LMFDB - Embedded newform 24.3.b.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,3,Mod(19,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("24.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	24.b (of order $2$, degree $1$, 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:	$0.653952634465$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.4752.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} - 6x + 6 $ x^4 + 3x^2 - 6x + 6
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$0.866025 + 0.719687i$ of defining polynomial
Character	$\chi$	$=$	24.19
Dual form			24.3.b.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.96622i) q^{2} +1.73205 q^{3} +(-3.73205 - 1.43937i) q^{4} +2.87875i q^{5} +(-0.633975 + 3.40559i) q^{6} -10.7436i q^{7} +(4.19615 - 6.81119i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-0.366025 + 1.96622i) q^{2} +1.73205 q^{3} +(-3.73205 - 1.43937i) q^{4} +2.87875i q^{5} +(-0.633975 + 3.40559i) q^{6} -10.7436i q^{7} +(4.19615 - 6.81119i) q^{8} +3.00000 q^{9} +(-5.66025 - 1.05369i) q^{10} -8.00000 q^{11} +(-6.46410 - 2.49307i) q^{12} +15.7298i q^{13} +(21.1244 + 3.93244i) q^{14} +4.98614i q^{15} +(11.8564 + 10.7436i) q^{16} -15.8564 q^{17} +(-1.09808 + 5.89866i) q^{18} +1.07180 q^{19} +(4.14359 - 10.7436i) q^{20} -18.6085i q^{21} +(2.92820 - 15.7298i) q^{22} +21.4873i q^{23} +(7.26795 - 11.7973i) q^{24} +16.7128 q^{25} +(-30.9282 - 5.75749i) q^{26} +5.19615 q^{27} +(-15.4641 + 40.0958i) q^{28} -40.0958i q^{29} +(-9.80385 - 1.82505i) q^{30} -9.20092i q^{31} +(-25.4641 + 19.3799i) q^{32} -13.8564 q^{33} +(5.80385 - 31.1772i) q^{34} +30.9282 q^{35} +(-11.1962 - 4.31812i) q^{36} +9.97227i q^{37} +(-0.392305 + 2.10739i) q^{38} +27.2448i q^{39} +(19.6077 + 12.0797i) q^{40} +51.5692 q^{41} +(36.5885 + 6.81119i) q^{42} -12.7846 q^{43} +(29.8564 + 11.5150i) q^{44} +8.63624i q^{45} +(-42.2487 - 7.86488i) q^{46} -1.54272i q^{47} +(20.5359 + 18.6085i) q^{48} -66.4256 q^{49} +(-6.11731 + 32.8611i) q^{50} -27.4641 q^{51} +(22.6410 - 58.7043i) q^{52} +28.5808i q^{53} +(-1.90192 + 10.2168i) q^{54} -23.0300i q^{55} +(-73.1769 - 45.0819i) q^{56} +1.85641 q^{57} +(78.8372 + 14.6761i) q^{58} -11.2154 q^{59} +(7.17691 - 18.6085i) q^{60} +1.54272i q^{61} +(18.0910 + 3.36777i) q^{62} -32.2309i q^{63} +(-28.7846 - 57.1616i) q^{64} -45.2820 q^{65} +(5.07180 - 27.2448i) q^{66} -43.2154 q^{67} +(59.1769 + 22.8233i) q^{68} +37.2170i q^{69} +(-11.3205 + 60.8117i) q^{70} -84.4063i q^{71} +(12.5885 - 20.4336i) q^{72} +105.426 q^{73} +(-19.6077 - 3.65011i) q^{74} +28.9474 q^{75} +(-4.00000 - 1.54272i) q^{76} +85.9491i q^{77} +(-53.5692 - 9.97227i) q^{78} +73.6627i q^{79} +(-30.9282 + 34.1316i) q^{80} +9.00000 q^{81} +(-18.8756 + 101.396i) q^{82} +12.2872 q^{83} +(-26.7846 + 69.4479i) q^{84} -45.6466i q^{85} +(4.67949 - 25.1374i) q^{86} -69.4479i q^{87} +(-33.5692 + 54.4895i) q^{88} +33.1384 q^{89} +(-16.9808 - 3.16108i) q^{90} +168.995 q^{91} +(30.9282 - 80.1916i) q^{92} -15.9365i q^{93} +(3.03332 + 0.564673i) q^{94} +3.08543i q^{95} +(-44.1051 + 33.5669i) q^{96} -69.1384 q^{97} +(24.3135 - 130.607i) q^{98} -24.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 8 q^{4} - 6 q^{6} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 - 4 * q^8 + 12 * q^9	$ 4 q + 2 q^{2} - 8 q^{4} - 6 q^{6} - 4 q^{8} + 12 q^{9} + 12 q^{10} - 32 q^{11} - 12 q^{12} + 36 q^{14} - 8 q^{16} - 8 q^{17} + 6 q^{18} + 32 q^{19} + 72 q^{20} - 16 q^{22} + 36 q^{24} - 44 q^{25} - 96 q^{26} - 48 q^{28} - 60 q^{30} - 88 q^{32} + 44 q^{34} + 96 q^{35} - 24 q^{36} + 40 q^{38} + 120 q^{40} + 40 q^{41} + 84 q^{42} + 32 q^{43} + 64 q^{44} - 72 q^{46} + 96 q^{48} - 44 q^{49} - 118 q^{50} - 96 q^{51} - 48 q^{52} - 18 q^{54} - 168 q^{56} - 48 q^{57} + 156 q^{58} - 128 q^{59} - 96 q^{60} + 204 q^{62} - 32 q^{64} + 96 q^{65} + 48 q^{66} - 256 q^{67} + 112 q^{68} + 24 q^{70} - 12 q^{72} + 200 q^{73} - 120 q^{74} + 192 q^{75} - 16 q^{76} - 48 q^{78} - 96 q^{80} + 36 q^{81} - 124 q^{82} + 160 q^{83} - 24 q^{84} + 88 q^{86} + 32 q^{88} - 200 q^{89} + 36 q^{90} + 288 q^{91} + 96 q^{92} - 168 q^{94} - 24 q^{96} + 56 q^{97} + 170 q^{98} - 96 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 - 4 * q^8 + 12 * q^9 + 12 * q^10 - 32 * q^11 - 12 * q^12 + 36 * q^14 - 8 * q^16 - 8 * q^17 + 6 * q^18 + 32 * q^19 + 72 * q^20 - 16 * q^22 + 36 * q^24 - 44 * q^25 - 96 * q^26 - 48 * q^28 - 60 * q^30 - 88 * q^32 + 44 * q^34 + 96 * q^35 - 24 * q^36 + 40 * q^38 + 120 * q^40 + 40 * q^41 + 84 * q^42 + 32 * q^43 + 64 * q^44 - 72 * q^46 + 96 * q^48 - 44 * q^49 - 118 * q^50 - 96 * q^51 - 48 * q^52 - 18 * q^54 - 168 * q^56 - 48 * q^57 + 156 * q^58 - 128 * q^59 - 96 * q^60 + 204 * q^62 - 32 * q^64 + 96 * q^65 + 48 * q^66 - 256 * q^67 + 112 * q^68 + 24 * q^70 - 12 * q^72 + 200 * q^73 - 120 * q^74 + 192 * q^75 - 16 * q^76 - 48 * q^78 - 96 * q^80 + 36 * q^81 - 124 * q^82 + 160 * q^83 - 24 * q^84 + 88 * q^86 + 32 * q^88 - 200 * q^89 + 36 * q^90 + 288 * q^91 + 96 * q^92 - 168 * q^94 - 24 * q^96 + 56 * q^97 + 170 * q^98 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.366025	+	1.96622i	−0.183013	+	0.983111i
$2$	−0.366025	+	1.96622i	−0.183013	+	0.983111i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−3.73205	−	1.43937i	−0.933013	−	0.359843i
$5$			2.87875i			0.575749i	0.957668	+	0.287875i	$0.0929487\pi$
$5$			2.87875i			0.575749i	−0.957668	+	0.287875i	$0.907051\pi$
$6$	−0.633975	+	3.40559i	−0.105662	+	0.567599i
$7$		−	10.7436i		−	1.53480i	−0.641166	−	0.767402i	$-0.721549\pi$
$7$		−	10.7436i		−	1.53480i	0.641166	−	0.767402i	$-0.278451\pi$
$8$	4.19615	−	6.81119i	0.524519	−	0.851399i
$9$	3.00000			0.333333
$10$	−5.66025	−	1.05369i	−0.566025	−	0.105369i
$11$	−8.00000			−0.727273			−0.363636	−	0.931541i	$-0.618465\pi$
$11$	−8.00000			−0.727273			−0.363636	+	0.931541i	$0.618465\pi$
$12$	−6.46410	−	2.49307i	−0.538675	−	0.207756i
$13$			15.7298i			1.20998i	0.796232	+	0.604991i	$0.206823\pi$
$13$			15.7298i			1.20998i	−0.796232	+	0.604991i	$0.793177\pi$
$14$	21.1244	+	3.93244i	1.50888	+	0.280889i
$15$			4.98614i			0.332409i
$16$	11.8564	+	10.7436i	0.741025	+	0.671477i
$17$	−15.8564			−0.932730			−0.466365	−	0.884592i	$-0.654437\pi$
$17$	−15.8564			−0.932730			−0.466365	+	0.884592i	$0.654437\pi$
$18$	−1.09808	+	5.89866i	−0.0610042	+	0.327704i
$19$	1.07180			0.0564104			0.0282052	−	0.999602i	$-0.491021\pi$
$19$	1.07180			0.0564104			0.0282052	+	0.999602i	$0.491021\pi$
$20$	4.14359	−	10.7436i	0.207180	−	0.537182i
$21$		−	18.6085i		−	0.886120i
$22$	2.92820	−	15.7298i	0.133100	−	0.714989i
$23$			21.4873i			0.934229i	0.884197	+	0.467114i	$0.154706\pi$
$23$			21.4873i			0.934229i	−0.884197	+	0.467114i	$0.845294\pi$
$24$	7.26795	−	11.7973i	0.302831	−	0.491555i
$25$	16.7128			0.668513
$26$	−30.9282	−	5.75749i	−1.18955	−	0.221442i
$27$	5.19615			0.192450
$28$	−15.4641	+	40.0958i	−0.552289	+	1.43199i
$29$		−	40.0958i		−	1.38261i	−0.722562	−	0.691307i	$-0.757035\pi$
$29$		−	40.0958i		−	1.38261i	0.722562	−	0.691307i	$-0.242965\pi$
$30$	−9.80385	−	1.82505i	−0.326795	−	0.0608351i
$31$		−	9.20092i		−	0.296804i	−0.988927	−	0.148402i	$-0.952587\pi$
$31$		−	9.20092i		−	0.296804i	0.988927	−	0.148402i	$-0.0474129\pi$
$32$	−25.4641	+	19.3799i	−0.795753	+	0.605621i
$33$	−13.8564			−0.419891
$34$	5.80385	−	31.1772i	0.170701	−	0.916976i
$35$	30.9282			0.883663
$36$	−11.1962	−	4.31812i	−0.311004	−	0.119948i
$37$			9.97227i			0.269521i	0.990878	+	0.134760i	$0.0430265\pi$
$37$			9.97227i			0.269521i	−0.990878	+	0.134760i	$0.956974\pi$
$38$	−0.392305	+	2.10739i	−0.0103238	+	0.0554576i
$39$			27.2448i			0.698584i
$40$	19.6077	+	12.0797i	0.490192	+	0.301992i
$41$	51.5692			1.25779			0.628893	−	0.777492i	$-0.283508\pi$
$41$	51.5692			1.25779			0.628893	+	0.777492i	$0.283508\pi$
$42$	36.5885	+	6.81119i	0.871154	+	0.162171i
$43$	−12.7846			−0.297317			−0.148658	−	0.988889i	$-0.547495\pi$
$43$	−12.7846			−0.297317			−0.148658	+	0.988889i	$0.547495\pi$
$44$	29.8564	+	11.5150i	0.678555	+	0.261704i
$45$			8.63624i			0.191916i
$46$	−42.2487	−	7.86488i	−0.918450	−	0.170976i
$47$		−	1.54272i		−	0.0328237i	−0.999865	−	0.0164119i	$-0.994776\pi$
$47$		−	1.54272i		−	0.0328237i	0.999865	−	0.0164119i	$-0.00522430\pi$
$48$	20.5359	+	18.6085i	0.427831	+	0.387677i
$49$	−66.4256			−1.35563
$50$	−6.11731	+	32.8611i	−0.122346	+	0.657222i
$51$	−27.4641			−0.538512
$52$	22.6410	−	58.7043i	0.435404	−	1.12893i
