LMFDB - Embedded newform 225.2.q.a.211.11

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			211.11
Character	$\chi$	$=$	225.211
Dual form			225.2.q.a.16.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.973390 - 0.433381i) q^{2} +(-1.71069 + 0.271186i) q^{3} +(-0.578592 - 0.642592i) q^{4} +(-2.03848 + 0.919011i) q^{5} +(1.78270 + 0.477410i) q^{6} +(-0.798426 - 1.38291i) q^{7} +(0.943229 + 2.90296i) q^{8} +(2.85292 - 0.927831i) q^{9} +O(q^{10})$	\(q+(-0.973390 - 0.433381i) q^{2} +(-1.71069 + 0.271186i) q^{3} +(-0.578592 - 0.642592i) q^{4} +(-2.03848 + 0.919011i) q^{5} +(1.78270 + 0.477410i) q^{6} +(-0.798426 - 1.38291i) q^{7} +(0.943229 + 2.90296i) q^{8} +(2.85292 - 0.927831i) q^{9} +(2.38252 - 0.0111154i) q^{10} +(4.35427 + 1.93865i) q^{11} +(1.16405 + 0.942368i) q^{12} +(0.904123 - 0.402542i) q^{13} +(0.177851 + 1.69214i) q^{14} +(3.23799 - 2.12495i) q^{15} +(0.159189 - 1.51458i) q^{16} +(0.0927524 + 0.285463i) q^{17} +(-3.17910 - 0.333258i) q^{18} +(0.468623 + 1.44227i) q^{19} +(1.77000 + 0.778180i) q^{20} +(1.74089 + 2.14922i) q^{21} +(-3.39823 - 3.77412i) q^{22} +(0.597633 + 5.68610i) q^{23} +(-2.40082 - 4.71027i) q^{24} +(3.31084 - 3.74678i) q^{25} -1.05452 q^{26} +(-4.62884 + 2.36090i) q^{27} +(-0.426686 + 1.31321i) q^{28} +(5.78936 - 1.23057i) q^{29} +(-4.07274 + 0.665123i) q^{30} +(2.67051 + 0.567634i) q^{31} +(2.24101 - 3.88154i) q^{32} +(-7.97454 - 2.13560i) q^{33} +(0.0334298 - 0.318064i) q^{34} +(2.89849 + 2.08529i) q^{35} +(-2.24689 - 1.29642i) q^{36} +(1.92560 + 1.39903i) q^{37} +(0.168901 - 1.60699i) q^{38} +(-1.43751 + 0.933810i) q^{39} +(-4.59061 - 5.05080i) q^{40} +(-10.2958 + 4.58400i) q^{41} +(-0.763133 - 2.84649i) q^{42} +(3.80449 + 6.58957i) q^{43} +(-1.27359 - 3.91970i) q^{44} +(-4.96294 + 4.51323i) q^{45} +(1.88252 - 5.79380i) q^{46} +(-5.69960 + 1.21149i) q^{47} +(0.138411 + 2.63415i) q^{48} +(2.22503 - 3.85387i) q^{49} +(-4.84652 + 2.21222i) q^{50} +(-0.236084 - 0.463185i) q^{51} +(-0.781789 - 0.348075i) q^{52} +(0.598625 - 1.84238i) q^{53} +(5.52884 - 0.292028i) q^{54} +(-10.6578 + 0.0497227i) q^{55} +(3.26145 - 3.62220i) q^{56} +(-1.19279 - 2.34020i) q^{57} +(-6.16861 - 1.31118i) q^{58} +(5.31370 - 2.36581i) q^{59} +(-3.23895 - 0.851225i) q^{60} +(12.1540 + 5.41129i) q^{61} +(-2.35344 - 1.70988i) q^{62} +(-3.56095 - 3.20453i) q^{63} +(-6.32771 + 4.59735i) q^{64} +(-1.47310 + 1.65147i) q^{65} +(6.83681 + 5.53479i) q^{66} +(1.02420 + 0.217699i) q^{67} +(0.129770 - 0.224768i) q^{68} +(-2.56436 - 9.56508i) q^{69} +(-1.91764 - 3.28595i) q^{70} +(-5.09100 + 15.6685i) q^{71} +(5.38441 + 7.40674i) q^{72} +(7.42742 - 5.39634i) q^{73} +(-1.26805 - 2.19633i) q^{74} +(-4.64774 + 7.30743i) q^{75} +(0.655651 - 1.13562i) q^{76} +(-0.795582 - 7.56945i) q^{77} +(1.80395 - 0.285971i) q^{78} +(-10.9470 + 2.32686i) q^{79} +(1.06741 + 3.23374i) q^{80} +(7.27826 - 5.29405i) q^{81} +12.0085 q^{82} +(3.98246 - 4.42297i) q^{83} +(0.373804 - 2.36220i) q^{84} +(-0.451418 - 0.496671i) q^{85} +(-0.847457 - 8.06302i) q^{86} +(-9.57009 + 3.67511i) q^{87} +(-1.52074 + 14.4689i) q^{88} +(1.01962 - 0.740795i) q^{89} +(6.78682 - 2.24229i) q^{90} +(-1.27856 - 0.928926i) q^{91} +(3.30805 - 3.67397i) q^{92} +(-4.72234 - 0.246840i) q^{93} +(6.07297 + 1.29085i) q^{94} +(-2.28075 - 2.50938i) q^{95} +(-2.78105 + 7.24785i) q^{96} +(1.87620 - 0.398799i) q^{97} +(-3.83602 + 2.78703i) q^{98} +(14.2211 + 1.49077i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.973390	−	0.433381i	−0.688291	−	0.306447i	0.0326268	−	0.999468i	$-0.489613\pi$
$2$	−0.973390	−	0.433381i	−0.688291	−	0.306447i	−0.720918	+	0.693021i	$0.756279\pi$
$3$	−1.71069	+	0.271186i	−0.987667	+	0.156570i
$3$	−1.71069	+	0.271186i	−0.987667	+	0.156570i
$4$	−0.578592	−	0.642592i	−0.289296	−	0.321296i
$5$	−2.03848	+	0.919011i	−0.911638	+	0.410994i
$5$	−2.03848	+	0.919011i	−0.911638	+	0.410994i
$6$	1.78270	+	0.477410i	0.727782	+	0.194902i
$7$	−0.798426	−	1.38291i	−0.301777	−	0.522693i	0.674762	−	0.738036i	$-0.264246\pi$
$7$	−0.798426	−	1.38291i	−0.301777	−	0.522693i	−0.976538	+	0.215343i	$0.930913\pi$
$8$	0.943229	+	2.90296i	0.333482	+	1.02635i
$9$	2.85292	−	0.927831i	0.950972	−	0.309277i
$10$	2.38252	−	0.0111154i	0.753420	−	0.00351501i
$11$	4.35427	+	1.93865i	1.31286	+	0.584524i	0.939305	−	0.343083i	$-0.111471\pi$
$11$	4.35427	+	1.93865i	1.31286	+	0.584524i	0.373557	+	0.927607i	$0.378138\pi$
$12$	1.16405	+	0.942368i	0.336033	+	0.272038i
$13$	0.904123	−	0.402542i	0.250759	−	0.111645i	−0.277508	−	0.960723i	$-0.589509\pi$
$13$	0.904123	−	0.402542i	0.250759	−	0.111645i	0.528267	+	0.849078i	$0.322842\pi$
$14$	0.177851	+	1.69214i	0.0475327	+	0.452243i
$15$	3.23799	−	2.12495i	0.836045	−	0.548660i
$16$	0.159189	−	1.51458i	0.0397972	−	0.378645i
$17$	0.0927524	+	0.285463i	0.0224958	+	0.0692348i	0.961674	−	0.274195i	$-0.0884113\pi$
$17$	0.0927524	+	0.285463i	0.0224958	+	0.0692348i	−0.939178	+	0.343430i	$0.888411\pi$
$18$	−3.17910	−	0.333258i	−0.749322	−	0.0785497i
$19$	0.468623	+	1.44227i	0.107510	+	0.330880i	0.990311	−	0.138866i	$-0.0443456\pi$
$19$	0.468623	+	1.44227i	0.107510	+	0.330880i	−0.882802	+	0.469746i	$0.844346\pi$
$20$	1.77000	+	0.778180i	0.395784	+	0.174006i
$21$	1.74089	+	2.14922i	0.379893	+	0.468997i
$22$	−3.39823	−	3.77412i	−0.724506	−	0.804645i
$23$	0.597633	+	5.68610i	0.124615	+	1.18563i	0.860832	+	0.508889i	$0.169944\pi$
$23$	0.597633	+	5.68610i	0.124615	+	1.18563i	−0.736217	+	0.676745i	$0.763390\pi$
$24$	−2.40082	−	4.71027i	−0.490064	−	0.961480i
$25$	3.31084	−	3.74678i	0.662167	−	0.749356i
$26$	−1.05452			−0.206808
$27$	−4.62884	+	2.36090i	−0.890820	+	0.454356i
$28$	−0.426686	+	1.31321i	−0.0806361	+	0.248173i
$29$	5.78936	−	1.23057i	1.07506	−	0.228511i	0.363825	−	0.931467i	$-0.381471\pi$
$29$	5.78936	−	1.23057i	1.07506	−	0.228511i	0.711233	+	0.702957i	$0.248137\pi$
$30$	−4.07274	+	0.665123i	−0.743578	+	0.121434i
