027	+	0.796205i	$0.706838\pi$
$338$	1041.00	−	1803.06i	0.167523	−	0.290159i
$339$	693.000	+	1200.31i	0.111028	+	0.192307i
$340$	−216.000	−	374.123i	−0.0344537	−	0.0596755i
$341$	−2016.00	+	3491.81i	−0.320154	+	0.554523i
$342$	−1656.00			−0.261831
$343$		0			0
$344$	1312.00			0.205635
$345$	−4860.00	+	8417.77i	−0.758416	+	1.31362i
$346$	−1038.00	−	1797.87i	−0.161281	−	0.279347i
$347$	5016.00	+	8687.97i	0.776003	+	1.34408i	0.934229	+	0.356673i	$0.116089\pi$
$347$	5016.00	+	8687.97i	0.776003	+	1.34408i	−0.158226	+	0.987403i	$0.550578\pi$
$348$	684.000	−	1184.72i	0.105363	−	0.182494i
$349$	−5942.00			−0.911370			−0.455685	−	0.890141i	$-0.650606\pi$
$349$	−5942.00			−0.911370			−0.455685	+	0.890141i	$0.650606\pi$
$350$		0			0
$351$	918.000			0.139599
$352$	1152.00	−	1995.32i	0.174437	−	0.302134i
$353$	−45.0000	−	77.9423i	−0.00678501	−	0.0117520i	0.862613	−	0.505864i	$-0.168826\pi$
$353$	−45.0000	−	77.9423i	−0.00678501	−	0.0117520i	−0.869398	+	0.494113i	$0.835493\pi$
$354$	−1476.00	−	2556.51i	−0.221606	−	0.383833i
$355$	324.000	−	561.184i	0.0484398	−	0.0839002i
$356$	−1560.00			−0.232247
$357$		0			0
$358$	−5136.00			−0.758229
$359$	−5298.00	+	9176.41i	−0.778880	+	1.34906i	0.153708	+	0.988116i	$0.450878\pi$
$359$	−5298.00	+	9176.41i	−0.778880	+	1.34906i	−0.932588	+	0.360943i	$0.882455\pi$
$360$	648.000	+	1122.37i	0.0948683	+	0.164317i
$361$	−802.500	−	1389.97i	−0.117000	−	0.202649i
$362$	−2698.00	+	4673.07i	−0.391723	+	0.678484i
$363$	11559.0			1.67132
$364$		0			0
$365$	18180.0			2.60708
$366$	−750.000	+	1299.04i	−0.107112	+	0.185524i
$367$	2008.00	+	3477.96i	0.285604	+	0.494681i	0.972756	−	0.231833i	$-0.0744724\pi$
$367$	2008.00	+	3477.96i	0.285604	+	0.494681i	−0.687151	+	0.726514i	$0.741139\pi$
$368$	1440.00	+	2494.15i	0.203981	+	0.353306i
$369$	27.0000	−	46.7654i	0.00380912	−	0.00659758i
$370$	1224.00			0.171980
$371$		0			0
$372$	−672.000			−0.0936602
$373$	−1639.00	+	2838.83i	−0.227518	+	0.394073i	−0.957072	−	0.289851i	$-0.906394\pi$
$373$	−1639.00	+	2838.83i	−0.227518	+	0.394073i	0.729554	+	0.683923i	$0.239728\pi$
$374$	−432.000	−	748.246i	−0.0597278	−	0.103452i
$375$	1998.00	+	3460.64i	0.275137	+	0.476551i
$376$	672.000	−	1163.94i	0.0921696	−	0.159642i
$377$	−3876.00			−0.529507
$378$		0			0
$379$	4628.00			0.627241			0.313621	−	0.949548i	$-0.398458\pi$
$379$	4628.00			0.627241			0.313621	+	0.949548i	$0.398458\pi$
$380$	−3312.00	+	5736.55i	−0.447111	+	0.774418i
$381$	−1596.00	−	2764.35i	−0.214608	−	0.371712i
$382$	4116.00	+	7129.12i	0.551290	+	0.954863i
$383$	−1440.00	+	2494.15i	−0.192116	+	0.332755i	−0.945951	−	0.324308i	$-0.894868\pi$
$383$	−1440.00	+	2494.15i	−0.192116	+	0.332755i	0.753835	+	0.657064i	$0.228202\pi$
$384$	384.000			0.0510310
$385$		0			0
$386$	−6620.00			−0.872925
$387$	−738.000	+	1278.25i	−0.0969371	+	0.167900i
$388$	−140.000	−	242.487i	−0.0183181	−	0.0317279i
$389$	−3987.00	−	6905.69i	−0.519663	−	0.900083i	−0.999739	−	0.0228557i	$-0.992724\pi$
$389$	−3987.00	−	6905.69i	−0.519663	−	0.900083i	0.480076	−	0.877227i	$-0.340609\pi$
$390$	1836.00	−	3180.05i	0.238383	−	0.412892i
$391$	1080.00			0.139688
$392$		0			0
$393$	−540.000			−0.0693114
$394$	−1278.00	+	2213.56i	−0.163413	+	0.283040i
$395$	504.000	+	872.954i	0.0642000	+	0.111198i
$396$	1296.00	+	2244.74i	0.164461	+	0.284854i
$397$	−6173.00	+	10691.9i	−0.780388	+	1.35167i	0.151328	+	0.988484i	$0.451645\pi$
$397$	−6173.00	+	10691.9i	−0.780388	+	1.35167i	−0.931716	+	0.363188i	$0.881688\pi$
$398$	−5872.00			−0.739540
$399$		0			0
$400$	3184.00			0.398000
$401$	−4869.00	+	8433.36i	−0.606350	+	1.05023i	0.385487	+	0.922713i	$0.374034\pi$
$401$	−4869.00	+	8433.36i	−0.606350	+	1.05023i	−0.991837	+	0.127515i	$0.959300\pi$
$402$	372.000	+	644.323i	0.0461534	+	0.0799401i
$403$	952.000	+	1648.91i	0.117674	+	0.203817i
$404$	−2700.00	+	4676.54i	−0.332500	+	0.575907i
$405$	−1458.00			−0.178885
$406$		0			0
$407$	2448.00			0.298140
$408$	72.0000	−	124.708i	0.00873660	−	0.0151322i
$409$	−215.000	−	372.391i	−0.0259928	−	0.0450209i	0.852736	−	0.522342i	$-0.174941\pi$
$409$	−215.000	−	372.391i	−0.0259928	−	0.0450209i	−0.878729	+	0.477321i	$0.841608\pi$
$410$	−108.000	−	187.061i	−0.0130091	−	0.0225325i
$411$	4077.00	−	7061.57i	0.489303	−	0.847498i
$412$	−8000.00			−0.956630
$413$		0			0
$414$	−3240.00			−0.384631
$415$	−2052.00	+	3554.17i	−0.242720	+	0.420403i
$416$	−544.000	−	942.236i	−0.0641149	−	0.111050i
$417$	−2022.00	−	3502.21i	−0.237453	−	0.411280i
$418$	−6624.00	+	11473.1i	−0.775097	+	1.34251i
$419$	1812.00			0.211270			0.105635	−	0.994405i	$-0.466313\pi$
$419$	1812.00			0.211270			0.105635	+	0.994405i	$0.466313\pi$
$420$		0			0
$421$	−10690.0			−1.23753			−0.618763	−	0.785577i	$-0.712366\pi$
$421$	−10690.0			−1.23753			−0.618763	+	0.785577i	$0.712366\pi$
$422$	3508.00	−	6076.03i	0.404661	−	0.700893i
$423$	756.000	+	1309.43i	0.0868983	+	0.150512i
$424$	−2616.00	−	4531.04i	−0.299633	−	0.518979i
$425$	597.000	−	1034.03i	0.0681382	−	0.118019i
$426$	216.000			0.0245663
$427$		0			0
$428$	2784.00			0.314415
$429$	3672.00	−	6360.09i	0.413254	−	0.715776i
$430$	2952.00	+	5113.01i	0.331065	+	0.573422i
$431$	2058.00	+	3564.56i	0.230001	+	0.398373i	0.957808	−	0.287409i	$-0.0927938\pi$