$53$			28.5808i			0.539260i	0.962964	+	0.269630i	$0.0869014\pi$
$53$			28.5808i			0.539260i	−0.962964	+	0.269630i	$0.913099\pi$
$54$	−1.90192	+	10.2168i	−0.0352208	+	0.189200i
$55$		−	23.0300i		−	0.418727i
$56$	−73.1769	−	45.0819i	−1.30673	−	0.805034i
$57$	1.85641			0.0325685
$58$	78.8372	+	14.6761i	1.35926	+	0.253036i
$59$	−11.2154			−0.190091			−0.0950457	−	0.995473i	$-0.530300\pi$
$59$	−11.2154			−0.190091			−0.0950457	+	0.995473i	$0.530300\pi$
$60$	7.17691	−	18.6085i	0.119615	−	0.310142i
$61$			1.54272i			0.0252904i	0.999920	+	0.0126452i	$0.00402520\pi$
$61$			1.54272i			0.0252904i	−0.999920	+	0.0126452i	$0.995975\pi$
$62$	18.0910	+	3.36777i	0.291791	+	0.0543189i
$63$		−	32.2309i		−	0.511602i
$64$	−28.7846	−	57.1616i	−0.449760	−	0.893150i
$65$	−45.2820			−0.696647
$66$	5.07180	−	27.2448i	0.0768454	−	0.412799i
$67$	−43.2154			−0.645006			−0.322503	−	0.946568i	$-0.604524\pi$
$67$	−43.2154			−0.645006			−0.322503	+	0.946568i	$0.604524\pi$
$68$	59.1769	+	22.8233i	0.870249	+	0.335637i
$69$			37.2170i			0.539377i
$70$	−11.3205	+	60.8117i	−0.161722	+	0.868738i
$71$		−	84.4063i		−	1.18882i	−0.804162	−	0.594411i	$-0.797385\pi$
$71$		−	84.4063i		−	1.18882i	0.804162	−	0.594411i	$-0.202615\pi$
$72$	12.5885	−	20.4336i	0.174840	−	0.283800i
$73$	105.426			1.44419			0.722093	−	0.691796i	$-0.243180\pi$
$73$	105.426			1.44419			0.722093	+	0.691796i	$0.243180\pi$
$74$	−19.6077	−	3.65011i	−0.264969	−	0.0493258i
$75$	28.9474			0.385966
$76$	−4.00000	−	1.54272i	−0.0526316	−	0.0202989i
$77$			85.9491i			1.11622i
$78$	−53.5692	−	9.97227i	−0.686785	−	0.127850i
$79$			73.6627i			0.932439i	0.884669	+	0.466220i	$0.154384\pi$
$79$			73.6627i			0.932439i	−0.884669	+	0.466220i	$0.845616\pi$
$80$	−30.9282	+	34.1316i	−0.386603	+	0.426645i
$81$	9.00000			0.111111
$82$	−18.8756	+	101.396i	−0.230191	+	1.23654i
$83$	12.2872			0.148038			0.0740192	−	0.997257i	$-0.476417\pi$
$83$	12.2872			0.148038			0.0740192	+	0.997257i	$0.476417\pi$
$84$	−26.7846	+	69.4479i	−0.318864	+	0.826761i
$85$		−	45.6466i		−	0.537019i
$86$	4.67949	−	25.1374i	0.0544127	−	0.292295i
$87$		−	69.4479i		−	0.798252i
$88$	−33.5692	+	54.4895i	−0.381468	+	0.619199i
$89$	33.1384			0.372342			0.186171	−	0.982517i	$-0.440392\pi$
$89$	33.1384			0.372342			0.186171	+	0.982517i	$0.440392\pi$
$90$	−16.9808	−	3.16108i	−0.188675	−	0.0351232i
$91$	168.995			1.85709
$92$	30.9282	−	80.1916i	0.336176	−	0.871647i
$93$		−	15.9365i		−	0.171360i
$94$	3.03332	+	0.564673i	0.0322694	+	0.00600716i
$95$			3.08543i			0.0324782i
$96$	−44.1051	+	33.5669i	−0.459428	+	0.349655i
$97$	−69.1384			−0.712767			−0.356384	−	0.934340i	$-0.615990\pi$
$97$	−69.1384			−0.712767			−0.356384	+	0.934340i	$0.615990\pi$
$98$	24.3135	−	130.607i	0.248097	−	1.33273i
$99$	−24.0000			−0.242424
$100$	−62.3731	−	24.0560i	−0.623731	−	0.240560i
$101$		−	97.2574i		−	0.962944i	−0.876461	−	0.481472i	$-0.840102\pi$
$101$		−	97.2574i		−	0.962944i	0.876461	−	0.481472i	$-0.159898\pi$
$102$	10.0526	−	54.0005i	0.0985545	−	0.529417i
$103$			139.667i			1.35599i	0.735065	+	0.677996i	$0.237151\pi$
$103$			139.667i			1.35599i	−0.735065	+	0.677996i	$0.762849\pi$
$104$	107.138	+	66.0045i	1.03018	+	0.634659i
$105$	53.5692			0.510183
$106$	−56.1962	−	10.4613i	−0.530152	−	0.0986915i
$107$	−197.779			−1.84841			−0.924203	−	0.381901i	$-0.875269\pi$
$107$	−197.779			−1.84841			−0.924203	+	0.381901i	$0.875269\pi$
$108$	−19.3923	−	7.47921i	−0.179558	−	0.0692519i
$109$		−	190.713i		−	1.74966i	−0.484427	−	0.874832i	$-0.660972\pi$
$109$		−	190.713i		−	1.74966i	0.484427	−	0.874832i	$-0.339028\pi$
$110$	45.2820	+	8.42956i	0.411655	+	0.0766323i
$111$			17.2725i			0.155608i
$112$	115.426	−	127.381i	1.03059	−	1.13733i
$113$	−113.713			−1.00631			−0.503154	−	0.864197i	$-0.667827\pi$
$113$	−113.713			−1.00631			−0.503154	+	0.864197i	$0.667827\pi$
$114$	−0.679492	+	3.65011i	−0.00596046	+	0.0320185i
$115$	−61.8564			−0.537882
$116$	−57.7128	+	149.639i	−0.497524	+	1.29000i
$117$			47.1893i			0.403327i
$118$	4.10512	−	22.0519i	0.0347891	−	0.186881i
$119$			170.355i			1.43156i
$120$	33.9615	+	20.9226i	0.283013	+	0.174355i
$121$	−57.0000			−0.471074
$122$	−3.03332	−	0.564673i	−0.0248633	−	0.00462847i
$123$	89.3205			0.726183
$124$	−13.2436	+	34.3383i	−0.106803	+	0.276922i
$125$			120.081i			0.960645i
$126$	63.3731	+	11.7973i	0.502961	+	0.0936296i
$127$		−	36.8590i		−	0.290229i	−0.989415	−	0.145114i	$-0.953645\pi$
$127$		−	36.8590i		−	0.290229i	0.989415	−	0.145114i	$-0.0463550\pi$
$128$	122.928	−	35.6743i	0.960377	−	0.278706i
$129$	−22.1436			−0.171656
$130$	16.5744	−	89.0345i	0.127495	−	0.684881i
$131$	194.641			1.48581			0.742905	−	0.669397i	$-0.233448\pi$
$131$	194.641			1.48581			0.742905	+	0.669397i	$0.233448\pi$
$132$	51.7128	+	19.9445i	0.391764	+	0.151095i
$133$		−	11.5150i		−	0.0865789i
$134$	15.8179	−	84.9710i	0.118044	−	0.634112i
$135$			14.9584i			0.110803i
$136$	−66.5359	+	108.001i	−0.489235	+	0.794125i
$137$	16.4308			0.119933			0.0599664	−	0.998200i	$-0.480901\pi$
$137$	16.4308			0.119933			0.0599664	+	0.998200i	$0.480901\pi$
$138$	−73.1769	−	13.6224i	−0.530267	−	0.0987129i
$139$	−113.492			−0.816491			−0.408246	−	0.912872i	$-0.633859\pi$
$139$	−113.492			−0.816491			−0.408246	+	0.912872i	$0.633859\pi$
$140$	−115.426	−	44.5172i	−0.824469	−	0.317980i
$141$		−	2.67206i		−	0.0189508i
$142$	165.962	+	30.8949i	1.16874	+	0.217569i
$143$		−	125.838i		−	0.879987i
$144$	35.5692	+	32.2309i	0.247008	+	0.223826i
$145$	115.426			0.796039
$146$	−38.5885	+	207.290i	−0.264305	+	1.41980i
$147$	−115.053			−0.782670
$148$	14.3538	−	37.2170i	0.0969853	−	0.251466i
$149$		−	31.6662i		−	0.212525i	−0.994338	−	0.106262i	$-0.966112\pi$
$149$		−	31.6662i		−	0.212525i	0.994338	−	0.106262i	$-0.0338884\pi$
$150$	−10.5955	+	56.9171i	−0.0706367	+	0.379447i
$151$		−	90.5218i		−	0.599482i	−0.954021	−	0.299741i	$-0.903100\pi$
$151$		−	90.5218i		−	0.599482i	0.954021	−	0.299741i	$-0.0969003\pi$
$152$	4.49742	−	7.30021i	0.0295883	−	0.0480277i
$153$	−47.5692			−0.310910
$154$	−168.995	−	31.4595i	−1.09737	−	0.204283i
$155$	26.4871			0.170885
$156$	39.2154	−	101.679i	0.251381	−	0.651787i
$157$			231.016i			1.47144i	0.677287	+	0.735719i	$0.263156\pi$
$157$			231.016i			1.47144i	−0.677287	+	0.735719i	$0.736844\pi$
$158$	−144.837	−	26.9624i	−0.916691	−	0.170648i
$159$			49.5034i			0.311342i
$160$	−55.7898	−	73.3047i	−0.348686	−	0.458154i
$161$	230.851			1.43386
$162$	−3.29423	+	17.6960i	−0.0203347	+	0.109235i
$163$	22.3538			0.137140			0.0685700	−	0.997646i	$-0.478156\pi$
$163$	22.3538			0.137140			0.0685700	+	0.997646i	$0.478156\pi$
$164$	−192.459	−	74.2274i	−1.17353	−	0.452606i
$165$		−	39.8891i		−	0.241752i
$166$	−4.49742	+	24.1593i	−0.0270929	+	0.145538i
$167$		−	221.044i		−	1.32361i	−0.749674	−	0.661807i	$-0.769790\pi$
$167$		−	221.044i		−	1.32361i	0.749674	−	0.661807i	$-0.230210\pi$
$168$	−126.746	−	78.0842i	−0.754441	−	0.464787i
$169$	−78.4256			−0.464057
$170$	89.7513	+	16.7078i	0.527949	+	0.0982812i
$171$	3.21539			0.0188035
$172$	47.7128	+	18.4018i	0.277400	+	0.106987i
$173$		−	231.525i		−	1.33830i	−0.743130	−	0.669148i	$-0.766659\pi$
$173$		−	231.525i		−	1.33830i	0.743130	−	0.669148i	$-0.233341\pi$
$174$	136.550	+	25.4197i	0.784770	+	0.146090i
$175$		−	179.556i		−	1.02604i
$176$	−94.8513	−	85.9491i	−0.538928	−	0.488347i
$177$	−19.4256			−0.109749
$178$	−12.1295	+	65.1575i	−0.0681433	+	0.366053i
$179$	193.646			1.08182			0.540911	−	0.841080i	$-0.318080\pi$
$179$	193.646			1.08182			0.540911	+	0.841080i	$0.318080\pi$
$180$	12.4308	−	32.2309i	0.0690599	−	0.179061i
$181$			270.492i			1.49443i	0.664583	+	0.747214i	$0.268609\pi$
$181$			270.492i			1.49443i	−0.664583	+	0.747214i	$0.731391\pi$
$182$	−61.8564	+	332.281i	−0.339870	+	1.82572i
$183$			2.67206i			0.0146014i
$184$	146.354	+	90.1638i	0.795401	+	0.490021i
$185$	−28.7077			−0.155177
$186$	31.3346	+	5.83315i	0.168466	+	0.0313610i
$187$	126.851			0.678349
$188$	−2.22055	+	5.75749i	−0.0118114	+	0.0306250i
$189$		−	55.8255i		−	0.295373i
$190$	−6.06664	−	1.12935i	−0.0319297	−	0.00594393i
$191$			311.510i			1.63094i	0.578798	+	0.815471i	$0.303522\pi$
$191$			311.510i			1.63094i	−0.578798	+	0.815471i	$0.696478\pi$
$192$	−49.8564	−	99.0068i	−0.259669	−	0.515660i
$193$	48.2769			0.250139			0.125070	−	0.992148i	$-0.460085\pi$
$193$	48.2769			0.250139			0.125070	+	0.992148i	$0.460085\pi$
$194$	25.3064	−	135.941i	0.130445	−	0.700729i