$31$	2.67051	+	0.567634i	0.479637	+	0.101950i	0.441385	−	0.897318i	$-0.354487\pi$
$31$	2.67051	+	0.567634i	0.479637	+	0.101950i	0.0382528	+	0.999268i	$0.487821\pi$
$32$	2.24101	−	3.88154i	0.396158	−	0.686166i
$33$	−7.97454	−	2.13560i	−1.38819	−	0.371761i
$34$	0.0334298	−	0.318064i	0.00573317	−	0.0545475i
$35$	2.89849	+	2.08529i	0.489935	+	0.352478i
$36$	−2.24689	−	1.29642i	−0.374482	−	0.216071i
$37$	1.92560	+	1.39903i	0.316567	+	0.230000i	0.734709	−	0.678382i	$-0.237319\pi$
$37$	1.92560	+	1.39903i	0.316567	+	0.230000i	−0.418142	+	0.908382i	$0.637319\pi$
$38$	0.168901	−	1.60699i	0.0273994	−	0.260688i
$39$	−1.43751	+	0.933810i	−0.230186	+	0.149529i
$40$	−4.59061	−	5.05080i	−0.725839	−	0.798602i
$41$	−10.2958	+	4.58400i	−1.60794	+	0.715901i	−0.997118	−	0.0758673i	$-0.975827\pi$
$41$	−10.2958	+	4.58400i	−1.60794	+	0.715901i	−0.610822	+	0.791768i	$0.709161\pi$
$42$	−0.763133	−	2.84649i	−0.117754	−	0.439223i
$43$	3.80449	+	6.58957i	0.580179	+	1.00490i	0.995458	+	0.0952056i	$0.0303508\pi$
$43$	3.80449	+	6.58957i	0.580179	+	1.00490i	−0.415278	+	0.909694i	$0.636316\pi$
$44$	−1.27359	−	3.91970i	−0.192001	−	0.590918i
$45$	−4.96294	+	4.51323i	−0.739831	+	0.672793i
$46$	1.88252	−	5.79380i	0.277562	−	0.854249i
$47$	−5.69960	+	1.21149i	−0.831372	+	0.176714i	−0.603889	−	0.797069i	$-0.706383\pi$
$47$	−5.69960	+	1.21149i	−0.831372	+	0.176714i	−0.227483	+	0.973782i	$0.573050\pi$
$48$	0.138411	+	2.63415i	0.0199779	+	0.380206i
$49$	2.22503	−	3.85387i	0.317862	−	0.550552i
$50$	−4.84652	+	2.21222i	−0.685401	+	0.312856i
$51$	−0.236084	−	0.463185i	−0.0330584	−	0.0648588i
$52$	−0.781789	−	0.348075i	−0.108415	−	0.0482693i
$53$	0.598625	−	1.84238i	0.0822275	−	0.253070i	−0.901488	−	0.432805i	$-0.857524\pi$
$53$	0.598625	−	1.84238i	0.0822275	−	0.253070i	0.983715	+	0.179735i	$0.0575239\pi$
$54$	5.52884	−	0.292028i	0.752379	−	0.0397400i
$55$	−10.6578	+	0.0497227i	−1.43709	+	0.00670461i
$56$	3.26145	−	3.62220i	0.435829	−	0.484037i
$57$	−1.19279	−	2.34020i	−0.157989	−	0.309967i
$58$	−6.16861	−	1.31118i	−0.809979	−	0.172166i
$59$	5.31370	−	2.36581i	0.691784	−	0.308002i	−0.0305627	−	0.999533i	$-0.509730\pi$
$59$	5.31370	−	2.36581i	0.691784	−	0.308002i	0.722347	+	0.691531i	$0.243063\pi$
$60$	−3.23895	−	0.851225i	−0.418147	−	0.109893i
$61$	12.1540	+	5.41129i	1.55616	+	0.692845i	0.991212	−	0.132284i	$-0.0422311\pi$
$61$	12.1540	+	5.41129i	1.55616	+	0.692845i	0.564944	+	0.825129i	$0.308898\pi$
$62$	−2.35344	−	1.70988i	−0.298888	−	0.217155i
$63$	−3.56095	−	3.20453i	−0.448638	−	0.403733i
$64$	−6.32771	+	4.59735i	−0.790963	+	0.574668i
$65$	−1.47310	+	1.65147i	−0.182716	+	0.204840i
$66$	6.83681	+	5.53479i	0.841553	+	0.681286i
$67$	1.02420	+	0.217699i	0.125125	+	0.0265962i	0.270049	−	0.962847i	$-0.412960\pi$
$67$	1.02420	+	0.217699i	0.125125	+	0.0265962i	−0.144923	+	0.989443i	$0.546294\pi$
$68$	0.129770	−	0.224768i	0.0157369	−	0.0272572i
$69$	−2.56436	−	9.56508i	−0.308712	−	1.15150i
$70$	−1.91764	−	3.28595i	−0.229202	−	0.392746i
$71$	−5.09100	+	15.6685i	−0.604191	+	1.85951i	−0.101930	+	0.994792i	$0.532502\pi$
$71$	−5.09100	+	15.6685i	−0.604191	+	1.85951i	−0.502260	+	0.864716i	$0.667498\pi$
$72$	5.38441	+	7.40674i	0.634559	+	0.872893i
$73$	7.42742	−	5.39634i	0.869314	−	0.631594i	−0.0610888	−	0.998132i	$-0.519457\pi$
$73$	7.42742	−	5.39634i	0.869314	−	0.631594i	0.930403	+	0.366539i	$0.119457\pi$
$74$	−1.26805	−	2.19633i	−0.147408	−	0.255318i
$75$	−4.64774	+	7.30743i	−0.536675	+	0.843789i
$76$	0.655651	−	1.13562i	0.0752084	−	0.130265i
$77$	−0.795582	−	7.56945i	−0.0906649	−	0.862619i
$78$	1.80395	−	0.285971i	0.204258	−	0.0323799i
$79$	−10.9470	+	2.32686i	−1.23164	+	0.261792i	−0.777353	−	0.629065i	$-0.783438\pi$
$79$	−10.9470	+	2.32686i	−1.23164	+	0.261792i	−0.454284	+	0.890857i	$0.650105\pi$
$80$	1.06741	+	3.23374i	0.119340	+	0.361544i
$81$	7.27826	−	5.29405i	0.808695	−	0.588228i
$82$	12.0085			1.32612
$83$	3.98246	−	4.42297i	0.437132	−	0.485485i	−0.483816	−	0.875170i	$-0.660750\pi$
$83$	3.98246	−	4.42297i	0.437132	−	0.485485i	0.920948	+	0.389685i	$0.127416\pi$
$84$	0.373804	−	2.36220i	0.0407854	−	0.257737i
$85$	−0.451418	−	0.496671i	−0.0489631	−	0.0538715i
$86$	−0.847457	−	8.06302i	−0.0913837	−	0.869457i
$87$	−9.57009	+	3.67511i	−1.02602	+	0.394014i
$88$	−1.52074	+	14.4689i	−0.162111	+	1.54239i
$89$	1.01962	−	0.740795i	0.108079	−	0.0785241i	−0.532433	−	0.846472i	$-0.678722\pi$
$89$	1.01962	−	0.740795i	0.108079	−	0.0785241i	0.640512	+	0.767948i	$0.278722\pi$
$90$	6.78682	−	2.24229i	0.715394	−	0.236358i
$91$	−1.27856	−	0.928926i	−0.134029	−	0.0973779i
$92$	3.30805	−	3.67397i	0.344889	−	0.383038i
$93$	−4.72234	−	0.246840i	−0.489684	−	0.0255961i
$94$	6.07297	+	1.29085i	0.626379	+	0.133141i
$95$	−2.28075	−	2.50938i	−0.234000	−	0.257457i
$96$	−2.78105	+	7.24785i	−0.283840	+	0.739730i
$97$	1.87620	−	0.398799i	0.190499	−	0.0404919i	−0.111674	−	0.993745i	$-0.535621\pi$
$97$	1.87620	−	0.398799i	0.190499	−	0.0404919i	0.302173	+	0.953253i	$0.402288\pi$
$98$	−3.83602	+	2.78703i	−0.387496	+	0.281533i
$99$	14.2211	+	1.49077i	1.42928	+	0.149828i
$100$	−4.32327	+	0.0403405i	−0.432327	+	0.00403405i
$101$	−2.94567	−	5.10205i	−0.293105	−	0.507673i	0.681437	−	0.731877i	$-0.261355\pi$
$101$	−2.94567	−	5.10205i	−0.293105	−	0.507673i	−0.974542	+	0.224204i	$0.928022\pi$
$102$	0.0290665	+	0.553174i	0.00287801	+	0.0547724i
$103$	8.59006	+	9.54023i	0.846404	+	0.940027i	0.998833	−	0.0482876i	$-0.0153764\pi$
$103$	8.59006	+	9.54023i	0.846404	+	0.940027i	−0.152430	+	0.988314i	$0.548710\pi$
$104$	2.02136	+	2.24495i	0.198210	+	0.220135i
$105$	−5.52392	−	2.78125i	−0.539080	−	0.271422i
$106$	−1.38115	+	1.53392i	−0.134149	+	0.148988i
$107$	19.9558			1.92920			0.964600	−	0.263716i	$-0.0849480\pi$
$107$	19.9558			1.92920			0.964600	+	0.263716i	$0.0849480\pi$
$108$	4.19531	+	1.60845i	0.403693	+	0.154773i
$109$	6.54028	+	4.75180i	0.626446	+	0.455139i	0.855167	−	0.518353i	$-0.173454\pi$