$431$	2058.00	+	3564.56i	0.230001	+	0.398373i	−0.727807	+	0.685782i	$0.759460\pi$
$432$	−216.000	+	374.123i	−0.0240563	+	0.0416667i
$433$	−9938.00			−1.10298			−0.551489	−	0.834182i	$-0.685940\pi$
$433$	−9938.00			−1.10298			−0.551489	+	0.834182i	$0.685940\pi$
$434$		0			0
$435$	6156.00			0.678523
$436$	2228.00	−	3859.01i	0.244729	−	0.423883i
$437$	−8280.00	−	14341.4i	−0.906376	−	1.56989i
$438$	3030.00	+	5248.11i	0.330546	+	0.572522i
$439$	892.000	−	1544.99i	0.0969769	−	0.167969i	−0.813455	−	0.581628i	$-0.802416\pi$
$439$	892.000	−	1544.99i	0.0969769	−	0.167969i	0.910432	+	0.413659i	$0.135749\pi$
$440$	10368.0			1.12335
$441$		0			0
$442$	−408.000			−0.0439063
$443$	5856.00	−	10142.9i	0.628052	−	1.08782i	−0.359890	−	0.932995i	$-0.617186\pi$
$443$	5856.00	−	10142.9i	0.628052	−	1.08782i	0.987942	−	0.154823i	$-0.0494808\pi$
$444$	204.000	+	353.338i	0.0218050	+	0.0377673i
$445$	−3510.00	−	6079.50i	−0.373910	−	0.647631i
$446$	−1888.00	+	3270.11i	−0.200447	+	0.347185i
$447$	1674.00			0.177131
$448$		0			0
$449$	7650.00			0.804066			0.402033	−	0.915625i	$-0.368304\pi$
$449$	7650.00			0.804066			0.402033	+	0.915625i	$0.368304\pi$
$450$	−1791.00	+	3102.10i	−0.187619	+	0.324966i
$451$	−216.000	−	374.123i	−0.0225522	−	0.0390616i
$452$	924.000	+	1600.41i	0.0961533	+	0.166542i
$453$	−2892.00	+	5009.09i	−0.299951	+	0.519531i
$454$	−7128.00			−0.736858
$455$		0			0
$456$	−2208.00			−0.226752
$457$	−1837.00	+	3181.78i	−0.188033	+	0.325683i	−0.944594	−	0.328240i	$-0.893545\pi$
$457$	−1837.00	+	3181.78i	−0.188033	+	0.325683i	0.756561	+	0.653923i	$0.226878\pi$
$458$	1334.00	+	2310.56i	0.136100	+	0.235732i
$459$	81.0000	+	140.296i	0.00823694	+	0.0142668i
$460$	−6480.00	+	11223.7i	−0.656808	+	1.13762i
$461$	3102.00			0.313394			0.156697	−	0.987647i	$-0.449915\pi$
$461$	3102.00			0.313394			0.156697	+	0.987647i	$0.449915\pi$
$462$		0			0
$463$	8984.00			0.901775			0.450888	−	0.892581i	$-0.351108\pi$
$463$	8984.00			0.901775			0.450888	+	0.892581i	$0.351108\pi$
$464$	912.000	−	1579.63i	0.0912468	−	0.158044i
$465$	−1512.00	−	2618.86i	−0.150790	−	0.261176i
$466$	−2658.00	−	4603.79i	−0.264226	−	0.457653i
$467$	1806.00	−	3128.08i	0.178954	−	0.309958i	−0.762568	−	0.646908i	$-0.776062\pi$
$467$	1806.00	−	3128.08i	0.178954	−	0.309958i	0.941523	+	0.336950i	$0.109395\pi$
$468$	1224.00			0.120896
$469$		0			0
$470$	6048.00			0.593561
$471$	−3615.00	+	6261.36i	−0.353653	+	0.612544i
$472$	−1968.00	−	3408.68i	−0.191916	−	0.332409i
$473$	5904.00	+	10226.0i	0.573924	+	0.994066i
$474$	−168.000	+	290.985i	−0.0162795	+	0.0281970i
$475$	−18308.0			−1.76848
$476$		0			0
$477$	5886.00			0.564993
$478$	588.000	−	1018.45i	0.0562646	−	0.0974532i
$479$	−4644.00	−	8043.64i	−0.442985	−	0.767272i	0.554924	−	0.831901i	$-0.312747\pi$
$479$	−4644.00	−	8043.64i	−0.442985	−	0.767272i	−0.997909	+	0.0646283i	$0.979414\pi$
$480$	864.000	+	1496.49i	0.0821584	+	0.142302i
$481$	578.000	−	1001.13i	0.0547911	−	0.0949010i
$482$	−11380.0			−1.07540
$483$		0			0
$484$	15412.0			1.44741
$485$	630.000	−	1091.19i	0.0589831	−	0.102162i
$486$	−243.000	−	420.888i	−0.0226805	−	0.0392837i
$487$	2924.00	+	5064.52i	0.272072	+	0.471243i	0.969392	−	0.245517i	$-0.0789578\pi$
$487$	2924.00	+	5064.52i	0.272072	+	0.471243i	−0.697320	+	0.716760i	$0.745624\pi$
$488$	−1000.00	+	1732.05i	−0.0927620	+	0.160669i
$489$	2220.00			0.205300
$490$		0			0
$491$	−5952.00			−0.547067			−0.273534	−	0.961862i	$-0.588192\pi$
$491$	−5952.00			−0.547067			−0.273534	+	0.961862i	$0.588192\pi$
$492$	36.0000	−	62.3538i	0.00329879	−	0.00571367i
$493$	−342.000	−	592.361i	−0.0312432	−	0.0541148i
$494$	3128.00	+	5417.85i	0.284889	+	0.493443i
$495$	−5832.00	+	10101.3i	−0.529553	+	0.917213i
$496$	−896.000			−0.0811121
$497$		0			0
$498$	−1368.00			−0.123095
$499$	−5374.00	+	9308.04i	−0.482111	+	0.835040i	−0.999789	−	0.0205349i	$-0.993463\pi$
$499$	−5374.00	+	9308.04i	−0.482111	+	0.835040i	0.517678	+	0.855575i	$0.326796\pi$
$500$	2664.00	+	4614.18i	0.238275	+	0.412705i
$501$	5976.00	+	10350.7i	0.532910	+	0.923027i
$502$	180.000	−	311.769i	0.0160036	−	0.0277190i
$503$	16488.0			1.46156			0.730779	−	0.682614i	$-0.239157\pi$
$503$	16488.0			1.46156			0.730779	+	0.682614i	$0.239157\pi$
$504$		0			0
$505$	−24300.0			−2.14126
$506$	−12960.0	+	22447.4i	−1.13862	+	1.97215i
$507$	1561.50	+	2704.60i	0.136782	+	0.236914i
$508$	−2128.00	−	3685.80i	−0.185856	−	0.321912i
$509$	7029.00	−	12174.6i	0.612092	−	1.06017i	−0.378795	−	0.925481i	$-0.623661\pi$
$509$	7029.00	−	12174.6i	0.612092	−	1.06017i	0.990887	−	0.134694i	$-0.0430052\pi$
$510$	648.000			0.0562626
$511$		0			0
$512$	512.000			0.0441942
$513$	1242.00	−	2151.21i	0.106892	−	0.185143i
$514$	5310.00	+	9197.19i	0.455669	+	0.789243i
$515$	−18000.0	−	31176.9i	−1.54015	−	2.66761i
$516$	−984.000	+	1704.34i	−0.0839500	+	0.145406i
$517$	12096.0			1.02898
$518$		0			0
$519$	3114.00			0.263371
$520$	2448.00	−	4240.06i	0.206446	−	0.357575i
$521$	−7233.00	−	12527.9i	−0.608222	−	1.05347i	−0.991533	−	0.129852i	$-0.958550\pi$
$521$	−7233.00	−	12527.9i	−0.608222	−	1.05347i	0.383312	−	0.923619i	$-0.374783\pi$
$522$	1026.00	+	1777.08i	0.0860284	+	0.149005i
$523$	9262.00	−	16042.3i	0.774377	−	1.34126i	−0.160768	−	0.986992i	$-0.551397\pi$