$195$	−78.4308			−0.402209
$196$	247.904	+	95.6113i	1.26482	+	0.487813i
$197$			251.883i			1.27859i	0.768960	+	0.639297i	$0.220775\pi$
$197$			251.883i			1.27859i	−0.768960	+	0.639297i	$0.779225\pi$
$198$	8.78461	−	47.1893i	0.0443667	−	0.238330i
$199$		−	72.1200i		−	0.362412i	−0.983445	−	0.181206i	$-0.942000\pi$
$199$		−	72.1200i		−	0.362412i	0.983445	−	0.181206i	$-0.0580001\pi$
$200$	70.1295	−	113.834i	0.350648	−	0.569171i
$201$	−74.8513			−0.372394
$202$	191.229	+	35.5987i	0.946681	+	0.176231i
$203$	−430.774			−2.12204
$204$	102.497	+	39.5311i	0.502438	+	0.193780i
$205$			148.455i			0.724170i
$206$	−274.617	−	51.1217i	−1.33309	−	0.248164i
$207$			64.4618i			0.311410i
$208$	−168.995	+	186.499i	−0.812475	+	0.896628i
$209$	−8.57437			−0.0410257
$210$	−19.6077	+	105.329i	−0.0933700	+	0.501566i
$211$	−264.918			−1.25554			−0.627768	−	0.778401i	$-0.716031\pi$
$211$	−264.918			−1.25554			−0.627768	+	0.778401i	$0.716031\pi$
$212$	41.1384	−	106.665i	0.194049	−	0.503137i
$213$		−	146.196i		−	0.686367i
$214$	72.3923	−	388.878i	0.338282	−	1.81719i
$215$		−	36.8037i		−	0.171180i
$216$	21.8038	−	35.3920i	0.100944	−	0.163852i
$217$	−98.8513			−0.455536
$218$	374.985	+	69.8059i	1.72011	+	0.320211i
$219$	182.603			0.833802
$220$	−33.1487	+	85.9491i	−0.150676	+	0.390678i
$221$		−	249.418i		−	1.12859i
$222$	−33.9615	−	6.32217i	−0.152980	−	0.0284782i
$223$		−	30.6882i		−	0.137615i	−0.997630	−	0.0688076i	$-0.978081\pi$
$223$		−	30.6882i		−	0.137615i	0.997630	−	0.0688076i	$-0.0219195\pi$
$224$	208.210	+	273.577i	0.929510	+	1.22133i
$225$	50.1384			0.222838
$226$	41.6218	−	223.585i	0.184167	−	0.989312i
$227$	295.846			1.30329			0.651643	−	0.758525i	$-0.274080\pi$
$227$	295.846			1.30329			0.651643	+	0.758525i	$0.274080\pi$
$228$	−6.92820	−	2.67206i	−0.0303869	−	0.0117196i
$229$		−	256.718i		−	1.12104i	−0.828141	−	0.560519i	$-0.810602\pi$
$229$		−	256.718i		−	1.12104i	0.828141	−	0.560519i	$-0.189398\pi$
$230$	22.6410	−	121.623i	0.0984392	−	0.528797i
$231$			148.868i			0.644451i
$232$	−273.100	−	168.248i	−1.17716	−	0.725207i
$233$	−404.564			−1.73633			−0.868163	−	0.496279i	$-0.834699\pi$
$233$	−404.564			−1.73633			−0.868163	+	0.496279i	$0.834699\pi$
$234$	−92.7846	−	17.2725i	−0.396515	−	0.0738140i
$235$	4.44109			0.0188983
$236$	41.8564	+	16.1431i	0.177358	+	0.0684031i
$237$			127.588i			0.538344i
$238$	−334.956	−	62.3544i	−1.40738	−	0.261993i
$239$			115.150i			0.481799i	0.970550	+	0.240899i	$0.0774424\pi$
$239$			115.150i			0.481799i	−0.970550	+	0.240899i	$0.922558\pi$
$240$	−53.5692	+	59.1177i	−0.223205	+	0.246324i
$241$	251.415			1.04322			0.521609	−	0.853185i	$-0.325332\pi$
$241$	251.415			1.04322			0.521609	+	0.853185i	$0.325332\pi$
$242$	20.8634	−	112.075i	0.0862126	−	0.463118i
$243$	15.5885			0.0641500
$244$	2.22055	−	5.75749i	0.00910059	−	0.0235963i
$245$		−	191.223i		−	0.780500i
$246$	−32.6936	+	175.624i	−0.132901	+	0.713918i
$247$			16.8591i			0.0682555i
$248$	−62.6692	−	38.6084i	−0.252698	−	0.155679i
$249$	21.2820			0.0854700
$250$	−236.105	−	43.9526i	−0.944420	−	0.175810i
$251$	6.85125			0.0272958			0.0136479	−	0.999907i	$-0.495656\pi$
$251$	6.85125			0.0272958			0.0136479	+	0.999907i	$0.495656\pi$
$252$	−46.3923	+	120.287i	−0.184096	+	0.477331i
$253$		−	171.898i		−	0.679439i
$254$	72.4730	+	13.4913i	0.285327	+	0.0531155i
$255$		−	79.0622i		−	0.310048i
$256$	25.1487	+	254.762i	0.0982373	+	0.995163i
$257$	248.277			0.966058			0.483029	−	0.875604i	$-0.339537\pi$
$257$	248.277			0.966058			0.483029	+	0.875604i	$0.339537\pi$
$258$	8.10512	−	43.5392i	0.0314152	−	0.168757i
$259$	107.138			0.413662
$260$	168.995	+	65.1778i	0.649980	+	0.250684i
$261$		−	120.287i		−	0.460871i
$262$	−71.2436	+	382.707i	−0.271922	+	1.46071i
$263$			498.835i			1.89671i	0.317208	+	0.948356i	$0.397255\pi$
$263$			498.835i			1.89671i	−0.317208	+	0.948356i	$0.602745\pi$
$264$	−58.1436	+	94.3786i	−0.220241	+	0.357495i
$265$	−82.2769			−0.310479
$266$	22.6410	+	4.21478i	0.0851166	+	0.0158450i
$267$	57.3975			0.214972
$268$	161.282	+	62.2031i	0.601799	+	0.232101i
$269$			234.611i			0.872158i	0.899908	+	0.436079i	$0.143633\pi$
$269$			234.611i			0.872158i	−0.899908	+	0.436079i	$0.856367\pi$
$270$	−29.4115	−	5.47516i	−0.108932	−	0.0202784i
$271$			101.321i			0.373878i	0.982372	+	0.186939i	$0.0598566\pi$
$271$			101.321i			0.373878i	−0.982372	+	0.186939i	$0.940143\pi$
$272$	−188.000	−	170.355i	−0.691176	−	0.626307i
$273$	292.708			1.07219
$274$	−6.01408	+	32.3065i	−0.0219492	+	0.117907i
$275$	−133.703			−0.486191
$276$	53.5692	−	138.896i	0.194091	−	0.503246i
$277$		−	169.942i		−	0.613509i	−0.951789	−	0.306755i	$-0.900757\pi$
$277$		−	169.942i		−	0.613509i	0.951789	−	0.306755i	$-0.0992431\pi$
$278$	41.5411	−	223.151i	0.149428	−	0.802701i
$279$		−	27.6027i		−	0.0989346i
$280$	129.779	−	210.658i	0.463498	−	0.752349i
$281$	−111.128			−0.395474			−0.197737	−	0.980255i	$-0.563359\pi$
$281$	−111.128			−0.395474			−0.197737	+	0.980255i	$0.563359\pi$
$282$	5.25387	+	0.978043i	0.0186307	+	0.00346824i
$283$	550.620			1.94566			0.972828	−	0.231531i	$-0.0743734\pi$
$283$	550.620			1.94566			0.972828	+	0.231531i	$0.0743734\pi$
$284$	−121.492	+	315.009i	−0.427790	+	1.10919i
$285$			5.34413i			0.0187513i
$286$	247.426	+	46.0600i	0.865125	+	0.161049i
$287$		−	554.041i		−	1.93046i
$288$	−76.3923	+	58.1396i	−0.265251	+	0.201874i
$289$	−37.5744			−0.130015
$290$	−42.2487	+	226.952i	−0.145685	+	0.782594i
$291$	−119.751			−0.411516
$292$	−393.454	−	151.747i	−1.34744	−	0.519681i
$293$			223.509i			0.762829i	0.924404	+	0.381414i	$0.124563\pi$
$293$			223.509i			0.762829i	−0.924404	+	0.381414i	$0.875437\pi$
$294$	42.1122	−	226.219i	0.143239	−	0.769452i
$295$		−	32.2863i		−	0.109445i
$296$	67.9230	+	41.8452i	0.229470	+	0.141369i
$297$	−41.5692			−0.139964
$298$	62.2628	+	11.5906i	0.208936	+	0.0388948i
$299$	−337.990			−1.13040
$300$	−108.033	−	41.6662i	−0.360111	−	0.138887i
$301$			137.353i			0.456323i
$302$	177.986	+	33.1333i	0.589357	+	0.109713i
$303$		−	168.455i		−	0.555956i
$304$	12.7077	+	11.5150i	0.0418015	+	0.0378783i
$305$	−4.44109			−0.0145610
$306$	17.4115	−	93.5316i	0.0569005	−	0.305659i
$307$	−371.790			−1.21104			−0.605521	−	0.795829i	$-0.707035\pi$
$307$	−371.790			−1.21104			−0.605521	+	0.795829i	$0.707035\pi$
$308$	123.713	−	320.766i	0.401665	−	1.04145i
$309$			241.911i			0.782883i
$310$	−9.69496	+	52.0795i	−0.0312741	+	0.167998i
$311$		−	330.023i		−	1.06117i	−0.847633	−	0.530583i	$-0.821973\pi$
$311$		−	330.023i		−	1.06117i	0.847633	−	0.530583i	$-0.178027\pi$
$312$	185.569	+	114.323i	0.594773	+	0.366420i
$313$	−80.2769			−0.256476			−0.128238	−	0.991743i	$-0.540932\pi$
$313$	−80.2769			−0.256476			−0.128238	+	0.991743i	$0.540932\pi$
$314$	−454.228	−	84.5576i	−1.44659	−	0.269292i
$315$	92.7846			0.294554
$316$	106.028	−	274.913i	0.335532	−	0.869978i
$317$			68.8833i			0.217297i	0.994080	+	0.108649i	$0.0346524\pi$
$317$			68.8833i			0.217297i	−0.994080	+	0.108649i	$0.965348\pi$
$318$	−97.3346	−	18.1195i	−0.306084	−	0.0569795i
$319$			320.766i			1.00554i
$320$	164.554	−	82.8636i	0.514230	−	0.258949i
$321$	−342.564			−1.06718
$322$	−84.4974	+	453.905i	−0.262414	+	1.40964i
$323$	−16.9948			−0.0526156
$324$	−33.5885	−	12.9544i	−0.103668	−	0.0399826i
$325$			262.889i			0.808888i
$326$	−8.18207	+	43.9526i	−0.0250984	+	0.134824i
$327$		−	330.325i		−	1.01017i
$328$	216.392	−	351.248i	0.659733	−	1.07088i
$329$	−16.5744			−0.0503780
$330$	78.4308	+	14.6004i	0.237669	+	0.0442437i
$331$	−396.056			−1.19654			−0.598272	−	0.801293i	$-0.704146\pi$
$331$	−396.056			−1.19654			−0.598272	+	0.801293i	$0.704146\pi$
$332$	−45.8564	−	17.6859i	−0.138122	−	0.0532706i
$333$			29.9168i			0.0898403i
$334$	434.620	+	80.9075i	1.30126	+	0.242238i
$335$		−	124.406i		−	0.371362i
$336$	199.923	−	220.630i	0.595009	−	0.656637i
$337$	231.723			0.687606			0.343803	−	0.939042i	$-0.388285\pi$
$337$	231.723			0.687606			0.343803	+	0.939042i	$0.388285\pi$
$338$	28.7058	−	154.202i	0.0849283	−	0.456219i
$339$	−196.956			−0.580992
$340$	−65.7025	+	170.355i	−0.193243	+	0.501045i
$341$			73.6073i			0.215857i
$342$	−1.17691	+	6.32217i	−0.00344127	+	0.0184859i
$343$			187.215i			0.545815i
$344$	−53.6462	+	87.0784i	−0.155948	+	0.253135i
$345$	−107.138			−0.310546
$346$	455.229	+	84.7441i	1.31569	+	0.244925i
$347$	462.123			1.33177			0.665883	−	0.746056i	$-0.268055\pi$