$109$	6.54028	+	4.75180i	0.626446	+	0.455139i	−0.228721	+	0.973492i	$0.573454\pi$
$110$	10.3957	+	4.57047i	0.991191	+	0.435777i
$111$	−3.67351	−	1.87111i	−0.348674	−	0.177598i
$112$	−2.22164	+	0.989136i	−0.209925	+	0.0934646i
$113$	11.9044	−	5.30018i	1.11987	−	0.498599i	0.238557	−	0.971129i	$-0.423326\pi$
$113$	11.9044	−	5.30018i	1.11987	−	0.498599i	0.881315	+	0.472530i	$0.156659\pi$
$114$	0.146856	+	2.79486i	0.0137543	+	0.261763i
$115$	−6.44386	−	11.0418i	−0.600893	−	1.02965i
$116$	−4.14043	−	3.00820i	−0.384429	−	0.279304i
$117$	2.20590	−	1.98729i	0.203935	−	0.183725i
$118$	−6.19760			−0.570535
$119$	0.320714	−	0.356189i	0.0293998	−	0.0326518i
$120$	9.22282	+	7.39544i	0.841924	+	0.675108i
$121$	7.84090	+	8.70820i	0.712809	+	0.791654i
$122$	−9.48540	−	10.5346i	−0.858767	−	0.953758i
$123$	16.3699	−	10.6339i	1.47602	−	0.958826i
$124$	−1.18038	−	2.04447i	−0.106001	−	0.183599i
$125$	−3.30576	+	10.6804i	−0.295676	+	0.955288i
$126$	2.07741	+	4.66251i	0.185071	+	0.415370i
$127$	−8.64345	+	6.27983i	−0.766982	+	0.557245i	−0.901044	−	0.433728i	$-0.857198\pi$
$127$	−8.64345	+	6.27983i	−0.766982	+	0.557245i	0.134062	+	0.990973i	$0.457198\pi$
$128$	−0.616423	+	0.131025i	−0.0544846	+	0.0115811i
$129$	−8.29530	−	10.2410i	−0.730361	−	0.901668i
$130$	2.14962	−	0.969114i	0.188534	−	0.0849970i
$131$	−17.3455	−	3.68690i	−1.51548	−	0.322126i	−0.626266	−	0.779610i	$-0.715417\pi$
$131$	−17.3455	−	3.68690i	−1.51548	−	0.322126i	−0.889218	+	0.457484i	$0.848751\pi$
$132$	3.24169	+	6.36002i	0.282153	+	0.553568i
$133$	1.62038	−	1.79961i	0.140505	−	0.156046i
$134$	−0.902595	−	0.655773i	−0.0779723	−	0.0566502i
$135$	7.26612	−	9.06662i	0.625368	−	0.780330i
$136$	−0.741200	+	0.538513i	−0.0635574	+	0.0461771i
$137$	1.79963	−	17.1223i	0.153753	−	1.46286i	−0.596981	−	0.802255i	$-0.703633\pi$
$137$	1.79963	−	17.1223i	0.153753	−	1.46286i	0.750734	−	0.660605i	$-0.229700\pi$
$138$	−1.64921	+	10.4219i	−0.140390	+	0.887171i
$139$	0.899749	+	8.56054i	0.0763157	+	0.726095i	0.964047	+	0.265733i	$0.0856139\pi$
$139$	0.899749	+	8.56054i	0.0763157	+	0.726095i	−0.887731	+	0.460363i	$0.847719\pi$
$140$	−0.337057	−	3.06908i	−0.0284865	−	0.259384i
$141$	9.42170	−	3.61813i	0.793450	−	0.304702i
$142$	11.7460	−	13.0452i	0.985699	−	1.09473i
$143$	4.71719			0.394471
$144$	−0.951122	−	4.46867i	−0.0792602	−	0.372389i
$145$	−10.6706	+	7.82898i	−0.886147	+	0.650161i
$146$	−9.56845	+	2.03384i	−0.791891	+	0.168322i
$147$	−2.76122	+	7.19617i	−0.227742	+	0.593530i
$148$	−0.215132	−	2.04685i	−0.0176838	−	0.168250i
$149$	−4.79551	+	8.30607i	−0.392863	+	0.680460i	−0.992826	−	0.119569i	$-0.961849\pi$
$149$	−4.79551	+	8.30607i	−0.392863	+	0.680460i	0.599962	+	0.800028i	$0.295182\pi$
$150$	7.69097	−	5.09874i	0.627965	−	0.416310i
$151$	−7.37063	−	12.7663i	−0.599814	−	1.03891i	−0.992848	−	0.119384i	$-0.961908\pi$
$151$	−7.37063	−	12.7663i	−0.599814	−	1.03891i	0.393034	−	0.919524i	$-0.371425\pi$
$152$	−3.74484	+	2.72079i	−0.303747	+	0.220685i
$153$	0.529476	+	0.728342i	0.0428056	+	0.0588830i
$154$	−2.50605	+	7.71282i	−0.201943	+	0.621517i
$155$	−5.96545	+	1.29711i	−0.479157	+	0.104187i
$156$	1.43179	+	0.383437i	0.114635	+	0.0306995i
$157$	−6.76957	+	11.7252i	−0.540270	+	0.935775i	0.458618	+	0.888634i	$0.348345\pi$
$157$	−6.76957	+	11.7252i	−0.540270	+	0.935775i	−0.998888	+	0.0471419i	$0.984989\pi$
$158$	11.6641	+	2.47929i	0.927950	+	0.197242i
$159$	−0.524434	+	3.31408i	−0.0415903	+	0.262823i
$160$	−1.00108	+	9.97198i	−0.0791425	+	0.788354i
$161$	7.38623	−	5.36641i	0.582116	−	0.422932i
$162$	−9.37893	+	1.99891i	−0.736878	+	0.157050i
$163$	2.23732	+	1.62551i	0.175240	+	0.127320i	0.671948	−	0.740598i	$-0.265458\pi$
$163$	2.23732	+	1.62551i	0.175240	+	0.127320i	−0.496708	+	0.867918i	$0.665458\pi$
$164$	8.90273	+	3.96375i	0.695187	+	0.309517i
$165$	18.2186	−	2.97530i	1.41832	−	0.231627i
$166$	−5.79333	+	2.57935i	−0.449649	+	0.200197i
$167$	−2.90321	−	0.617096i	−0.224657	−	0.0477524i	0.0942076	−	0.995553i	$-0.469968\pi$
$167$	−2.90321	−	0.617096i	−0.224657	−	0.0477524i	−0.318865	+	0.947800i	$0.603302\pi$
$168$	−4.59703	+	7.08093i	−0.354669	+	0.546305i
$169$	−8.04330	+	8.93299i	−0.618715	+	0.687153i
$170$	0.224158	+	0.679090i	0.0171921	+	0.0520838i
$171$	2.67513	+	3.67988i	0.204572	+	0.281408i
$172$	2.03315	−	6.25741i	0.155027	−	0.477123i
$173$	−11.4424	−	5.09449i	−0.869951	−	0.387327i	−0.0773039	−	0.997008i	$-0.524631\pi$
$173$	−11.4424	−	5.09449i	−0.869951	−	0.387327i	−0.792647	+	0.609680i	$0.791298\pi$
$174$	10.9082	+	0.570176i	0.826945	+	0.0432250i
$175$	−7.82494	−	1.58708i	−0.591510	−	0.119972i
$176$	3.62939	−	6.28628i	0.273575	−	0.473846i
$177$	−8.44851	+	5.48817i	−0.635029	+	0.412516i
$178$	−1.31353	+	0.279200i	−0.0984533	+	0.0209269i
$179$	−3.60018	+	11.0802i	−0.269090	+	0.828174i	0.721633	+	0.692276i	$0.243392\pi$
$179$	−3.60018	+	11.0802i	−0.269090	+	0.828174i	−0.990723	+	0.135898i	$0.956608\pi$
$180$	5.77168	+	0.577822i	0.430196	+	0.0430683i
$181$	−6.84051	−	21.0529i	−0.508451	−	1.56485i	−0.794891	−	0.606752i	$-0.792472\pi$
$181$	−6.84051	−	21.0529i	−0.508451	−	1.56485i	0.286440	−	0.958098i	$-0.407528\pi$
$182$	0.841955	+	1.45831i	0.0624099	+	0.108097i
$183$	−22.2591	−	5.96105i	−1.64544	−	0.440654i
$184$	−15.9428	+	7.09820i	−1.17532	+	0.523286i
$185$	−5.21104	−	1.08226i	−0.383123	−	0.0795691i
$186$	4.48971	+	2.28685i	0.329201	+	0.167680i
$187$	−0.149542	+	1.42280i	−0.0109356	+	0.104045i
$188$	4.07623	+	2.96156i	0.297290	+	0.215994i
$189$	6.96071	+	4.51628i	0.506317	+	0.328511i
$190$	1.13254	+	3.43104i	0.0821629	+	0.248914i
$191$	−1.19373	+	11.3576i	−0.0863753	+	0.821806i	0.862479	+	0.506092i	$0.168911\pi$
$191$	−1.19373	+	11.3576i	−0.0863753	+	0.821806i	−0.948855	+	0.315714i	$0.897756\pi$
$192$	9.57800	−	9.58062i	0.691233	−	0.691422i
$193$	8.87230	−	15.3673i	0.638642	−	1.10616i	−0.347089	−	0.937832i	$-0.612830\pi$
$193$	8.87230	−	15.3673i	0.638642	−	1.10616i	0.985731	−	0.168328i	$-0.0538369\pi$