$523$	9262.00	−	16042.3i	0.774377	−	1.34126i	0.935144	−	0.354267i	$-0.115270\pi$
$524$	−720.000			−0.0600255
$525$		0			0
$526$	1656.00			0.137272
$527$	−168.000	+	290.985i	−0.0138865	+	0.0240522i
$528$	1728.00	+	2992.98i	0.142427	+	0.246691i
$529$	−10116.5	−	17522.3i	−0.831470	−	1.44015i
$530$	11772.0	−	20389.7i	0.964798	−	1.67108i
$531$	4428.00			0.361881
$532$		0			0
$533$	−204.000			−0.0165783
$534$	1170.00	−	2026.50i	0.0948143	−	0.164223i
$535$	6264.00	+	10849.6i	0.506199	+	0.876762i
$536$	496.000	+	859.097i	0.0399700	+	0.0692301i
$537$	3852.00	−	6671.86i	0.309546	−	0.536149i
$538$	8268.00			0.662563
$539$		0			0
$540$	−1944.00			−0.154919
$541$	−2179.00	+	3774.14i	−0.173165	+	0.299931i	−0.939525	−	0.342481i	$-0.888733\pi$
$541$	−2179.00	+	3774.14i	−0.173165	+	0.299931i	0.766359	+	0.642412i	$0.222066\pi$
$542$	−2968.00	−	5140.73i	−0.235215	−	0.407404i
$543$	−4047.00	−	7009.61i	−0.319841	−	0.553980i
$544$	96.0000	−	166.277i	0.00756611	−	0.0131049i
$545$	20052.0			1.57602
$546$		0			0
$547$	−2140.00			−0.167276			−0.0836378	−	0.996496i	$-0.526654\pi$
$547$	−2140.00			−0.167276			−0.0836378	+	0.996496i	$0.526654\pi$
$548$	5436.00	−	9415.43i	0.423749	−	0.733955i
$549$	−1125.00	−	1948.56i	−0.0874569	−	0.151480i
$550$	14328.0	+	24816.8i	1.11081	+	1.92399i
$551$	−5244.00	+	9082.87i	−0.405448	+	0.702257i
$552$	−4320.00			−0.333100
$553$		0			0
$554$	−9572.00			−0.734071
$555$	−918.000	+	1590.02i	−0.0702107	+	0.121608i
$556$	−2696.00	−	4669.61i	−0.205640	−	0.356179i
$557$	−1011.00	−	1751.10i	−0.0769074	−	0.133208i	0.825007	−	0.565123i	$-0.191171\pi$
$557$	−1011.00	−	1751.10i	−0.0769074	−	0.133208i	−0.901914	+	0.431915i	$0.857838\pi$
$558$	504.000	−	872.954i	0.0382366	−	0.0662277i
$559$	5576.00			0.421896
$560$		0			0
$561$	1296.00			0.0975350
$562$	4398.00	−	7617.56i	0.330104	−	0.571757i
$563$	3678.00	+	6370.48i	0.275327	+	0.476881i	0.970218	−	0.242235i	$-0.0778805\pi$
$563$	3678.00	+	6370.48i	0.275327	+	0.476881i	−0.694890	+	0.719116i	$0.744547\pi$
$564$	1008.00	+	1745.91i	0.0752561	+	0.130347i
$565$	−4158.00	+	7201.87i	−0.309608	+	0.536256i
$566$	−9544.00			−0.708771
$567$		0			0
$568$	288.000			0.0212750
$569$	−5601.00	+	9701.22i	−0.412665	+	0.714756i	−0.995180	−	0.0980635i	$-0.968735\pi$
$569$	−5601.00	+	9701.22i	−0.412665	+	0.714756i	0.582516	+	0.812820i	$0.302068\pi$
$570$	−4968.00	−	8604.83i	−0.365064	−	0.632310i
$571$	5282.00	+	9148.69i	0.387119	+	0.670509i	0.992061	−	0.125760i	$-0.0401370\pi$
$571$	5282.00	+	9148.69i	0.387119	+	0.670509i	−0.604942	+	0.796270i	$0.706804\pi$
$572$	4896.00	−	8480.12i	0.357888	−	0.619881i
$573$	−12348.0			−0.900253
$574$		0			0
$575$	−35820.0			−2.59791
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	−9287.00	−	16085.6i	−0.670057	−	1.16057i	−0.977888	−	0.209132i	$-0.932936\pi$
$577$	−9287.00	−	16085.6i	−0.670057	−	1.16057i	0.307831	−	0.951441i	$-0.400397\pi$
$578$	4877.00	+	8447.21i	0.350963	+	0.607885i
$579$	4965.00	−	8599.63i	0.356370	−	0.617251i
$580$	8208.00			0.587618
$581$		0			0
$582$	420.000			0.0299133
$583$	23544.0	−	40779.4i	1.67254	−	2.89693i
$584$	4040.00	+	6997.49i	0.286261	+	0.495818i
$585$	2754.00	+	4770.07i	0.194639	+	0.337125i
$586$	6522.00	−	11296.4i	0.459763	−	0.796334i
$587$	−13188.0			−0.927303			−0.463652	−	0.886018i	$-0.653461\pi$
$587$	−13188.0			−0.927303			−0.463652	+	0.886018i	$0.653461\pi$
$588$		0			0
$589$	5152.00			0.360415
$590$	8856.00	−	15339.0i	0.617959	−	1.07034i
$591$	−1917.00	−	3320.34i	−0.133426	−	0.231101i
$592$	272.000	+	471.118i	0.0188837	+	0.0327075i
$593$	−11253.0	+	19490.8i	−0.779267	+	1.34973i	0.153098	+	0.988211i	$0.451075\pi$
$593$	−11253.0	+	19490.8i	−0.779267	+	1.34973i	−0.932365	+	0.361519i	$0.882258\pi$
$594$	−3888.00			−0.268563
$595$		0			0
$596$	2232.00			0.153400
$597$	4404.00	−	7627.95i	0.301916	−	0.522933i
$598$	6120.00	+	10600.2i	0.418504	+	0.724870i
$599$	−5298.00	−	9176.41i	−0.361386	−	0.625939i	0.626803	−	0.779178i	$-0.284363\pi$
$599$	−5298.00	−	9176.41i	−0.361386	−	0.625939i	−0.988189	+	0.153238i	$0.951030\pi$
$600$	−2388.00	+	4136.14i	−0.162483	+	0.281428i
$601$	−14618.0			−0.992148			−0.496074	−	0.868280i	$-0.665225\pi$
$601$	−14618.0			−0.992148			−0.496074	+	0.868280i	$0.665225\pi$
$602$		0			0
$603$	−1116.00			−0.0753682
$604$	−3856.00	+	6678.79i	−0.259766	+	0.449927i
$605$	34677.0	+	60062.3i	2.33028	+	4.03617i
$606$	−4050.00	−	7014.81i	−0.271485	−	0.470226i
$607$	2584.00	−	4475.62i	0.172786	−	0.299275i	−0.766607	−	0.642117i	$-0.778056\pi$
$607$	2584.00	−	4475.62i	0.172786	−	0.299275i	0.939393	+	0.342842i	$0.111390\pi$
$608$	−2944.00			−0.196373
$609$		0			0
$610$	−9000.00			−0.597376
$611$	2856.00	−	4946.74i	0.189102	−	0.327534i
$612$	108.000	+	187.061i	0.00713340	+	0.0123554i
$613$	−2863.00	−	4958.86i	−0.188639	−	0.326732i	0.756158	−	0.654389i	$-0.227074\pi$
$613$	−2863.00	−	4958.86i	−0.188639	−	0.326732i	−0.944797	+	0.327657i	$0.893741\pi$
$614$	−6244.00	+	10814.9i	−0.410403	+	0.710839i
$615$	324.000			0.0212438
$616$		0			0
$617$	−7806.00			−0.509332			−0.254666	−	0.967029i	$-0.581965\pi$
$617$	−7806.00			−0.509332			−0.254666	+	0.967029i	$0.581965\pi$
$618$	6000.00	−	10392.3i	0.390543	−	0.676440i
$619$	−9026.00	−	15633.5i	−0.586083	−	1.01513i	−0.994739	−	0.102438i	$-0.967336\pi$