$347$	462.123			1.33177			0.665883	+	0.746056i	$0.268055\pi$
$348$	−99.9615	+	259.183i	−0.287246	+	0.744779i
$349$		−	266.993i		−	0.765022i	−0.923951	−	0.382511i	$-0.875059\pi$
$349$		−	266.993i		−	0.765022i	0.923951	−	0.382511i	$-0.124941\pi$
$350$	353.047	+	65.7222i	1.00871	+	0.187778i
$351$			81.7343i			0.232861i
$352$	203.713	−	155.039i	0.578730	−	0.440452i
$353$	262.862			0.744650			0.372325	−	0.928102i	$-0.378561\pi$
$353$	262.862			0.744650			0.372325	+	0.928102i	$0.378561\pi$
$354$	7.11027	−	38.1951i	0.0200855	−	0.107896i
$355$	242.985			0.684463
$356$	−123.674	−	47.6986i	−0.347400	−	0.133985i
$357$			295.064i			0.826510i
$358$	−70.8794	+	380.751i	−0.197987	+	1.06355i
$359$		−	164.185i		−	0.457339i	−0.973504	−	0.228669i	$-0.926563\pi$
$359$		−	164.185i		−	0.457339i	0.973504	−	0.228669i	$-0.0734374\pi$
$360$	58.8231	+	36.2390i	0.163397	+	0.100664i
$361$	−359.851			−0.996818
$362$	−531.846	−	99.0068i	−1.46919	−	0.273499i
$363$	−98.7269			−0.271975
$364$	−630.697	−	243.247i	−1.73269	−	0.668260i
$365$			303.494i			0.831490i
$366$	−5.25387	−	0.978043i	−0.0143548	−	0.00267225i
$367$			242.475i			0.660696i	0.943859	+	0.330348i	$0.107166\pi$
$367$			242.475i			0.660696i	−0.943859	+	0.330348i	$0.892834\pi$
$368$	−230.851	+	254.762i	−0.627313	+	0.692287i
$369$	154.708			0.419262
$370$	10.5077	−	56.4456i	0.0283993	−	0.152556i
$371$	307.061			0.827659
$372$	−22.9385	+	59.4757i	−0.0616627	+	0.159881i
$373$		−	328.480i		−	0.880643i	−0.897840	−	0.440321i	$-0.854864\pi$
$373$		−	328.480i		−	0.880643i	0.897840	−	0.440321i	$-0.145136\pi$
$374$	−46.4308	+	249.418i	−0.124146	+	0.666892i
$375$			207.986i			0.554629i
$376$	−10.5077	−	6.47347i	−0.0279461	−	0.0172167i
$377$	630.697			1.67294
$378$	109.765	+	20.4336i	0.290385	+	0.0540571i
$379$	36.2102			0.0955415			0.0477708	−	0.998858i	$-0.484788\pi$
$379$	36.2102			0.0955415			0.0477708	+	0.998858i	$0.484788\pi$
$380$	4.44109	−	11.5150i	0.0116871	−	0.0303026i
$381$		−	63.8417i		−	0.167564i
$382$	−612.497	−	114.021i	−1.60340	−	0.298483i
$383$			164.295i			0.428969i	0.976727	+	0.214485i	$0.0688072\pi$
$383$			164.295i			0.428969i	−0.976727	+	0.214485i	$0.931193\pi$
$384$	212.918	−	61.7897i	0.554474	−	0.160911i
$385$	−247.426			−0.642664
$386$	−17.6706	+	94.9230i	−0.0457787	+	0.245915i
$387$	−38.3538			−0.0991055
$388$	258.028	+	99.5161i	0.665021	+	0.256485i
$389$		−	604.936i		−	1.55510i	−0.628819	−	0.777552i	$-0.716461\pi$
$389$		−	604.936i		−	1.55510i	0.628819	−	0.777552i	$-0.283539\pi$
$390$	28.7077	−	154.212i	0.0736094	−	0.395416i
$391$		−	340.711i		−	0.871383i
$392$	−278.732	+	452.438i	−0.711051	+	1.15418i
$393$	337.128			0.857832
$394$	−495.258	−	92.1956i	−1.25700	−	0.233999i
$395$	−212.056			−0.536851
$396$	89.5692	+	34.5450i	0.226185	+	0.0872348i
$397$		−	541.699i		−	1.36448i	−0.731128	−	0.682241i	$-0.761006\pi$
$397$		−	541.699i		−	1.36448i	0.731128	−	0.682241i	$-0.238994\pi$
$398$	141.804	+	26.3977i	0.356291	+	0.0663260i
$399$		−	19.9445i		−	0.0499863i
$400$	198.154	+	179.556i	0.495385	+	0.448891i
$401$	−379.569			−0.946557			−0.473278	−	0.880913i	$-0.656930\pi$
$401$	−379.569			−0.946557			−0.473278	+	0.880913i	$0.656930\pi$
$402$	27.3975	−	147.174i	0.0681529	−	0.366105i
$403$	144.728			0.359127
$404$	−139.990	+	362.969i	−0.346509	+	0.898439i
$405$			25.9087i			0.0639722i
$406$	157.674	−	846.998i	0.388360	−	2.08620i
$407$		−	79.7782i		−	0.196015i
$408$	−115.244	+	187.063i	−0.282460	+	0.458488i
$409$	251.415			0.614707			0.307354	−	0.951595i	$-0.400557\pi$
$409$	251.415			0.614707			0.307354	+	0.951595i	$0.400557\pi$
$410$	−291.895	−	54.3382i	−0.711939	−	0.132532i
$411$	28.4589			0.0692432
$412$	201.033	−	521.245i	0.487945	−	1.26516i
$413$			120.494i			0.291753i
$414$	−126.746	−	23.5947i	−0.306150	−	0.0569919i
$415$			35.3717i			0.0852330i
$416$	−304.841	−	400.544i	−0.732791	−	0.962847i
$417$	−196.574			−0.471401
$418$	3.13844	−	16.8591i	0.00750823	−	0.0403328i
$419$	268.133			0.639936			0.319968	−	0.947428i	$-0.396328\pi$
$419$	268.133			0.639936			0.319968	+	0.947428i	$0.396328\pi$
$420$	−199.923	−	77.1061i	−0.476007	−	0.183586i
$421$			218.261i			0.518434i	0.965819	+	0.259217i	$0.0834645\pi$
$421$			218.261i			0.518434i	−0.965819	+	0.259217i	$0.916536\pi$
$422$	96.9667	−	520.887i	0.229779	−	1.23433i
$423$		−	4.62815i		−	0.0109412i
$424$	194.669	+	119.929i	0.459125	+	0.282852i
$425$	−265.005			−0.623542
$426$	287.454	+	53.5115i	0.674774	+	0.125614i
$427$	16.5744			0.0388159
$428$	738.123	+	284.679i	1.72459	+	0.665137i
$429$		−	217.958i		−	0.508061i
$430$	72.3641	+	13.4711i	0.168289	+	0.0313281i
$431$			550.955i			1.27832i	0.769074	+	0.639159i	$0.220718\pi$
$431$			550.955i			1.27832i	−0.769074	+	0.639159i	$0.779282\pi$
$432$	61.6077	+	55.8255i	0.142610	+	0.129226i
$433$	−263.128			−0.607686			−0.303843	−	0.952722i	$-0.598270\pi$
$433$	−263.128			−0.607686			−0.303843	+	0.952722i	$0.598270\pi$
$434$	36.1821	−	194.363i	0.0833688	−	0.447842i
$435$	199.923			0.459593
$436$	−274.508	+	711.752i	−0.629605	+	1.63246i
$437$			23.0300i			0.0527002i
$438$	−66.8372	+	359.037i	−0.152596	+	0.819719i
$439$			440.489i			1.00339i	0.865044	+	0.501696i	$0.167290\pi$
$439$			440.489i			1.00339i	−0.865044	+	0.501696i	$0.832710\pi$
$440$	−156.862	−	96.6373i	−0.356504	−	0.219630i
$441$	−199.277			−0.451875
$442$	490.410	+	91.2932i	1.10953	+	0.206546i
$443$	−228.708			−0.516270			−0.258135	−	0.966109i	$-0.583108\pi$
$443$	−228.708			−0.516270			−0.258135	+	0.966109i	$0.583108\pi$
$444$	24.8616	−	64.4618i	0.0559945	−	0.145184i
$445$			95.3972i			0.214376i
$446$	60.3397	+	11.2327i	0.135291	+	0.0251853i
$447$		−	54.8475i		−	0.122701i
$448$	−614.123	+	309.251i	−1.37081	+	0.690293i
$449$	−108.410			−0.241448			−0.120724	−	0.992686i	$-0.538522\pi$
$449$	−108.410			−0.241448			−0.120724	+	0.992686i	$0.538522\pi$
$450$	−18.3519	+	98.5833i	−0.0407821	+	0.219074i
$451$	−412.554			−0.914753
$452$	424.382	+	163.675i	0.938898	+	0.362113i
$453$		−	156.788i		−	0.346111i
$454$	−108.287	+	581.699i	−0.238518	+	1.28127i
$455$			486.493i			1.06922i
$456$	7.78976	−	12.6443i	0.0170828	−	0.0277288i
$457$	561.692			1.22909			0.614543	−	0.788883i	$-0.289340\pi$
$457$	561.692			1.22909			0.614543	+	0.788883i	$0.289340\pi$
$458$	504.764	+	93.9652i	1.10210	+	0.205164i
$459$	−82.3923			−0.179504
$460$	230.851	+	89.0345i	0.501851	+	0.193553i
$461$		−	335.160i		−	0.727028i	−0.931589	−	0.363514i	$-0.881577\pi$
$461$		−	335.160i		−	0.727028i	0.931589	−	0.363514i	$-0.118423\pi$
$462$	−292.708	−	54.4895i	−0.633566	−	0.117943i
$463$		−	389.912i		−	0.842142i	−0.907028	−	0.421071i	$-0.861654\pi$
$463$		−	389.912i		−	0.842142i	0.907028	−	0.421071i	$-0.138346\pi$
$464$	430.774	−	475.392i	0.928393	−	1.02455i
$465$	45.8770			0.0986603
$466$	148.081	−	795.462i	0.317770	−	1.70700i
$467$	−546.410			−1.17004			−0.585022	−	0.811018i	$-0.698914\pi$
$467$	−546.410			−1.17004			−0.585022	+	0.811018i	$0.698914\pi$
$468$	67.9230	−	176.113i	0.145135	−	0.376310i
$469$			464.290i			0.989958i
$470$	−1.62555	+	8.73217i	−0.00345862	+	0.0185791i
$471$			400.131i			0.849535i
$472$	−47.0615	+	76.3902i	−0.0997065	+	0.161844i
$473$	102.277			0.216230
$474$	−250.865	−	46.7003i	−0.529252	−	0.0985238i
$475$	17.9127			0.0377110
$476$	245.205	−	635.775i	0.515137	−	1.33566i
$477$			85.7424i			0.179753i
$478$	−226.410	−	42.1478i	−0.473661	−	0.0881753i
$479$		−	368.369i		−	0.769037i	−0.923117	−	0.384519i	$-0.874367\pi$
$479$		−	368.369i		−	0.769037i	0.923117	−	0.384519i	$-0.125633\pi$
$480$	−96.6307	−	126.967i	−0.201314	−	0.264516i
$481$	−156.862			−0.326116
$482$	−92.0244	+	494.338i	−0.190922	+	1.02560i
$483$	399.846			0.827839
$484$	212.727	+	82.0443i	0.439518	+	0.169513i
$485$		−	199.032i		−	0.410375i
$486$	−5.70577	+	30.6504i	−0.0117403	+	0.0630666i
$487$			90.6326i			0.186104i	0.995661	+	0.0930519i	$0.0296623\pi$
$487$			90.6326i			0.186104i	−0.995661	+	0.0930519i	$0.970338\pi$
$488$	10.5077	+	6.47347i	0.0215322	+	0.0132653i
$489$	38.7180			0.0791778
$490$	375.986	+	69.9923i	0.767318	+	0.142841i
$491$	−17.6462			−0.0359392			−0.0179696	−	0.999839i	$-0.505720\pi$
$491$	−17.6462			−0.0359392			−0.0179696	+	0.999839i	$0.505720\pi$
$492$	−333.349	−	128.566i	−0.677538	−	0.261312i
$493$			635.775i			1.28960i
$494$	−33.1487	−	6.17086i	−0.0671027	−	0.0124916i
$495$		−	69.0899i		−	0.139576i
$496$	98.8513	−	109.090i	0.199297	−	0.219939i
$497$	−906.831			−1.82461
