LMFDB - Embedded newform 225.2.q.a.16.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.17
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.322402 - 0.143543i) q^{2} +(-0.648399 - 1.60611i) q^{3} +(-1.25492 + 1.39373i) q^{4} +(-1.80765 - 1.31620i) q^{5} +(-0.439590 - 0.424739i) q^{6} +(1.84787 - 3.20061i) q^{7} +(-0.422642 + 1.30076i) q^{8} +(-2.15916 + 2.08280i) q^{9} +O(q^{10})$	\(q+(0.322402 - 0.143543i) q^{2} +(-0.648399 - 1.60611i) q^{3} +(-1.25492 + 1.39373i) q^{4} +(-1.80765 - 1.31620i) q^{5} +(-0.439590 - 0.424739i) q^{6} +(1.84787 - 3.20061i) q^{7} +(-0.422642 + 1.30076i) q^{8} +(-2.15916 + 2.08280i) q^{9} +(-0.771722 - 0.164872i) q^{10} +(-5.06633 + 2.25567i) q^{11} +(3.05217 + 1.11185i) q^{12} +(-3.83460 - 1.70728i) q^{13} +(0.136334 - 1.29713i) q^{14} +(-0.941886 + 3.75671i) q^{15} +(-0.341623 - 3.25032i) q^{16} +(0.721064 - 2.21921i) q^{17} +(-0.397147 + 0.981428i) q^{18} +(1.49906 - 4.61362i) q^{19} +(4.10290 - 0.867648i) q^{20} +(-6.33868 - 0.892610i) q^{21} +(-1.30961 + 1.45447i) q^{22} +(0.0122903 - 0.116934i) q^{23} +(2.36319 - 0.164602i) q^{24} +(1.53521 + 4.75848i) q^{25} -1.48135 q^{26} +(4.74519 + 2.11736i) q^{27} +(2.14186 + 6.59196i) q^{28} +(1.63010 + 0.346488i) q^{29} +(0.235582 + 1.34637i) q^{30} +(8.52984 - 1.81307i) q^{31} +(-1.94440 - 3.36779i) q^{32} +(6.90785 + 6.67448i) q^{33} +(-0.0860783 - 0.818980i) q^{34} +(-7.55297 + 3.35341i) q^{35} +(-0.193284 - 5.62304i) q^{36} +(2.35522 - 1.71117i) q^{37} +(-0.178952 - 1.70262i) q^{38} +(-0.255714 + 7.26578i) q^{39} +(2.47605 - 1.79503i) q^{40} +(-3.36731 - 1.49922i) q^{41} +(-2.17173 + 0.622091i) q^{42} +(-2.06835 + 3.58248i) q^{43} +(3.21404 - 9.89180i) q^{44} +(6.64439 - 0.923075i) q^{45} +(-0.0128226 - 0.0394639i) q^{46} +(4.22717 + 0.898512i) q^{47} +(-4.99886 + 2.65619i) q^{48} +(-3.32927 - 5.76646i) q^{49} +(1.17800 + 1.31377i) q^{50} +(-4.03182 + 0.280825i) q^{51} +(7.19162 - 3.20191i) q^{52} +(-3.62572 - 11.1588i) q^{53} +(1.83379 + 0.00150320i) q^{54} +(12.1271 + 2.59085i) q^{55} +(3.38223 + 3.75634i) q^{56} +(-8.38195 + 0.583822i) q^{57} +(0.575283 - 0.122280i) q^{58} +(-7.00923 - 3.12071i) q^{59} +(-4.05385 - 6.02712i) q^{60} +(-1.35990 + 0.605466i) q^{61} +(2.48978 - 1.80893i) q^{62} +(2.67637 + 10.7594i) q^{63} +(4.17780 + 3.03535i) q^{64} +(4.68450 + 8.13328i) q^{65} +(3.18518 + 1.16030i) q^{66} +(0.659374 - 0.140154i) q^{67} +(2.18810 + 3.78991i) q^{68} +(-0.195777 + 0.0560804i) q^{69} +(-1.95373 + 2.16532i) q^{70} +(1.99156 + 6.12940i) q^{71} +(-1.79666 - 3.68882i) q^{72} +(-9.08610 - 6.60143i) q^{73} +(0.513701 - 0.889757i) q^{74} +(6.64720 - 5.55110i) q^{75} +(4.54895 + 7.87902i) q^{76} +(-2.14240 + 20.3835i) q^{77} +(0.960506 + 2.37921i) q^{78} +(-8.44849 - 1.79578i) q^{79} +(-3.66056 + 6.32510i) q^{80} +(0.323926 - 8.99417i) q^{81} -1.30083 q^{82} +(2.71620 + 3.01664i) q^{83} +(9.19861 - 7.71427i) q^{84} +(-4.22437 + 3.06249i) q^{85} +(-0.152600 + 1.45190i) q^{86} +(-0.500457 - 2.84278i) q^{87} +(-0.792843 - 7.54340i) q^{88} +(-7.85033 - 5.70360i) q^{89} +(2.00966 - 1.25135i) q^{90} +(-12.5502 + 9.11824i) q^{91} +(0.147551 + 0.163872i) q^{92} +(-8.44273 - 12.5242i) q^{93} +(1.49182 - 0.317097i) q^{94} +(-8.78224 + 6.36675i) q^{95} +(-4.14829 + 5.30658i) q^{96} +(9.42543 + 2.00344i) q^{97} +(-1.90110 - 1.38123i) q^{98} +(6.24089 - 15.4225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.322402	−	0.143543i	0.227973	−	0.101500i	−0.289572	−	0.957156i	$-0.593513\pi$
$2$	0.322402	−	0.143543i	0.227973	−	0.101500i	0.517544	+	0.855656i	$0.326846\pi$
$3$	−0.648399	−	1.60611i	−0.374353	−	0.927286i
$3$	−0.648399	−	1.60611i	−0.374353	−	0.927286i
$4$	−1.25492	+	1.39373i	−0.627461	+	0.696866i
$5$	−1.80765	−	1.31620i	−0.808406	−	0.588625i
$5$	−1.80765	−	1.31620i	−0.808406	−	0.588625i
$6$	−0.439590	−	0.424739i	−0.179462	−	0.173399i
$7$	1.84787	−	3.20061i	0.698430	−	1.20972i	−0.270580	−	0.962697i	$-0.587216\pi$
$7$	1.84787	−	3.20061i	0.698430	−	1.20972i	0.969011	−	0.247019i	$-0.0794512\pi$
$8$	−0.422642	+	1.30076i	−0.149426	+	0.459887i
$9$	−2.15916	+	2.08280i	−0.719719	+	0.694265i
$10$	−0.771722	−	0.164872i	−0.244040	−	0.0521371i
$11$	−5.06633	+	2.25567i	−1.52755	+	0.680111i	−0.986930	−	0.161152i	$-0.948479\pi$
$11$	−5.06633	+	2.25567i	−1.52755	+	0.680111i	−0.540625	+	0.841264i	$0.681812\pi$
$12$	3.05217	+	1.11185i	0.881087	+	0.320962i
$13$	−3.83460	−	1.70728i	−1.06353	−	0.473513i	−0.201036	−	0.979584i	$-0.564431\pi$
$13$	−3.83460	−	1.70728i	−1.06353	−	0.473513i	−0.862492	+	0.506071i	$0.831097\pi$
$14$	0.136334	−	1.29713i	0.0364368	−	0.346673i
$15$	−0.941886	+	3.75671i	−0.243194	+	0.969978i
$16$	−0.341623	−	3.25032i	−0.0854057	−	0.812581i
$17$	0.721064	−	2.21921i	0.174884	−	0.538237i	−0.824744	−	0.565506i	$-0.808681\pi$
$17$	0.721064	−	2.21921i	0.174884	−	0.538237i	0.999628	+	0.0272687i	$0.00868099\pi$
$18$	−0.397147	+	0.981428i	−0.0936084	+	0.231325i
$19$	1.49906	−	4.61362i	0.343907	−	1.05844i	−0.618259	−	0.785974i	$-0.712162\pi$
$19$	1.49906	−	4.61362i	0.343907	−	1.05844i	0.962166	−	0.272463i	$-0.0878382\pi$
$20$	4.10290	−	0.867648i	0.917437	−	0.194012i
$21$	−6.33868	−	0.892610i	−1.38321	−	0.194783i
$22$	−1.30961	+	1.45447i	−0.279209	+	0.310093i
$23$	0.0122903	−	0.116934i	0.00256270	−	0.0243824i	−0.993166	−	0.116712i	$-0.962765\pi$
$23$	0.0122903	−	0.116934i	0.00256270	−	0.0243824i	0.995729	+	0.0923294i	$0.0294313\pi$
$24$	2.36319	−	0.164602i	0.482385	−	0.0335992i
$25$	1.53521	+	4.75848i	0.307042	+	0.951696i
$26$	−1.48135			−0.290517
$27$	4.74519	+	2.11736i	0.913212	+	0.407485i
$28$	2.14186	+	6.59196i	0.404773	+	1.24576i
$29$	1.63010	+	0.346488i	0.302702	+	0.0643413i	0.356759	−	0.934197i	$-0.383882\pi$
$29$	1.63010	+	0.346488i	0.302702	+	0.0643413i	−0.0540567	+	0.998538i	$0.517215\pi$
$30$	0.235582	+	1.34637i	0.0430111	+	0.245812i
$31$	8.52984	−	1.81307i	1.53200	−	0.325638i	0.636707	−	0.771106i	$-0.280296\pi$
$31$	8.52984	−	1.81307i	1.53200	−	0.325638i	0.895298	+	0.445469i	$0.146963\pi$
$32$	−1.94440	−	3.36779i	−0.343724	−	0.595347i
$33$	6.90785	+	6.67448i	1.20250	+	1.16188i
$34$	−0.0860783	−	0.818980i	−0.0147623	−	0.140454i
$35$	−7.55297	+	3.35341i	−1.27668	+	0.566830i
$36$	−0.193284	−	5.62304i	−0.0322140	−	0.937173i
$37$	2.35522	−	1.71117i	0.387195	−	0.281314i	−0.377110	−	0.926169i	$-0.623082\pi$
$37$	2.35522	−	1.71117i	0.387195	−	0.281314i	0.764305	+	0.644855i	$0.223082\pi$
$38$	−0.178952	−	1.70262i	−0.0290299	−	0.276201i
$39$	−0.255714	+	7.26578i	−0.0409471	+	1.16346i
$40$	2.47605	−	1.79503i	0.391498	−	0.283820i
$41$	−3.36731	−	1.49922i	−0.525885	−	0.234139i	0.126582	−	0.991956i	$-0.459599\pi$
$41$	−3.36731	−	1.49922i	−0.525885	−	0.234139i	−0.652467	+	0.757817i	$0.726266\pi$
$42$	−2.17173	+	0.622091i	−0.335105	+	0.0959908i
$43$	−2.06835	+	3.58248i	−0.315420	+	0.546323i	−0.979527	−	0.201314i	$-0.935479\pi$
$43$	−2.06835	+	3.58248i	−0.315420	+	0.546323i	0.664107	+	0.747638i	$0.268812\pi$
$44$	3.21404	−	9.89180i	0.484535	−	1.49125i
$45$	6.64439	−	0.923075i	0.990487	−	0.137604i
$46$	−0.0128226	−	0.0394639i	−0.00189059	−	0.00581864i
$47$	4.22717	+	0.898512i	0.616596	+	0.131061i	0.505612	−	0.862761i	$-0.331267\pi$
$47$	4.22717	+	0.898512i	0.616596	+	0.131061i	0.110983	+	0.993822i	$0.464600\pi$
$48$	−4.99886	+	2.65619i	−0.721523	+	0.383388i
$49$	−3.32927	−	5.76646i	−0.475610	−	0.823781i
$50$	1.17800	+	1.31377i	0.166594	+	0.185796i
$51$	−4.03182	+	0.280825i	−0.564568	+	0.0393234i
$52$	7.19162	−	3.20191i	0.997298	−	0.444026i
$53$	−3.62572	−	11.1588i	−0.498031	−	1.53278i	−0.812179	−	0.583409i	$-0.801719\pi$
$53$	−3.62572	−	11.1588i	−0.498031	−	1.53278i	0.314148	−	0.949374i	$-0.398281\pi$
$54$	1.83379	+	0.00150320i	0.249547	+	0.000204560i
$55$	12.1271	+	2.59085i	1.63522	+	0.349350i
$56$	3.38223	+	3.75634i	0.451969	+	0.501963i
$57$	−8.38195	+	0.583822i	−1.11022	+	0.0773291i
$58$	0.575283	−	0.122280i	0.0755384	−	0.0160562i
$59$	−7.00923	−	3.12071i	−0.912524	−	0.406282i	−0.103887	−	0.994589i	$-0.533128\pi$
$59$	−7.00923	−	3.12071i	−0.912524	−	0.406282i	−0.808638	+	0.588307i	$0.799795\pi$
$60$	−4.05385	−	6.02712i	−0.523350	−	0.778097i
$61$	−1.35990	+	0.605466i	−0.174117	+	0.0775220i	−0.491944	−	0.870627i	$-0.663714\pi$
$61$	−1.35990	+	0.605466i	−0.174117	+	0.0775220i	0.317827	+	0.948149i	$0.397047\pi$
$62$	2.48978	−	1.80893i	0.316203	−	0.229735i
$63$	2.67637	+	10.7594i	0.337190	+	1.35555i
$64$	4.17780	+	3.03535i	0.522226	+	0.379419i
$65$	4.68450	+	8.13328i	0.581041	+	1.00881i
$66$	3.18518	+	1.16030i	0.392068	+	0.142823i
$67$	0.659374	−	0.140154i	0.0805553	−	0.0171226i	−0.167458	−	0.985879i	$-0.553556\pi$
$67$	0.659374	−	0.140154i	0.0805553	−	0.0171226i	0.248013	+	0.968757i	$0.420222\pi$
$68$	2.18810	+	3.78991i	0.265346	+	0.459594i
$69$	−0.195777	+	0.0560804i	−0.0235688	+	0.00675129i
$70$	−1.95373	+	2.16532i	−0.233516	+	0.258805i
$71$	1.99156	+	6.12940i	0.236355	+	0.727425i	0.996939	+	0.0781858i	$0.0249127\pi$
$71$	1.99156	+	6.12940i	0.236355	+	0.727425i	−0.760584	+	0.649240i	$0.775087\pi$
$72$	−1.79666	−	3.68882i	−0.211739	−	0.434731i
$73$	−9.08610	−	6.60143i	−1.06345	−	0.772639i	−0.0887240	−	0.996056i	$-0.528279\pi$
$73$	−9.08610	−	6.60143i	−1.06345	−	0.772639i	−0.974723	+	0.223417i	$0.928279\pi$
$74$	0.513701	−	0.889757i	0.0597166	−	0.103432i
$75$	6.64720	−	5.55110i	0.767552	−	0.640986i
$76$	4.54895	+	7.87902i	0.521801	+	0.903786i
$77$	−2.14240	+	20.3835i	−0.244149	+	2.32292i