$619$	−9026.00	−	15633.5i	−0.586083	−	1.01513i	0.408656	−	0.912688i	$-0.365998\pi$
$620$	−2016.00	−	3491.81i	−0.130588	−	0.226185i
$621$	2430.00	−	4208.88i	0.157025	−	0.271975i
$622$	1056.00			0.0680735
$623$		0			0
$624$	1632.00			0.104699
$625$	449.500	−	778.557i	0.0287680	−	0.0498276i
$626$	−5830.00	−	10097.9i	−0.372226	−	0.644715i
$627$	−9936.00	−	17209.7i	−0.632864	−	1.09615i
$628$	−4820.00	+	8348.48i	−0.306272	+	0.530479i
$629$	204.000			0.0129317
$630$		0			0
$631$	−6208.00			−0.391659			−0.195829	−	0.980638i	$-0.562740\pi$
$631$	−6208.00			−0.391659			−0.195829	+	0.980638i	$0.562740\pi$
$632$	−224.000	+	387.979i	−0.0140985	+	0.0244193i
$633$	5262.00	+	9114.05i	0.330404	+	0.572276i
$634$	−5046.00	−	8739.93i	−0.316092	−	0.547487i
$635$	9576.00	−	16586.1i	0.598444	−	1.03654i
$636$	7848.00			0.489298
$637$		0			0
$638$	16416.0			1.01868
$639$	−162.000	+	280.592i	−0.0100291	+	0.0173710i
$640$	1152.00	+	1995.32i	0.0711512	+	0.123238i
$641$	10755.0	+	18628.2i	0.662710	+	1.14785i	0.979901	+	0.199485i	$0.0639270\pi$
$641$	10755.0	+	18628.2i	0.662710	+	1.14785i	−0.317191	+	0.948362i	$0.602740\pi$
$642$	−2088.00	+	3616.52i	−0.128359	+	0.222325i
$643$	11140.0			0.683233			0.341616	−	0.939839i	$-0.389026\pi$
$643$	11140.0			0.683233			0.341616	+	0.939839i	$0.389026\pi$
$644$		0			0
$645$	−8856.00			−0.540627
$646$	−552.000	+	956.092i	−0.0336194	+	0.0582306i
$647$	4656.00	+	8064.43i	0.282915	+	0.490024i	0.972102	−	0.234561i	$-0.0753651\pi$
$647$	4656.00	+	8064.43i	0.282915	+	0.490024i	−0.689186	+	0.724584i	$0.742032\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	17712.0	−	30678.1i	1.07127	−	1.85550i
$650$	13532.0			0.816567
$651$		0			0
$652$	2960.00			0.177795
$653$	−2439.00	+	4224.47i	−0.146165	+	0.253164i	−0.929807	−	0.368048i	$-0.880026\pi$
$653$	−2439.00	+	4224.47i	−0.146165	+	0.253164i	0.783642	+	0.621212i	$0.213360\pi$
$654$	3342.00	+	5788.51i	0.199820	+	0.346099i
$655$	−1620.00	−	2805.92i	−0.0966391	−	0.167384i
$656$	48.0000	−	83.1384i	0.00285684	−	0.00494819i
$657$	−9090.00			−0.539779
$658$		0			0
$659$	−9744.00			−0.575982			−0.287991	−	0.957633i	$-0.592987\pi$
$659$	−9744.00			−0.575982			−0.287991	+	0.957633i	$0.592987\pi$
$660$	−7776.00	+	13468.4i	−0.458607	+	0.794330i
$661$	1495.00	+	2589.42i	0.0879709	+	0.152370i	0.906653	−	0.421876i	$-0.138628\pi$
$661$	1495.00	+	2589.42i	0.0879709	+	0.152370i	−0.818682	+	0.574247i	$0.805295\pi$
$662$	5020.00	+	8694.90i	0.294725	+	0.510478i
$663$	306.000	−	530.008i	0.0179247	−	0.0310464i
$664$	−1824.00			−0.106604
$665$		0			0
$666$	−612.000			−0.0356074
$667$	−10260.0	+	17770.8i	−0.595605	+	1.03162i
$668$	7968.00	+	13801.0i	0.461514	+	0.799365i
$669$	−2832.00	−	4905.17i	−0.163664	−	0.283475i
$670$	−2232.00	+	3865.94i	−0.128701	+	0.222917i
$671$	−18000.0			−1.03559
$672$		0			0
$673$	33266.0			1.90536			0.952682	−	0.303969i	$-0.0983118\pi$
$673$	33266.0			1.90536			0.952682	+	0.303969i	$0.0983118\pi$
$674$	7486.00	−	12966.1i	0.427819	−	0.741004i
$675$	−2686.50	−	4653.15i	−0.153190	−	0.265333i
$676$	2082.00	+	3606.13i	0.118457	+	0.205174i
$677$	2685.00	−	4650.56i	0.152427	−	0.264011i	−0.779692	−	0.626163i	$-0.784625\pi$
$677$	2685.00	−	4650.56i	0.152427	−	0.264011i	0.932119	+	0.362152i	$0.117958\pi$
$678$	−2772.00			−0.157018
$679$		0			0
$680$	864.000			0.0487248
$681$	5346.00	−	9259.54i	0.300821	−	0.521037i
$682$	−4032.00	−	6983.63i	−0.226383	−	0.392107i
$683$	−192.000	−	332.554i	−0.0107565	−	0.0186308i	0.860597	−	0.509286i	$-0.170091\pi$
$683$	−192.000	−	332.554i	−0.0107565	−	0.0186308i	−0.871354	+	0.490656i	$0.836757\pi$
$684$	1656.00	−	2868.28i	0.0925713	−	0.160338i
$685$	48924.0			2.72889
$686$		0			0
$687$	−4002.00			−0.222250
$688$	−1312.00	+	2272.45i	−0.0727028	+	0.125925i
$689$	−11118.0	−	19256.9i	−0.614749	−	1.06478i
$690$	−9720.00	−	16835.5i	−0.536281	−	0.928866i
$691$	−7262.00	+	12578.2i	−0.399797	+	0.692468i	−0.993701	−	0.112068i	$-0.964253\pi$
$691$	−7262.00	+	12578.2i	−0.399797	+	0.692468i	0.593904	+	0.804536i	$0.297586\pi$
$692$	4152.00			0.228086
$693$		0			0
$694$	−20064.0			−1.09743
$695$	12132.0	−	21013.2i	0.662148	−	1.14687i
$696$	1368.00	+	2369.45i	0.0745027	+	0.129043i
$697$	−18.0000	−	31.1769i	−0.000978190	−	0.00169428i
$698$	5942.00	−	10291.8i	0.322218	−	0.558098i
$699$	7974.00			0.431480
$700$		0			0
$701$	24750.0			1.33352			0.666758	−	0.745274i	$-0.267682\pi$
$701$	24750.0			1.33352			0.666758	+	0.745274i	$0.267682\pi$
$702$	−918.000	+	1590.02i	−0.0493557	+	0.0854865i
$703$	−1564.00	−	2708.93i	−0.0839081	−	0.145333i
$704$	2304.00	+	3990.65i	0.123346	+	0.213641i
$705$	−4536.00	+	7856.58i	−0.242320	+	0.419711i
$706$	180.000			0.00959545
$707$		0			0
$708$	5904.00			0.313398
$709$	521.000	−	902.398i	0.0275974	−	0.0478001i	−0.851897	−	0.523710i	$-0.824548\pi$
$709$	521.000	−	902.398i	0.0275974	−	0.0478001i	0.879494	+	0.475909i	$0.157881\pi$
$710$	648.000	+	1122.37i	0.0342521	+	0.0593264i
$711$	−252.000	−	436.477i	−0.0132922	−	0.0230227i
$712$	1560.00	−	2702.00i	0.0821116	−	0.142221i
$713$	10080.0			0.529452
$714$		0			0
$715$	44064.0			2.30476
$716$	5136.00	−	8895.81i	0.268074	−	0.464319i
$717$	882.000	+	1527.67i	0.0459399	+	0.0795702i
$718$	−10596.0	−	18352.8i	−0.550751	−	0.953929i