$498$	−7.78976	+	41.8452i	−0.0156421	+	0.0840265i
$499$	548.631			1.09946			0.549730	−	0.835342i	$-0.314731\pi$
$499$	548.631			1.09946			0.549730	+	0.835342i	$0.314731\pi$
$500$	172.841	−	448.147i	0.345682	−	0.896294i
$501$		−	382.859i		−	0.764189i
$502$	−2.50773	+	13.4711i	−0.00499548	+	0.0268348i
$503$		−	262.475i		−	0.521820i	−0.965363	−	0.260910i	$-0.915977\pi$
$503$		−	262.475i		−	0.521820i	0.965363	−	0.260910i	$-0.0840225\pi$
$504$	−219.531	−	135.246i	−0.435577	−	0.268345i
$505$	279.979			0.554415
$506$	337.990	+	62.9191i	0.667964	+	0.124346i
$507$	−135.837			−0.267923
$508$	−53.0539	+	137.560i	−0.104437	+	0.270787i
$509$			230.093i			0.452049i	0.974122	+	0.226025i	$0.0725730\pi$
$509$			230.093i			0.452049i	−0.974122	+	0.226025i	$0.927427\pi$
$510$	155.454	+	28.9388i	0.304811	+	0.0567427i
$511$		−	1132.65i		−	2.21654i
$512$	−510.123	−	43.8013i	−0.996334	−	0.0855493i
$513$	5.56922			0.0108562
$514$	−90.8756	+	488.167i	−0.176801	+	0.949742i
$515$	−402.067			−0.780712
$516$	82.6410	+	31.8729i	0.160157	+	0.0617692i
$517$			12.3417i			0.0238718i
$518$	−39.2154	+	210.658i	−0.0757054	+	0.406675i
$519$		−	401.013i		−	0.772665i
$520$	−190.010	+	308.425i	−0.365404	+	0.593124i
$521$	164.144			0.315055			0.157527	−	0.987515i	$-0.449648\pi$
$521$	164.144			0.315055			0.157527	+	0.987515i	$0.449648\pi$
$522$	236.512	+	44.0282i	0.453087	+	0.0843453i
$523$	−185.492			−0.354670			−0.177335	−	0.984151i	$-0.556748\pi$
$523$	−185.492			−0.354670			−0.177335	+	0.984151i	$0.556748\pi$
$524$	−726.410	−	280.161i	−1.38628	−	0.534659i
$525$		−	311.001i		−	0.592382i
$526$	−980.820	−	182.586i	−1.86468	−	0.347122i
$527$			145.893i			0.276838i
$528$	−164.287	−	148.868i	−0.311150	−	0.281947i
$529$	67.2975			0.127216
$530$	30.1154	−	161.775i	0.0568216	−	0.305235i
$531$	−33.6462			−0.0633638
$532$	−16.5744	+	42.9745i	−0.0311548	+	0.0807792i
$533$			811.172i			1.52190i
$534$	−21.0089	+	112.856i	−0.0393426	+	0.211341i
$535$		−	569.357i		−	1.06422i
$536$	−181.338	+	294.348i	−0.338318	+	0.549157i
$537$	335.405			0.624590
$538$	−461.296	−	85.8734i	−0.857428	−	0.159616i
$539$	531.405			0.985909
$540$	21.5307	−	55.8255i	0.0398717	−	0.103381i
$541$			891.253i			1.64742i	0.567013	+	0.823709i	$0.308099\pi$
$541$			891.253i			1.64742i	−0.567013	+	0.823709i	$0.691901\pi$
$542$	−199.219	−	37.0860i	−0.367563	−	0.0684244i
$543$			468.505i			0.862809i
$544$	403.769	−	307.295i	0.742223	−	0.564881i
$545$	549.015			1.00737
$546$	−107.138	+	575.528i	−0.196224	+	1.05408i
$547$	524.631			0.959105			0.479553	−	0.877513i	$-0.340799\pi$
$547$	524.631			0.959105			0.479553	+	0.877513i	$0.340799\pi$
$548$	−61.3205	−	23.6500i	−0.111899	−	0.0431570i
$549$			4.62815i			0.00843014i
$550$	48.9385	−	262.889i	0.0889791	−	0.477979i
$551$		−	42.9745i		−	0.0779937i
$552$	253.492	+	156.168i	0.459225	+	0.282914i
$553$	791.405			1.43111
$554$	334.144	+	62.2031i	0.603147	+	0.112280i
$555$	−49.7231			−0.0895912
$556$	423.559	+	163.358i	0.761797	+	0.293809i
$557$		−	570.804i		−	1.02478i	−0.858752	−	0.512391i	$-0.828760\pi$
$557$		−	570.804i		−	1.02478i	0.858752	−	0.512391i	$-0.171240\pi$
$558$	54.2731	+	10.1033i	0.0972636	+	0.0181063i
$559$		−	201.099i		−	0.359748i
$560$	366.697	+	332.281i	0.654817	+	0.593359i
$561$	219.713			0.391645
$562$	40.6757	−	218.502i	0.0723767	−	0.388794i
$563$	−161.877			−0.287526			−0.143763	−	0.989612i	$-0.545920\pi$
$563$	−161.877			−0.287526			−0.143763	+	0.989612i	$0.545920\pi$
$564$	−3.84610	+	9.97227i	−0.00681932	+	0.0176813i
$565$		−	327.350i		−	0.579381i
$566$	−201.541	+	1082.64i	−0.356080	+	1.91279i
$567$		−	96.6927i		−	0.170534i
$568$	−574.908	−	354.182i	−1.01216	−	0.623560i
$569$	624.123			1.09688			0.548438	−	0.836191i	$-0.315222\pi$
$569$	624.123			1.09688			0.548438	+	0.836191i	$0.315222\pi$
$570$	−10.5077	−	1.95609i	−0.0184346	−	0.00343173i
$571$	−593.031			−1.03858			−0.519291	−	0.854597i	$-0.673804\pi$
$571$	−593.031			−1.03858			−0.519291	+	0.854597i	$0.673804\pi$
$572$	−181.128	+	469.634i	−0.316658	+	0.821039i
$573$			539.551i			0.941625i
$574$	1089.37	+	202.793i	1.89785	+	0.353298i
$575$			359.113i			0.624544i
$576$	−86.3538	−	171.485i	−0.149920	−	0.297717i
$577$	−1003.68			−1.73948			−0.869742	−	0.493507i	$-0.835715\pi$
$577$	−1003.68			−1.73948			−0.869742	+	0.493507i	$0.835715\pi$
$578$	13.7532	−	73.8795i	0.0237944	−	0.127819i
$579$	83.6180			0.144418
$580$	−430.774	−	166.141i	−0.742714	−	0.286449i
$581$		−	132.009i		−	0.227210i
$582$	43.8320	−	235.458i	0.0753127	−	0.404566i
$583$		−	228.646i		−	0.392189i
$584$	442.382	−	718.074i	0.757503	−	1.22958i
$585$	−135.846			−0.232216
$586$	−439.468	−	81.8099i	−0.749945	−	0.139607i
$587$	859.215			1.46374			0.731870	−	0.681444i	$-0.238648\pi$
$587$	859.215			1.46374			0.731870	+	0.681444i	$0.238648\pi$
$588$	429.382	+	165.604i	0.730241	+	0.281639i
$589$		−	9.86151i		−	0.0167428i
$590$	63.4820	+	11.8176i	0.107597	+	0.0200298i
$591$			436.274i			0.738196i
$592$	−107.138	+	118.235i	−0.180977	+	0.199722i
$593$	−1007.42			−1.69885			−0.849423	−	0.527713i	$-0.823050\pi$
$593$	−1007.42			−1.69885			−0.849423	+	0.527713i	$0.823050\pi$
$594$	15.2154	−	81.7343i	0.0256151	−	0.137600i
$595$	−490.410			−0.824219
$596$	−45.5795	+	118.180i	−0.0764757	+	0.198289i
$597$		−	124.915i		−	0.209239i
$598$	123.713	−	664.562i	0.206878	−	1.11131i
$599$		−	86.0598i		−	0.143672i	−0.997416	−	0.0718362i	$-0.977114\pi$
$599$		−	86.0598i		−	0.143672i	0.997416	−	0.0718362i	$-0.0228859\pi$
$600$	121.468	−	197.167i	0.202446	−	0.328611i
$601$	−406.000			−0.675541			−0.337770	−	0.941229i	$-0.609673\pi$
$601$	−406.000			−0.675541			−0.337770	+	0.941229i	$0.609673\pi$
$602$	−270.067	−	50.2747i	−0.448616	−	0.0835129i
$603$	−129.646			−0.215002
$604$	−130.295	+	337.832i	−0.215720	+	0.559325i
$605$		−	164.089i		−	0.271221i
$606$	331.219	+	61.6587i	0.546566	+	0.101747i
$607$			1187.80i			1.95684i	0.206617	+	0.978422i	$0.433755\pi$
$607$			1187.80i			1.95684i	−0.206617	+	0.978422i	$0.566245\pi$
$608$	−27.2923	+	20.7713i	−0.0448887	+	0.0341633i
$609$	−746.123			−1.22516
$610$	1.62555	−	8.73217i	0.00266484	−	0.0143150i
$611$	24.2666			0.0397162
$612$	177.531	+	68.4699i	0.290083	+	0.111879i
$613$		−	500.378i		−	0.816277i	−0.912920	−	0.408139i	$-0.866178\pi$
$613$		−	500.378i		−	0.816277i	0.912920	−	0.408139i	$-0.133822\pi$
$614$	136.084	−	731.021i	0.221636	−	1.19059i
$615$			257.131i			0.418099i
$616$	585.415	+	360.655i	0.950350	+	0.585479i
$617$	88.8306			0.143972			0.0719859	−	0.997406i	$-0.477066\pi$
$617$	88.8306			0.143972			0.0719859	+	0.997406i	$0.477066\pi$
$618$	−475.650	−	88.5455i	−0.769660	−	0.143277i
$619$	−424.231			−0.685349			−0.342674	−	0.939454i	$-0.611333\pi$
$619$	−424.231			−0.685349			−0.342674	+	0.939454i	$0.611333\pi$
$620$	−98.8513	−	38.1249i	−0.159438	−	0.0614917i
$621$			111.651i			0.179792i
$622$	648.897	+	120.797i	1.04324	+	0.194207i
$623$		−	356.027i		−	0.571472i
$624$	−292.708	+	323.025i	−0.469083	+	0.517668i
$625$	72.1384			0.115422
$626$	29.3834	−	157.842i	0.0469383	−	0.252144i
$627$	−14.8513			−0.0236862
$628$	332.518	−	862.163i	0.529487	−	1.37287i
$629$		−	158.124i		−	0.251390i
$630$	−33.9615	+	182.435i	−0.0539072	+	0.289579i
$631$			90.6326i			0.143633i	0.997418	+	0.0718166i	$0.0228796\pi$
$631$			90.6326i			0.143633i	−0.997418	+	0.0718166i	$0.977120\pi$
$632$	501.731	+	309.100i	0.793878	+	0.489082i
$633$	−458.851			−0.724883
$634$	−135.440	−	25.2130i	−0.213627	−	0.0397682i
$635$	106.108			0.167099
$636$	71.2539	−	184.749i	0.112034	−	0.290486i
$637$		−	1044.86i		−	1.64028i
$638$	−630.697	−	117.409i	−0.988554	−	0.184026i
$639$		−	253.219i		−	0.396274i
$640$	102.697	+	353.879i	0.160465	+	0.552936i
$641$	1090.40			1.70109			0.850546	−	0.525901i	$-0.176272\pi$
$641$	1090.40			1.70109			0.850546	+	0.525901i	$0.176272\pi$
$642$	125.387	−	673.557i	0.195307	−	1.04915i
$643$	−454.200			−0.706376			−0.353188	−	0.935552i	$-0.614902\pi$
$643$	−454.200			−0.706376			−0.353188	+	0.935552i	$0.614902\pi$
$644$	−861.549	−	332.281i	−1.33781	−	0.515965i
$645$		−	63.7458i		−	0.0988307i
$646$	6.22055	−	33.4156i	0.00962933	−	0.0517270i
$647$			610.789i			0.944032i	0.881590	+	0.472016i	$0.156474\pi$
$647$			610.789i			0.944032i	−0.881590	+	0.472016i	$0.843526\pi$
$648$	37.7654	−	61.3007i	0.0582799	−	0.0945999i
$649$	89.7231			0.138248
$650$	−516.897	−	96.2239i	−0.795227	−	0.148037i
$651$	−171.215			−0.263004