$78$	0.960506	+	2.37921i	0.108756	+	0.269392i
$79$	−8.44849	−	1.79578i	−0.950529	−	0.202041i	−0.293545	−	0.955945i	$-0.594835\pi$
$79$	−8.44849	−	1.79578i	−0.950529	−	0.202041i	−0.656984	+	0.753904i	$0.728168\pi$
$80$	−3.66056	+	6.32510i	−0.409263	+	0.707168i
$81$	0.323926	−	8.99417i	0.0359918	−	0.999352i
$82$	−1.30083			−0.143653
$83$	2.71620	+	3.01664i	0.298141	+	0.331120i	0.873539	−	0.486754i	$-0.161819\pi$
$83$	2.71620	+	3.01664i	0.298141	+	0.331120i	−0.575397	+	0.817874i	$0.695153\pi$
$84$	9.19861	−	7.71427i	1.00365	−	0.841696i
$85$	−4.22437	+	3.06249i	−0.458197	+	0.332173i
$86$	−0.152600	+	1.45190i	−0.0164553	+	0.156562i
$87$	−0.500457	−	2.84278i	−0.0536547	−	0.304778i
$88$	−0.792843	−	7.54340i	−0.0845174	−	0.804129i
$89$	−7.85033	−	5.70360i	−0.832133	−	0.604580i	0.0880291	−	0.996118i	$-0.471943\pi$
$89$	−7.85033	−	5.70360i	−0.832133	−	0.604580i	−0.920162	+	0.391538i	$0.871943\pi$
$90$	2.00966	−	1.25135i	0.211837	−	0.131904i
$91$	−12.5502	+	9.11824i	−1.31562	+	0.955852i
$92$	0.147551	+	0.163872i	0.0153833	+	0.0170849i
$93$	−8.44273	−	12.5242i	−0.875470	−	1.29870i
$94$	1.49182	−	0.317097i	0.153870	−	0.0327060i
$95$	−8.78224	+	6.36675i	−0.901039	+	0.653215i
$96$	−4.14829	+	5.30658i	−0.423383	+	0.541601i
$97$	9.42543	+	2.00344i	0.957008	+	0.203418i	0.659839	−	0.751407i	$-0.270624\pi$
$97$	9.42543	+	2.00344i	0.957008	+	0.203418i	0.297168	+	0.954825i	$0.403958\pi$
$98$	−1.90110	−	1.38123i	−0.192040	−	0.139525i
$99$	6.24089	−	15.4225i	0.627233	−	1.55002i
$100$	−8.55862	−	3.83185i	−0.855862	−	0.383185i
$101$	6.50797	−	11.2721i	0.647568	−	1.12162i	−0.336134	−	0.941814i	$-0.609120\pi$
$101$	6.50797	−	11.2721i	0.647568	−	1.12162i	0.983702	−	0.179806i	$-0.0575470\pi$
$102$	−1.25956	+	0.669277i	−0.124715	+	0.0662683i
$103$	−4.13474	+	4.59210i	−0.407408	+	0.452473i	−0.911575	−	0.411134i	$-0.865133\pi$
$103$	−4.13474	+	4.59210i	−0.407408	+	0.452473i	0.504167	+	0.863606i	$0.331800\pi$
$104$	3.84141	−	4.26632i	0.376682	−	0.418347i
$105$	10.2833	+	9.95653i	1.00354	+	0.971658i
$106$	−2.77071	−	3.07718i	−0.269115	−	0.298882i
$107$	4.72593			0.456873			0.228437	−	0.973559i	$-0.426639\pi$
$107$	4.72593			0.456873			0.228437	+	0.973559i	$0.426639\pi$
$108$	−8.90587	+	3.95641i	−0.856968	+	0.380705i
$109$	0.143913	−	0.104559i	0.0137844	−	0.0100150i	−0.580872	−	0.813995i	$-0.697288\pi$
$109$	0.143913	−	0.104559i	0.0137844	−	0.0100150i	0.594656	+	0.803980i	$0.297288\pi$
$110$	4.28169	−	0.905458i	0.408243	−	0.0863320i
$111$	−4.27543	−	2.67321i	−0.405806	−	0.253730i
$112$	−11.0343	−	4.91278i	−1.04264	−	0.464214i
$113$	7.93576	+	3.53323i	0.746534	+	0.332378i	0.744502	−	0.667620i	$-0.232687\pi$
$113$	7.93576	+	3.53323i	0.746534	+	0.332378i	0.00203114	+	0.999998i	$0.499353\pi$
$114$	−2.61855	+	1.39139i	−0.245250	+	0.130316i
$115$	−0.176126	+	0.195199i	−0.0164238	+	0.0182024i
$116$	−2.52856	+	1.83711i	−0.234771	+	0.170571i
$117$	11.8354	−	4.30042i	1.09419	−	0.397574i
$118$	−2.70774			−0.249268
$119$	−5.77038	−	6.40866i	−0.528970	−	0.587481i
$120$	−4.48848	−	2.81291i	−0.409741	−	0.256782i
$121$	13.2192	−	14.6814i	1.20174	−	1.33467i
$122$	−0.351524	+	0.390407i	−0.0318255	+	0.0353458i
$123$	−0.224552	+	6.38035i	−0.0202472	+	0.575297i
$124$	−8.17735	+	14.1636i	−0.734348	+	1.27193i
$125$	3.48801	−	10.6223i	0.311977	−	0.950090i
$126$	2.40729	+	3.08467i	0.214459	+	0.274804i
$127$	−2.28222	−	1.65813i	−0.202514	−	0.147135i	0.481906	−	0.876223i	$-0.339945\pi$
$127$	−2.28222	−	1.65813i	−0.202514	−	0.147135i	−0.684420	+	0.729088i	$0.739945\pi$
$128$	9.39026	+	1.99596i	0.829990	+	0.176420i
$129$	7.09496	+	0.999109i	0.624677	+	0.0879667i
$130$	2.67777	+	1.94976i	0.234856	+	0.171005i
$131$	−12.4804	+	2.65278i	−1.09041	+	0.231775i	−0.717827	−	0.696222i	$-0.754863\pi$
$131$	−12.4804	+	2.65278i	−1.09041	+	0.231775i	−0.372588	+	0.927997i	$0.621530\pi$
$132$	−17.9713	+	1.25174i	−1.56420	+	0.108950i
$133$	−11.9963	−	13.3233i	−1.04021	−	1.15527i
$134$	0.192465	−	0.139834i	0.0166265	−	0.0120798i
$135$	−5.79077	−	10.0731i	−0.498390	−	0.866953i
$136$	2.58190	+	1.87586i	0.221396	+	0.160854i
$137$	−0.336803	−	3.20447i	−0.0287751	−	0.273776i	−0.999444	−	0.0333546i	$-0.989381\pi$
$137$	−0.336803	−	3.20447i	−0.0287751	−	0.273776i	0.970669	−	0.240422i	$-0.0772857\pi$
$138$	−0.0550691	+	0.0461828i	−0.00468779	+	0.00393134i
$139$	−2.36782	+	22.5283i	−0.200836	+	1.91082i	0.175740	+	0.984437i	$0.443768\pi$
$139$	−2.36782	+	22.5283i	−0.200836	+	1.91082i	−0.376576	+	0.926386i	$0.622898\pi$
$140$	4.80464	−	14.7351i	0.406066	−	1.24534i
$141$	−1.29778	−	7.37188i	−0.109293	−	0.620824i
$142$	1.52191	+	1.69025i	0.127716	+	0.141843i
$143$	23.2784			1.94664
$144$	7.50738	+	6.30643i	0.625615	+	0.525536i
$145$	−2.49060	−	2.77188i	−0.206833	−	0.230192i
$146$	−3.87696	−	0.824074i	−0.320860	−	0.0682008i
$147$	−7.10286	+	9.08613i	−0.585834	+	0.749411i
$148$	−0.570708	+	5.42992i	−0.0469119	+	0.446337i
$149$	6.71097	+	11.6237i	0.549784	+	0.952254i	0.998289	+	0.0584738i	$0.0186234\pi$
$149$	6.71097	+	11.6237i	0.549784	+	0.952254i	−0.448505	+	0.893780i	$0.648043\pi$
$150$	1.34625	−	2.74384i	0.109921	−	0.224034i
$151$	−5.28514	+	9.15413i	−0.430098	+	0.744952i	−0.996881	−	0.0789149i	$-0.974854\pi$
$151$	−5.28514	+	9.15413i	−0.430098	+	0.744952i	0.566783	+	0.823867i	$0.308188\pi$
$152$	5.36763	+	3.89982i	0.435373	+	0.316317i
$153$	3.06526	+	6.29345i	0.247812	+	0.508795i
$154$	2.23519	+	6.87921i	0.180117	+	0.554343i
$155$	−17.8054	−	7.94961i	−1.43016	−	0.638528i
$156$	−9.80565	−	9.47439i	−0.785081	−	0.758558i
$157$	−9.96211	−	17.2549i	−0.795063	−	1.37709i	−0.922799	−	0.385281i	$-0.874104\pi$
$157$	−9.96211	−	17.2549i	−0.795063	−	1.37709i	0.127736	−	0.991808i	$-0.459229\pi$
$158$	−2.98158	+	0.633754i	−0.237202	+	0.0504188i
$159$	−15.5714	+	13.0587i	−1.23489	+	1.03562i
$160$	−0.917914	+	8.64702i	−0.0725675	+	0.683607i
$161$	−0.351549	−	0.255415i	−0.0277060	−	0.0201296i
$162$	−1.18661	−	2.94623i	−0.0932290	−	0.231478i
$163$	5.33592	−	3.87677i	0.417941	−	0.303652i	−0.358868	−	0.933388i	$-0.616837\pi$
$163$	5.33592	−	3.87677i	0.417941	−	0.303652i	0.776809	+	0.629736i	$0.216837\pi$
$164$	6.31523	−	2.81172i	0.493136	−	0.219559i
$165$	−3.70200	−	21.1573i	−0.288201	−	1.64709i
$166$	1.30872	+	0.582681i	0.101577	+	0.0452249i
$167$	4.26590	−	0.906745i	0.330105	−	0.0701661i	−0.0398777	−	0.999205i	$-0.512697\pi$
$167$	4.26590	−	0.906745i	0.330105	−	0.0701661i	0.369983	+	0.929039i	$0.379363\pi$
$168$	3.84006	−	7.86783i	0.296267	−	0.607016i
$169$	3.09070	+	3.43257i	0.237746	+	0.264044i
$170$	−0.922346	+	1.59373i	−0.0707407	+	0.122233i
$171$	6.37253	+	13.0838i	0.487319	+	1.00054i
$172$	−2.39741	−	7.37846i	−0.182801	−	0.562602i
$173$	1.16330	−	0.517936i	0.0884444	−	0.0393780i	−0.362038	−	0.932163i	$-0.617919\pi$
$173$	1.16330	−	0.517936i	0.0884444	−	0.0393780i	0.450482	+	0.892786i	$0.351252\pi$
$174$	−0.569408	−	0.844680i	−0.0431667	−	0.0640350i
$175$	18.0669	+	3.87946i	1.36573	+	0.293259i
$176$	9.06244	+	15.6966i	0.683107	+	1.18318i
$177$	−0.467418	+	13.2810i	−0.0351333	+	0.998264i
$178$	−3.34967	−	0.711994i	−0.251068	−	0.0533662i
$179$	−1.80122	−	5.54358i	−0.134629	−	0.414347i	0.860903	−	0.508770i	$-0.169899\pi$
$179$	−1.80122	−	5.54358i	−0.134629	−	0.414347i	−0.995532	+	0.0944227i	$0.969899\pi$
$180$	−7.05168	+	10.4189i	−0.525601	+	0.776578i
$181$	−0.488485	+	1.50340i	−0.0363088	+	0.111747i	−0.967568	−	0.252610i	$-0.918711\pi$
$181$	−0.488485	+	1.50340i	−0.0363088	+	0.111747i	0.931259	+	0.364357i	$0.118711\pi$
$182$	−2.73735	+	4.74122i	−0.202906	+	0.351443i
$183$	1.85420	+	1.79156i	0.137067	+	0.132436i
$184$	0.146908	+	0.0654078i	0.0108302	+	0.00482193i
$185$	−6.50966	−	0.00675687i	−0.478599	−	0.000496775i
$186$	−4.51971	−	2.82595i	−0.331401	−	0.207209i
$187$	1.35266	+	12.8697i	0.0989164	+	0.941127i
$188$	−6.55706	+	4.76398i	−0.478222	+	0.347449i
$189$	15.5453	−	11.2749i	1.13076	−	0.820128i
$190$	−1.91751	+	3.31328i	−0.139111	+	0.240370i
$191$	0.207758	+	1.97668i	0.0150328	+	0.143028i	0.999464	−	0.0327440i	$-0.0104246\pi$
$191$	0.207758	+	1.97668i	0.0150328	+	0.143028i	−0.984431	+	0.175772i	$0.943758\pi$
$192$	2.16622	−	8.67812i	0.156333	−	0.626289i
$193$	−0.278612	−	0.482570i	−0.0200549	−	0.0347362i	0.855824	−	0.517268i	$-0.173051\pi$
$193$	−0.278612	−	0.482570i	−0.0200549	−	0.0347362i	−0.875879	+	0.482531i	$0.839717\pi$
$194$	3.32636	−	0.707039i	0.238818	−	0.0507624i
$195$	10.0255	−	12.7974i	0.717941	−	0.916443i
$196$	12.2149	+	2.59635i	0.872492	+	0.185454i
$197$	4.27834	+	13.1674i	0.304819	+	0.938137i	0.979745	+	0.200251i	$0.0641758\pi$
$197$	4.27834	+	13.1674i	0.304819	+	0.938137i	−0.674925	+	0.737886i	$0.735824\pi$
$198$	−0.201707	−	5.86807i	−0.0143347	−	0.417026i
$199$	−9.32321			−0.660905			−0.330452	−	0.943823i	$-0.607201\pi$
$199$	−9.32321			−0.660905			−0.330452	+	0.943823i	$0.607201\pi$
$200$	−6.83847	−	0.0141964i	−0.483553	−	0.00100383i
$201$	−0.652640	−	0.968149i	−0.0460337	−	0.0682880i
$202$	0.480151	−	4.56833i	0.0337833	−	0.321427i
$203$	4.12119	−	4.57705i	0.289251	−	0.321246i
$204$	4.66823	−	5.97170i	0.326841	−	0.418102i
$205$	4.11364	+	7.14214i	0.287309	+	0.498829i
$206$	−0.673887	+	2.07401i	−0.0469520	+	0.144503i
$207$	0.217013	+	0.278077i	0.0150834	+	0.0193277i
$208$	−4.23921	+	13.0469i	−0.293936	+	0.904643i
$209$	2.81211	+	26.7555i	0.194518	+	1.85072i
$210$	4.74453	+	1.73392i	0.327404	+	0.119652i
$211$	2.49845	−	23.7712i	0.172001	−	1.63648i	−0.479297	−	0.877653i	$-0.659108\pi$