$719$	−18480.0	+	32008.3i	−0.958536	+	1.66023i	−0.232477	+	0.972602i	$0.574683\pi$
$719$	−18480.0	+	32008.3i	−0.958536	+	1.66023i	−0.726059	+	0.687632i	$0.758650\pi$
$720$	−2592.00			−0.134164
$721$		0			0
$722$	3210.00			0.165462
$723$	8535.00	−	14783.1i	0.439032	−	0.760426i
$724$	−5396.00	−	9346.15i	−0.276990	−	0.479761i
$725$	11343.0	+	19646.7i	0.581060	+	1.00643i
$726$	−11559.0	+	20020.8i	−0.590902	+	1.02347i
$727$	16288.0			0.830933			0.415467	−	0.909608i	$-0.363618\pi$
$727$	16288.0			0.830933			0.415467	+	0.909608i	$0.363618\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−18180.0	+	31488.7i	−0.921742	+	1.59650i
$731$	492.000	+	852.169i	0.0248937	+	0.0431171i
$732$	−1500.00	−	2598.08i	−0.0757399	−	0.131185i
$733$	−3905.00	+	6763.66i	−0.196773	+	0.340820i	−0.947480	−	0.319814i	$-0.896379\pi$
$733$	−3905.00	+	6763.66i	−0.196773	+	0.340820i	0.750707	+	0.660635i	$0.229713\pi$
$734$	−8032.00			−0.403905
$735$		0			0
$736$	−5760.00			−0.288473
$737$	−4464.00	+	7731.87i	−0.223112	+	0.386441i
$738$	54.0000	+	93.5307i	0.00269345	+	0.00466520i
$739$	18350.0	+	31783.1i	0.913418	+	1.58209i	0.809202	+	0.587531i	$0.199900\pi$
$739$	18350.0	+	31783.1i	0.913418	+	1.58209i	0.104216	+	0.994555i	$0.466767\pi$
$740$	−1224.00	+	2120.03i	−0.0608042	+	0.105316i
$741$	−9384.00			−0.465222
$742$		0			0
$743$	29508.0			1.45699			0.728495	−	0.685051i	$-0.240220\pi$
$743$	29508.0			1.45699			0.728495	+	0.685051i	$0.240220\pi$
$744$	672.000	−	1163.94i	0.0331139	−	0.0573549i
$745$	5022.00	+	8698.36i	0.246969	+	0.427763i
$746$	−3278.00	−	5677.66i	−0.160880	−	0.278651i
$747$	1026.00	−	1777.08i	0.0502535	−	0.0870416i
$748$	1728.00			0.0844678
$749$		0			0
$750$	−7992.00			−0.389102
$751$	7568.00	−	13108.2i	0.367723	−	0.636916i	−0.621486	−	0.783425i	$-0.713471\pi$
$751$	7568.00	−	13108.2i	0.367723	−	0.636916i	0.989209	+	0.146510i	$0.0468040\pi$
$752$	1344.00	+	2327.88i	0.0651737	+	0.112884i
$753$	270.000	+	467.654i	0.0130669	+	0.0226325i
$754$	3876.00	−	6713.43i	0.187209	−	0.324256i
$755$	−34704.0			−1.67286
$756$		0			0
$757$	3422.00			0.164299			0.0821497	−	0.996620i	$-0.473821\pi$
$757$	3422.00			0.164299			0.0821497	+	0.996620i	$0.473821\pi$
$758$	−4628.00	+	8015.93i	−0.221763	+	0.384105i
$759$	−19440.0	−	33671.1i	−0.929680	−	1.61025i
$760$	−6624.00	−	11473.1i	−0.316155	−	0.547596i
$761$	15723.0	−	27233.0i	0.748960	−	1.29724i	−0.199362	−	0.979926i	$-0.563887\pi$
$761$	15723.0	−	27233.0i	0.748960	−	1.29724i	0.948322	−	0.317310i	$-0.102780\pi$
$762$	6384.00			0.303501
$763$		0			0
$764$	−16464.0			−0.779642
$765$	−486.000	+	841.777i	−0.0229691	+	0.0397837i
$766$	−2880.00	−	4988.31i	−0.135847	−	0.235294i
$767$	−8364.00	−	14486.9i	−0.393750	−	0.681996i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	18718.0			0.877748			0.438874	−	0.898549i	$-0.355377\pi$
$769$	18718.0			0.877748			0.438874	+	0.898549i	$0.355377\pi$
$770$		0			0
$771$	−15930.0			−0.744105
$772$	6620.00	−	11466.2i	0.308626	−	0.534555i
$773$	−843.000	−	1460.12i	−0.0392246	−	0.0679390i	0.845747	−	0.533585i	$-0.179155\pi$
$773$	−843.000	−	1460.12i	−0.0392246	−	0.0679390i	−0.884971	+	0.465646i	$0.845822\pi$
$774$	−1476.00	−	2556.51i	−0.0685449	−	0.118723i
$775$	5572.00	−	9650.99i	0.258261	−	0.447321i
$776$	560.000			0.0259057
$777$		0			0
$778$	15948.0			0.734915
$779$	−276.000	+	478.046i	−0.0126941	+	0.0219869i
$780$	3672.00	+	6360.09i	0.168562	+	0.291959i
$781$	1296.00	+	2244.74i	0.0593784	+	0.102846i
$782$	−1080.00	+	1870.61i	−0.0493871	+	0.0855410i
$783$	−3078.00			−0.140484
$784$		0			0
$785$	−43380.0			−1.97235
$786$	540.000	−	935.307i	0.0245053	−	0.0424444i
$787$	2746.00	+	4756.21i	0.124377	+	0.215426i	0.921489	−	0.388404i	$-0.126974\pi$
$787$	2746.00	+	4756.21i	0.124377	+	0.215426i	−0.797113	+	0.603831i	$0.793640\pi$
$788$	−2556.00	−	4427.12i	−0.115550	−	0.200139i
$789$	−1242.00	+	2151.21i	−0.0560410	+	0.0970659i
$790$	−2016.00			−0.0907925
$791$		0			0
$792$	−5184.00			−0.232583
$793$	−4250.00	+	7361.22i	−0.190318	+	0.329640i
$794$	−12346.0	−	21383.9i	−0.551818	−	0.955776i
$795$	17658.0	+	30584.6i	0.787754	+	1.36443i
$796$	5872.00	−	10170.6i	0.261467	−	0.452874i
$797$	17310.0			0.769325			0.384662	−	0.923057i	$-0.374318\pi$
$797$	17310.0			0.769325			0.384662	+	0.923057i	$0.374318\pi$
$798$		0			0
$799$	1008.00			0.0446314
$800$	−3184.00	+	5514.85i	−0.140714	+	0.243724i
$801$	1755.00	+	3039.75i	0.0774156	+	0.134088i
$802$	−9738.00	−	16866.7i	−0.428754	−	0.742624i
$803$	−36360.0	+	62977.4i	−1.59790	+	2.76765i
$804$	−1488.00			−0.0652708
$805$		0			0
$806$	−3808.00			−0.166416
$807$	−6201.00	+	10740.4i	−0.270490	+	0.468503i
$808$	−5400.00	−	9353.07i	−0.235113	−	0.407228i
$809$	−17877.0	−	30963.9i	−0.776912	−	1.34565i	−0.933714	−	0.358021i	$-0.883452\pi$
$809$	−17877.0	−	30963.9i	−0.776912	−	1.34565i	0.156801	−	0.987630i	$-0.449882\pi$
$810$	1458.00	−	2525.33i	0.0632456	−	0.109545i
$811$	−33644.0			−1.45672			−0.728360	−	0.685194i	$-0.759717\pi$
$811$	−33644.0			−1.45672			−0.728360	+	0.685194i	$0.759717\pi$
$812$		0			0
$813$	8904.00			0.384104
$814$	−2448.00	+	4240.06i	−0.105408	+	0.182573i
$815$	6660.00	+	11535.5i	0.286245	+	0.495791i
$816$	144.000	+	249.415i	0.00617771	+	0.0107001i