$194$	−1.99911	−	0.424923i	−0.143527	−	0.0305077i
$195$	2.07216	−	3.22464i	0.148391	−	0.230922i
$196$	−3.76385	+	0.800031i	−0.268846	+	0.0571450i
$197$	−2.97775	+	9.16457i	−0.212156	+	0.652948i	0.787187	+	0.616714i	$0.211536\pi$
$197$	−2.97775	+	9.16457i	−0.212156	+	0.652948i	−0.999343	+	0.0362347i	$0.988464\pi$
$198$	−13.1966	−	7.61426i	−0.937843	−	0.541122i
$199$	3.11193			0.220599			0.110299	−	0.993898i	$-0.464819\pi$
$199$	3.11193			0.220599			0.110299	+	0.993898i	$0.464819\pi$
$200$	13.9996	+	6.07716i	0.989923	+	0.429720i
$201$	−1.81112	−	0.0946683i	−0.127746	−	0.00667738i
$202$	0.656153	+	6.24288i	0.0461668	+	0.439248i
$203$	−6.32415	−	7.02368i	−0.443868	−	0.492966i
$204$	−0.161042	+	0.419701i	−0.0112752	+	0.0293849i
$205$	16.7752	−	18.8064i	1.17163	−	1.31350i
$206$	−4.22692	−	13.0091i	−0.294504	−	0.906389i
$207$	6.98074	+	15.6675i	0.485195	+	1.08896i
$208$	−0.465755	−	1.43345i	−0.0322943	−	0.0993917i
$209$	−0.755547	+	7.18855i	−0.0522623	+	0.497242i
$210$	4.17159	+	5.10120i	0.287867	+	0.352016i
$211$	−0.896864	−	8.53309i	−0.0617427	−	0.587442i	−0.981030	−	0.193856i	$-0.937901\pi$
$211$	−0.896864	−	8.53309i	−0.0617427	−	0.587442i	0.919287	−	0.393587i	$-0.128766\pi$
$212$	−1.53026	+	0.681315i	−0.105099	+	0.0467929i
$213$	4.46004	−	28.1845i	0.305597	−	1.93117i
$214$	−19.4248	−	8.64847i	−1.32785	−	0.591197i
$215$	−13.8113	−	9.93637i	−0.941921	−	0.677655i
$216$	−11.2197	−	11.2105i	−0.763401	−	0.762775i
$217$	−1.34721	−	4.14630i	−0.0914549	−	0.281469i
$218$	−4.30691	−	7.45979i	−0.291701	−	0.505241i
$219$	−11.2426	+	11.2457i	−0.759704	+	0.759912i
$220$	6.19844	+	6.81981i	0.417899	+	0.459792i
$221$	0.198770	+	0.220757i	0.0133707	+	0.0148497i
$222$	2.76485	+	3.41335i	0.185565	+	0.229089i
$223$	−10.8831	−	4.84546i	−0.728785	−	0.324476i	0.00858684	−	0.999963i	$-0.497267\pi$
$223$	−10.8831	−	4.84546i	−0.728785	−	0.324476i	−0.737372	+	0.675487i	$0.763933\pi$
$224$	−7.15712			−0.478205
$225$	5.96916	−	13.7611i	0.397944	−	0.917410i
$226$	−13.8846			−0.923591
$227$	−20.2359	−	9.00961i	−1.34310	−	0.597989i	−0.395804	−	0.918335i	$-0.629534\pi$
$227$	−20.2359	−	9.00961i	−1.34310	−	0.597989i	−0.947300	+	0.320347i	$0.896201\pi$
$228$	−0.813651	+	2.12050i	−0.0538853	+	0.140433i
$229$	−10.1750	−	11.3005i	−0.672386	−	0.746760i	0.306343	−	0.951921i	$-0.400895\pi$
$229$	−10.1750	−	11.3005i	−0.672386	−	0.746760i	−0.978728	+	0.205161i	$0.934228\pi$
$230$	1.48708	+	13.5406i	0.0980550	+	0.892842i
$231$	3.41373	+	12.7332i	0.224607	+	0.837785i
$232$	9.03298	+	15.6456i	0.593044	+	1.02718i
$233$	−4.57150	−	14.0696i	−0.299489	−	0.921732i	−0.981677	−	0.190555i	$-0.938971\pi$
$233$	−4.57150	−	14.0696i	−0.299489	−	0.921732i	0.682188	−	0.731177i	$-0.261029\pi$
$234$	−3.00845	+	0.978416i	−0.196669	+	0.0639610i
$235$	10.5052	−	7.70759i	0.685282	−	0.502788i
$236$	−4.59471	−	2.04570i	−0.299090	−	0.133164i
$237$	18.0959	−	6.94922i	1.17546	−	0.451401i
$238$	−0.466546	+	0.207720i	−0.0302417	+	0.0134645i
$239$	0.530735	+	5.04960i	0.0343304	+	0.326632i	0.998186	+	0.0602064i	$0.0191759\pi$
$239$	0.530735	+	5.04960i	0.0343304	+	0.326632i	−0.963856	+	0.266425i	$0.914157\pi$
$240$	−2.70296	−	5.24246i	−0.174475	−	0.338400i
$241$	−1.40061	+	13.3259i	−0.0902211	+	0.858397i	0.852031	+	0.523492i	$0.175371\pi$
$241$	−1.40061	+	13.3259i	−0.0902211	+	0.858397i	−0.942252	+	0.334905i	$0.891296\pi$
$242$	−3.85828	−	11.8746i	−0.248020	−	0.763326i
$243$	−11.0152	+	11.0302i	−0.706623	+	0.707590i
$244$	−3.55494	−	10.9410i	−0.227581	−	0.700424i
$245$	−0.993945	+	9.90088i	−0.0635008	+	0.632544i
$246$	−20.5428	+	3.25654i	−1.30976	+	0.207629i
$247$	1.00427	+	1.11535i	0.0639001	+	0.0709682i
$248$	0.871082	+	8.28779i	0.0553137	+	0.526275i
$249$	−5.61331	+	8.64632i	−0.355729	+	0.547939i
$250$	7.84650	−	8.96359i	0.496256	−	0.566907i
$251$	25.6881			1.62142			0.810709	−	0.585450i	$-0.199082\pi$
$251$	25.6881			1.62142			0.810709	+	0.585450i	$0.199082\pi$
$252$	0.00113289	+	4.14236i	7.13654e−5	+	0.260944i
$253$	−8.42108	+	25.9174i	−0.529429	+	1.62941i
$254$	11.1350	−	2.36682i	0.698673	−	0.148507i
$255$	0.906926	+	0.727231i	0.0567939	+	0.0455409i
$256$	15.9579	+	3.39196i	0.997370	+	0.211997i
$257$	−9.78552	+	16.9490i	−0.610404	+	1.05725i	0.380768	+	0.924670i	$0.375660\pi$
$257$	−9.78552	+	16.9490i	−0.610404	+	1.05725i	−0.991172	+	0.132580i	$0.957674\pi$
$258$	3.63632	+	13.5635i	0.226387	+	0.844426i
$259$	0.397291	−	3.77997i	0.0246865	−	0.234876i
$260$	1.91355	−	0.00892748i	0.118673	−	0.000553659i
$261$	15.3748	−	8.88225i	0.951677	−	0.549798i
$262$	15.2861	+	11.1060i	0.944379	+	0.686131i
$263$	0.779304	−	7.41458i	0.0480540	−	0.457203i	−0.943865	−	0.330331i	$-0.892840\pi$
$263$	0.779304	−	7.41458i	0.0480540	−	0.457203i	0.991919	−	0.126872i	$-0.0404937\pi$
$264$	−1.32225	−	25.1641i	−0.0813787	−	1.54875i
$265$	0.472879	+	4.30581i	0.0290487	+	0.264504i
$266$	−2.35718	+	1.04948i	−0.144528	+	0.0643481i
$267$	−1.54335	+	1.54378i	−0.0944517	+	0.0944776i
$268$	−0.452699	−	0.784098i	−0.0276530	−	0.0478964i
$269$	−1.24097	−	3.81931i	−0.0756631	−	0.232867i	0.906071	−	0.423126i	$-0.139067\pi$
$269$	−1.24097	−	3.81931i	−0.0756631	−	0.232867i	−0.981734	+	0.190259i	$0.939067\pi$
$270$	−11.0021	+	5.67636i	−0.669565	+	0.345452i
$271$	7.44164	−	22.9030i	0.452047	−	1.39126i	−0.422519	−	0.906354i	$-0.638854\pi$
$271$	7.44164	−	22.9030i	0.452047	−	1.39126i	0.874567	−	0.484905i	$-0.161146\pi$
$272$	0.447121	−	0.0950385i	0.0271107	−	0.00576256i
$273$	2.43913	+	1.24238i	0.147623	+	0.0751920i
$274$	−9.17224	+	15.8868i	−0.554115	+	0.959756i
$275$	21.6800	−	9.89595i	1.30735	−	0.596748i
$276$	−4.66272	+	7.18212i	−0.280663	+	0.432313i
$277$	16.8715	+	7.51166i	1.01371	+	0.451332i	0.845246	−	0.534377i	$-0.179454\pi$
$277$	16.8715	+	7.51166i	1.01371	+	0.451332i	0.168461	+	0.985708i	$0.446120\pi$
$278$	2.83417	−	8.72268i	0.169982	−	0.523152i
$279$	8.14540	−	0.858369i	0.487653	−	0.0513892i
$280$	−3.31956	+	10.3811i	−0.198382	+	0.620390i