$211$	2.49845	−	23.7712i	0.172001	−	1.63648i	0.651297	−	0.758823i	$-0.274225\pi$
$212$	20.1024	+	8.95018i	1.38064	+	0.614701i
$213$	8.55314	−	7.17295i	0.586051	−	0.491483i
$214$	1.52365	−	0.678373i	0.104155	−	0.0463726i
$215$	8.45413	−	3.75351i	0.576567	−	0.255987i
$216$	−4.75968	+	5.27745i	−0.323855	+	0.359085i
$217$	9.95912	−	30.6510i	0.676069	−	2.08073i
$218$	0.0313893	−	0.0543678i	0.00212595	−	0.00368225i
$219$	−4.71120	+	18.8736i	−0.318353	+	1.27536i
$220$	−18.8295	+	13.6506i	−1.26948	+	0.920323i
$221$	−6.55380	+	7.27873i	−0.440856	+	0.489620i
$222$	−1.76213	−	0.248142i	−0.118266	−	0.0166542i
$223$	22.9260	−	10.2073i	1.53524	−	0.683532i	0.547095	−	0.837070i	$-0.315734\pi$
$223$	22.9260	−	10.2073i	1.53524	−	0.683532i	0.988143	+	0.153539i	$0.0490669\pi$
$224$	−14.3720			−0.960269
$225$	−13.2257	−	7.07678i	−0.881713	−	0.471785i
$226$	3.06567			0.203926
$227$	11.7651	−	5.23816i	0.780877	−	0.347669i	0.0227210	−	0.999742i	$-0.492767\pi$
$227$	11.7651	−	5.23816i	0.780877	−	0.347669i	0.758156	+	0.652073i	$0.226100\pi$
$228$	9.70501	−	12.4149i	0.642730	−	0.822194i
$229$	2.26335	−	2.51370i	0.149566	−	0.166110i	−0.663706	−	0.747994i	$-0.731017\pi$
$229$	2.26335	−	2.51370i	0.149566	−	0.166110i	0.813272	+	0.581884i	$0.197684\pi$
$230$	−0.0287638	+	0.0882142i	−0.00189663	+	0.00581667i
$231$	34.1273	−	9.77574i	2.24541	−	0.643197i
$232$	−1.13965	+	1.97392i	−0.0748214	+	0.129594i
$233$	7.67143	−	23.6102i	0.502572	−	1.54676i	−0.302243	−	0.953231i	$-0.597735\pi$
$233$	7.67143	−	23.6102i	0.502572	−	1.54676i	0.804815	−	0.593526i	$-0.202265\pi$
$234$	3.19847	−	3.08535i	0.209090	−	0.201696i
$235$	−6.45862	−	7.18802i	−0.421314	−	0.468894i
$236$	13.1455	−	5.85275i	0.855698	−	0.380981i
$237$	2.59377	+	14.7336i	0.168484	+	0.957047i
$238$	−2.78030	−	1.23787i	−0.180220	−	0.0802391i
$239$	1.31584	−	12.5194i	0.0851147	−	0.809813i	−0.865806	−	0.500379i	$-0.833194\pi$
$239$	1.31584	−	12.5194i	0.0851147	−	0.809813i	0.950921	−	0.309433i	$-0.100139\pi$
$240$	12.5323	+	1.77806i	0.808955	+	0.114773i
$241$	−1.24674	−	11.8620i	−0.0803097	−	0.764096i	−0.958367	−	0.285540i	$-0.907827\pi$
$241$	−1.24674	−	11.8620i	−0.0803097	−	0.764096i	0.878057	−	0.478556i	$-0.158840\pi$
$242$	2.15448	−	6.63081i	0.138495	−	0.426245i
$243$	−14.6556	+	5.31155i	−0.940159	+	0.340736i
$244$	0.862711	−	2.65515i	0.0552294	−	0.169979i
$245$	−1.57169	+	14.8058i	−0.100411	+	0.945905i
$246$	0.843456	+	2.08927i	0.0537768	+	0.133207i
$247$	−13.6250	+	15.1321i	−0.866938	+	0.962833i
$248$	−1.24670	+	11.8615i	−0.0791653	+	0.753208i
$249$	3.08387	−	6.31849i	0.195432	−	0.400418i
$250$	−0.400215	−	3.92534i	−0.0253118	−	0.248260i
$251$	25.9859			1.64021			0.820107	−	0.572210i	$-0.193914\pi$
$251$	25.9859			1.64021			0.820107	+	0.572210i	$0.193914\pi$
$252$	−18.3543	−	9.77203i	−1.15621	−	0.615580i
$253$	0.201498	+	0.620148i	0.0126681	+	0.0389884i
$254$	−0.973803	−	0.206988i	−0.0611018	−	0.0129876i
$255$	7.65776	+	4.79907i	0.479547	+	0.300529i
$256$	−6.78846	+	1.44293i	−0.424279	+	0.0901833i
$257$	−10.6268	−	18.4062i	−0.662884	−	1.14815i	−0.979854	−	0.199714i	$-0.935999\pi$
$257$	−10.6268	−	18.4062i	−0.662884	−	1.14815i	0.316970	−	0.948436i	$-0.397335\pi$
$258$	2.43084	−	0.696315i	0.151338	−	0.0433507i
$259$	−1.12463	−	10.7001i	−0.0698812	−	0.664875i
$260$	−17.2143	−	3.67769i	−1.06759	−	0.228081i
$261$	−4.24131	+	2.64704i	−0.262530	+	0.163848i
$262$	−3.64291	+	2.64673i	−0.225060	+	0.163515i
$263$	1.18423	+	11.2672i	0.0730230	+	0.694768i	0.968390	+	0.249439i	$0.0802464\pi$
$263$	1.18423	+	11.2672i	0.0730230	+	0.694768i	−0.895367	+	0.445328i	$0.853087\pi$
$264$	−11.6014	+	6.16452i	−0.714019	+	0.379400i
$265$	−8.13326	+	24.9435i	−0.499622	+	1.53226i
$266$	−5.78010	−	2.57347i	−0.354401	−	0.157789i
$267$	−4.07044	+	16.3067i	−0.249107	+	0.997952i
$268$	−0.632126	+	1.09487i	−0.0386132	+	0.0668801i
$269$	−6.24902	+	19.2325i	−0.381010	+	1.17263i	0.558324	+	0.829623i	$0.311444\pi$
$269$	−6.24902	+	19.2325i	−0.381010	+	1.17263i	−0.939334	+	0.343004i	$0.888556\pi$
$270$	−3.31287	−	2.41636i	−0.201615	−	0.147055i
$271$	8.26847	+	25.4477i	0.502274	+	1.54584i	0.805306	+	0.592859i	$0.202001\pi$
$271$	8.26847	+	25.4477i	0.502274	+	1.54584i	−0.303033	+	0.952980i	$0.597999\pi$
$272$	−7.45948	−	1.58556i	−0.452297	−	0.0961387i
$273$	22.7824	+	14.2447i	1.37885	+	0.862127i
$274$	−0.568564	−	0.984782i	−0.0343482	−	0.0594928i
$275$	−18.5115	−	20.6451i	−1.11628	−	1.24495i
$276$	0.167524	−	0.343238i	0.0100838	−	0.0206605i
$277$	−11.5048	+	5.12229i	−0.691259	+	0.307768i	−0.722132	−	0.691755i	$-0.756838\pi$
$277$	−11.5048	+	5.12229i	−0.691259	+	0.307768i	0.0308731	+	0.999523i	$0.490171\pi$
$278$	2.47038	+	7.60304i	0.148163	+	0.456000i
$279$	−14.6410	+	21.6806i	−0.876534	+	1.29798i
$280$	−1.16977	−	11.2419i	−0.0699072	−	0.671830i
$281$	12.7349	+	14.1436i	0.759703	+	0.843735i	0.991645	−	0.128994i	$-0.0411749\pi$
$281$	12.7349	+	14.1436i	0.759703	+	0.843735i	−0.231943	+	0.972729i	$0.574508\pi$
$282$	−1.47659	−	2.19042i	−0.0879294	−	0.130438i
$283$	19.2572	−	4.09324i	1.14472	−	0.243318i	0.403759	−	0.914865i	$-0.367703\pi$
$283$	19.2572	−	4.09324i	1.14472	−	0.243318i	0.740961	+	0.671548i	$0.234370\pi$
$284$	−11.0420	−	4.91621i	−0.655222	−	0.291724i
$285$	15.9201	+	9.97702i	0.943024	+	0.590988i
$286$	7.50500	−	3.34144i	0.443780	−	0.197584i
$287$	−11.0208	+	8.00707i	−0.650536	+	0.472642i
$288$	11.2127	+	3.22182i	0.660714	+	0.189847i
$289$	9.34834	+	6.79196i	0.549902	+	0.399527i
$290$	−1.20086	−	0.536150i	−0.0705168	−	0.0314838i
$291$	−2.89370	−	16.4373i	−0.169632	−	0.963570i
$292$	20.6030	−	4.37930i	1.20570	−	0.256279i
$293$	−8.01286	−	13.8787i	−0.468116	−	0.810801i	0.531220	−	0.847234i	$-0.321734\pi$
$293$	−8.01286	−	13.8787i	−0.468116	−	0.810801i	−0.999336	+	0.0364328i	$0.988401\pi$
$294$	−0.985730	+	3.94895i	−0.0574889	+	0.230307i
$295$	8.56276	+	14.8667i	0.498543	+	0.865575i
$296$	1.23040	+	3.78677i	0.0715154	+	0.220102i
$297$	−28.8167	−	0.0236218i	−1.67212	−	0.00137067i
$298$	3.83213	+	2.78421i	0.221989	+	0.161285i
$299$	−0.246767	+	0.427413i	−0.0142709	+	0.0247179i
$300$	−0.604964	+	16.2306i	−0.0349276	+	0.937076i
$301$	7.64409	+	13.2399i	0.440598	+	0.763138i
$302$	−0.389931	+	3.70995i	−0.0224380	+	0.213484i
$303$	−22.3240	−	3.14366i	−1.28248	−	0.180598i
$304$	−15.5079	−	3.29630i	−0.889437	−	0.189056i
$305$	3.25514	+	0.695434i	0.186389	+	0.0398205i
$306$	1.89163	+	1.58902i	0.108137	+	0.0908385i
$307$	−11.3485			−0.647692			−0.323846	−	0.946110i	$-0.604976\pi$
$307$	−11.3485			−0.647692			−0.323846	+	0.946110i	$0.604976\pi$
$308$	−25.7207	−	28.5657i	−1.46557	−	1.62768i
$309$	10.0564	+	3.66333i	0.572086	+	0.208399i
$310$	−6.88159	−	0.00714292i	−0.390848	−	0.000405691i
$311$	1.11184	−	10.5785i	0.0630468	−	0.599850i	−0.916695	−	0.399587i	$-0.869154\pi$
$311$	1.11184	−	10.5785i	0.0630468	−	0.599850i	0.979742	−	0.200263i	$-0.0641798\pi$
$312$	−9.34294	−	3.40344i	−0.528940	−	0.192682i
$313$	−2.17284	−	20.6731i	−0.122816	−	1.16852i	−0.866217	−	0.499669i	$-0.833455\pi$
$313$	−2.17284	−	20.6731i	−0.122816	−	1.16852i	0.743401	−	0.668846i	$-0.233212\pi$
$314$	−5.68861	−	4.13302i	−0.321027	−	0.233240i
$315$	9.32359	−	22.9718i	0.525325	−	1.29432i
$316$	13.1050	−	9.52137i	0.737216	−	0.535619i
$317$	−11.7370	−	13.0353i	−0.659217	−	0.732135i	0.317121	−	0.948385i	$-0.397284\pi$
$317$	−11.7370	−	13.0353i	−0.659217	−	0.732135i	−0.976338	+	0.216250i	$0.930617\pi$
$318$	−3.14576	+	6.44529i	−0.176405	+	0.361434i
$319$	−9.04018	+	1.92155i	−0.506153	+	0.107586i
$320$	−3.55687	−	10.9857i	−0.198835	−	0.614120i
$321$	−3.06429	−	7.59035i	−0.171032	−	0.423652i
$322$	−0.150003	−	0.0318842i	−0.00835935	−	0.00177683i
$323$	−9.15767	−	6.65343i	−0.509546	−	0.370207i
$324$	12.1290	+	11.7385i	0.673831	+	0.652136i
$325$	2.23711	−	20.8679i	0.124093	−	1.15754i
$326$	1.16383	−	2.01581i	0.0644585	−	0.111645i
$327$	−0.261247	−	0.163344i	−0.0144470	−	0.00903296i
$328$	3.37329	−	3.74642i	0.186259	−	0.206861i
$329$	10.6871	−	11.8692i	0.589197	−	0.654369i
$330$	−4.23051	−	6.28976i	−0.232882	−	0.346240i
$331$	−0.838053	−	0.930752i	−0.0460636	−	0.0511588i	0.719673	−	0.694313i	$-0.244292\pi$
$331$	−0.838053	−	0.930752i	−0.0460636	−	0.0511588i	−0.765736	+	0.643155i	$0.777625\pi$
$332$	−7.61301			−0.417818
$333$	−1.52128	+	8.60011i	−0.0833655	+	0.471283i
$334$	1.24518	−	0.904675i	0.0681331	−	0.0495016i
$335$	−1.37639	−	0.614521i	−0.0752002	−	0.0335749i
$336$	−0.735833	+	20.9077i	−0.0401430	+	1.14061i
$337$	−15.8316	−	7.04866i	−0.862400	−	0.383965i	−0.0726229	−	0.997359i	$-0.523137\pi$
$337$	−15.8316	−	7.04866i	−0.862400	−	0.383965i	−0.789777	+	0.613394i	$0.789804\pi$
$338$	1.48917	+	0.663020i	0.0810000	+	0.0360635i
$339$	0.529204	−	15.0366i	0.0287424	−	0.816677i
$340$	1.03296	−	9.73082i	0.0560203	−	0.527728i
$341$	−39.1252	+	28.4262i	−2.11875	+	1.53936i
$342$	3.93259	+	3.30350i	0.212650	+	0.178633i
$343$	1.26195			0.0681390
$344$	−3.78577	−	4.20452i	−0.204115	−	0.226693i
$345$	0.427711	+	0.156309i	0.0230272	+	0.00841542i
$346$	0.300706	−	0.333967i	0.0161660	−	0.0179542i
$347$	−2.33602	+	2.59441i	−0.125404	+	0.139275i	−0.802577	−	0.596549i	$-0.796538\pi$
$347$	−2.33602	+	2.59441i	−0.125404	+	0.139275i	0.677173	+	0.735824i	$0.263205\pi$
$348$	4.59011	+	2.86996i	0.246056	+	0.153846i
$349$	2.58364	−	4.47500i	0.138299	−	0.239541i	−0.788554	−	0.614966i	$-0.789170\pi$