$817$	7544.00	−	13066.6i	0.323049	−	0.559538i
$818$	860.000			0.0367594
$819$		0			0
$820$	432.000			0.0183977
$821$	−14367.0	+	24884.4i	−0.610733	+	1.05782i	0.380384	+	0.924829i	$0.375792\pi$
$821$	−14367.0	+	24884.4i	−0.610733	+	1.05782i	−0.991117	+	0.132992i	$0.957542\pi$
$822$	8154.00	+	14123.1i	0.345990	+	0.599271i
$823$	14336.0	+	24830.7i	0.607195	+	1.05169i	0.991700	+	0.128570i	$0.0410387\pi$
$823$	14336.0	+	24830.7i	0.607195	+	1.05169i	−0.384505	+	0.923123i	$0.625628\pi$
$824$	8000.00	−	13856.4i	0.338220	−	0.585814i
$825$	−42984.0			−1.81395
$826$		0			0
$827$	−15912.0			−0.669062			−0.334531	−	0.942385i	$-0.608578\pi$
$827$	−15912.0			−0.669062			−0.334531	+	0.942385i	$0.608578\pi$
$828$	3240.00	−	5611.84i	0.135988	−	0.235538i
$829$	8767.00	+	15184.9i	0.367299	+	0.636180i	0.989142	−	0.146962i	$-0.0469494\pi$
$829$	8767.00	+	15184.9i	0.367299	+	0.636180i	−0.621844	+	0.783141i	$0.713616\pi$
$830$	−4104.00	−	7108.34i	−0.171629	−	0.297270i
$831$	7179.00	−	12434.4i	0.299683	−	0.519067i
$832$	2176.00			0.0906721
$833$		0			0
$834$	8088.00			0.335809
$835$	−35856.0	+	62104.4i	−1.48605	+	2.57391i
$836$	−13248.0	−	22946.2i	−0.548076	−	0.949296i
$837$	756.000	+	1309.43i	0.0312201	+	0.0540747i
$838$	−1812.00	+	3138.48i	−0.0746951	+	0.129376i
$839$	−40656.0			−1.67295			−0.836473	−	0.548009i	$-0.815386\pi$
$839$	−40656.0			−1.67295			−0.836473	+	0.548009i	$0.815386\pi$
$840$		0			0
$841$	−11393.0			−0.467137
$842$	10690.0	−	18515.6i	0.437532	−	0.757827i
$843$	6597.00	+	11426.3i	0.269529	+	0.466838i
$844$	7016.00	+	12152.1i	0.286138	+	0.495606i
$845$	−9369.00	+	16227.6i	−0.381424	+	0.660646i
$846$	−3024.00			−0.122893
$847$		0			0
$848$	10464.0			0.423744
$849$	7158.00	−	12398.0i	0.289354	−	0.501177i
$850$	1194.00	+	2068.07i	0.0481810	+	0.0834520i
$851$	−3060.00	−	5300.08i	−0.123261	−	0.213495i
$852$	−216.000	+	374.123i	−0.00868549	+	0.0150437i
$853$	−23870.0			−0.958140			−0.479070	−	0.877777i	$-0.659026\pi$
$853$	−23870.0			−0.958140			−0.479070	+	0.877777i	$0.659026\pi$
$854$		0			0
$855$	14904.0			0.596147
$856$	−2784.00	+	4822.03i	−0.111163	+	0.192539i
$857$	−14805.0	−	25643.0i	−0.590116	−	1.02211i	−0.994216	−	0.107396i	$-0.965749\pi$
$857$	−14805.0	−	25643.0i	−0.590116	−	1.02211i	0.404101	−	0.914715i	$-0.367585\pi$
$858$	7344.00	+	12720.2i	0.292214	+	0.506130i
$859$	−22742.0	+	39390.3i	−0.903314	+	1.56459i	−0.0801503	+	0.996783i	$0.525540\pi$
$859$	−22742.0	+	39390.3i	−0.903314	+	1.56459i	−0.823164	+	0.567804i	$0.807793\pi$
$860$	−11808.0			−0.468197
$861$		0			0
$862$	−8232.00			−0.325270
$863$	−23082.0	+	39979.2i	−0.910452	+	1.57695i	−0.0970261	+	0.995282i	$0.530933\pi$
$863$	−23082.0	+	39979.2i	−0.910452	+	1.57695i	−0.813426	+	0.581668i	$0.802400\pi$
$864$	−432.000	−	748.246i	−0.0170103	−	0.0294628i
$865$	9342.00	+	16180.8i	0.367211	+	0.636028i
$866$	9938.00	−	17213.1i	0.389962	−	0.675434i
$867$	−14631.0			−0.573120
$868$		0			0
$869$	−4032.00			−0.157395
$870$	−6156.00	+	10662.5i	−0.239894	+	0.415509i
$871$	2108.00	+	3651.16i	0.0820056	+	0.142038i
$872$	4456.00	+	7718.02i	0.173050	+	0.299731i
$873$	−315.000	+	545.596i	−0.0122121	+	0.0211519i
$874$	33120.0			1.28181
$875$		0			0
$876$	−12120.0			−0.467462
$877$	1493.00	−	2585.95i	0.0574858	−	0.0995683i	−0.835850	−	0.548957i	$-0.815025\pi$
$877$	1493.00	−	2585.95i	0.0574858	−	0.0995683i	0.893336	+	0.449389i	$0.148358\pi$
$878$	1784.00	+	3089.98i	0.0685730	+	0.118772i
$879$	9783.00	+	16944.7i	0.375395	+	0.650204i
$880$	−10368.0	+	17957.9i	−0.397165	+	0.687910i
$881$	−6534.00			−0.249871			−0.124935	−	0.992165i	$-0.539872\pi$
$881$	−6534.00			−0.249871			−0.124935	+	0.992165i	$0.539872\pi$
$882$		0			0
$883$	29756.0			1.13405			0.567027	−	0.823699i	$-0.308094\pi$
$883$	29756.0			1.13405			0.567027	+	0.823699i	$0.308094\pi$
$884$	408.000	−	706.677i	0.0155232	−	0.0268870i
$885$	13284.0	+	23008.6i	0.504561	+	0.873926i
$886$	11712.0	+	20285.8i	0.444100	+	0.769203i
$887$	14976.0	−	25939.2i	0.566905	−	0.981909i	−0.429964	−	0.902846i	$-0.641474\pi$
$887$	14976.0	−	25939.2i	0.566905	−	0.981909i	0.996870	−	0.0790627i	$-0.0251927\pi$
$888$	−816.000			−0.0308369
$889$		0			0
$890$	14040.0			0.528789
$891$	2916.00	−	5050.66i	0.109640	−	0.189903i
$892$	−3776.00	−	6540.22i	−0.141737	−	0.245497i
$893$	−7728.00	−	13385.3i	−0.289594	−	0.501592i
$894$	−1674.00	+	2899.45i	−0.0626252	+	0.108470i
$895$	46224.0			1.72637
$896$		0			0
$897$	−18360.0			−0.683414
$898$	−7650.00	+	13250.2i	−0.284280	+	0.492388i
$899$	−3192.00	−	5528.71i	−0.118420	−	0.205109i
$900$	−3582.00	−	6204.21i	−0.132667	−	0.229785i
$901$	1962.00	−	3398.28i	0.0725457	−	0.125653i
$902$	864.000			0.0318936
$903$		0			0
$904$	−3696.00			−0.135981
$905$	24282.0	−	42057.7i	0.891891	−	1.54480i
$906$	−5784.00	−	10018.2i	−0.212098	−	0.367364i
$907$	18134.0	+	31409.0i	0.663869	+	1.14986i	0.979591	+	0.201004i	$0.0644203\pi$
$907$	18134.0	+	31409.0i	0.663869	+	1.14986i	−0.315721	+	0.948852i	$0.602246\pi$
$908$	7128.00	−	12346.1i	0.260519	−	0.451232i
$909$	12150.0			0.443333
$910$		0			0
$911$	−23604.0			−0.858436			−0.429218	−	0.903201i	$-0.641211\pi$
$911$	−23604.0			−0.858436			−0.429218	+	0.903201i	$0.641211\pi$
$912$	2208.00	−	3824.37i	0.0801691	−	0.138857i