$281$	−4.37061	+	4.85406i	−0.260729	+	0.289569i	−0.859269	−	0.511524i	$-0.829081\pi$
$281$	−4.37061	+	4.85406i	−0.260729	+	0.289569i	0.598540	+	0.801093i	$0.295748\pi$
$282$	−10.7390	−	0.561336i	−0.639499	−	0.0334271i
$283$	24.3288	+	5.17125i	1.44620	+	0.307399i	0.863112	−	0.505013i	$-0.168512\pi$
$283$	24.3288	+	5.17125i	1.44620	+	0.307399i	0.583085	+	0.812411i	$0.301845\pi$
$284$	13.0141	−	5.79423i	0.772242	−	0.343824i
$285$	4.58216	+	3.67427i	0.271424	+	0.217645i
$286$	−4.59166	−	2.04434i	−0.271511	−	0.120884i
$287$	14.5598	+	10.5783i	0.859435	+	0.624416i
$288$	2.79200	−	13.1530i	0.164520	−	0.775048i
$289$	13.6804	−	9.93939i	0.804730	−	0.584670i
$290$	13.7796	−	2.99620i	0.809167	−	0.175943i
$291$	−3.10145	+	1.19102i	−0.181810	+	0.0698188i
$292$	−7.76509	−	1.65052i	−0.454417	−	0.0965894i
$293$	3.51196	−	6.08289i	0.205171	−	0.355366i	−0.745016	−	0.667046i	$-0.767558\pi$
$293$	3.51196	−	6.08289i	0.205171	−	0.355366i	0.950187	+	0.311680i	$0.100892\pi$
$294$	5.80643	−	5.80802i	0.338638	−	0.338730i
$295$	−8.65768	+	9.70601i	−0.504070	+	0.565106i
$296$	−2.24505	+	6.90956i	−0.130491	+	0.401610i
$297$	−24.7322	+	1.30633i	−1.43511	+	0.0758011i
$298$	8.26760	−	6.00676i	0.478929	−	0.347962i
$299$	2.82923	+	4.90036i	0.163618	+	0.283395i
$300$	7.38484	−	1.24142i	0.426364	−	0.0716736i
$301$	6.07521	−	10.5226i	0.350169	−	0.606511i
$302$	1.64182	+	15.6209i	0.0944763	+	0.898882i
$303$	6.42273	+	7.92920i	0.368976	+	0.455520i
$304$	2.25904	−	0.480173i	0.129565	−	0.0275398i
$305$	−29.7487	+	0.138790i	−1.70341	+	0.00794708i
$306$	−0.199737	−	0.938426i	−0.0114182	−	0.0536462i
$307$	20.8173			1.18810			0.594052	−	0.804427i	$-0.297527\pi$
$307$	20.8173			1.18810			0.594052	+	0.804427i	$0.297527\pi$
$308$	−4.40375	+	4.89086i	−0.250927	+	0.278683i
$309$	−17.2821	−	13.9909i	−0.983145	−	0.795912i
$310$	6.36886	+	1.32272i	0.361727	+	0.0751253i
$311$	0.714248	+	6.79561i	0.0405013	+	0.385344i	0.995931	+	0.0901238i	$0.0287263\pi$
$311$	0.714248	+	6.79561i	0.0405013	+	0.385344i	−0.955429	+	0.295220i	$0.904607\pi$
$312$	−4.06671	−	3.29224i	−0.230232	−	0.186386i
$313$	−3.31544	+	31.5443i	−0.187400	+	1.78299i	0.347108	+	0.937825i	$0.387164\pi$
$313$	−3.31544	+	31.5443i	−0.187400	+	1.78299i	−0.534507	+	0.845164i	$0.679503\pi$
$314$	11.6709	−	8.47942i	0.658628	−	0.478522i
$315$	10.2040	+	3.25984i	0.574928	+	0.183671i
$316$	7.82908	+	5.68816i	0.440420	+	0.319984i
$317$	5.22722	−	5.80542i	0.293590	−	0.326065i	−0.578246	−	0.815862i	$-0.696263\pi$
$317$	5.22722	−	5.80542i	0.293590	−	0.326065i	0.871836	+	0.489797i	$0.162929\pi$
$318$	1.94674	−	2.99861i	0.109168	−	0.168154i
$319$	27.5941	+	5.86531i	1.54497	+	0.328394i
$320$	8.67392	−	15.1869i	0.484887	−	0.848971i
$321$	−34.1382	+	5.41174i	−1.90541	+	0.302054i
$322$	−9.51538	+	2.02256i	−0.530271	+	0.112713i
$323$	−0.368249	+	0.267549i	−0.0204899	+	0.0148868i
$324$	−7.61305	−	1.61385i	−0.422947	−	0.0896585i
$325$	1.48517	−	4.72030i	0.0823825	−	0.261835i
$326$	−1.47332	−	2.55186i	−0.0815996	−	0.141335i
$327$	−12.4770	−	6.35521i	−0.689981	−	0.351444i
$328$	−23.0185	−	25.5646i	−1.27098	−	1.41157i
$329$	6.22609	+	6.91477i	0.343256	+	0.381224i
$330$	−19.0233	−	4.99948i	−1.04720	−	0.275212i
$331$	−14.3709	+	15.9605i	−0.789894	+	0.877266i	−0.994835	−	0.101508i	$-0.967633\pi$
$331$	−14.3709	+	15.9605i	−0.789894	+	0.877266i	0.204941	+	0.978774i	$0.434300\pi$
$332$	−5.14639			−0.282445
$333$	6.79166	+	2.20469i	0.372180	+	0.120816i
$334$	2.55852	+	1.85887i	0.139996	+	0.101713i
$335$	−2.28787	+	0.497470i	−0.125000	+	0.0271797i
$336$	3.53229	−	2.29458i	0.192702	−	0.125180i
$337$	−15.6867	+	6.98418i	−0.854511	+	0.380453i	−0.786767	−	0.617250i	$-0.788247\pi$
$337$	−15.6867	+	6.98418i	−0.854511	+	0.380453i	−0.0677437	+	0.997703i	$0.521580\pi$
$338$	11.7007	−	5.20947i	0.636432	−	0.283358i
$339$	−18.9274	+	12.2953i	−1.02799	+	0.667788i
$340$	−0.0579697	+	0.577447i	−0.00314385	+	0.0313164i
$341$	10.5277	+	7.64880i	0.570106	+	0.414206i
$342$	−1.00915	−	4.74131i	−0.0545687	−	0.256381i
$343$	−18.2841			−0.987246
$344$	−15.5408	+	17.2598i	−0.837901	+	0.930584i
$345$	14.0178	+	17.1416i	0.754694	+	0.922873i
$346$	8.93008	+	9.91786i	0.480084	+	0.533188i
$347$	12.4606	+	13.8389i	0.668920	+	0.742911i	0.978110	−	0.208089i	$-0.0667244\pi$
$347$	12.4606	+	13.8389i	0.668920	+	0.742911i	−0.309190	+	0.951000i	$0.600058\pi$
$348$	7.89877	+	4.02327i	0.423419	+	0.215670i
$349$	−8.55166	−	14.8119i	−0.457760	−	0.792863i	0.541083	−	0.840969i	$-0.318015\pi$
$349$	−8.55166	−	14.8119i	−0.457760	−	0.792863i	−0.998842	+	0.0481065i	$0.984681\pi$
$350$	6.92891	+	4.93603i	0.370366	+	0.263842i
$351$	−3.23468	+	3.99785i	−0.172654	+	0.213389i
$352$	17.2829	−	12.5568i	0.921182	−	0.669278i
$353$	19.6474	−	4.17618i	1.04573	−	0.222276i	0.347148	−	0.937810i	$-0.387150\pi$
$353$	19.6474	−	4.17618i	1.04573	−	0.222276i	0.698577	+	0.715535i	$0.253817\pi$
$354$	10.6022	−	1.68070i	0.563499	−	0.0893284i
$355$	−4.02159	−	36.6187i	−0.213444	−	1.94352i
$356$	−1.06597	−	0.226579i	−0.0564963	−	0.0120087i
$357$	−0.452049	+	0.696303i	−0.0239250	+	0.0368523i
$358$	8.30633	−	9.22512i	0.439003	−	0.487563i
$359$	−3.71885	−	2.70190i	−0.196273	−	0.142601i	0.485308	−	0.874343i	$-0.338707\pi$
$359$	−3.71885	−	2.70190i	−0.196273	−	0.142601i	−0.681581	+	0.731742i	$0.738707\pi$
$360$	−17.7829	−	10.1502i	−0.937242	−	0.534963i
$361$	13.5108	−	9.81615i	0.711094	−	0.516640i
$362$	−2.46546	+	23.4572i	−0.129581	+	1.23289i
$363$	−15.7749	−	12.7707i	−0.827967	−	0.670287i
$364$	0.142843	+	1.35906i	0.00748700	+	0.0712340i
$365$	−10.1814	+	17.8262i	−0.532918	+	0.933068i
$366$	19.0834	+	15.4491i	0.997506	+	0.807538i
$367$	11.7878	−	13.0917i	0.615318	−	0.683380i	−0.352275	−	0.935897i	$-0.614592\pi$
$367$	11.7878	−	13.0917i	0.615318	−	0.683380i	0.967592	+	0.252517i	$0.0812583\pi$
$368$	8.70719			0.453894
$369$	−25.1200	+	22.6306i	−1.30769	+	1.17810i
$370$	4.60335	+	3.31183i	0.239317	+	0.172174i