$349$	2.58364	−	4.47500i	0.138299	−	0.239541i	0.926853	+	0.375425i	$0.122503\pi$
$350$	6.38167	−	1.34263i	0.341115	−	0.0717664i
$351$	−14.5810	−	16.2206i	−0.778276	−	0.865790i
$352$	17.4476	+	12.6764i	0.929960	+	0.675655i
$353$	2.34215	+	0.497840i	0.124660	+	0.0264974i	0.269819	−	0.962911i	$-0.413036\pi$
$353$	2.34215	+	0.497840i	0.124660	+	0.0264974i	−0.145159	+	0.989408i	$0.546369\pi$
$354$	1.75570	+	4.34893i	0.0933143	+	0.231143i
$355$	4.46749	−	13.7011i	0.237110	−	0.727180i
$356$	17.8008	−	3.78369i	0.943443	−	0.200535i
$357$	−6.55148	+	13.4232i	−0.346741	+	0.710432i
$358$	−1.37646	−	1.52871i	−0.0727480	−	0.0807948i
$359$	26.0634	−	18.9362i	1.37557	−	0.999413i	0.378296	−	0.925685i	$-0.376510\pi$
$359$	26.0634	−	18.9362i	1.37557	−	0.999413i	0.997278	−	0.0737286i	$-0.0234899\pi$
$360$	−1.60750	+	9.03287i	−0.0847227	+	0.476074i
$361$	−3.66700	−	2.66423i	−0.193000	−	0.140223i
$362$	0.0583138	+	0.554819i	0.00306490	+	0.0291606i
$363$	−32.1511	−	11.7120i	−1.68750	−	0.614721i
$364$	3.04112	−	28.9343i	0.159398	−	1.51657i
$365$	7.73566	+	23.8923i	0.404903	+	1.25058i
$366$	0.854963	+	0.311446i	0.0446896	+	0.0162795i
$367$	7.87365	+	8.74458i	0.411001	+	0.456463i	0.912731	−	0.408561i	$-0.133969\pi$
$367$	7.87365	+	8.74458i	0.411001	+	0.456463i	−0.501730	+	0.865025i	$0.667303\pi$
$368$	−0.384272			−0.0200316
$369$	10.3931	−	3.77636i	0.541045	−	0.196589i
$370$	−2.09970	+	0.932234i	−0.109158	+	0.0484646i
$371$	−42.4149	−	9.01557i	−2.20207	−	0.468065i
$372$	28.0504	+	3.95004i	1.45435	+	0.204800i
$373$	0.376273	−	3.58000i	0.0194827	−	0.185366i	−0.980452	−	0.196756i	$-0.936959\pi$
$373$	0.376273	−	3.58000i	0.0194827	−	0.185366i	0.999935	+	0.0113908i	$0.00362588\pi$
$374$	2.28345	+	3.95506i	0.118075	+	0.204511i
$375$	−19.3222	+	1.28539i	−0.997795	+	0.0663772i
$376$	−2.95532	+	5.11877i	−0.152409	+	0.263980i
$377$	−5.65924	−	4.11168i	−0.291465	−	0.211762i
$378$	3.39342	−	5.86646i	0.174539	−	0.301738i
$379$	5.79630	+	17.8392i	0.297736	+	0.916336i	0.982289	+	0.187373i	$0.0599974\pi$
$379$	5.79630	+	17.8392i	0.297736	+	0.916336i	−0.684553	+	0.728963i	$0.740003\pi$
$380$	2.14748	−	20.2299i	0.110163	−	1.03777i
$381$	−1.18334	+	4.74061i	−0.0606245	+	0.242869i
$382$	0.350720	+	0.607464i	0.0179444	+	0.0310806i
$383$	16.5379	−	3.51524i	0.845048	−	0.179621i	0.235010	−	0.971993i	$-0.424488\pi$
$383$	16.5379	−	3.51524i	0.845048	−	0.179621i	0.610038	+	0.792372i	$0.291154\pi$
$384$	−2.88291	−	16.3759i	−0.147118	−	0.835681i
$385$	30.7016	−	34.0265i	1.56470	−	1.73415i
$386$	−0.159094	−	0.115589i	−0.00809769	−	0.00588332i
$387$	−2.99569	−	12.0431i	−0.152279	−	0.612185i
$388$	−14.6204	+	10.6224i	−0.742241	+	0.539269i
$389$	−6.08407	+	2.70880i	−0.308475	+	0.137342i	−0.555135	−	0.831760i	$-0.687333\pi$
$389$	−6.08407	+	2.70880i	−0.308475	+	0.137342i	0.246660	+	0.969102i	$0.420667\pi$
$390$	1.39526	−	5.56500i	0.0706519	−	0.281795i
$391$	−0.250639	−	0.111592i	−0.0126753	−	0.00564343i
$392$	8.90786	−	1.89342i	0.449915	−	0.0956323i
$393$	12.3529	+	18.3247i	0.623122	+	0.924361i
$394$	3.26942	+	3.63106i	0.164711	+	0.182930i
$395$	12.9083	+	14.3661i	0.649487	+	0.722836i
$396$	13.6630	+	28.0522i	0.686590	+	1.40967i
$397$	9.41994	+	28.9916i	0.472773	+	1.45505i	0.848937	+	0.528494i	$0.177243\pi$
$397$	9.41994	+	28.9916i	0.472773	+	1.45505i	−0.376164	+	0.926553i	$0.622757\pi$
$398$	−3.00582	+	1.33828i	−0.150668	+	0.0670818i
$399$	−13.6202	+	27.9062i	−0.681863	+	1.39706i
$400$	14.9421	−	6.61553i	0.747107	−	0.330777i
$401$	−16.1027	−	27.8907i	−0.804130	−	1.39279i	−0.916877	−	0.399171i	$-0.869298\pi$
$401$	−16.1027	−	27.8907i	−0.804130	−	1.39279i	0.112746	−	0.993624i	$-0.464035\pi$
$402$	−0.349383	−	0.218451i	−0.0174256	−	0.0108954i
$403$	−35.8040	−	7.61037i	−1.78352	−	0.379099i
$404$	7.54335	+	23.2160i	0.375296	+	1.15504i
$405$	−12.4237	+	15.8320i	−0.617339	+	0.786697i
$406$	0.671679	−	2.06722i	0.0333349	−	0.102594i
$407$	−8.07247	+	13.9819i	−0.400137	+	0.693058i
$408$	1.33873	−	5.36311i	0.0662770	−	0.265514i
$409$	4.04636	+	1.80156i	0.200080	+	0.0890812i	0.504330	−	0.863511i	$-0.331739\pi$
$409$	4.04636	+	1.80156i	0.200080	+	0.0890812i	−0.304251	+	0.952592i	$0.598406\pi$
$410$	2.35145	+	1.71216i	0.116130	+	0.0845574i
$411$	−4.92834	+	2.61872i	−0.243097	+	0.129172i
$412$	−1.21137	−	11.5255i	−0.0596801	−	0.567818i
$413$	−22.9404	+	16.6671i	−1.12882	+	0.820136i
$414$	0.109881	+	0.0585020i	0.00540037	+	0.00287521i
$415$	−0.939419	−	9.02811i	−0.0461143	−	0.443173i
$416$	1.70624	+	16.2338i	0.0836552	+	0.795926i
$417$	37.7181	−	10.8043i	1.84706	−	0.529091i
$418$	4.74718	+	8.22236i	0.232192	+	0.402169i
$419$	−16.3235	+	3.46968i	−0.797457	+	0.169505i	−0.588582	−	0.808438i	$-0.700314\pi$
$419$	−16.3235	+	3.46968i	−0.797457	+	0.169505i	−0.208875	+	0.977942i	$0.566980\pi$
$420$	−26.7814	+	1.83746i	−1.30680	+	0.0896587i
$421$	7.87200	+	1.67324i	0.383658	+	0.0815490i	0.395703	−	0.918378i	$-0.370501\pi$
$421$	7.87200	+	1.67324i	0.383658	+	0.0815490i	−0.0120454	+	0.999927i	$0.503834\pi$
$422$	−2.60667	−	8.02251i	−0.126891	−	0.390530i
$423$	−10.9985	+	6.86430i	−0.534767	+	0.333754i
$424$	16.0473			0.779326
$425$	11.6670	+	0.0242202i	0.565935	+	0.00117485i
$426$	1.72792	−	3.54031i	0.0837182	−	0.171529i
$427$	−0.575060	+	5.47133i	−0.0278291	+	0.264776i
$428$	−5.93068	+	6.58669i	−0.286670	+	0.318380i
$429$	−15.0937	−	37.3876i	−0.728730	−	1.80509i
$430$	2.18684	−	2.42367i	0.105459	−	0.116880i
$431$	0.708440	−	2.18035i	0.0341244	−	0.105024i	−0.932544	−	0.361058i	$-0.882416\pi$
$431$	0.708440	−	2.18035i	0.0341244	−	0.105024i	0.966668	+	0.256034i	$0.0824158\pi$
$432$	5.26103	−	16.1467i	0.253121	−	0.776860i
$433$	−4.01620	+	12.3606i	−0.193006	+	0.594012i	0.806988	+	0.590568i	$0.201096\pi$
$433$	−4.01620	+	12.3606i	−0.193006	+	0.594012i	−0.999994	+	0.00344378i	$0.998904\pi$
$434$	−1.18889	−	11.3115i	−0.0570684	−	0.542970i
$435$	−2.83702	+	5.79746i	−0.136025	+	0.277967i
$436$	−0.0348726	+	0.331791i	−0.00167009	+	0.0158899i
$437$	−0.521065	−	0.231993i	−0.0249259	−	0.0110977i
$438$	1.19027	+	6.76114i	0.0568732	+	0.323060i
$439$	−25.9750	+	11.5648i	−1.23972	+	0.551958i	−0.918640	−	0.395095i	$-0.870712\pi$
$439$	−25.9750	+	11.5648i	−1.23972	+	0.551958i	−0.321077	+	0.947053i	$0.604045\pi$
$440$	−8.49548	+	14.6794i	−0.405006	+	0.699812i
$441$	19.1988	+	5.51652i	0.914228	+	0.262691i
$442$	−1.06815	+	3.28742i	−0.0508067	+	0.156367i
$443$	4.68519	−	8.11498i	0.222600	−	0.385555i	−0.732997	−	0.680232i	$-0.761879\pi$
$443$	4.68519	−	8.11498i	0.222600	−	0.385555i	0.955597	+	0.294678i	$0.0952123\pi$
$444$	9.09108	−	2.60414i	0.431444	−	0.123587i
$445$	6.68356	+	20.6428i	0.316831	+	0.978560i
$446$	5.92620	−	6.58171i	0.280614	−	0.311653i
$447$	14.3176	−	18.3154i	0.677199	−	0.866287i
$448$	17.4350	−	7.76258i	0.823728	−	0.366747i
$449$	0.615561			0.0290501			0.0145251	−	0.999895i	$-0.495376\pi$
$449$	0.615561			0.0290501			0.0145251	+	0.999895i	$0.495376\pi$
$450$	−5.27981	−	0.383117i	−0.248893	−	0.0180603i
$451$	20.4416			0.962559
$452$	−14.8831	+	6.62640i	−0.700044	+	0.311680i
$453$	18.1294	+	2.55297i	0.851793	+	0.119949i
$454$	3.04119	−	3.37759i	0.142730	−	0.158518i
$455$	34.6878	+	0.0360051i	1.62619	+	0.00168795i
$456$	2.78315	−	11.1496i	0.130333	−	0.522129i
$457$	−7.68458	+	13.3101i	−0.359469	+	0.622619i	−0.987872	−	0.155269i	$-0.950376\pi$
$457$	−7.68458	+	13.3101i	−0.359469	+	0.622619i	0.628403	+	0.777888i	$0.283709\pi$
$458$	0.368884	−	1.13531i	0.0172368	−	0.0530495i
$459$	8.12044	−	9.00381i	0.379030	−	0.420262i
$460$	−0.0510319	−	0.490432i	−0.00237937	−	0.0228665i
$461$	−6.83665	+	3.04387i	−0.318415	+	0.141767i	−0.559720	−	0.828682i	$-0.689091\pi$
$461$	−6.83665	+	3.04387i	−0.318415	+	0.141767i	0.241305	+	0.970449i	$0.422425\pi$
$462$	9.59946	−	8.05043i	0.446607	−	0.374540i
$463$	13.1605	+	5.85945i	0.611622	+	0.272312i	0.689082	−	0.724684i	$-0.258014\pi$
$463$	13.1605	+	5.85945i	0.611622	+	0.272312i	−0.0774593	+	0.996996i	$0.524681\pi$
$464$	0.569320	−	5.41672i	0.0264300	−	0.251465i
$465$	−1.22295	+	33.7518i	−0.0567130	+	1.56520i
$466$	−0.915790	−	8.71316i	−0.0424231	−	0.403629i
$467$	2.08120	−	6.40526i	0.0963062	−	0.296400i	−0.891286	−	0.453442i	$-0.850196\pi$
$467$	2.08120	−	6.40526i	0.0963062	−	0.296400i	0.987592	+	0.157042i	$0.0501958\pi$
$468$	−8.85890	+	21.8921i	−0.409503	+	1.01196i
$469$	0.769860	−	2.36939i	0.0355488	−	0.109408i
$470$	−3.11406	−	1.39034i	−0.143641	−	0.0641317i
$471$	−21.2538	+	27.1883i	−0.979321	+	1.25277i
$472$	7.02168	−	7.79837i	0.323199	−	0.358949i
$473$	2.39801	−	22.8155i	0.110261	−	1.04906i
$474$	2.95113	+	4.37781i	0.135550	+	0.201079i
$475$	24.2552	+	0.0503526i	1.11290	+	0.00231034i
$476$	16.1733			0.741304
$477$	31.0701	+	16.5420i	1.42260	+	0.757408i
$478$	−1.37284	−	4.22516i	−0.0627921	−	0.193254i
$479$	−0.617776	−	0.131312i	−0.0282269	−	0.00599981i	0.193777	−	0.981046i	$-0.437926\pi$
$479$	−0.617776	−	0.131312i	−0.0282269	−	0.00599981i	−0.222003	+	0.975046i	$0.571260\pi$
$480$	14.4832	−	4.13245i	0.661065	−	0.188620i
$481$	−11.9528	+	2.54064i	−0.544999	+	0.115843i
$482$	−2.10465	−	3.64536i	−0.0958641	−	0.166042i
$483$	−0.182280	+	0.730237i	−0.00829405	+	0.0332269i
$484$	3.87288	+	36.8480i	0.176040	+	1.67491i
$485$	−14.4010	−	16.0273i	−0.653914	−	0.727763i
$486$	−3.96257	+	3.81616i	−0.179746	+	0.173105i
$487$	15.7164	−	11.4186i	0.712176	−	0.517426i	−0.171699	−	0.985150i	$-0.554926\pi$
$487$	15.7164	−	11.4186i	0.712176	−	0.517426i	0.883875	+	0.467723i	$0.154926\pi$