$652$	−83.4256	−	32.1755i	−0.127953	−	0.0493489i
$653$		−	673.612i		−	1.03157i	−0.856720	−	0.515783i	$-0.827501\pi$
$653$		−	673.612i		−	1.03157i	0.856720	−	0.515783i	$-0.172499\pi$
$654$	649.492	+	120.907i	0.993107	+	0.184874i
$655$			560.322i			0.855454i
$656$	611.426	+	554.041i	0.932051	+	0.844574i
$657$	316.277			0.481396
$658$	6.06664	−	32.5889i	0.00921982	−	0.0495272i
$659$	−819.328			−1.24329			−0.621645	−	0.783299i	$-0.713535\pi$
$659$	−819.328			−1.24329			−0.621645	+	0.783299i	$0.713535\pi$
$660$	−57.4153	+	148.868i	−0.0869929	+	0.225558i
$661$			370.628i			0.560707i	0.959897	+	0.280354i	$0.0904518\pi$
$661$			370.628i			0.560707i	−0.959897	+	0.280354i	$0.909548\pi$
$662$	144.967	−	778.734i	0.218983	−	1.17634i
$663$		−	432.004i		−	0.651590i
$664$	51.5589	−	83.6904i	0.0776490	−	0.126040i
$665$	33.1487			0.0498477
$666$	−58.8231	−	10.9503i	−0.0883230	−	0.0164419i
$667$	861.549			1.29168
$668$	−318.164	+	824.946i	−0.476294	+	1.23495i
$669$		−	53.1535i		−	0.0794521i
$670$	244.610	+	45.5358i	0.365090	+	0.0679639i
$671$		−	12.3417i		−	0.0183930i
$672$	360.631	+	473.849i	0.536653	+	0.705133i
$673$	−255.703			−0.379944			−0.189972	−	0.981789i	$-0.560840\pi$
$673$	−255.703			−0.379944			−0.189972	+	0.981789i	$0.560840\pi$
$674$	−84.8165	+	455.619i	−0.125841	+	0.675992i
$675$	86.8423			0.128655
$676$	292.688	+	112.884i	0.432971	+	0.166988i
$677$			934.323i			1.38009i	0.723765	+	0.690047i	$0.242410\pi$
$677$			934.323i			1.38009i	−0.723765	+	0.690047i	$0.757590\pi$
$678$	72.0910	−	387.260i	0.106329	−	0.571180i
$679$			742.798i			1.09396i
$680$	−310.908	−	191.540i	−0.457217	−	0.281677i
$681$	512.420			0.752453
$682$	−144.728	−	26.9422i	−0.212212	−	0.0395046i
$683$	1142.54			1.67283			0.836415	−	0.548096i	$-0.184647\pi$
$683$	1142.54			1.67283			0.836415	+	0.548096i	$0.184647\pi$
$684$	−12.0000	−	4.62815i	−0.0175439	−	0.00676630i
$685$			47.3001i			0.0690512i
$686$	−368.105	−	68.5253i	−0.536596	−	0.0998911i
$687$		−	444.648i		−	0.647232i
$688$	−151.580	−	137.353i	−0.220319	−	0.199641i
$689$	−449.569			−0.652495
$690$	39.2154	−	210.658i	0.0568339	−	0.305301i
$691$	1316.90			1.90578			0.952892	−	0.303309i	$-0.0980913\pi$
$691$	1316.90			1.90578			0.952892	+	0.303309i	$0.0980913\pi$
$692$	−333.251	+	864.063i	−0.481577	+	1.24865i
$693$			257.847i			0.372074i
$694$	−169.149	+	908.636i	−0.243730	+	1.30927i
$695$		−	326.716i		−	0.470094i
$696$	−473.023	−	291.414i	−0.679631	−	0.418698i
$697$	−817.703			−1.17317
$698$	524.967	+	97.7261i	0.752101	+	0.140009i
$699$	−700.726			−1.00247
$700$	−258.449	+	670.113i	−0.369212	+	0.957305i
$701$		−	318.493i		−	0.454341i	−0.973855	−	0.227170i	$-0.927053\pi$
$701$		−	318.493i		−	0.454341i	0.973855	−	0.227170i	$-0.0729474\pi$
$702$	−160.708	−	29.9168i	−0.228928	−	0.0426166i
$703$			10.6883i			0.0152038i
$704$	230.277	+	457.293i	0.327098	+	0.649563i
$705$	7.69219			0.0109109
$706$	−96.2140	+	516.844i	−0.136280	+	0.732074i
$707$	−1044.90			−1.47793
$708$	72.4974	+	27.9607i	0.102397	+	0.0394926i
$709$			289.831i			0.408788i	0.978889	+	0.204394i	$0.0655224\pi$
$709$			289.831i			0.408788i	−0.978889	+	0.204394i	$0.934478\pi$
$710$	−88.9385	+	477.761i	−0.125266	+	0.672903i
$711$			220.988i			0.310813i
$712$	139.054	−	225.712i	0.195300	−	0.317012i
$713$	197.703			0.277283
$714$	−580.161	−	108.001i	−0.812551	−	0.151262i
$715$	362.256			0.506652
$716$	−722.697	−	278.729i	−1.00935	−	0.389287i
$717$			199.445i			0.278167i
$718$	322.823	+	60.0957i	0.449614	+	0.0836988i
$719$		−	491.122i		−	0.683062i	−0.939870	−	0.341531i	$-0.889055\pi$
$719$		−	491.122i		−	0.683062i	0.939870	−	0.341531i	$-0.110945\pi$
$720$	−92.7846	+	102.395i	−0.128868	+	0.142215i
$721$	1500.53			2.08118
$722$	131.715	−	707.547i	0.182430	−	0.979982i
$723$	435.464			0.602302
$724$	389.338	−	1009.49i	0.537760	−	1.39432i
$725$		−	670.113i		−	0.924294i
$726$	36.1366	−	194.119i	0.0497749	−	0.267381i
$727$			774.918i			1.06591i	0.846143	+	0.532956i	$0.178919\pi$
$727$			774.918i			1.06591i	−0.846143	+	0.532956i	$0.821081\pi$
$728$	709.128	−	1151.06i	0.974077	−	1.58112i
$729$	27.0000			0.0370370
$730$	−596.736	−	111.086i	−0.817446	−	0.152173i
$731$	202.718			0.277316
$732$	3.84610	−	9.97227i	0.00525423	−	0.0136233i
$733$		−	858.966i		−	1.17185i	−0.810365	−	0.585925i	$-0.800731\pi$
$733$		−	858.966i		−	1.17185i	0.810365	−	0.585925i	$-0.199269\pi$
$734$	−476.760	−	88.7522i	−0.649537	−	0.120916i
$735$		−	331.207i		−	0.450622i
$736$	−416.420	−	547.154i	−0.565789	−	0.743416i
$737$	345.723			0.469095
$738$	−56.6269	+	304.189i	−0.0767303	+	0.412181i
$739$	63.1948			0.0855139			0.0427569	−	0.999086i	$-0.486386\pi$
$739$	63.1948			0.0855139			0.0427569	+	0.999086i	$0.486386\pi$
$740$	107.138	+	41.3210i	0.144782	+	0.0558393i
$741$			29.2008i			0.0394073i
$742$	−112.392	+	603.751i	−0.151472	+	0.813680i
$743$		−	1105.00i		−	1.48721i	−0.668620	−	0.743604i	$-0.733115\pi$
$743$		−	1105.00i		−	1.48721i	0.668620	−	0.743604i	$-0.266885\pi$
$744$	−108.546	−	66.8718i	−0.145895	−	0.0898814i
$745$	91.1591			0.122361
$746$	645.864	+	120.232i	0.865769	+	0.161169i
$747$	36.8616			0.0493461
$748$	−473.415	−	182.586i	−0.632908	−	0.244099i
$749$			2124.87i			2.83694i
$750$	−408.946	−	76.1281i	−0.545261	−	0.101504i
$751$		−	804.119i		−	1.07073i	−0.844621	−	0.535365i	$-0.820174\pi$
$751$		−	804.119i		−	1.07073i	0.844621	−	0.535365i	$-0.179826\pi$
$752$	16.5744	−	18.2911i	0.0220404	−	0.0243232i
$753$	11.8667			0.0157593
$754$	−230.851	+	1240.09i	−0.306169	+	1.64468i
$755$	260.589			0.345152
$756$	−80.3538	+	208.344i	−0.106288	+	0.275587i
$757$		−	1351.03i		−	1.78471i	−0.451334	−	0.892355i	$-0.649052\pi$
$757$		−	1351.03i		−	1.78471i	0.451334	−	0.892355i	$-0.350948\pi$
$758$	−13.2539	+	71.1973i	−0.0174853	+	0.0939279i
$759$		−	297.736i		−	0.392274i
$760$	21.0155	+	12.9469i	0.0276519	+	0.0170355i
$761$	−709.805			−0.932726			−0.466363	−	0.884593i	$-0.654436\pi$
$761$	−709.805			−0.932726			−0.466363	+	0.884593i	$0.654436\pi$
$762$	125.527	+	23.3677i	0.164734	+	0.0306663i
$763$	−2048.95			−2.68539
$764$	448.379	−	1162.57i	0.586884	−	1.52169i
$765$		−	136.940i		−	0.179006i
$766$	−323.041	−	60.1363i	−0.421724	−	0.0785069i
$767$		−	176.415i		−	0.230007i
$768$	43.5589	+	441.260i	0.0567173	+	0.574558i
$769$	−195.703			−0.254490			−0.127245	−	0.991871i	$-0.540613\pi$
$769$	−195.703			−0.254490			−0.127245	+	0.991871i	$0.540613\pi$
$770$	90.5641	−	486.493i	0.117616	−	0.631810i
$771$	430.028			0.557754
$772$	−180.172	−	69.4885i	−0.233383	−	0.0900110i
$773$			12.5484i			0.0162334i	0.999967	+	0.00811670i	$0.00258365\pi$
$773$			12.5484i			0.0162334i	−0.999967	+	0.00811670i	$0.997416\pi$
$774$	14.0385	−	75.4121i	0.0181376	−	0.0974317i
$775$		−	153.773i		−	0.198417i
$776$	−290.115	+	470.915i	−0.373860	+	0.606849i
$777$	185.569			0.238828
$778$	1189.44	+	221.422i	1.52884	+	0.284604i
$779$	55.2717			0.0709521
$780$	292.708	+	112.891i	0.375266	+	0.144732i
$781$			675.251i			0.864598i
$782$	669.913	+	124.709i	0.856666	+	0.159474i
$783$		−	208.344i		−	0.266084i
$784$	−787.569	−	713.652i	−1.00455	−	0.910271i
$785$	−665.036			−0.847180
$786$	−123.397	+	662.868i	−0.156994	+	0.843344i
$787$	−432.918			−0.550086			−0.275043	−	0.961432i	$-0.588692\pi$
$787$	−432.918			−0.550086			−0.275043	+	0.961432i	$0.588692\pi$
$788$	362.554	−	940.040i	0.460094	−	1.19294i
$789$			864.008i			1.09507i
$790$	77.6180	−	416.950i	0.0982506	−	0.527784i
$791$			1221.69i			1.54449i
$792$	−100.708	+	163.469i	−0.127156	+	0.206400i
$793$	−24.2666			−0.0306010
$794$	1065.10	+	198.276i	1.34144	+	0.249717i
$795$	−142.508			−0.179255
$796$	−103.808	+	269.155i	−0.130412	+	0.338135i
$797$			700.746i			0.879230i	0.898186	+	0.439615i	$0.144885\pi$
$797$			700.746i			0.879230i	−0.898186	+	0.439615i	$0.855115\pi$
$798$	39.2154	+	7.30021i	0.0491421	+	0.00914813i
$799$			24.4619i			0.0306157i
$800$	−425.577	+	323.892i	−0.531971	+	0.404865i
$801$	99.4153			0.124114
$802$	138.932	−	746.317i	0.173232	−	0.930570i
$803$	−843.405			−1.05032
$804$	279.349	+	107.739i	0.347449	+	0.134004i
$805$			664.562i			0.825543i
$806$	−52.9742	+	284.568i	−0.0657248	+	0.353062i
$807$			406.357i			0.503541i
$808$	−662.438	−	408.107i	−0.819849	−	0.505083i
$809$	−848.102			−1.04833			−0.524167	−	0.851615i	$-0.675623\pi$
$809$	−848.102			−1.04833			−0.524167	+	0.851615i	$0.675623\pi$
$810$	−50.9423	−	9.48325i	−0.0628917	−	0.0117077i