$371$	−3.02581	+	0.643156i	−0.157092	+	0.0333910i
$372$	2.57369	+	3.17736i	0.133440	+	0.164738i
$373$	−1.05604	−	10.0475i	−0.0546795	−	0.520240i	−0.987241	−	0.159230i	$-0.949099\pi$
$373$	−1.05604	−	10.0475i	−0.0546795	−	0.520240i	0.932562	−	0.361010i	$-0.117568\pi$
$374$	0.762176	−	1.32013i	0.0394112	−	0.0682621i
$375$	2.75873	−	19.1674i	0.142460	−	0.989800i
$376$	−8.89292	−	15.4030i	−0.458618	−	0.794349i
$377$	4.73894	−	3.44304i	0.244068	−	0.177326i
$378$	−4.81822	−	7.41275i	−0.247822	−	0.381270i
$379$	6.82808	−	21.0147i	0.350735	−	1.07945i	−0.607707	−	0.794162i	$-0.707910\pi$
$379$	6.82808	−	21.0147i	0.350735	−	1.07945i	0.958442	−	0.285289i	$-0.0920896\pi$
$380$	−0.292886	+	2.91750i	−0.0150248	+	0.149664i
$381$	13.0832	−	13.0868i	0.670275	−	0.670458i
$382$	6.08413	−	10.5380i	0.311291	−	0.539172i
$383$	−7.60202	−	1.61586i	−0.388445	−	0.0825666i	0.00954918	−	0.999954i	$-0.496960\pi$
$383$	−7.60202	−	1.61586i	−0.388445	−	0.0825666i	−0.397994	+	0.917388i	$0.630294\pi$
$384$	1.01898	−	0.391308i	0.0519994	−	0.0199689i
$385$	8.57819	+	14.6991i	0.437185	+	0.749134i
$386$	−15.2961	+	11.1133i	−0.778551	+	0.565650i
$387$	16.9679	+	15.2696i	0.862527	+	0.776196i
$388$	−1.34182	−	0.974889i	−0.0681205	−	0.0494925i
$389$	−11.4424	−	5.09450i	−0.580154	−	0.258301i	0.0956104	−	0.995419i	$-0.469520\pi$
$389$	−11.4424	−	5.09450i	−0.580154	−	0.258301i	−0.675764	+	0.737118i	$0.736186\pi$
$390$	−3.41452	+	2.24080i	−0.172901	+	0.113467i
$391$	−1.56774	+	0.698001i	−0.0792839	+	0.0352995i
$392$	13.2863	+	2.82410i	0.671061	+	0.142638i
$393$	30.6726	+	1.60328i	1.54723	+	0.0808746i
$394$	6.87026	−	7.63020i	0.346119	−	0.384404i
$395$	20.1769	−	14.8037i	1.01521	−	0.744855i
$396$	−7.27027	−	10.0009i	−0.365345	−	0.502565i
$397$	−8.80399	+	27.0959i	−0.441859	+	1.35990i	0.444032	+	0.896011i	$0.353548\pi$
$397$	−8.80399	+	27.0959i	−0.441859	+	1.35990i	−0.885891	+	0.463893i	$0.846452\pi$
$398$	−3.02912	−	1.34865i	−0.151836	−	0.0676019i
$399$	−2.28394	+	3.51801i	−0.114340	+	0.176121i
$400$	−5.14775	−	5.61097i	−0.257387	−	0.280549i
$401$	4.38488	−	7.59484i	0.218971	−	0.379268i	−0.735523	−	0.677500i	$-0.763063\pi$
$401$	4.38488	−	7.59484i	0.218971	−	0.379268i	0.954494	+	0.298232i	$0.0963968\pi$
$402$	1.72190	+	0.877053i	0.0858804	+	0.0437434i
$403$	2.64297	−	0.561780i	0.131655	−	0.0279842i
$404$	−1.57419	+	4.84487i	−0.0783190	+	0.241041i
$405$	−9.97133	+	17.4806i	−0.495479	+	0.868620i
$406$	3.11193	+	9.57755i	0.154443	+	0.475326i
$407$	5.67237	+	9.82484i	0.281169	+	0.486999i
$408$	1.12193	−	1.12223i	0.0555436	−	0.0555588i
$409$	−10.5929	+	4.71627i	−0.523786	+	0.233205i	−0.651558	−	0.758599i	$-0.725884\pi$
$409$	−10.5929	+	4.71627i	−0.523786	+	0.233205i	0.127772	+	0.991804i	$0.459218\pi$
$410$	−24.4791	+	11.0359i	−1.20894	+	0.545026i
$411$	1.56474	+	29.7790i	0.0771828	+	1.46889i
$412$	1.16033	−	11.0398i	0.0571654	−	0.543892i
$413$	−7.51431	−	5.45947i	−0.369755	−	0.268643i
$414$	−0.00499826	−	18.2759i	−0.000245651	−	0.898210i
$415$	−4.05343	+	12.6761i	−0.198975	+	0.622245i
$416$	0.463667	−	4.41149i	0.0227331	−	0.216291i
$417$	−3.86069	−	14.4004i	−0.189059	−	0.705192i
$418$	3.85082	−	6.66982i	0.188350	−	0.326232i
$419$	28.0034	+	5.95230i	1.36806	+	0.290789i	0.832647	−	0.553804i	$-0.186824\pi$
$419$	28.0034	+	5.95230i	1.36806	+	0.290789i	0.535408	+	0.844593i	$0.320158\pi$
$420$	1.40889	+	5.15883i	0.0687469	+	0.251725i
$421$	13.6168	−	2.89433i	0.663640	−	0.141061i	0.136237	−	0.990676i	$-0.456499\pi$
$421$	13.6168	−	2.89433i	0.663640	−	0.141061i	0.527403	+	0.849615i	$0.323166\pi$
$422$	−2.82508	+	8.69471i	−0.137523	+	0.423252i
$423$	−15.1364	+	8.74453i	−0.735958	+	0.425174i
$424$	5.91300			0.287160
$425$	1.37665	+	0.597597i	0.0667775	+	0.0289877i
$426$	−16.5560	+	25.5016i	−0.802141	+	1.23556i
$427$	−2.22069	−	21.1284i	−0.107467	−	1.02248i
$428$	−11.5463	−	12.8234i	−0.558110	−	0.619844i
$429$	−8.06964	+	1.27924i	−0.389606	+	0.0617621i
$430$	9.13753	+	15.6575i	0.440651	+	0.755072i
$431$	−3.32930	−	10.2465i	−0.160367	−	0.493559i	0.838298	−	0.545212i	$-0.183551\pi$
$431$	−3.32930	−	10.2465i	−0.160367	−	0.493559i	−0.998665	+	0.0516534i	$0.983551\pi$
$432$	2.83892	+	7.38657i	0.136587	+	0.355387i
$433$	−3.22740	−	9.93293i	−0.155099	−	0.477346i	0.843072	−	0.537801i	$-0.180745\pi$
$433$	−3.22740	−	9.93293i	−0.155099	−	0.477346i	−0.998171	+	0.0604550i	$0.980745\pi$
$434$	−0.485563	+	4.61982i	−0.0233078	+	0.221759i
$435$	16.1310	−	16.2867i	0.773422	−	0.780886i
$436$	−0.730693	−	6.95208i	−0.0349939	−	0.332944i
$437$	−7.92085	+	3.52659i	−0.378906	+	0.168700i
$438$	15.8171	−	6.07410i	0.755770	−	0.290232i
$439$	24.0422	+	10.7043i	1.14747	+	0.510887i	0.890253	−	0.455466i	$-0.150527\pi$
$439$	24.0422	+	10.7043i	1.14747	+	0.510887i	0.257219	+	0.966353i	$0.417194\pi$
$440$	−10.1970	−	30.8921i	−0.486125	−	1.47272i
$441$	2.77209	−	13.0592i	0.132004	−	0.621867i
$442$	−0.0978092	−	0.301026i	−0.00465231	−	0.0143183i
$443$	−1.09162	−	1.89074i	−0.0518643	−	0.0898316i	0.838928	−	0.544243i	$-0.183183\pi$
$443$	−1.09162	−	1.89074i	−0.0518643	−	0.0898316i	−0.890792	+	0.454411i	$0.849850\pi$
$444$	0.923102	+	3.44318i	0.0438085	+	0.163406i
$445$	−1.39767	+	2.44714i	−0.0662561	+	0.116005i
$446$	8.49355	+	9.43304i	0.402181	+	0.446668i
$447$	5.95114	−	15.5096i	0.281479	−	0.733578i
$448$	11.4099	+	5.08003i	0.539069	+	0.240009i
$449$	−32.5364			−1.53549			−0.767743	−	0.640758i	$-0.778620\pi$
$449$	−32.5364			−1.53549			−0.767743	+	0.640758i	$0.778620\pi$
$450$	−11.7741	+	10.8080i	−0.555039	+	0.509496i
$451$	−53.7176			−2.52946
$452$	−10.2936	−	4.58302i	−0.484172	−	0.215567i
$453$	16.0709	+	19.8404i	0.755077	+	0.932182i
$454$	15.7928	+	17.5397i	0.741195	+	0.823180i
$455$	3.46001	+	0.718593i	0.162208	+	0.0336882i
$456$	5.66842	−	5.66997i	0.265448	−	0.265521i
$457$	−10.4827	−	18.1566i	−0.490360	−	0.849328i	0.509579	−	0.860424i	$-0.329801\pi$