$488$	−0.212814	−	2.02479i	−0.00963366	−	0.0916581i
$489$	−9.68631	−	6.05636i	−0.438030	−	0.273878i
$490$	1.61854	+	4.99901i	0.0731183	+	0.225832i
$491$	25.5533	+	11.3770i	1.15320	+	0.513439i	0.892085	−	0.451868i	$-0.149242\pi$
$491$	25.5533	+	11.3770i	1.15320	+	0.513439i	0.261117	+	0.965307i	$0.415909\pi$
$492$	−8.61071	−	8.31981i	−0.388201	−	0.375086i
$493$	1.94434	−	3.36769i	0.0875685	−	0.151673i
$494$	−2.22063	+	6.83439i	−0.0999107	+	0.307494i
$495$	−31.5805	+	19.6642i	−1.41944	+	0.883839i
$496$	−8.80706	−	27.1053i	−0.395449	−	1.21707i
$497$	23.2980	+	4.95213i	1.04506	+	0.222134i
$498$	0.0872736	−	2.47976i	0.00391082	−	0.111121i
$499$	−14.3498	−	24.8546i	−0.642386	−	1.11264i	−0.984899	−	0.173132i	$-0.944611\pi$
$499$	−14.3498	−	24.8546i	−0.642386	−	1.11264i	0.342513	−	0.939513i	$-0.388722\pi$
$500$	10.4275	+	18.1915i	0.466332	+	0.813551i
$501$	−4.22234	−	6.26356i	−0.188640	−	0.279835i
$502$	8.37790	−	3.73008i	0.373924	−	0.166482i
$503$	10.0951	+	31.0695i	0.450118	+	1.38532i	0.876772	+	0.480907i	$0.159692\pi$
$503$	10.0951	+	31.0695i	0.450118	+	1.38532i	−0.426653	+	0.904415i	$0.640308\pi$
$504$	−15.1265	−	1.06605i	−0.673786	−	0.0474857i
$505$	−26.6006	+	11.8103i	−1.18371	+	0.525551i
$506$	0.153981	+	0.171013i	0.00684530	+	0.00760247i
$507$	3.50907	−	7.18966i	0.155843	−	0.319304i
$508$	5.17499	−	1.09998i	0.229603	−	0.0488037i
$509$	0.979668	+	0.436176i	0.0434230	+	0.0193332i	0.428333	−	0.903621i	$-0.359101\pi$
$509$	0.979668	+	0.436176i	0.0434230	+	0.0193332i	−0.384910	+	0.922954i	$0.625768\pi$
$510$	3.15775	+	0.448015i	0.139827	+	0.0198384i
$511$	−37.9186	+	16.8824i	−1.67742	+	0.746835i
$512$	−17.5147	+	12.7252i	−0.774047	+	0.562378i
$513$	16.8820	−	18.7185i	0.745357	−	0.826440i
$514$	−6.06819	−	4.40880i	−0.267657	−	0.194464i
$515$	13.5183	−	2.85874i	0.595688	−	0.125971i
$516$	−10.2961	+	8.63468i	−0.453261	+	0.380121i
$517$	−23.4430	+	4.98296i	−1.03102	+	0.219150i
$518$	−1.89851	−	3.28832i	−0.0834157	−	0.144480i
$519$	−1.58615	−	1.53256i	−0.0696241	−	0.0672720i
$520$	−12.5593	+	2.65594i	−0.550761	+	0.116471i
$521$	−11.7963	−	36.3052i	−0.516805	−	1.59056i	−0.779974	−	0.625812i	$-0.784768\pi$
$521$	−11.7963	−	36.3052i	−0.516805	−	1.59056i	0.263170	−	0.964750i	$-0.415232\pi$
$522$	−0.987442	+	1.46222i	−0.0432192	+	0.0639996i
$523$	−27.1301	−	19.7112i	−1.18632	−	0.861909i	−0.193446	−	0.981111i	$-0.561966\pi$
$523$	−27.1301	−	19.7112i	−1.18632	−	0.861909i	−0.992870	+	0.119202i	$0.961966\pi$
$524$	11.9646	−	20.7233i	0.522677	−	0.905303i
$525$	−5.48374	−	31.5328i	−0.239330	−	1.37621i
$526$	1.99913	+	3.46259i	0.0871661	+	0.150976i
$527$	2.12698	−	20.2368i	0.0926526	−	0.881530i
$528$	19.3344	−	24.7329i	0.841420	−	1.07636i
$529$	22.4839	+	4.77909i	0.977560	+	0.207787i
$530$	0.958272	+	9.20929i	0.0416247	+	0.400026i
$531$	21.6338	−	7.86069i	0.938829	−	0.341125i
$532$	33.6236			1.45777
$533$	10.3527	+	11.4978i	0.448426	+	0.498027i
$534$	1.02838	+	5.84158i	0.0445025	+	0.252790i
$535$	−8.54284	−	6.22030i	−0.369339	−	0.268927i
$536$	−0.0963722	+	0.916920i	−0.00416264	+	0.0396049i
$537$	−7.73568	+	6.48740i	−0.333819	+	0.279952i
$538$	0.745988	+	7.09760i	0.0321618	+	0.305999i
$539$	29.8744	+	21.7050i	1.28678	+	0.934902i
$540$	21.3062	+	4.57015i	0.916871	+	0.196668i
$541$	−26.4907	+	19.2466i	−1.13892	+	0.827475i	−0.986969	−	0.160912i	$-0.948556\pi$
$541$	−26.4907	+	19.2466i	−1.13892	+	0.827475i	−0.151953	+	0.988388i	$0.548556\pi$
$542$	6.31860	+	7.01752i	0.271407	+	0.301428i
$543$	2.73136	−	0.190245i	0.117214	−	0.00816421i
$544$	−8.87587	+	1.88662i	−0.380550	+	0.0808884i
$545$	−0.397767		0.000412872i	−0.0170385		1.76855e-5i
$546$	9.38981	+	1.32227i	0.401847	+	0.0565878i
$547$	−2.93767	−	0.624420i	−0.125606	−	0.0266983i	0.144680	−	0.989479i	$-0.453785\pi$
$547$	−2.93767	−	0.624420i	−0.125606	−	0.0266983i	−0.270285	+	0.962780i	$0.587118\pi$
$548$	4.88884	+	3.55195i	0.208841	+	0.151732i
$549$	1.67518	−	4.13969i	0.0714948	−	0.176678i
$550$	−8.93157	−	3.99883i	−0.380844	−	0.170511i
$551$	4.04218	−	7.00125i	0.172203	−	0.298263i
$552$	0.00979673	−	0.278361i	0.000416976	−	0.0118478i
$553$	−21.3593	+	23.7219i	−0.908291	+	1.00876i
$554$	−2.97392	+	3.30287i	−0.126350	+	0.140326i
$555$	4.21000	+	10.4596i	0.178705	+	0.443985i
$556$	−28.4270	−	31.5713i	−1.20557	−	1.33892i
$557$	33.7372			1.42949			0.714746	−	0.699384i	$-0.246542\pi$
$557$	33.7372			1.42949			0.714746	+	0.699384i	$0.246542\pi$
$558$	−1.60820	+	9.09148i	−0.0680804	+	0.384873i
$559$	14.0476	−	10.2062i	0.594149	−	0.431675i
$560$	13.4799	+	23.4040i	0.569631	+	0.988999i
$561$	19.7931	−	10.5172i	0.835664	−	0.444038i
$562$	6.13597	+	2.73191i	0.258830	+	0.115239i
$563$	29.5179	+	13.1422i	1.24403	+	0.553879i	0.919908	−	0.392135i	$-0.128263\pi$
$563$	29.5179	+	13.1422i	1.24403	+	0.553879i	0.324125	+	0.946014i	$0.394930\pi$
$564$	11.9030	+	7.44237i	0.501209	+	0.313380i
$565$	−9.69464	−	16.8319i	−0.407857	−	0.708125i
$566$	5.62100	−	4.08389i	0.236268	−	0.171659i
$567$	−28.1883	−	17.6568i	−1.18380	−	0.741518i
$568$	−8.81457			−0.369851
$569$	−0.128506	−	0.142720i	−0.00538726	−	0.00598315i	0.740445	−	0.672117i	$-0.234615\pi$
$569$	−0.128506	−	0.142720i	−0.00538726	−	0.00598315i	−0.745832	+	0.666134i	$0.767948\pi$
$570$	6.56479	+	0.931401i	0.274969	+	0.0390121i
$571$	8.78172	−	9.75309i	0.367503	−	0.408154i	−0.530823	−	0.847483i	$-0.678117\pi$
$571$	8.78172	−	9.75309i	0.367503	−	0.408154i	0.898326	+	0.439329i	$0.144784\pi$
$572$	−29.2126	+	32.4439i	−1.22144	+	1.35655i
$573$	3.04006	−	1.61536i	0.127000	−	0.0674827i
$574$	−2.40377	+	4.16345i	−0.100331	+	0.173779i
$575$	0.575296	−	0.121035i	0.0239915	−	0.00504752i
$576$	−15.3426	+	2.14771i	−0.639273	+	0.0894878i
$577$	−14.6600	−	10.6511i	−0.610303	−	0.443411i	0.239218	−	0.970966i	$-0.423109\pi$
$577$	−14.6600	−	10.6511i	−0.610303	−	0.443411i	−0.849521	+	0.527555i	$0.823109\pi$
$578$	3.98886	+	0.847858i	0.165915	+	0.0352662i
$579$	−0.594408	+	0.760379i	−0.0247027	+	0.0316003i
$580$	6.98877	+	0.00725417i	0.290193	+	0.000301213i
$581$	14.6743	−	3.11912i	0.608792	−	0.129403i
$582$	−3.29238	−	4.88404i	−0.136474	−	0.202450i
$583$	43.5398	+	48.3558i	1.80323	+	2.00269i
$584$	12.4270	−	9.02876i	0.514234	−	0.373613i
$585$	−27.0545	−	7.80418i	−1.11857	−	0.322663i
$586$	−4.57554	−	3.32433i	−0.189014	−	0.137327i
$587$	−4.01695	−	38.2188i	−0.165797	−	1.57746i	−0.688688	−	0.725057i	$-0.741813\pi$
$587$	−4.01695	−	38.2188i	−0.165797	−	1.57746i	0.522891	−	0.852400i	$-0.324853\pi$
$588$	−3.75010	−	21.3019i	−0.154651	−	0.878475i
$589$	4.42188	−	42.0713i	0.182200	−	1.73352i
$590$	4.89466	+	3.56395i	0.201510	+	0.146725i
$591$	18.3741	−	15.4092i	0.755811	−	0.633849i
$592$	−6.36644	−	7.07064i	−0.261659	−	0.290602i
$593$	−17.8242			−0.731954			−0.365977	−	0.930624i	$-0.619265\pi$
$593$	−17.8242			−0.731954			−0.365977	+	0.930624i	$0.619265\pi$
$594$	−9.29396	+	4.12881i	−0.381336	+	0.169407i
$595$	1.99574	+	19.1796i	0.0818172	+	0.786288i
$596$	−24.6221	−	5.23360i	−1.00856	−	0.214377i
$597$	6.04516	+	14.9741i	0.247412	+	0.612848i
$598$	−0.0182062	+	0.173220i	−0.000744506	+	0.00708350i
$599$	5.99511	+	10.3838i	0.244953	+	0.424272i	0.962119	−	0.272632i	$-0.0878940\pi$
$599$	5.99511	+	10.3838i	0.244953	+	0.424272i	−0.717165	+	0.696903i	$0.754561\pi$
$600$	4.41125	+	10.9925i	0.180089	+	0.448768i
$601$	−14.4186	+	24.9737i	−0.588145	+	1.01870i	0.406330	+	0.913726i	$0.366808\pi$
$601$	−14.4186	+	24.9737i	−0.588145	+	1.01870i	−0.994475	+	0.104971i	$0.966525\pi$
$602$	4.36496	+	3.17133i	0.177903	+	0.129254i
$603$	−1.13178	+	1.67596i	−0.0460896	+	0.0682502i
$604$	−6.12597	−	18.8538i	−0.249262	−	0.767150i
$605$	−43.2193	+	9.13967i	−1.75712	+	0.371581i
$606$	−7.64856	+	2.19093i	−0.310701	+	0.0890003i
$607$	12.1552	+	21.0534i	0.493365	+	0.854533i	0.999971	−	0.00764499i	$-0.00243350\pi$
$607$	12.1552	+	21.0534i	0.493365	+	0.854533i	−0.506606	+	0.862178i	$0.669100\pi$
$608$	−18.4525	+	3.92220i	−0.748347	+	0.159066i
$609$	−10.0234	−	3.65132i	−0.406169	−	0.147959i
$610$	1.14929	−	0.243042i	0.0465333	−	0.00984050i
$611$	−14.6755	−	10.6624i	−0.593707	−	0.431354i
$612$	−12.6181	−	3.62563i	−0.510055	−	0.146558i
$613$	−11.7449	+	8.53317i	−0.474372	+	0.344652i	−0.799143	−	0.601141i	$-0.794713\pi$
$613$	−11.7449	+	8.53317i	−0.474372	+	0.344652i	0.324771	+	0.945793i	$0.394713\pi$
$614$	−3.65877	+	1.62899i	−0.147656	+	0.0657407i
$615$	8.80376	−	11.2379i	0.355002	−	0.453156i
$616$	−25.6086	−	11.4017i	−1.03180	−	0.459386i
$617$	12.0865	−	2.56907i	0.486586	−	0.103427i	0.0419153	−	0.999121i	$-0.486654\pi$
$617$	12.0865	−	2.56907i	0.486586	−	0.103427i	0.444671	+	0.895694i	$0.353321\pi$
$618$	3.76803	−	0.262452i	0.151573	−	0.0105574i
$619$	−19.3417	−	21.4812i	−0.777410	−	0.863402i	0.216190	−	0.976351i	$-0.430637\pi$
$619$	−19.3417	−	21.4812i	−0.777410	−	0.863402i	−0.993601	+	0.112950i	$0.963970\pi$
$620$	33.4240	−	14.8398i	1.34234	−	0.595979i
$621$	0.305910	−	0.528851i	0.0122758	−	0.0212221i
$622$	−1.16000	−	3.57012i	−0.0465118	−	0.143149i
$623$	−32.7614	+	14.5863i	−1.31256	+	0.584388i
$624$	23.7035	−	1.65100i	0.948899	−	0.0660929i
$625$	−20.2863	+	14.6105i	−0.811450	+	0.584421i
$626$	−3.66800	−	6.35317i	−0.146603	−	0.253924i
$627$	41.1488	−	21.8648i	1.64332	−	0.873195i
$628$	36.5504	+	7.76902i	1.45852	+	0.310018i
$629$	−2.09917	−	6.46058i	−0.0836994	−	0.257600i
$630$	−0.291493	−	8.74449i	−0.0116134	−	0.348389i