$811$	1242.18			1.53166			0.765832	−	0.643041i	$-0.222327\pi$
$811$	1242.18			1.53166			0.765832	+	0.643041i	$0.222327\pi$
$812$	1607.67	+	620.045i	1.97989	+	0.763602i
$813$			175.493i			0.215858i
$814$	156.862	+	29.2008i	0.192705	+	0.0358733i
$815$			64.3510i			0.0789583i
$816$	−325.626	−	295.064i	−0.399051	−	0.361598i
$817$	−13.7025			−0.0167717
$818$	−92.0244	+	494.338i	−0.112499	+	0.604325i
$819$	506.985			0.619029
$820$	213.682	−	554.041i	0.260588	−	0.675659i
$821$			208.303i			0.253719i	0.991921	+	0.126859i	$0.0404897\pi$
$821$			208.303i			0.253719i	−0.991921	+	0.126859i	$0.959510\pi$
$822$	−10.4167	+	55.9566i	−0.0126724	+	0.0680737i
$823$		−	778.114i		−	0.945461i	−0.881207	−	0.472730i	$-0.843268\pi$
$823$		−	778.114i		−	0.945461i	0.881207	−	0.472730i	$-0.156732\pi$
$824$	951.300	+	586.065i	1.15449	+	0.711244i
$825$	−231.580			−0.280702
$826$	−236.918	−	44.1039i	−0.286826	−	0.0533945i
$827$	−1280.57			−1.54845			−0.774225	−	0.632910i	$-0.781860\pi$
$827$	−1280.57			−1.54845			−0.774225	+	0.632910i	$0.781860\pi$
$828$	92.7846	−	240.575i	0.112059	−	0.290549i
$829$		−	9.78043i		−	0.0117979i	−0.999983	−	0.00589893i	$-0.998122\pi$
$829$		−	9.78043i		−	0.0117979i	0.999983	−	0.00589893i	$-0.00187770\pi$
$830$	−69.5486	−	12.9469i	−0.0837935	−	0.0155987i
$831$		−	294.348i		−	0.354210i
$832$	899.138	−	452.775i	1.08070	−	0.544201i
$833$	1053.27			1.26443
$834$	71.9512	−	386.509i	0.0862724	−	0.463440i
$835$	636.328			0.762070
$836$	32.0000	+	12.3417i	0.0382775	+	0.0147628i
$837$		−	47.8094i		−	0.0571199i
$838$	−98.1436	+	527.209i	−0.117116	+	0.629128i
$839$		−	1232.38i		−	1.46886i	−0.678682	−	0.734432i	$-0.737449\pi$
$839$		−	1232.38i		−	1.46886i	0.678682	−	0.734432i	$-0.262551\pi$
$840$	224.785	−	364.870i	0.267601	−	0.434369i
$841$	−766.672			−0.911619
$842$	−429.149	−	79.8890i	−0.509678	−	0.0948800i
$843$	−192.480			−0.228327
$844$	988.687	+	381.316i	1.17143	+	0.451796i
$845$		−	225.768i		−	0.267181i
$846$	9.09996	+	1.69402i	0.0107565	+	0.00200239i
$847$			612.387i			0.723007i
$848$	−307.061	+	338.865i	−0.362101	+	0.399606i
$849$	953.703			1.12332
$850$	96.9986	−	521.059i	0.114116	−	0.613010i
$851$	−214.277			−0.251794
$852$	−210.431	+	545.611i	−0.246984	+	0.640389i
$853$			412.170i			0.483201i	0.970376	+	0.241600i	$0.0776723\pi$
$853$			412.170i			0.483201i	−0.970376	+	0.241600i	$0.922328\pi$
$854$	−6.06664	+	32.5889i	−0.00710380	+	0.0381603i
$855$			9.25630i			0.0108261i
$856$	−829.913	+	1347.11i	−0.969524	+	1.57373i
$857$	−136.451			−0.159220			−0.0796099	−	0.996826i	$-0.525367\pi$
$857$	−136.451			−0.159220			−0.0796099	+	0.996826i	$0.525367\pi$
$858$	428.554	+	79.7782i	0.499480	+	0.0929816i
$859$	−649.646			−0.756282			−0.378141	−	0.925748i	$-0.623437\pi$
$859$	−649.646			−0.756282			−0.378141	+	0.925748i	$0.623437\pi$
$860$	−52.9742	+	137.353i	−0.0615979	+	0.159713i
$861$		−	959.627i		−	1.11455i
$862$	−1083.30	−	201.664i	−1.25673	−	0.233949i
$863$			1192.38i			1.38167i	0.723015	+	0.690833i	$0.242756\pi$
$863$			1192.38i			1.38167i	−0.723015	+	0.690833i	$0.757244\pi$
$864$	−132.315	+	100.701i	−0.153143	+	0.116552i
$865$	666.502			0.770523
$866$	96.3116	−	517.368i	0.111214	−	0.597423i
$867$	−65.0807			−0.0750643
$868$	368.918	+	142.284i	0.425021	+	0.163922i
$869$		−	589.302i		−	0.678138i
$870$	−73.1769	+	393.093i	−0.0841114	+	0.451831i
$871$		−	679.768i		−	0.780446i
$872$	−1298.98	−	800.262i	−1.48966	−	0.917732i
$873$	−207.415			−0.237589
$874$	−45.2820	−	8.42956i	−0.0518101	−	0.00964480i
$875$	1290.10			1.47440
$876$	−681.482	−	262.833i	−0.777947	−	0.300038i
$877$		−	744.451i		−	0.848861i	−0.905460	−	0.424431i	$-0.860474\pi$
$877$		−	744.451i		−	0.848861i	0.905460	−	0.424431i	$-0.139526\pi$
$878$	−866.099	−	161.230i	−0.986445	−	0.183633i
$879$			387.129i			0.440419i
$880$	247.426	−	273.053i	0.281165	−	0.310287i
$881$	651.108			0.739055			0.369528	−	0.929220i	$-0.379520\pi$
$881$	651.108			0.739055			0.369528	+	0.929220i	$0.379520\pi$
$882$	72.9404	−	391.822i	0.0826989	−	0.444243i
$883$	1171.44			1.32666			0.663330	−	0.748327i	$-0.269143\pi$
$883$	1171.44			1.32666			0.663330	+	0.748327i	$0.269143\pi$
$884$	−359.005	+	930.839i	−0.406114	+	1.05299i
$885$		−	55.9215i		−	0.0631881i
$886$	83.7128	−	449.690i	0.0944840	−	0.507551i
$887$			1026.87i			1.15769i	0.815437	+	0.578845i	$0.196496\pi$
$887$			1026.87i			1.15769i	−0.815437	+	0.578845i	$0.803504\pi$
$888$	117.646	+	72.4780i	0.132484	+	0.0816193i
$889$	−396.000			−0.445444
$890$	−187.572	−	34.9178i	−0.210755	−	0.0392335i
$891$	−72.0000			−0.0808081
$892$	−44.1718	+	114.530i	−0.0495199	+	0.128397i
$893$		−	1.65348i		−	0.00185160i
$894$	107.842	+	20.0756i	0.120629	+	0.0224559i
$895$			557.458i			0.622859i
$896$	−383.272	−	1320.70i	−0.427759	−	1.47399i
$897$	−585.415			−0.652637
$898$	39.6809	−	213.158i	0.0441881	−	0.237370i
$899$	−368.918			−0.410365
$900$	−187.119	−	72.1680i	−0.207910	−	0.0801866i
$901$		−	453.189i		−	0.502984i
$902$	151.005	−	811.172i	0.167411	−	0.899304i
$903$			237.903i			0.263458i
$904$	−477.156	+	774.520i	−0.527828	+	0.856769i
$905$	−778.677			−0.860416
$906$	308.281	+	57.3885i	0.340266	+	0.0633428i
$907$	−470.508			−0.518752			−0.259376	−	0.965776i	$-0.583517\pi$
$907$	−470.508			−0.518752			−0.259376	+	0.965776i	$0.583517\pi$
$908$	−1104.11	−	425.833i	−1.21598	−	0.468979i
$909$		−	291.772i		−	0.320981i
$910$	−956.554	−	178.069i	−1.05116	−	0.195680i
$911$		−	553.930i		−	0.608046i	−0.952665	−	0.304023i	$-0.901670\pi$
$911$		−	553.930i		−	0.608046i	0.952665	−	0.304023i	$-0.0983300\pi$
$912$	22.0103	+	19.9445i	0.0241341	+	0.0218690i
$913$	−98.2975			−0.107664
$914$	−205.594	+	1104.41i	−0.224938	+	1.20833i
$915$	−7.69219			−0.00840677
$916$	−369.513	+	958.084i	−0.403398	+	1.04594i
$917$		−	2091.15i		−	2.28043i
$918$	30.1577	−	162.001i	0.0328515	−	0.176472i
$919$		−	910.123i		−	0.990341i	−0.868796	−	0.495170i	$-0.835106\pi$
$919$		−	910.123i		−	0.990341i	0.868796	−	0.495170i	$-0.164894\pi$
$920$	−259.559	+	421.316i	−0.282129	+	0.457952i
$921$	−643.959			−0.699195
$922$	658.999	+	122.677i	0.714749	+	0.133055i
$923$	1327.69			1.43845
$924$	214.277	−	555.583i	0.231901	−	0.601281i
$925$			166.665i			0.180178i
$926$	766.652	+	142.718i	0.827918	+	0.154123i
$927$			419.002i			0.451997i
$928$	777.051	+	1021.00i	0.837340	+	1.10022i
$929$	1278.69			1.37641			0.688206	−	0.725515i	$-0.258398\pi$
$929$	1278.69			1.37641			0.688206	+	0.725515i	$0.258398\pi$
$930$	−16.7922	+	90.2044i	−0.0180561	+	0.0969940i
$931$	−71.1948			−0.0764713
$932$	1509.85	+	582.319i	1.62001	+	0.624806i
$933$		−	571.616i		−	0.612664i
$934$	200.000	−	1074.36i	0.214133	−	1.15028i
$935$			365.173i			0.390559i
$936$	321.415	+	198.014i	0.343392	+	0.211553i
$937$	634.554			0.677219			0.338609	−	0.940927i	$-0.390044\pi$
$937$	634.554			0.677219			0.338609	+	0.940927i	$0.390044\pi$
$938$	−912.897	−	169.942i	−0.973238	−	0.181175i
$939$	−139.044			−0.148076
$940$	−16.5744	−	6.39239i	−0.0176323	−	0.00680041i
$941$		−	1136.25i		−	1.20749i	−0.797177	−	0.603745i	$-0.793674\pi$
$941$		−	1136.25i		−	1.20749i	0.797177	−	0.603745i	$-0.206326\pi$
$942$	−786.746	−	146.458i	−0.835187	−	0.155476i
$943$			1108.08i			1.17506i
$944$	−132.974	−	120.494i	−0.140863	−	0.127642i
$945$	160.708			0.170061
$946$	−37.4359	+	201.099i	−0.0395729	+	0.212578i
$947$	775.615			0.819023			0.409512	−	0.912305i	$-0.365699\pi$
$947$	775.615			0.819023			0.409512	+	0.912305i	$0.365699\pi$
$948$	183.646	−	476.163i	0.193720	−	0.502282i
$949$			1658.32i			1.74744i
$950$	−6.55652	+	35.2204i	−0.00690160	+	0.0370741i
$951$			119.309i			0.125457i
$952$	1160.32	+	714.837i	1.21883	+	0.750879i
$953$	599.590			0.629160			0.314580	−	0.949231i	$-0.398136\pi$
$953$	599.590			0.629160			0.314580	+	0.949231i	$0.398136\pi$
$954$	−168.588	−	31.3839i	−0.176717	−	0.0328972i
$955$	−896.758			−0.939014
$956$	165.744	−	429.745i	0.173372	−	0.449524i
$957$			555.583i			0.580547i
$958$	724.295	+	134.832i	0.756049	+	0.140744i
$959$		−	176.526i		−	0.184073i
$960$	285.015	−	143.524i	0.296891	−	0.149504i
$961$	876.343			0.911908
$962$	57.4153	−	308.425i	0.0596833	−	0.320608i
$963$	−593.338			−0.616135
$964$	−938.295	−	361.881i	−0.973335	−	0.375395i
$965$			138.977i			0.144018i
$966$	−146.354	+	786.186i	−0.151505	+	0.813857i
$967$			1407.53i			1.45556i	0.685811	+	0.727780i	$0.259448\pi$
$967$			1407.53i			1.45556i	−0.685811	+	0.727780i	$0.740552\pi$