$913$	−8208.00	−	14216.7i	−0.297530	−	0.515338i
$914$	−3674.00	−	6363.55i	−0.132960	−	0.230293i
$915$	6750.00	−	11691.3i	0.243878	−	0.422409i
$916$	−5336.00			−0.192474
$917$		0			0
$918$	−324.000			−0.0116488
$919$	−17092.0	+	29604.2i	−0.613507	+	1.06263i	0.377137	+	0.926157i	$0.376908\pi$
$919$	−17092.0	+	29604.2i	−0.613507	+	1.06263i	−0.990644	+	0.136468i	$0.956425\pi$
$920$	−12960.0	−	22447.4i	−0.464433	−	0.804422i
$921$	−9366.00	−	16222.4i	−0.335093	−	0.580397i
$922$	−3102.00	+	5372.82i	−0.110801	+	0.191914i
$923$	1224.00			0.0436495
$924$		0			0
$925$	−6766.00			−0.240502
$926$	−8984.00	+	15560.7i	−0.318826	+	0.552222i
$927$	9000.00	+	15588.5i	0.318877	+	0.552311i
$928$	1824.00	+	3159.26i	0.0645213	+	0.111754i
$929$	−26961.0	+	46697.8i	−0.952165	+	1.64920i	−0.211440	+	0.977391i	$0.567815\pi$
$929$	−26961.0	+	46697.8i	−0.952165	+	1.64920i	−0.740725	+	0.671808i	$0.765518\pi$
$930$	6048.00			0.213249
$931$		0			0
$932$	10632.0			0.373672
$933$	−792.000	+	1371.78i	−0.0277909	+	0.0481353i
$934$	3612.00	+	6256.17i	0.126540	+	0.219174i
$935$	3888.00	+	6734.21i	0.135991	+	0.235543i
$936$	−1224.00	+	2120.03i	−0.0427433	+	0.0740335i
$937$	−40538.0			−1.41336			−0.706680	−	0.707533i	$-0.749808\pi$
$937$	−40538.0			−1.41336			−0.706680	+	0.707533i	$0.749808\pi$
$938$		0			0
$939$	17490.0			0.607843
$940$	−6048.00	+	10475.4i	−0.209855	+	0.363480i
$941$	−1803.00	−	3122.89i	−0.0624613	−	0.108186i	0.833104	−	0.553117i	$-0.186562\pi$
$941$	−1803.00	−	3122.89i	−0.0624613	−	0.108186i	−0.895565	+	0.444931i	$0.853228\pi$
$942$	−7230.00	−	12522.7i	−0.250070	−	0.433134i
$943$	−540.000	+	935.307i	−0.0186477	+	0.0322988i
$944$	7872.00			0.271411
$945$		0			0
$946$	−23616.0			−0.811652
$947$	−7032.00	+	12179.8i	−0.241298	+	0.417941i	−0.961084	−	0.276255i	$-0.910906\pi$
$947$	−7032.00	+	12179.8i	−0.241298	+	0.417941i	0.719786	+	0.694196i	$0.244240\pi$
$948$	−336.000	−	581.969i	−0.0115114	−	0.0199383i
$949$	17170.0	+	29739.3i	0.587315	+	1.01726i
$950$	18308.0	−	31710.4i	0.625253	−	1.08297i
$951$	15138.0			0.516176
$952$		0			0
$953$	33066.0			1.12394			0.561969	−	0.827158i	$-0.310044\pi$
$953$	33066.0			1.12394			0.561969	+	0.827158i	$0.310044\pi$
$954$	−5886.00	+	10194.9i	−0.199755	+	0.345986i
$955$	−37044.0	−	64162.1i	−1.25520	−	2.17407i
$956$	1176.00	+	2036.89i	0.0397851	+	0.0689098i
$957$	−12312.0	+	21325.0i	−0.415873	+	0.720313i
$958$	18576.0			0.626475
$959$		0			0
$960$	−3456.00			−0.116190
$961$	13327.5	−	23083.9i	0.447367	−	0.774862i
$962$	1156.00	+	2002.25i	0.0387432	+	0.0671052i
$963$	−3132.00	−	5424.78i	−0.104805	−	0.181528i
$964$	11380.0	−	19710.7i	0.380213	−	0.658548i
$965$	59580.0			1.98751
$966$		0			0
$967$	−26368.0			−0.876875			−0.438437	−	0.898762i	$-0.644468\pi$
$967$	−26368.0			−0.876875			−0.438437	+	0.898762i	$0.644468\pi$
$968$	−15412.0	+	26694.4i	−0.511736	+	0.886353i
$969$	−828.000	−	1434.14i	−0.0274501	−	0.0475450i
$970$	1260.00	+	2182.38i	0.0417074	+	0.0722393i
$971$	27942.0	−	48397.0i	0.923482	−	1.59952i	0.129499	−	0.991580i	$-0.458663\pi$
$971$	27942.0	−	48397.0i	0.923482	−	1.59952i	0.793984	−	0.607939i	$-0.208003\pi$
$972$	972.000			0.0320750
$973$		0			0
$974$	−11696.0			−0.384768
$975$	−10149.0	+	17578.6i	−0.333362	+	0.577400i
$976$	−2000.00	−	3464.10i	−0.0655927	−	0.113610i
$977$	25563.0	+	44276.4i	0.837086	+	1.44988i	0.892321	+	0.451402i	$0.149076\pi$
$977$	25563.0	+	44276.4i	0.837086	+	1.44988i	−0.0552350	+	0.998473i	$0.517591\pi$
$978$	−2220.00	+	3845.15i	−0.0725846	+	0.125720i
$979$	28080.0			0.916691
$980$		0			0
$981$	−10026.0			−0.326305
$982$	5952.00	−	10309.2i	0.193417	−	0.335009i
$983$	−7092.00	−	12283.7i	−0.230112	−	0.398565i	0.727729	−	0.685865i	$-0.240576\pi$
$983$	−7092.00	−	12283.7i	−0.230112	−	0.398565i	−0.957841	+	0.287300i	$0.907242\pi$
$984$	72.0000	+	124.708i	0.00233260	+	0.00404018i
$985$	11502.0	−	19922.0i	0.372065	−	0.644436i
$986$	1368.00			0.0441846
$987$		0			0
$988$	−12512.0			−0.402894
$989$	14760.0	−	25565.1i	0.474561	−	0.821964i
$990$	−11664.0	−	20202.6i	−0.374451	−	0.648568i
$991$	−25840.0	−	44756.2i	−0.828289	−	1.43464i	−0.899379	−	0.437169i	$-0.855981\pi$
$991$	−25840.0	−	44756.2i	−0.828289	−	1.43464i	0.0710900	−	0.997470i	$-0.477352\pi$
$992$	896.000	−	1551.92i	0.0286774	−	0.0496708i
$993$	−15060.0			−0.481284
$994$		0			0
$995$	52848.0			1.68381
$996$	1368.00	−	2369.45i	0.0435208	−	0.0753803i
$997$	26047.0	+	45114.7i	0.827399	+	1.43310i	0.900072	+	0.435741i	$0.143514\pi$
$997$	26047.0	+	45114.7i	0.827399	+	1.43310i	−0.0726730	+	0.997356i	$0.523153\pi$
$998$	−10748.0	−	18616.1i	−0.340904	−	0.590463i
$999$	459.000	−	795.011i	0.0145367	−	0.0251782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.e.b.79.1		2
3.2	odd	2		882.4.g.o.667.1		2
7.2	even	3		294.4.a.i.1.1		1
7.3	odd	6		294.4.e.c.67.1		2
7.4	even	3	inner	294.4.e.b.67.1		2
7.5	odd	6		42.4.a.a.1.1	✓	1
7.6	odd	2		294.4.e.c.79.1		2
21.2	odd	6		882.4.a.g.1.1		1
21.5	even	6		126.4.a.a.1.1		1
21.11	odd	6		882.4.g.o.361.1		2
21.17	even	6		882.4.g.w.361.1		2
21.20	even	2		882.4.g.w.667.1		2
28.19	even	6		336.4.a.l.1.1		1
28.23	odd	6		2352.4.a.a.1.1		1
35.12	even	12		1050.4.g.a.799.2		2
35.19	odd	6		1050.4.a.g.1.1		1
35.33	even	12		1050.4.g.a.799.1		2
56.5	odd	6		1344.4.a.o.1.1		1