$631$	−5.35180	+	16.4711i	−0.213052	+	0.655706i	0.786234	+	0.617928i	$0.212028\pi$
$631$	−5.35180	+	16.4711i	−0.213052	+	0.655706i	−0.999286	+	0.0377776i	$0.987972\pi$
$632$	5.90656	−	10.2305i	0.234950	−	0.406946i
$633$	−39.7991	+	11.4004i	−1.58187	+	0.453126i
$634$	−5.65516	−	2.51784i	−0.224595	−	0.0999962i
$635$	1.94302	+	6.00118i	0.0771063	+	0.238150i
$636$	1.34055	−	38.0899i	0.0531563	−	1.51036i
$637$	2.92149	+	27.7961i	0.115754	+	1.10132i
$638$	−2.63875	+	1.91716i	−0.104469	+	0.0759012i
$639$	−17.0664	−	9.08632i	−0.675135	−	0.359449i
$640$	−14.3472	−	15.9675i	−0.567124	−	0.631171i
$641$	−1.88795	−	17.9626i	−0.0745694	−	0.709480i	−0.966388	−	0.257088i	$-0.917237\pi$
$641$	−1.88795	−	17.9626i	−0.0745694	−	0.709480i	0.891819	−	0.452393i	$-0.149430\pi$
$642$	−2.07747	−	2.00729i	−0.0819913	−	0.0792214i
$643$	20.8929	+	36.1876i	0.823937	+	1.42710i	0.902729	+	0.430209i	$0.141560\pi$
$643$	20.8929	+	36.1876i	0.823937	+	1.42710i	−0.0787922	+	0.996891i	$0.525106\pi$
$644$	0.797148	−	0.169439i	0.0314120	−	0.00667683i
$645$	−11.5102	−	11.1445i	−0.453213	−	0.438813i
$646$	−3.90750	−	0.830565i	−0.153739	−	0.0326781i
$647$	−7.01532	−	21.5909i	−0.275801	−	0.848827i	−0.989006	−	0.147872i	$-0.952758\pi$
$647$	−7.01532	−	21.5909i	−0.275801	−	0.848827i	0.713206	−	0.700955i	$-0.247242\pi$
$648$	11.5623	+	4.22266i	0.454211	+	0.165882i
$649$	42.5504			1.67025
$650$	−2.27418	−	7.04898i	−0.0892008	−	0.276484i
$651$	−55.6863	+	3.87867i	−2.18252	+	0.152017i
$652$	−1.29298	+	12.3019i	−0.0506370	+	0.481779i
$653$	−32.0888	+	35.6383i	−1.25573	+	1.39463i	−0.370935	+	0.928659i	$0.620963\pi$
$653$	−32.0888	+	35.6383i	−1.25573	+	1.39463i	−0.884798	+	0.465974i	$0.845704\pi$
$654$	−0.107673	−	0.0151625i	−0.00421036	−	0.000592900i
$655$	26.0518	+	11.6314i	1.01793	+	0.454477i
$656$	−3.72261	+	11.4570i	−0.145343	+	0.447321i
$657$	33.3678	−	4.67094i	1.30180	−	0.182231i
$658$	1.74180	−	5.36069i	0.0679022	−	0.208982i
$659$	2.46211	+	23.4255i	0.0959104	+	0.912526i	0.931639	+	0.363384i	$0.118379\pi$
$659$	2.46211	+	23.4255i	0.0959104	+	0.912526i	−0.835729	+	0.549142i	$0.814955\pi$
$660$	34.1333	+	21.3912i	1.32864	+	0.832650i
$661$	−0.139806	+	1.33017i	−0.00543783	+	0.0517375i	−0.996904	−	0.0786243i	$-0.974947\pi$
$661$	−0.139806	+	1.33017i	−0.00543783	+	0.0517375i	0.991466	+	0.130362i	$0.0416139\pi$
$662$	−0.403792	−	0.179780i	−0.0156938	−	0.00698735i
$663$	15.9399	+	5.80658i	0.619054	+	0.225509i
$664$	−5.07190	+	2.25815i	−0.196828	+	0.0876334i
$665$	4.14903	+	39.8735i	0.160893	+	1.54623i
$666$	0.744019	+	2.99106i	0.0288302	+	0.115901i
$667$	0.0605506	−	0.186356i	0.00234453	−	0.00721572i
$668$	−4.08962	+	7.08342i	−0.158232	+	0.274066i
$669$	−31.2592	−	30.2032i	−1.20855	−	1.16772i
$670$	−0.531961		0.000552162i	−0.0205514		2.13319e-5i
$671$	5.52396	−	6.13498i	0.213250	−	0.236838i
$672$	9.31878	+	23.0830i	0.359480	+	0.890444i
$673$	−15.8434	+	7.05392i	−0.610717	+	0.271909i	−0.688701	−	0.725046i	$-0.741819\pi$
$673$	−15.8434	+	7.05392i	−0.610717	+	0.271909i	0.0779835	+	0.996955i	$0.475152\pi$
$674$	−6.11591			−0.235576
$675$	−2.79054	+	25.8305i	−0.107408	+	0.994215i
$676$	−8.66267			−0.333180
$677$	5.03836	−	2.24322i	0.193640	−	0.0862141i	−0.307626	−	0.951507i	$-0.599535\pi$
$677$	5.03836	−	2.24322i	0.193640	−	0.0862141i	0.501266	+	0.865293i	$0.332868\pi$
$678$	−1.98778	−	4.92380i	−0.0763402	−	0.189097i
$679$	23.8292	−	26.4650i	0.914482	−	1.01563i
$680$	−2.19816	−	6.78921i	−0.0842956	−	0.260354i
$681$	−16.0415	−	15.4996i	−0.614713	−	0.593946i
$682$	−8.53369	+	14.7808i	−0.326772	+	0.565985i
$683$	−1.88003	+	5.78612i	−0.0719372	+	0.221400i	−0.980561	−	0.196217i	$-0.937134\pi$
$683$	−1.88003	+	5.78612i	−0.0719372	+	0.221400i	0.908623	+	0.417616i	$0.137134\pi$
$684$	−26.2323	−	7.53751i	−1.00302	−	0.288204i
$685$	−3.60892	+	6.23587i	−0.137890	+	0.238260i
$686$	0.406855	−	0.181144i	0.0155338	−	0.00691610i
$687$	−5.50482	−	2.00529i	−0.210022	−	0.0765068i
$688$	12.3508	+	5.49894i	0.470871	+	0.209645i
$689$	−5.14798	+	48.9798i	−0.196123	+	1.86598i
$690$	0.160332	−	0.0110003i	0.00610373	−	0.000418773i
$691$	−2.09183	−	19.9024i	−0.0795769	−	0.757124i	−0.959443	−	0.281902i	$-0.909035\pi$
$691$	−2.09183	−	19.9024i	−0.0795769	−	0.757124i	0.879866	−	0.475221i	$-0.157632\pi$
$692$	−0.737992	+	2.27131i	−0.0280542	+	0.0863421i
$693$	−37.8290	−	48.4734i	−1.43700	−	1.84135i
$694$	−0.380729	+	1.17176i	−0.0144523	+	0.0444795i
$695$	33.9320	−	37.6067i	1.28711	−	1.42650i
$696$	3.90928	+	0.550502i	0.148181	+	0.0208667i
$697$	−5.75513	+	6.39172i	−0.217991	+	0.242104i
$698$	0.190618	−	1.81361i	0.00721501	−	0.0686462i
$699$	−42.8947	+	2.98771i	−1.62243	+	0.113006i
$700$	−28.0795	+	20.3120i	−1.06131	+	0.767722i
$701$	42.2502			1.59577			0.797885	−	0.602810i	$-0.205952\pi$
$701$	42.2502			1.59577			0.797885	+	0.602810i	$0.205952\pi$
$702$	−7.02928	−	3.13655i	−0.265303	−	0.118381i
$703$	−4.36406	−	13.4312i	−0.164594	−	0.506568i
$704$	−28.0129	−	5.95432i	−1.05578	−	0.224412i
$705$	−7.35696	+	15.0339i	−0.277079	+	0.566211i
$706$	0.826576	−	0.175694i	0.0311086	−	0.00661234i
$707$	−24.0518	−	41.6590i	−0.904562	−	1.56675i
$708$	−17.9237	−	17.3181i	−0.673612	−	0.650855i
$709$	−1.76170	−	16.7614i	−0.0661619	−	0.629489i	−0.976484	−	0.215589i	$-0.930833\pi$
$709$	−1.76170	−	16.7614i	−0.0661619	−	0.629489i	0.910322	−	0.413900i	$-0.135834\pi$
$710$	−0.526366	−	5.05854i	−0.0197542	−	0.189844i
$711$	21.9819	−	13.7191i	0.824384	−	0.514506i
$712$	10.7369	−	7.80079i	0.402381	−	0.292347i
$713$	−0.107176	−	1.01971i	−0.00401377	−	0.0381885i
$714$	−0.185407	+	5.26809i	−0.00693868	+	0.197153i
$715$	−42.0793	−	30.6392i	−1.57367	−	1.14584i
$716$	9.98667	+	4.44635i	0.373219	+	0.166168i
$717$	−20.9607	+	6.00418i	−0.782791	+	0.224230i
$718$	5.68475	−	9.84627i	0.212153	−	0.367460i
$719$	4.45302	−	13.7050i	0.166070	−	0.511110i	−0.833044	−	0.553207i	$-0.813404\pi$
$719$	4.45302	−	13.7050i	0.166070	−	0.511110i	0.999114	+	0.0420971i	$0.0134039\pi$
$720$	−5.27017	−	21.2811i	−0.196408	−	0.793099i
$721$	7.05703	+	21.7193i	0.262818	+	0.808869i
$722$	−1.56468	−	0.332582i	−0.0582312	−	0.0123774i
$723$	−18.2432	+	9.69368i	−0.678472	+	0.360512i
$724$	−1.48233	−	2.56747i	−0.0550904	−	0.0954194i
$725$	0.853787	+	8.28873i	0.0317089	+	0.307836i
$726$	−12.0468	+	0.839083i	−0.447097	+	0.0311413i
$727$	−24.4060	+	10.8662i	−0.905168	+	0.403007i	−0.805899	−	0.592054i	$-0.798317\pi$
$727$	−24.4060	+	10.8662i	−0.905168	+	0.403007i	−0.0992697	+	0.995061i	$0.531651\pi$
$728$	−6.55639	−	20.1785i	−0.242996	−	0.747865i
$729$	18.0336	+	20.0945i	0.667911	+	0.744241i
$730$	5.92355	+	6.59251i	0.219240	+	0.244000i
$731$	6.45886	+	7.17329i	0.238890	+	0.265314i
$732$	−4.82384	+	0.335991i	−0.178294	+	0.0124186i
$733$	21.4865	−	4.56709i	0.793622	−	0.168689i	0.206776	−	0.978388i	$-0.433703\pi$
$733$	21.4865	−	4.56709i	0.793622	−	0.168689i	0.586846	+	0.809699i	$0.300370\pi$
$734$	3.79370	+	1.68906i	0.140028	+	0.0623445i
$735$	24.7987	−	7.07574i	0.914714	−	0.260993i
$736$	−0.417707	+	0.185975i	−0.0153969	+	0.00685513i
$737$	−3.02446	+	2.19740i	−0.111407	+	0.0809422i
$738$	2.80870	−	2.70936i	0.103390	−	0.0997330i
$739$	18.5616	+	13.4858i	0.682800	+	0.496083i	0.874285	−	0.485412i	$-0.161331\pi$
$739$	18.5616	+	13.4858i	0.682800	+	0.496083i	−0.191486	+	0.981495i	$0.561331\pi$
$740$	8.17853	−	9.06424i	0.300649	−	0.333208i
$741$	33.1382	+	12.0716i	1.21736	+	0.443460i
$742$	−14.9688	+	3.18171i	−0.549521	+	0.116804i
$743$	−17.1287	−	29.6678i	−0.628392	−	1.08841i	−0.987874	−	0.155255i	$-0.950380\pi$
$743$	−17.1287	−	29.6678i	−0.628392	−	1.08841i	0.359483	−	0.933152i	$-0.382953\pi$
$744$	19.8592	−	5.68867i	0.728075	−	0.208557i
$745$	3.16813	−	29.8447i	0.116071	−	1.09343i
$746$	−0.392572	−	1.20821i	−0.0143731	−	0.0442358i
$747$	−12.1478	−	0.856125i	−0.444463	−	0.0313240i
$748$	−19.6344	−	14.2653i	−0.717906	−	0.521589i
$749$	8.73293	−	15.1259i	0.319094	−	0.552687i
$750$	−6.04501	+	3.18797i	−0.220733	+	0.116408i
$751$	23.4392	+	40.5978i	0.855308	+	1.48144i	0.876359	+	0.481658i	$0.159965\pi$
$751$	23.4392	+	40.5978i	0.855308	+	1.48144i	−0.0210514	+	0.999778i	$0.506701\pi$
$752$	1.47636	−	14.0466i	0.0538373	−	0.512227i
$753$	−16.8492	−	41.7361i	−0.614020	−	1.52095i
$754$	−2.41475	−	0.513271i	−0.0879400	−	0.0186922i
$755$	21.6024	−	9.59115i	0.786192	−	0.349058i
$756$	−3.79401	+	35.8152i	−0.137987	+	1.30258i
$757$	−35.2445			−1.28098			−0.640492	−	0.767965i	$-0.721269\pi$
$757$	−35.2445			−1.28098			−0.640492	+	0.767965i	$0.721269\pi$
$758$	4.42942	+	4.91937i	0.160884	+	0.178679i
$759$	0.865373	−	0.725732i	0.0314111	−	0.0263424i
$760$	−4.56986	−	14.1144i	−0.165766	−	0.511984i
$761$	−3.37164	+	32.0790i	−0.122222	+	1.16286i	0.745742	+	0.666235i	$0.232095\pi$
$761$	−3.37164	+	32.0790i	−0.122222	+	1.16286i	−0.867964	+	0.496627i	$0.834572\pi$
$762$	0.298968	+	1.69824i	0.0108305	+	0.0615208i
$763$	−0.0687195	−	0.653823i	−0.00248781	−	0.0236700i
$764$	−3.01569	−	2.19103i	−0.109104	−	0.0792686i
$765$	2.74254	−	15.4109i	0.0991567	−	0.557182i
$766$	4.82727	−	3.50722i	0.174416	−	0.126721i
$767$	21.5497	+	23.9334i	0.778115	+	0.864184i
$768$	6.71913	+	9.96740i	0.242456	+	0.359668i
$769$	3.77336	−	0.802052i	0.136071	−	0.0289227i	−0.139373	−	0.990240i	$-0.544509\pi$
$769$	3.77336	−	0.802052i	0.136071	−	0.0289227i	0.275443	+	0.961317i	$0.411175\pi$
$770$	5.01401	−	15.3772i	0.180692	−	0.554156i
$771$	−22.6719	+	29.0024i	−0.816510	+	1.04450i
$772$	1.02221	+	0.217278i	0.0367902	+	0.00781999i