$968$	−239.181	+	388.238i	−0.247087	+	0.401072i
$969$	−29.4359			−0.0303776
$970$	391.341	+	72.8508i	0.403444	+	0.0751039i
$971$	653.661			0.673184			0.336592	−	0.941651i	$-0.390726\pi$
$971$	653.661			0.673184			0.336592	+	0.941651i	$0.390726\pi$
$972$	−58.1769	−	22.4376i	−0.0598528	−	0.0230840i
$973$			1219.32i			1.25315i
$974$	−178.204	−	33.1738i	−0.182961	−	0.0340594i
$975$			455.337i			0.467012i
$976$	−16.5744	+	18.2911i	−0.0169819	+	0.0187408i
$977$	−1003.57			−1.02719			−0.513597	−	0.858031i	$-0.671687\pi$
$977$	−1003.57			−1.02719			−0.513597	+	0.858031i	$0.671687\pi$
$978$	−14.1718	+	76.1281i	−0.0144906	+	0.0778406i
$979$	−265.108			−0.270794
$980$	−275.241	+	713.652i	−0.280858	+	0.728217i
$981$		−	572.140i		−	0.583221i
$982$	6.45895	−	34.6963i	0.00657734	−	0.0353323i
$983$			105.672i			0.107500i	0.998554	+	0.0537498i	$0.0171173\pi$
$983$			105.672i			0.107500i	−0.998554	+	0.0537498i	$0.982883\pi$
$984$	374.802	−	608.379i	0.380897	−	0.618271i
$985$	−725.108			−0.736150
$986$	−1250.07	−	232.710i	−1.26782	−	0.236014i
$987$	−28.7077			−0.0290858
$988$	24.2666	−	62.9191i	0.0245613	−	0.0636833i
$989$		−	274.706i		−	0.277762i
$990$	135.846	+	25.2887i	0.137218	+	0.0255441i
$991$		−	1728.18i		−	1.74388i	−0.489615	−	0.871938i	$-0.662863\pi$
$991$		−	1728.18i		−	1.74388i	0.489615	−	0.871938i	$-0.337137\pi$
$992$	178.313	+	234.293i	0.179751	+	0.236183i
$993$	−685.990			−0.690825
$994$	331.923	−	1783.03i	0.333927	−	1.79379i
$995$	207.615			0.208659
$996$	−79.4256	−	30.6328i	−0.0797446	−	0.0307558i
$997$		−	135.205i		−	0.135612i	−0.997699	−	0.0678060i	$-0.978400\pi$
$997$		−	135.205i		−	0.135612i	0.997699	−	0.0678060i	$-0.0215999\pi$
$998$	−200.813	+	1078.73i	−0.201215	+	1.08089i
$999$			51.8175i			0.0518693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.3.b.a.19.2	yes	4
3.2	odd	2		72.3.b.b.19.3		4
4.3	odd	2		96.3.b.a.79.2		4
5.2	odd	4		600.3.p.a.499.1		8
5.3	odd	4		600.3.p.a.499.8		8
5.4	even	2		600.3.g.a.451.3		4
8.3	odd	2	inner	24.3.b.a.19.1	✓	4
8.5	even	2		96.3.b.a.79.1		4
12.11	even	2		288.3.b.b.271.2		4
16.3	odd	4		768.3.g.h.511.3		8
16.5	even	4		768.3.g.h.511.2		8
16.11	odd	4		768.3.g.h.511.6		8
16.13	even	4		768.3.g.h.511.7		8
20.3	even	4		2400.3.p.a.1999.4		8
20.7	even	4		2400.3.p.a.1999.5		8
20.19	odd	2		2400.3.g.a.751.3		4
24.5	odd	2		288.3.b.b.271.3		4
24.11	even	2		72.3.b.b.19.4		4
40.3	even	4		600.3.p.a.499.2		8
40.13	odd	4		2400.3.p.a.1999.1		8
40.19	odd	2		600.3.g.a.451.4		4
40.27	even	4		600.3.p.a.499.7		8
40.29	even	2		2400.3.g.a.751.4		4
40.37	odd	4		2400.3.p.a.1999.8		8
48.5	odd	4		2304.3.g.z.1279.6		8
48.11	even	4		2304.3.g.z.1279.5		8
48.29	odd	4		2304.3.g.z.1279.4		8
48.35	even	4		2304.3.g.z.1279.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.3.b.a.19.1	✓	4	8.3	odd	2	inner
24.3.b.a.19.2	yes	4	1.1	even	1	trivial
72.3.b.b.19.3		4	3.2	odd	2
72.3.b.b.19.4		4	24.11	even	2
96.3.b.a.79.1		4	8.5	even	2
96.3.b.a.79.2		4	4.3	odd	2
288.3.b.b.271.2		4	12.11	even	2
288.3.b.b.271.3		4	24.5	odd	2
600.3.g.a.451.3		4	5.4	even	2
600.3.g.a.451.4		4	40.19	odd	2
600.3.p.a.499.1		8	5.2	odd	4
600.3.p.a.499.2		8	40.3	even	4
600.3.p.a.499.7		8	40.27	even	4
600.3.p.a.499.8		8	5.3	odd	4
768.3.g.h.511.2		8	16.5	even	4
768.3.g.h.511.3		8	16.3	odd	4
768.3.g.h.511.6		8	16.11	odd	4
768.3.g.h.511.7		8	16.13	even	4
2304.3.g.z.1279.3		8	48.35	even	4
2304.3.g.z.1279.4		8	48.29	odd	4
2304.3.g.z.1279.5		8	48.11	even	4
2304.3.g.z.1279.6		8	48.5	odd	4
2400.3.g.a.751.3		4	20.19	odd	2
2400.3.g.a.751.4		4	40.29	even	2
2400.3.p.a.1999.1		8	40.13	odd	4
2400.3.p.a.1999.4		8	20.3	even	4
2400.3.p.a.1999.5		8	20.7	even	4
2400.3.p.a.1999.8		8	40.37	odd	4

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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	24.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.96622i) q^{2} +1.73205 q^{3} +(-3.73205 - 1.43937i) q^{4} +2.87875i q^{5} +(-0.633975 + 3.40559i) q^{6} -10.7436i q^{7} +(4.19615 - 6.81119i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-0.366025 + 1.96622i) q^{2} +1.73205 q^{3} +(-3.73205 - 1.43937i) q^{4} +2.87875i q^{5} +(-0.633975 + 3.40559i) q^{6} -10.7436i q^{7} +(4.19615 - 6.81119i) q^{8} +3.00000 q^{9} +(-5.66025 - 1.05369i) q^{10} -8.00000 q^{11} +(-6.46410 - 2.49307i) q^{12} +15.7298i q^{13} +(21.1244 + 3.93244i) q^{14} +4.98614i q^{15} +(11.8564 + 10.7436i) q^{16} -15.8564 q^{17} +(-1.09808 + 5.89866i) q^{18} +1.07180 q^{19} +(4.14359 - 10.7436i) q^{20} -18.6085i q^{21} +(2.92820 - 15.7298i) q^{22} +21.4873i q^{23} +(7.26795 - 11.7973i) q^{24} +16.7128 q^{25} +(-30.9282 - 5.75749i) q^{26} +5.19615 q^{27} +(-15.4641 + 40.0958i) q^{28} -40.0958i q^{29} +(-9.80385 - 1.82505i) q^{30} -9.20092i q^{31} +(-25.4641 + 19.3799i) q^{32} -13.8564 q^{33} +(5.80385 - 31.1772i) q^{34} +30.9282 q^{35} +(-11.1962 - 4.31812i) q^{36} +9.97227i q^{37} +(-0.392305 + 2.10739i) q^{38} +27.2448i q^{39} +(19.6077 + 12.0797i) q^{40} +51.5692 q^{41} +(36.5885 + 6.81119i) q^{42} -12.7846 q^{43} +(29.8564 + 11.5150i) q^{44} +8.63624i q^{45} +(-42.2487 - 7.86488i) q^{46} -1.54272i q^{47} +(20.5359 + 18.6085i) q^{48} -66.4256 q^{49} +(-6.11731 + 32.8611i) q^{50} -27.4641 q^{51} +(22.6410 - 58.7043i) q^{52} +28.5808i q^{53} +(-1.90192 + 10.2168i) q^{54} -23.0300i q^{55} +(-73.1769 - 45.0819i) q^{56} +1.85641 q^{57} +(78.8372 + 14.6761i) q^{58} -11.2154 q^{59} +(7.17691 - 18.6085i) q^{60} +1.54272i q^{61} +(18.0910 + 3.36777i) q^{62} -32.2309i q^{63} +(-28.7846 - 57.1616i) q^{64} -45.2820 q^{65} +(5.07180 - 27.2448i) q^{66} -43.2154 q^{67} +(59.1769 + 22.8233i) q^{68} +37.2170i q^{69} +(-11.3205 + 60.8117i) q^{70} -84.4063i q^{71} +(12.5885 - 20.4336i) q^{72} +105.426 q^{73} +(-19.6077 - 3.65011i) q^{74} +28.9474 q^{75} +(-4.00000 - 1.54272i) q^{76} +85.9491i q^{77} +(-53.5692 - 9.97227i) q^{78} +73.6627i q^{79} +(-30.9282 + 34.1316i) q^{80} +9.00000 q^{81} +(-18.8756 + 101.396i) q^{82} +12.2872 q^{83} +(-26.7846 + 69.4479i) q^{84} -45.6466i q^{85} +(4.67949 - 25.1374i) q^{86} -69.4479i q^{87} +(-33.5692 + 54.4895i) q^{88} +33.1384 q^{89} +(-16.9808 - 3.16108i) q^{90} +168.995 q^{91} +(30.9282 - 80.1916i) q^{92} -15.9365i q^{93} +(3.03332 + 0.564673i) q^{94} +3.08543i q^{95} +(-44.1051 + 33.5669i) q^{96} -69.1384 q^{97} +(24.3135 - 130.607i) q^{98} -24.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 8 q^{4} - 6 q^{6} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 - 4 * q^8 + 12 * q^9	\( 4 q + 2 q^{2} - 8 q^{4} - 6 q^{6} - 4 q^{8} + 12 q^{9} + 12 q^{10} - 32 q^{11} - 12 q^{12} + 36 q^{14} - 8 q^{16} - 8 q^{17} + 6 q^{18} + 32 q^{19} + 72 q^{20} - 16 q^{22} + 36 q^{24} - 44 q^{25} - 96 q^{26} - 48 q^{28} - 60 q^{30} - 88 q^{32} + 44 q^{34} + 96 q^{35} - 24 q^{36} + 40 q^{38} + 120 q^{40} + 40 q^{41} + 84 q^{42} + 32 q^{43} + 64 q^{44} - 72 q^{46} + 96 q^{48} - 44 q^{49} - 118 q^{50} - 96 q^{51} - 48 q^{52} - 18 q^{54} - 168 q^{56} - 48 q^{57} + 156 q^{58} - 128 q^{59} - 96 q^{60} + 204 q^{62} - 32 q^{64} + 96 q^{65} + 48 q^{66} - 256 q^{67} + 112 q^{68} + 24 q^{70} - 12 q^{72} + 200 q^{73} - 120 q^{74} + 192 q^{75} - 16 q^{76} - 48 q^{78} - 96 q^{80} + 36 q^{81} - 124 q^{82} + 160 q^{83} - 24 q^{84} + 88 q^{86} + 32 q^{88} - 200 q^{89} + 36 q^{90} + 288 q^{91} + 96 q^{92} - 168 q^{94} - 24 q^{96} + 56 q^{97} + 170 q^{98} - 96 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 - 4 * q^8 + 12 * q^9 + 12 * q^10 - 32 * q^11 - 12 * q^12 + 36 * q^14 - 8 * q^16 - 8 * q^17 + 6 * q^18 + 32 * q^19 + 72 * q^20 - 16 * q^22 + 36 * q^24 - 44 * q^25 - 96 * q^26 - 48 * q^28 - 60 * q^30 - 88 * q^32 + 44 * q^34 + 96 * q^35 - 24 * q^36 + 40 * q^38 + 120 * q^40 + 40 * q^41 + 84 * q^42 + 32 * q^43 + 64 * q^44 - 72 * q^46 + 96 * q^48 - 44 * q^49 - 118 * q^50 - 96 * q^51 - 48 * q^52 - 18 * q^54 - 168 * q^56 - 48 * q^57 + 156 * q^58 - 128 * q^59 - 96 * q^60 + 204 * q^62 - 32 * q^64 + 96 * q^65 + 48 * q^66 - 256 * q^67 + 112 * q^68 + 24 * q^70 - 12 * q^72 + 200 * q^73 - 120 * q^74 + 192 * q^75 - 16 * q^76 - 48 * q^78 - 96 * q^80 + 36 * q^81 - 124 * q^82 + 160 * q^83 - 24 * q^84 + 88 * q^86 + 32 * q^88 - 200 * q^89 + 36 * q^90 + 288 * q^91 + 96 * q^92 - 168 * q^94 - 24 * q^96 + 56 * q^97 + 170 * q^98 - 96 * q^99

Introduction

L-functions

Modular forms

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Database

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