56.19	even	6		1344.4.a.a.1.1		1
84.47	odd	6		1008.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.a.a.1.1	✓	1	7.5	odd	6
126.4.a.a.1.1		1	21.5	even	6
294.4.a.i.1.1		1	7.2	even	3
294.4.e.b.67.1		2	7.4	even	3	inner
294.4.e.b.79.1		2	1.1	even	1	trivial
294.4.e.c.67.1		2	7.3	odd	6
294.4.e.c.79.1		2	7.6	odd	2
336.4.a.l.1.1		1	28.19	even	6
882.4.a.g.1.1		1	21.2	odd	6
882.4.g.o.361.1		2	21.11	odd	6
882.4.g.o.667.1		2	3.2	odd	2
882.4.g.w.361.1		2	21.17	even	6
882.4.g.w.667.1		2	21.20	even	2
1008.4.a.b.1.1		1	84.47	odd	6
1050.4.a.g.1.1		1	35.19	odd	6
1050.4.g.a.799.1		2	35.33	even	12
1050.4.g.a.799.2		2	35.12	even	12
1344.4.a.a.1.1		1	56.19	even	6
1344.4.a.o.1.1		1	56.5	odd	6
2352.4.a.a.1.1		1	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(9.00000 - 15.5885i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(9.00000 - 15.5885i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(18.0000 + 31.1769i) q^{10} +(36.0000 + 62.3538i) q^{11} +(-6.00000 + 10.3923i) q^{12} +34.0000 q^{13} -54.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(46.0000 - 79.6743i) q^{19} -72.0000 q^{20} -144.000 q^{22} +(90.0000 - 155.885i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-99.5000 - 172.339i) q^{25} +(-34.0000 + 58.8897i) q^{26} +27.0000 q^{27} -114.000 q^{29} +(54.0000 - 93.5307i) q^{30} +(28.0000 + 48.4974i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(108.000 - 187.061i) q^{33} -12.0000 q^{34} +36.0000 q^{36} +(17.0000 - 29.4449i) q^{37} +(92.0000 + 159.349i) q^{38} +(-51.0000 - 88.3346i) q^{39} +(72.0000 - 124.708i) q^{40} -6.00000 q^{41} +164.000 q^{43} +(144.000 - 249.415i) q^{44} +(81.0000 + 140.296i) q^{45} +(180.000 + 311.769i) q^{46} +(84.0000 - 145.492i) q^{47} +48.0000 q^{48} +398.000 q^{50} +(9.00000 - 15.5885i) q^{51} +(-68.0000 - 117.779i) q^{52} +(-327.000 - 566.381i) q^{53} +(-27.0000 + 46.7654i) q^{54} +1296.00 q^{55} -276.000 q^{57} +(114.000 - 197.454i) q^{58} +(-246.000 - 426.084i) q^{59} +(108.000 + 187.061i) q^{60} +(-125.000 + 216.506i) q^{61} -112.000 q^{62} +64.0000 q^{64} +(306.000 - 530.008i) q^{65} +(216.000 + 374.123i) q^{66} +(62.0000 + 107.387i) q^{67} +(12.0000 - 20.7846i) q^{68} -540.000 q^{69} +36.0000 q^{71} +(-36.0000 + 62.3538i) q^{72} +(505.000 + 874.686i) q^{73} +(34.0000 + 58.8897i) q^{74} +(-298.500 + 517.017i) q^{75} -368.000 q^{76} +204.000 q^{78} +(-28.0000 + 48.4974i) q^{79} +(144.000 + 249.415i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(6.00000 - 10.3923i) q^{82} -228.000 q^{83} +108.000 q^{85} +(-164.000 + 284.056i) q^{86} +(171.000 + 296.181i) q^{87} +(288.000 + 498.831i) q^{88} +(195.000 - 337.750i) q^{89} -324.000 q^{90} -720.000 q^{92} +(84.0000 - 145.492i) q^{93} +(168.000 + 290.985i) q^{94} +(-828.000 - 1434.14i) q^{95} +(-48.0000 + 83.1384i) q^{96} +70.0000 q^{97} -648.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} - 4 q^{4} + 18 q^{5} + 12 q^{6} + 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 + 18 * q^5 + 12 * q^6 + 16 * q^8 - 9 * q^9	\( 2 q - 2 q^{2} - 3 q^{3} - 4 q^{4} + 18 q^{5} + 12 q^{6} + 16 q^{8} - 9 q^{9} + 36 q^{10} + 72 q^{11} - 12 q^{12} + 68 q^{13} - 108 q^{15} - 16 q^{16} + 6 q^{17} - 18 q^{18} + 92 q^{19} - 144 q^{20} - 288 q^{22} + 180 q^{23} - 24 q^{24} - 199 q^{25} - 68 q^{26} + 54 q^{27} - 228 q^{29} + 108 q^{30} + 56 q^{31} - 32 q^{32} + 216 q^{33} - 24 q^{34} + 72 q^{36} + 34 q^{37} + 184 q^{38} - 102 q^{39} + 144 q^{40} - 12 q^{41} + 328 q^{43} + 288 q^{44} + 162 q^{45} + 360 q^{46} + 168 q^{47} + 96 q^{48} + 796 q^{50} + 18 q^{51} - 136 q^{52} - 654 q^{53} - 54 q^{54} + 2592 q^{55} - 552 q^{57} + 228 q^{58} - 492 q^{59} + 216 q^{60} - 250 q^{61} - 224 q^{62} + 128 q^{64} + 612 q^{65} + 432 q^{66} + 124 q^{67} + 24 q^{68} - 1080 q^{69} + 72 q^{71} - 72 q^{72} + 1010 q^{73} + 68 q^{74} - 597 q^{75} - 736 q^{76} + 408 q^{78} - 56 q^{79} + 288 q^{80} - 81 q^{81} + 12 q^{82} - 456 q^{83} + 216 q^{85} - 328 q^{86} + 342 q^{87} + 576 q^{88} + 390 q^{89} - 648 q^{90} - 1440 q^{92} + 168 q^{93} + 336 q^{94} - 1656 q^{95} - 96 q^{96} + 140 q^{97} - 1296 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 + 18 * q^5 + 12 * q^6 + 16 * q^8 - 9 * q^9 + 36 * q^10 + 72 * q^11 - 12 * q^12 + 68 * q^13 - 108 * q^15 - 16 * q^16 + 6 * q^17 - 18 * q^18 + 92 * q^19 - 144 * q^20 - 288 * q^22 + 180 * q^23 - 24 * q^24 - 199 * q^25 - 68 * q^26 + 54 * q^27 - 228 * q^29 + 108 * q^30 + 56 * q^31 - 32 * q^32 + 216 * q^33 - 24 * q^34 + 72 * q^36 + 34 * q^37 + 184 * q^38 - 102 * q^39 + 144 * q^40 - 12 * q^41 + 328 * q^43 + 288 * q^44 + 162 * q^45 + 360 * q^46 + 168 * q^47 + 96 * q^48 + 796 * q^50 + 18 * q^51 - 136 * q^52 - 654 * q^53 - 54 * q^54 + 2592 * q^55 - 552 * q^57 + 228 * q^58 - 492 * q^59 + 216 * q^60 - 250 * q^61 - 224 * q^62 + 128 * q^64 + 612 * q^65 + 432 * q^66 + 124 * q^67 + 24 * q^68 - 1080 * q^69 + 72 * q^71 - 72 * q^72 + 1010 * q^73 + 68 * q^74 - 597 * q^75 - 736 * q^76 + 408 * q^78 - 56 * q^79 + 288 * q^80 - 81 * q^81 + 12 * q^82 - 456 * q^83 + 216 * q^85 - 328 * q^86 + 342 * q^87 + 576 * q^88 + 390 * q^89 - 648 * q^90 - 1440 * q^92 + 168 * q^93 + 336 * q^94 - 1656 * q^95 - 96 * q^96 + 140 * q^97 - 1296 * q^99

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