$773$	26.4160	+	19.1924i	0.950118	+	0.690301i	0.950835	−	0.309699i	$-0.100228\pi$
$773$	26.4160	+	19.1924i	0.950118	+	0.690301i	−0.000716800		1.00000i	$0.500228\pi$
$774$	−2.69451	−	3.45271i	−0.0968522	−	0.124105i
$775$	21.7226	+	37.8056i	0.780298	+	1.35802i
$776$	−6.58956	+	11.4135i	−0.236552	+	0.409719i
$777$	−16.4564	+	8.74424i	−0.590369	+	0.313698i
$778$	−1.57269	+	1.74665i	−0.0563836	+	0.0626203i
$779$	−11.9646	+	13.2881i	−0.428677	+	0.476094i
$780$	5.25497	+	30.0326i	0.188158	+	1.07534i
$781$	−23.9158	−	26.5612i	−0.855775	−	0.950435i
$782$	−0.0968246			−0.00346244
$783$	7.00149	+	5.09565i	0.250213	+	0.182104i
$784$	−17.6055	+	12.7912i	−0.628769	+	0.456827i
$785$	−4.70293	+	44.3030i	−0.167855	+	1.58124i
$786$	6.61298	+	4.13476i	0.235877	+	0.147482i
$787$	32.3557	+	14.4057i	1.15336	+	0.513507i	0.892134	−	0.451771i	$-0.149208\pi$
$787$	32.3557	+	14.4057i	1.15336	+	0.513507i	0.261222	+	0.965279i	$0.415874\pi$
$788$	−23.7208	−	10.5612i	−0.845018	−	0.376226i
$789$	17.3285	−	9.20767i	0.616912	−	0.327802i
$790$	6.22381	+	2.77876i	0.221433	+	0.0988639i
$791$	25.9728	−	18.8703i	0.923485	−	0.670951i
$792$	17.4232	+	14.6361i	0.619108	+	0.520070i
$793$	6.24838			0.221886
$794$	7.19854	+	7.99478i	0.255466	+	0.283724i
$795$	45.3355	−	3.11043i	1.60788	−	0.110316i
$796$	11.6999	−	12.9941i	0.414692	−	0.460562i
$797$	34.0708	−	37.8394i	1.20685	−	1.34034i	0.282276	−	0.959333i	$-0.408911\pi$
$797$	34.0708	−	37.8394i	1.20685	−	1.34034i	0.924572	−	0.381007i	$-0.124423\pi$
$798$	−0.385452	+	10.9521i	−0.0136448	+	0.387700i
$799$	5.04205	−	8.73308i	0.178375	−	0.308954i
$800$	13.0405	−	14.4226i	0.461052	−	0.509917i
$801$	28.8295	−	4.03566i	1.01864	−	0.142593i
$802$	−9.19504	−	6.68059i	−0.324688	−	0.235900i
$803$	60.9238	+	12.9498i	2.14995	+	0.456987i
$804$	2.16835	+	0.305346i	0.0764719	+	0.0107687i
$805$	0.299300	+	0.924413i	0.0105489	+	0.0325813i
$806$	−12.6357	+	2.68580i	−0.445073	+	0.0946031i
$807$	34.9413	−	2.43374i	1.22999	−	0.0856717i
$808$	11.9118	+	13.2294i	0.419055	+	0.465408i
$809$	−34.2150	+	24.8586i	−1.20293	+	0.873983i	−0.994570	−	0.104069i	$-0.966814\pi$
$809$	−34.2150	+	24.8586i	−1.20293	+	0.873983i	−0.208364	+	0.978051i	$0.566814\pi$
$810$	−1.73287	+	6.88759i	−0.0608867	+	0.242005i
$811$	32.2883	+	23.4589i	1.13380	+	0.823752i	0.986243	−	0.165302i	$-0.0528599\pi$
$811$	32.2883	+	23.4589i	1.13380	+	0.823752i	0.147554	+	0.989054i	$0.452860\pi$
$812$	1.20740	+	11.4877i	0.0423716	+	0.403139i
$813$	35.5105	−	29.7803i	1.24541	−	1.04444i
$814$	−0.595577	+	5.66654i	−0.0208750	+	0.198612i
$815$	−14.7481	−	0.0153082i	−0.516604	−	0.000536222i
$816$	2.29014	+	13.0088i	0.0801708	+	0.455399i
$817$	13.4276	+	14.9129i	0.469774	+	0.521737i
$818$	1.56315			0.0546544
$819$	8.10640	−	45.8272i	0.283260	−	1.60133i
$820$	−15.1165	−	3.22952i	−0.527892	−	0.112780i
$821$	22.0647	+	4.68999i	0.770063	+	0.163682i	0.576158	−	0.817338i	$-0.304551\pi$
$821$	22.0647	+	4.68999i	0.770063	+	0.163682i	0.193905	+	0.981020i	$0.437885\pi$
$822$	−1.21301	+	1.55171i	−0.0423085	+	0.0541220i
$823$	4.63521	−	44.1010i	0.161573	−	1.53727i	−0.550306	−	0.834963i	$-0.685489\pi$
$823$	4.63521	−	44.1010i	0.161573	−	1.53727i	0.711879	−	0.702302i	$-0.247845\pi$
$824$	−4.22569	−	7.31911i	−0.147209	−	0.254973i
$825$	−21.1554	+	43.1176i	−0.736536	+	1.50116i
$826$	−5.00357	+	8.66644i	−0.174096	+	0.301544i
$827$	−11.8580	−	8.61536i	−0.412344	−	0.299586i	0.362206	−	0.932098i	$-0.382024\pi$
$827$	−11.8580	−	8.61536i	−0.412344	−	0.299586i	−0.774550	+	0.632513i	$0.782024\pi$
$828$	−0.659900	−	0.0465071i	−0.0229331	−	0.00161623i
$829$	−1.89376	−	5.82838i	−0.0657728	−	0.202428i	0.912769	−	0.408476i	$-0.133940\pi$
$829$	−1.89376	−	5.82838i	−0.0657728	−	0.202428i	−0.978542	+	0.206048i	$0.933940\pi$
$830$	−1.59879	−	2.77583i	−0.0554948	−	0.0963506i
$831$	15.6867	+	15.1567i	0.544165	+	0.525781i
$832$	−10.8380	−	18.7720i	−0.375741	−	0.650803i
$833$	−15.1976	+	3.23035i	−0.526566	+	0.111925i
$834$	10.6095	−	8.89749i	0.367377	−	0.308095i
$835$	−8.90473	−	3.97572i	−0.308161	−	0.137585i
$836$	−40.8190	−	29.6567i	−1.41175	−	1.02570i
$837$	44.3146	+	9.45733i	1.53174	+	0.326893i
$838$	−4.76469	+	3.46175i	−0.164594	+	0.119584i
$839$	−21.0628	+	9.37778i	−0.727170	+	0.323757i	−0.736720	−	0.676198i	$-0.763627\pi$
$839$	−21.0628	+	9.37778i	−0.727170	+	0.323757i	0.00955052	+	0.999954i	$0.496960\pi$
$840$	−17.2972	+	9.16799i	−0.596809	+	0.316326i
$841$	−23.9556	−	10.6657i	−0.826057	−	0.367784i
$842$	2.77813	−	0.590510i	0.0957406	−	0.0203503i
$843$	14.4588	−	29.6243i	0.497987	−	1.02032i
$844$	29.9953	+	33.3132i	1.03248	+	1.14669i
$845$	−1.06894	−	10.2729i	−0.0367728	−	0.353398i
$846$	−2.56063	+	3.79182i	−0.0880363	+	0.130365i
$847$	−22.5620	−	69.4387i	−0.775239	−	2.38594i
$848$	−35.0312	+	15.5969i	−1.20298	+	0.535599i
$849$	−19.0605	−	28.2750i	−0.654155	−	0.970396i
$850$	3.76495	−	1.66691i	0.129137	−	0.0571745i
$851$	−0.171147	−	0.296436i	−0.00586685	−	0.0101617i
$852$	−0.736346	+	20.9223i	−0.0252268	+	0.716786i
$853$	−26.3151	−	5.59344i	−0.901010	−	0.191516i	−0.265958	−	0.963985i	$-0.585688\pi$
$853$	−26.3151	−	5.59344i	−0.901010	−	0.191516i	−0.635053	+	0.772469i	$0.719022\pi$
$854$	0.599969	+	1.84651i	0.0205305	+	0.0631864i
$855$	5.70160	−	32.0384i	0.194991	−	1.09569i
$856$	−1.99738	+	6.14729i	−0.0682689	+	0.210110i
$857$	−23.5084	+	40.7177i	−0.803031	+	1.39089i	0.114582	+	0.993414i	$0.463447\pi$
$857$	−23.5084	+	40.7177i	−0.803031	+	1.39089i	−0.917613	+	0.397476i	$0.869886\pi$
$858$	−10.2329	−	9.88725i	−0.349347	−	0.337545i
$859$	4.04413	+	1.80056i	0.137984	+	0.0614343i	0.474567	−	0.880219i	$-0.342605\pi$
$859$	4.04413	+	1.80056i	0.137984	+	0.0614343i	−0.336583	+	0.941654i	$0.609271\pi$
$860$	−5.37789	+	16.4932i	−0.183384	+	0.562412i
$861$	20.0061	+	12.5088i	0.681805	+	0.426298i
$862$	−0.0845712	−	0.804642i	−0.00288051	−	0.0274062i
$863$	−39.5333	+	28.7226i	−1.34573	+	0.977730i	−0.346517	+	0.938044i	$0.612636\pi$
$863$	−39.5333	+	28.7226i	−1.34573	+	0.977730i	−0.999212	+	0.0396859i	$0.987364\pi$
$864$	−2.09571	−	20.0978i	−0.0712974	−	0.683741i
$865$	−2.78456	−	0.594898i	−0.0946779	−	0.0202271i
$866$	0.479440	+	4.56157i	0.0162920	+	0.155008i
$867$	4.84717	−	19.4183i	0.164619	−	0.659481i
$868$	30.2214	+	52.3450i	1.02578	+	1.77671i
$869$	46.8535	−	9.95902i	1.58940	−	0.337836i
$870$	−0.0824803	+	2.27634i	−0.00279634	+	0.0771753i
$871$	−2.76772	−	0.588297i	−0.0937806	−	0.0199337i
$872$	0.0751823	+	0.231387i	0.00254600	+	0.00783577i
$873$	−24.5237	+	15.3055i	−0.830003	+	0.518013i
$874$	−0.201293			−0.00680885
$875$	−27.5525	−	30.7925i	−0.931445	−	1.04098i
$876$	−20.3926	−	30.2511i	−0.689001	−	1.02209i
$877$	−0.223810	+	2.12941i	−0.00755751	+	0.0719049i	−0.997651	−	0.0685077i	$-0.978176\pi$
$877$	−0.223810	+	2.12941i	−0.00755751	+	0.0719049i	0.990093	+	0.140413i	$0.0448429\pi$
$878$	−6.71434	+	7.45703i	−0.226598	+	0.251662i
$879$	−17.0951	+	21.8684i	−0.576604	+	0.737604i
$880$	4.27821	−	40.3020i	0.144219	−	1.35858i
$881$	0.263101	−	0.809740i	0.00886408	−	0.0272808i	−0.946527	−	0.322626i	$-0.895435\pi$
$881$	0.263101	−	0.809740i	0.00886408	−	0.0272808i	0.955391	+	0.295345i	$0.0954345\pi$
$882$	6.98158	−	0.977307i	0.235082	−	0.0329076i
$883$	11.6665	−	35.9059i	0.392611	−	1.20833i	−0.538196	−	0.842820i	$-0.680894\pi$
$883$	11.6665	−	35.9059i	0.392611	−	1.20833i	0.930807	−	0.365512i	$-0.119106\pi$
$884$	−1.92009	−	18.2685i	−0.0645798	−	0.614436i
$885$	18.3255	−	23.3923i	0.616005	−	0.786323i
$886$	0.345668	−	3.28881i	0.0116129	−	0.110490i
$887$	−7.85445	−	3.49703i	−0.263727	−	0.117419i	0.270614	−	0.962688i	$-0.412773\pi$
$887$	−7.85445	−	3.49703i	−0.263727	−	0.117419i	−0.534341	+	0.845269i	$0.679440\pi$
$888$	5.28418	−	4.43149i	0.177325	−	0.148711i
$889$	−9.52427	+	4.24048i	−0.319434	+	0.142221i
$890$	5.11790	+	5.69589i	0.171553	+	0.190927i
$891$	18.6468	+	46.2981i	0.624691	+	1.55104i
$892$	−14.5441	+	44.7621i	−0.486972	+	1.49875i
$893$	10.4822	−	18.1556i	0.350772	−	0.607555i
$894$	1.98698	−	7.96009i	0.0664547	−	0.266225i
$895$	−4.04051	+	12.3916i	−0.135059	+	0.414207i
$896$	23.7403	−	26.3663i	0.793108	−	0.880836i
$897$	0.846474	+	0.119200i	0.0282629	+	0.00397997i
$898$	0.198458	−	0.0883593i	0.00662263	−	0.00294859i
$899$	14.5327			0.484693
$900$	26.4604	−	9.55228i	0.882012	−	0.318409i
$901$	−27.3781			−0.912098
$902$	6.59042	−	2.93425i	0.219437	−	0.0976997i
$903$	16.3084	−	20.8620i	0.542708	−	0.694243i
$904$	−7.94985	+	8.82921i	−0.264408	+	0.293655i
$905$	2.86180	−	2.07468i	0.0951294	−	0.0689648i
$906$	6.21141	−	1.77926i	0.206360	−	0.0591118i
$907$	22.8025	−	39.4951i	0.757145	−	1.31141i	−0.187156	−	0.982330i	$-0.559927\pi$
$907$	22.8025	−	39.4951i	0.757145	−	1.31141i	0.944301	−	0.329083i	$-0.106740\pi$
$908$	−7.46370	+	22.9709i	−0.247691	+	0.762316i
$909$	9.42582	+	37.8931i	0.312635	+	1.25684i
$910$	11.1886	−	4.96757i	0.370898	−	0.164673i
$911$	11.1860	−	4.98033i	0.370609	−	0.165006i	−0.212977	−	0.977057i	$-0.568316\pi$
$911$	11.1860	−	4.98033i	0.370609	−	0.165006i	0.583586	+	0.812052i	$0.301649\pi$
$912$	4.76108	+	27.0446i	0.157655	+	0.895537i
$913$	−20.5657	−	9.15644i	−0.680626	−	0.303034i
$914$	−0.566960	+	5.39426i	−0.0187534	+	0.178426i
$915$	−0.993689	−	5.67903i	−0.0328504	−	0.187743i
$916$	0.663103	+	6.30900i	0.0219095	+	0.208455i
$917$	−14.5716	+	44.8468i	−0.481197	+	1.48097i
$918$	1.32562	−	4.06847i	0.0437518	−	0.134280i