$457$	−10.4827	−	18.1566i	−0.490360	−	0.849328i	−0.999938	+	0.0110963i	$0.996468\pi$
$458$	5.00685	+	15.4095i	0.233955	+	0.720038i
$459$	−1.10329	−	1.10238i	−0.0514969	−	0.0514547i
$460$	−3.36700	+	10.5295i	−0.156987	+	0.490939i
$461$	13.3684	+	5.95197i	0.622626	+	0.277211i	0.693705	−	0.720260i	$-0.255977\pi$
$461$	13.3684	+	5.95197i	0.622626	+	0.277211i	−0.0710784	+	0.997471i	$0.522644\pi$
$462$	2.19546	−	13.8738i	0.102142	−	0.645470i
$463$	−24.2009	+	10.7749i	−1.12471	+	0.500753i	−0.882896	−	0.469569i	$-0.844409\pi$
$463$	−24.2009	+	10.7749i	−1.12471	+	0.500753i	−0.241814	+	0.970323i	$0.577743\pi$
$464$	−0.942191	−	8.96434i	−0.0437401	−	0.416159i
$465$	9.85327	−	3.83671i	0.456935	−	0.177923i
$466$	−1.64766	+	15.6764i	−0.0763264	+	0.726197i
$467$	−6.73062	−	20.7147i	−0.311456	−	0.958562i	−0.977189	−	0.212372i	$-0.931881\pi$
$467$	−6.73062	−	20.7147i	−0.311456	−	0.958562i	0.665733	−	0.746190i	$-0.268119\pi$
$468$	−2.55333	−	0.267660i	−0.118028	−	0.0123726i
$469$	−0.516684	−	1.59019i	−0.0238583	−	0.0734282i
$470$	−13.5660	+	2.94975i	−0.625751	+	0.136062i
$471$	8.40090	−	21.8940i	0.387093	−	1.00882i
$472$	11.8799	+	13.1940i	0.546816	+	0.607301i
$473$	3.79094	+	36.0683i	0.174307	+	1.65842i
$474$	−20.6261	−	1.07814i	−0.947387	−	0.0495206i
$475$	6.95542	+	3.01931i	0.319136	+	0.138535i
$476$	−0.414447			−0.0189962
$477$	−0.00158940	−	5.81158i	−7.27738e−5	−	0.266094i
$478$	1.67179	−	5.14524i	0.0764660	−	0.235338i
$479$	−6.19057	+	1.31585i	−0.282854	+	0.0601225i	−0.347154	−	0.937808i	$-0.612852\pi$
$479$	−6.19057	+	1.31585i	−0.282854	+	0.0601225i	0.0642999	+	0.997931i	$0.479519\pi$
$480$	−0.991723	−	17.3304i	−0.0452657	−	0.791023i
$481$	2.30415	+	0.489763i	0.105060	+	0.0223313i
$482$	7.13853	−	12.3643i	0.325151	−	0.563178i
$483$	−11.1802	+	11.1833i	−0.508719	+	0.508858i
$484$	1.05913	−	10.0770i	0.0481425	−	0.458045i
$485$	−3.45810	+	2.53719i	−0.157024	+	0.115208i
$486$	15.5024	−	5.96296i	0.703201	−	0.270485i
$487$	−18.7250	−	13.6045i	−0.848512	−	0.616480i	0.0762233	−	0.997091i	$-0.475714\pi$
$487$	−18.7250	−	13.6045i	−0.848512	−	0.616480i	−0.924735	+	0.380611i	$0.875714\pi$
$488$	−4.24480	+	40.3866i	−0.192153	+	1.82821i
$489$	−4.26817	−	2.17401i	−0.193013	−	0.0983120i
$490$	5.25835	−	9.20666i	0.237548	−	0.415914i
$491$	9.25616	−	4.12111i	0.417725	−	0.185983i	−0.187101	−	0.982341i	$-0.559909\pi$
$491$	9.25616	−	4.12111i	0.417725	−	0.185983i	0.604826	+	0.796358i	$0.293243\pi$
$492$	−16.3047	−	4.36645i	−0.735074	−	0.196855i
$493$	0.888258	+	1.53851i	0.0400051	+	0.0692909i
$494$	−0.494172	−	1.52090i	−0.0222338	−	0.0684287i
$495$	−30.3595	+	10.0305i	−1.36456	+	0.450835i
$496$	1.28484	−	3.95434i	0.0576911	−	0.177555i
$497$	25.7330	−	5.46971i	1.15428	−	0.245350i
$498$	9.21109	−	5.98355i	0.412759	−	0.268129i
$499$	2.03652	−	3.52736i	0.0911674	−	0.157906i	−0.816835	−	0.576871i	$-0.804274\pi$
$499$	2.03652	−	3.52736i	0.0911674	−	0.157906i	0.908003	+	0.418965i	$0.137607\pi$
$500$	8.77585	−	4.05537i	0.392468	−	0.181362i
$501$	5.13384	+	0.268349i	0.229363	+	0.0119890i
$502$	−25.0045	−	11.1327i	−1.11601	−	0.496878i
$503$	6.77990	−	20.8664i	0.302301	−	0.930386i	−0.678370	−	0.734721i	$-0.737313\pi$
$503$	6.77990	−	20.8664i	0.302301	−	0.930386i	0.980671	−	0.195666i	$-0.0626867\pi$
$504$	5.94384	−	13.3599i	0.264760	−	0.595098i
$505$	10.6935	+	7.69334i	0.475856	+	0.342349i
$506$	19.4291	−	21.5782i	0.863730	−	0.959269i
$507$	11.3371	−	17.4628i	0.503497	−	0.775550i
$508$	9.03640	+	1.92075i	0.400925	+	0.0852193i
$509$	−10.2484	+	4.56289i	−0.454253	+	0.202247i	−0.621092	−	0.783738i	$-0.713311\pi$
$509$	−10.2484	+	4.56289i	−0.454253	+	0.202247i	0.166839	+	0.985984i	$0.446644\pi$
$510$	−0.567624	−	1.10092i	−0.0251348	−	0.0487497i
$511$	−13.3929	−	5.96291i	−0.592468	−	0.263784i
$512$	−13.0436	−	9.47672i	−0.576451	−	0.418816i
$513$	−5.57425	−	5.56968i	−0.246109	−	0.245907i
$514$	16.8705	−	12.2571i	0.744126	−	0.540639i
$515$	−26.2783	−	11.5532i	−1.15796	−	0.509097i
$516$	−1.78117	+	11.2558i	−0.0784117	+	0.495511i
$517$	−27.1662	−	5.77436i	−1.19477	−	0.253956i
$518$	−2.02489	+	3.50721i	−0.0889685	+	0.154098i
$519$	20.9560	+	5.61207i	0.919866	+	0.246342i
$520$	−6.18364	−	2.71864i	−0.271170	−	0.119220i
$521$	−0.276314	+	0.850408i	−0.0121056	+	0.0372571i	−0.956927	−	0.290329i	$-0.906235\pi$
$521$	−0.276314	+	0.850408i	−0.0121056	+	0.0372571i	0.944821	+	0.327586i	$0.106235\pi$
$522$	−18.8151	+	1.98275i	−0.823514	+	0.0867825i
$523$	−9.65472	+	7.01456i	−0.422171	+	0.306725i	−0.778511	−	0.627631i	$-0.784025\pi$
$523$	−9.65472	+	7.01456i	−0.422171	+	0.306725i	0.356340	+	0.934357i	$0.384025\pi$
$524$	7.66680	+	13.2793i	0.334926	+	0.580108i
$525$	13.8164	+	0.592983i	0.602998	+	0.0258799i
$526$	−3.97191	+	6.87955i	−0.173183	+	0.299962i
$527$	0.0856578	+	0.814980i	0.00373131	+	0.0355011i
$528$	−4.50400	+	11.7381i	−0.196011	+	0.510836i
$529$	−9.47718	+	2.01444i	−0.412051	+	0.0875842i
$530$	1.40576	−	4.39617i	0.0610623	−	0.190957i
$531$	12.9645	−	11.6797i	0.562610	−	0.506855i
$532$	−2.09396			−0.0907845
$533$	−7.46346	+	8.28901i	−0.323278	+	0.359037i
$534$	2.17133	−	0.833836i	0.0939626	−	0.0360836i
$535$	−40.6796	+	18.3396i	−1.75873	+	0.792890i
$536$	0.334078	+	3.17854i	0.0144300	+	0.137292i
$537$	3.15399	−	19.9311i	0.136105	−	0.860091i
$538$	−0.447270	+	4.25549i	−0.0192832	+	0.183467i
$539$	17.1597	−	12.4672i	0.739120	−	0.537002i
$540$	−10.0302	+	0.576727i	−0.431633	+	0.0248184i
$541$	24.7363	+	17.9720i	1.06350	+	0.772675i	0.974732	−	0.223378i	$-0.0717084\pi$
$541$	24.7363	+	17.9720i	1.06350	+	0.772675i	0.0887638	+	0.996053i	$0.471708\pi$
$542$	−17.1694	+	19.0685i	−0.737487	+	0.819062i
$543$	17.4112	+	34.1599i	0.747188	+	1.46594i
$544$	1.31589	+	0.279702i	0.0564185	+	0.0119921i
$545$	−17.6992	−	3.67587i	−0.758151	−	0.157457i
$546$	−1.83580	−	2.26639i	−0.0785649	−	0.0969924i
$547$	−0.403221	+	0.0857073i	−0.0172405	+	0.00366458i	−0.216524	−	0.976277i	$-0.569472\pi$