$919$	0.377667	−	1.16234i	0.0124581	−	0.0383421i	−0.944634	−	0.328125i	$-0.893583\pi$
$919$	0.377667	−	1.16234i	0.0124581	−	0.0383421i	0.957092	+	0.289783i	$0.0935832\pi$
$920$	−0.179469	−	0.311596i	−0.00591692	−	0.0102730i
$921$	7.35834	+	18.2269i	0.242466	+	0.600596i
$922$	−1.76722	+	1.96270i	−0.0582004	+	0.0646381i
$923$	2.82772	−	26.9039i	0.0930755	−	0.885554i
$924$	−29.2023	+	59.8321i	−0.960685	+	1.96833i
$925$	11.7583	+	8.58026i	0.386610	+	0.282117i
$926$	5.08407			0.167073
$927$	−0.636836	−	18.5269i	−0.0209164	−	0.608503i
$928$	−2.00266	−	6.16355i	−0.0657405	−	0.202328i
$929$	45.5102	+	9.67350i	1.49314	+	0.317377i	0.880904	−	0.473296i	$-0.156936\pi$
$929$	45.5102	+	9.67350i	1.49314	+	0.317377i	0.612239	+	0.790673i	$0.290269\pi$
$930$	4.45054	+	11.0572i	0.145939	+	0.362580i
$931$	−31.5950	+	6.71573i	−1.03549	+	0.220099i
$932$	23.2793	+	40.3209i	0.762539	+	1.32076i
$933$	−17.7111	+	5.07333i	−0.579835	+	0.166093i
$934$	−0.248446	−	2.36381i	−0.00812941	−	0.0773462i
$935$	14.4940	−	25.0443i	0.474006	−	0.819038i
$936$	0.591658	+	17.2125i	0.0193389	+	0.562610i
$937$	1.51656	−	1.10185i	0.0495440	−	0.0359958i	−0.562738	−	0.826636i	$-0.690252\pi$
$937$	1.51656	−	1.10185i	0.0495440	−	0.0359958i	0.612282	+	0.790640i	$0.290252\pi$
$938$	−0.0919034	−	0.874402i	−0.00300075	−	0.0285502i
$939$	−31.7944	+	16.8942i	−1.03757	+	0.551323i
$940$	18.1232	+	0.0188115i	0.591115	+	0.000613563i
$941$	−7.43469	−	3.31014i	−0.242364	−	0.107907i	0.281960	−	0.959426i	$-0.409015\pi$
$941$	−7.43469	−	3.31014i	−0.242364	−	0.107907i	−0.524324	+	0.851519i	$0.675682\pi$
$942$	−2.94958	+	11.8164i	−0.0961025	+	0.384998i
$943$	−0.216695	+	0.375327i	−0.00705657	+	0.0122223i
$944$	−7.74881	+	23.8484i	−0.252202	+	0.776199i
$945$	−42.9406	−	0.0797709i	−1.39686	−	0.00259495i
$946$	−2.50188	−	7.69999i	−0.0813431	−	0.250348i
$947$	−25.1385	−	5.34335i	−0.816890	−	0.173635i	−0.219527	−	0.975606i	$-0.570452\pi$
$947$	−25.1385	−	5.34335i	−0.816890	−	0.173635i	−0.597363	+	0.801971i	$0.703785\pi$
$948$	−23.7896	−	14.8744i	−0.772651	−	0.483100i
$949$	23.5711	+	40.8264i	0.765151	+	1.32528i
$950$	7.82714	−	3.46542i	0.253946	−	0.112433i
$951$	−13.3258	+	27.3030i	−0.432119	+	0.885360i
$952$	10.7749	−	4.79730i	0.349217	−	0.155481i
$953$	−11.4194	−	35.1453i	−0.369910	−	1.13847i	−0.946849	−	0.321679i	$-0.895753\pi$
$953$	−11.4194	−	35.1453i	−0.369910	−	1.13847i	0.576939	−	0.816788i	$-0.304247\pi$
$954$	12.3915	+	0.873305i	0.401191	+	0.0282743i
$955$	2.22617	−	3.84661i	0.0720371	−	0.124473i
$956$	15.7974	+	17.5448i	0.510925	+	0.567440i
$957$	8.94786	+	13.2736i	0.289243	+	0.429073i
$958$	−0.218021	+	0.0463418i	−0.00704394	+	0.00149724i
$959$	−10.8786	−	4.84348i	−0.351289	−	0.156404i
$960$	−15.3379	+	12.8358i	−0.495030	+	0.414275i
$961$	41.1510	−	18.3216i	1.32745	−	0.591020i
$962$	−3.48890	+	2.53484i	−0.112487	+	0.0817264i
$963$	−10.2040	+	9.84315i	−0.328821	+	0.317191i
$964$	18.0970	+	13.1482i	0.582864	+	0.423476i
$965$	−0.131528	+	1.23903i	−0.00423403	+	0.0398858i
$966$	0.0460525	+	0.261595i	0.00148172	+	0.00841667i
$967$	−16.7536	+	3.56108i	−0.538758	+	0.114517i	−0.469251	−	0.883065i	$-0.655476\pi$
$967$	−16.7536	+	3.56108i	−0.538758	+	0.114517i	−0.0695072	+	0.997581i	$0.522143\pi$
$968$	13.5099	+	23.3999i	0.434225	+	0.752100i
$969$	−4.74831	+	19.0223i	−0.152538	+	0.611083i
$970$	−6.94350	−	3.10009i	−0.222942	−	0.0995377i
$971$	−15.8028	−	48.6359i	−0.507134	−	1.56080i	−0.797152	−	0.603778i	$-0.793661\pi$
$971$	−15.8028	−	48.6359i	−0.507134	−	1.56080i	0.290018	−	0.957021i	$-0.406339\pi$
$972$	10.9888	−	27.0916i	0.352466	−	0.868964i
$973$	67.7288	+	49.2078i	2.17128	+	1.57753i
$974$	3.42793	−	5.93735i	0.109838	−	0.190245i
$975$	−34.9666	+	9.93768i	−1.11983	+	0.318261i
$976$	2.43253	+	4.21327i	0.0778635	+	0.134864i
$977$	1.64344	−	15.6363i	0.0525782	−	0.500249i	−0.936266	−	0.351293i	$-0.885742\pi$
$977$	1.64344	−	15.6363i	0.0525782	−	0.500249i	0.988844	−	0.148956i	$-0.0475912\pi$
$978$	−3.99223	−	0.562184i	−0.127657	−	0.0179767i
$979$	52.6378	+	11.1885i	1.68231	+	0.357586i
$980$	−18.6629	−	20.7706i	−0.596165	−	0.663492i
$981$	−0.0929563	+	0.525502i	−0.00296787	+	0.0167780i
$982$	9.87151			0.315012
$983$	−7.82324	−	8.68859i	−0.249523	−	0.277123i	0.605352	−	0.795958i	$-0.293032\pi$
$983$	−7.82324	−	8.68859i	−0.249523	−	0.277123i	−0.854874	+	0.518835i	$0.826366\pi$
$984$	−8.20438	−	2.98869i	−0.261546	−	0.0952760i
$985$	9.59722	−	29.4332i	0.305793	−	0.937820i
$986$	0.143451	−	1.36484i	0.00456841	−	0.0434655i
$987$	−25.9926	−	9.46859i	−0.827355	−	0.301389i
$988$	−3.99178	−	37.9792i	−0.126995	−	1.20828i
$989$	0.393493	+	0.285890i	0.0125124	+	0.00909076i
$990$	−7.35897	+	10.8729i	−0.233883	+	0.345564i
$991$	−4.67546	+	3.39692i	−0.148521	+	0.107907i	−0.659564	−	0.751648i	$-0.729259\pi$
$991$	−4.67546	+	3.39692i	−0.148521	+	0.107907i	0.511043	+	0.859555i	$0.329259\pi$
$992$	−22.6914	−	25.2014i	−0.720454	−	0.800145i
$993$	−0.951495	+	1.94950i	−0.0301948	+	0.0618655i
$994$	8.22215	−	1.74767i	0.260791	−	0.0554328i
$995$	16.8531	+	12.2712i	0.534280	+	0.389025i
$996$	4.93627	+	12.2273i	0.156412	+	0.387437i
$997$	9.79843	+	2.08272i	0.310319	+	0.0659604i	0.360439	−	0.932783i	$-0.382627\pi$
$997$	9.79843	+	2.08272i	0.310319	+	0.0659604i	−0.0501196	+	0.998743i	$0.515960\pi$
$998$	−8.19410	−	5.95336i	−0.259380	−	0.188450i
$999$	14.7991	−	3.13297i	0.468223	−	0.0991227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.17	✓	224
3.2	odd	2		675.2.r.a.316.12		224
9.4	even	3	inner	225.2.q.a.166.12	yes	224
9.5	odd	6		675.2.r.a.91.17		224
25.11	even	5	inner	225.2.q.a.61.12	yes	224
75.11	odd	10		675.2.r.a.586.17		224
225.86	odd	30		675.2.r.a.361.12		224
225.211	even	15	inner	225.2.q.a.211.17	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.17	✓	224	1.1	even	1	trivial
225.2.q.a.61.12	yes	224	25.11	even	5	inner
225.2.q.a.166.12	yes	224	9.4	even	3	inner
225.2.q.a.211.17	yes	224	225.211	even	15	inner
675.2.r.a.91.17		224	9.5	odd	6
675.2.r.a.316.12		224	3.2	odd	2
675.2.r.a.361.12		224	225.86	odd	30
675.2.r.a.586.17		224	75.11	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.322402 - 0.143543i) q^{2} +(-0.648399 - 1.60611i) q^{3} +(-1.25492 + 1.39373i) q^{4} +(-1.80765 - 1.31620i) q^{5} +(-0.439590 - 0.424739i) q^{6} +(1.84787 - 3.20061i) q^{7} +(-0.422642 + 1.30076i) q^{8} +(-2.15916 + 2.08280i) q^{9} +O(q^{10})\)	\(q+(0.322402 - 0.143543i) q^{2} +(-0.648399 - 1.60611i) q^{3} +(-1.25492 + 1.39373i) q^{4} +(-1.80765 - 1.31620i) q^{5} +(-0.439590 - 0.424739i) q^{6} +(1.84787 - 3.20061i) q^{7} +(-0.422642 + 1.30076i) q^{8} +(-2.15916 + 2.08280i) q^{9} +(-0.771722 - 0.164872i) q^{10} +(-5.06633 + 2.25567i) q^{11} +(3.05217 + 1.11185i) q^{12} +(-3.83460 - 1.70728i) q^{13} +(0.136334 - 1.29713i) q^{14} +(-0.941886 + 3.75671i) q^{15} +(-0.341623 - 3.25032i) q^{16} +(0.721064 - 2.21921i) q^{17} +(-0.397147 + 0.981428i) q^{18} +(1.49906 - 4.61362i) q^{19} +(4.10290 - 0.867648i) q^{20} +(-6.33868 - 0.892610i) q^{21} +(-1.30961 + 1.45447i) q^{22} +(0.0122903 - 0.116934i) q^{23} +(2.36319 - 0.164602i) q^{24} +(1.53521 + 4.75848i) q^{25} -1.48135 q^{26} +(4.74519 + 2.11736i) q^{27} +(2.14186 + 6.59196i) q^{28} +(1.63010 + 0.346488i) q^{29} +(0.235582 + 1.34637i) q^{30} +(8.52984 - 1.81307i) q^{31} +(-1.94440 - 3.36779i) q^{32} +(6.90785 + 6.67448i) q^{33} +(-0.0860783 - 0.818980i) q^{34} +(-7.55297 + 3.35341i) q^{35} +(-0.193284 - 5.62304i) q^{36} +(2.35522 - 1.71117i) q^{37} +(-0.178952 - 1.70262i) q^{38} +(-0.255714 + 7.26578i) q^{39} +(2.47605 - 1.79503i) q^{40} +(-3.36731 - 1.49922i) q^{41} +(-2.17173 + 0.622091i) q^{42} +(-2.06835 + 3.58248i) q^{43} +(3.21404 - 9.89180i) q^{44} +(6.64439 - 0.923075i) q^{45} +(-0.0128226 - 0.0394639i) q^{46} +(4.22717 + 0.898512i) q^{47} +(-4.99886 + 2.65619i) q^{48} +(-3.32927 - 5.76646i) q^{49} +(1.17800 + 1.31377i) q^{50} +(-4.03182 + 0.280825i) q^{51} +(7.19162 - 3.20191i) q^{52} +(-3.62572 - 11.1588i) q^{53} +(1.83379 + 0.00150320i) q^{54} +(12.1271 + 2.59085i) q^{55} +(3.38223 + 3.75634i) q^{56} +(-8.38195 + 0.583822i) q^{57} +(0.575283 - 0.122280i) q^{58} +(-7.00923 - 3.12071i) q^{59} +(-4.05385 - 6.02712i) q^{60} +(-1.35990 + 0.605466i) q^{61} +(2.48978 - 1.80893i) q^{62} +(2.67637 + 10.7594i) q^{63} +(4.17780 + 3.03535i) q^{64} +(4.68450 + 8.13328i) q^{65} +(3.18518 + 1.16030i) q^{66} +(0.659374 - 0.140154i) q^{67} +(2.18810 + 3.78991i) q^{68} +(-0.195777 + 0.0560804i) q^{69} +(-1.95373 + 2.16532i) q^{70} +(1.99156 + 6.12940i) q^{71} +(-1.79666 - 3.68882i) q^{72} +(-9.08610 - 6.60143i) q^{73} +(0.513701 - 0.889757i) q^{74} +(6.64720 - 5.55110i) q^{75} +(4.54895 + 7.87902i) q^{76} +(-2.14240 + 20.3835i) q^{77} +(0.960506 + 2.37921i) q^{78} +(-8.44849 - 1.79578i) q^{79} +(-3.66056 + 6.32510i) q^{80} +(0.323926 - 8.99417i) q^{81} -1.30083 q^{82} +(2.71620 + 3.01664i) q^{83} +(9.19861 - 7.71427i) q^{84} +(-4.22437 + 3.06249i) q^{85} +(-0.152600 + 1.45190i) q^{86} +(-0.500457 - 2.84278i) q^{87} +(-0.792843 - 7.54340i) q^{88} +(-7.85033 - 5.70360i) q^{89} +(2.00966 - 1.25135i) q^{90} +(-12.5502 + 9.11824i) q^{91} +(0.147551 + 0.163872i) q^{92} +(-8.44273 - 12.5242i) q^{93} +(1.49182 - 0.317097i) q^{94} +(-8.78224 + 6.36675i) q^{95} +(-4.14829 + 5.30658i) q^{96} +(9.42543 + 2.00344i) q^{97} +(-1.90110 - 1.38123i) q^{98} +(6.24089 - 15.4225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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