$547$	−0.403221	+	0.0857073i	−0.0172405	+	0.00366458i	0.199283	+	0.979942i	$0.436139\pi$
$548$	−12.0439	+	8.75042i	−0.514491	+	0.373799i
$549$	39.6950	+	4.16114i	1.69414	+	0.177593i
$550$	−25.3918	+	0.236931i	−1.08271	+	0.0101028i
$551$	4.48784	+	7.77317i	0.191189	+	0.331148i
$552$	25.3483	−	16.4663i	1.07889	−	0.700852i
$553$	11.9582	+	13.2810i	0.508516	+	0.564765i
$554$	−13.1671	−	14.6235i	−0.559416	−	0.621295i
$555$	9.20797	+	0.438241i	0.390856	+	0.0186023i
$556$	4.98034	−	5.53123i	0.211214	−	0.234576i
$557$	−11.0413			−0.467833			−0.233917	−	0.972257i	$-0.575154\pi$
$557$	−11.0413			−0.467833			−0.233917	+	0.972257i	$0.575154\pi$
$558$	−8.30066	−	2.69454i	−0.351395	−	0.114069i
$559$	6.09230	+	4.42632i	0.257677	+	0.187213i
$560$	3.61974	−	4.05805i	0.152962	−	0.171484i
$561$	−0.130023	−	2.47452i	−0.00548958	−	0.104474i
$562$	6.35797	−	2.83075i	0.268195	−	0.119408i
$563$	−28.1794	+	12.5463i	−1.18762	+	0.528762i	−0.902901	−	0.429849i	$-0.858567\pi$
$563$	−28.1794	+	12.5463i	−1.18762	+	0.528762i	−0.284719	+	0.958611i	$0.591900\pi$
$564$	−7.77630	−	3.96088i	−0.327441	−	0.166783i
$565$	−19.3960	+	21.7446i	−0.815996	+	0.914803i
$566$	−21.4403	−	15.5773i	−0.901203	−	0.654762i
$567$	−13.1324	−	5.83830i	−0.551508	−	0.245186i
$568$	−50.2870			−2.11000
$569$	4.77576	−	5.30402i	0.200210	−	0.222356i	−0.634676	−	0.772778i	$-0.718867\pi$
$569$	4.77576	−	5.30402i	0.200210	−	0.222356i	0.834886	+	0.550422i	$0.185533\pi$
$570$	−2.86787	−	5.56232i	−0.120122	−	0.232980i
$571$	0.561367	+	0.623461i	0.0234925	+	0.0260910i	0.754777	−	0.655982i	$-0.227745\pi$
$571$	0.561367	+	0.623461i	0.0234925	+	0.0260910i	−0.731284	+	0.682073i	$0.761079\pi$
$572$	−2.72933	−	3.03122i	−0.114119	−	0.126742i
$573$	−1.03792	−	19.7530i	−0.0433598	−	0.825194i
$574$	−9.58789	−	16.6067i	−0.400191	−	0.693151i
$575$	23.2832	+	16.5866i	0.970978	+	0.691707i
$576$	−13.7868	+	18.9869i	−0.574452	+	0.791120i
$577$	−21.7584	+	15.8084i	−0.905813	+	0.658112i	−0.939952	−	0.341305i	$-0.889131\pi$
$577$	−21.7584	+	15.8084i	−0.905813	+	0.658112i	0.0341394	+	0.999417i	$0.489131\pi$
$578$	−17.6239	+	3.74608i	−0.733058	+	0.155816i
$579$	−11.0104	+	28.6947i	−0.457575	+	1.19251i
$580$	11.2048	+	2.32707i	0.465253	+	0.0966261i
$581$	−9.29630	−	1.97599i	−0.385676	−	0.0819779i
$582$	3.53508	+	0.184781i	0.146534	+	0.00765942i
$583$	6.17830	−	6.86170i	0.255879	−	0.284183i
$584$	22.6711	+	16.4715i	0.938137	+	0.681597i
$585$	−2.67034	+	6.07831i	−0.110405	+	0.251307i
$586$	−6.05471	+	4.39901i	−0.250118	+	0.181721i
$587$	−0.0950816	+	0.904641i	−0.00392444	+	0.0373385i	−0.996309	−	0.0858408i	$-0.972642\pi$
$587$	−0.0950816	+	0.904641i	−0.00392444	+	0.0373385i	0.992384	+	0.123179i	$0.0393090\pi$
$588$	6.22182	−	2.38931i	0.256583	−	0.0985334i
$589$	0.432778	+	4.11761i	0.0178323	+	0.169663i
$590$	12.6337	−	5.69566i	0.520122	−	0.234487i
$591$	2.60870	−	16.4853i	0.107307	−	0.678113i
$592$	2.42548	−	2.69377i	0.0996867	−	0.110713i
$593$	35.9174			1.47495			0.737476	−	0.675373i	$-0.236017\pi$
$593$	35.9174			1.47495			0.737476	+	0.675373i	$0.236017\pi$
$594$	24.6402	+	9.44689i	1.01100	+	0.387611i
$595$	−0.326429	+	1.02083i	−0.0133823	+	0.0418498i
$596$	8.11205	−	1.72427i	0.332283	−	0.0706289i
$597$	−5.32355	+	0.843913i	−0.217878	+	0.0345391i
$598$	−0.630216	−	5.99610i	−0.0257714	−	0.245199i
$599$	21.6849	−	37.5593i	0.886020	−	1.53463i	0.0414800	−	0.999139i	$-0.486793\pi$
$599$	21.6849	−	37.5593i	0.886020	−	1.53463i	0.844540	−	0.535492i	$-0.179874\pi$
$600$	−25.5971	−	6.59962i	−1.04500	−	0.269428i
$601$	−9.27357	−	16.0623i	−0.378277	−	0.655195i	0.612535	−	0.790444i	$-0.290150\pi$
$601$	−9.27357	−	16.0623i	−0.378277	−	0.655195i	−0.990812	+	0.135249i	$0.956817\pi$
$602$	−10.4738	+	7.60968i	−0.426882	+	0.310148i
$603$	3.12393	−	0.329202i	0.127216	−	0.0134061i
$604$	−3.93893	+	12.1228i	−0.160273	+	0.493270i
$605$	−23.9865	−	10.5457i	−0.975189	−	0.428742i
$606$	−2.81546	−	10.5017i	−0.114370	−	0.426602i
$607$	−10.0739	+	17.4485i	−0.408886	+	0.708212i	−0.994765	−	0.102187i	$-0.967416\pi$
$607$	−10.0739	+	17.4485i	−0.408886	+	0.708212i	0.585879	+	0.810398i	$0.300749\pi$
$608$	6.64844	+	1.41317i	0.269630	+	0.0573116i
$609$	12.7234	+	10.3003i	0.515577	+	0.417390i
$610$	29.0172	+	12.7574i	1.17487	+	0.516533i
$611$	−4.66547	+	3.38966i	−0.188745	+	0.137131i
$612$	0.161676	−	0.761650i	0.00653536	−	0.0307879i
$613$	6.07494	+	4.41370i	0.245365	+	0.178268i	0.703670	−	0.710527i	$-0.251543\pi$
$613$	6.07494	+	4.41370i	0.245365	+	0.178268i	−0.458305	+	0.888795i	$0.651543\pi$
$614$	−20.2633	−	9.02181i	−0.817761	−	0.364091i
$615$	−23.5970	+	36.7211i	−0.951524	+	1.48074i
$616$	21.2234	−	9.44927i	0.855115	−	0.380722i
$617$	9.59800	+	2.04012i	0.386401	+	0.0821320i	0.397016	−	0.917812i	$-0.370046\pi$
$617$	9.59800	+	2.04012i	0.386401	+	0.0821320i	−0.0106153	+	0.999944i	$0.503379\pi$
$618$	10.7589	+	21.1083i	0.432785	+	0.849101i
$619$	1.03695	−	1.15165i	0.0416787	−	0.0462889i	−0.721945	−	0.691950i	$-0.756752\pi$
$619$	1.03695	−	1.15165i	0.0416787	−	0.0462889i	0.763624	+	0.645662i	$0.223418\pi$
$620$	4.28508	+	3.08285i	0.172093	+	0.123810i
$621$	−16.1907	−	24.9091i	−0.649710	−	0.999567i
$622$	2.24985	−	6.92432i	0.0902107	−	0.277640i
$623$	−1.83854	−	0.818573i	−0.0736597	−	0.0327954i
$624$	1.18549	+	2.32588i	0.0474577	+	0.0931096i
$625$	−3.07671	−	24.8100i	−0.123068	−	0.992398i
$626$	16.8979	−	29.2681i	0.675377	−	1.16979i
$627$	−0.656930	−	12.5023i	−0.0262353	−	0.499292i
$628$	11.4514	−	2.43406i	0.456959	−	0.0971296i
$629$	−0.220767	+	0.679452i	−0.00880257	+	0.0270915i
$630$	−8.51967	−	7.59530i	−0.339432	−	0.302604i
$631$	3.50012	+	10.7722i	0.139337	+	0.428836i	0.996239	−	0.0866429i	$-0.0276139\pi$
$631$	3.50012	+	10.7722i	0.139337	+	0.428836i	−0.856902	+	0.515479i	$0.827614\pi$
$632$	−17.0803	−	29.5840i	−0.679419	−	1.17679i
$633$	3.84832	+	14.3543i	0.152957	+	0.570530i
$634$	−7.60409	+	3.38556i	−0.301997	+	0.134458i
$635$	11.8483	−	20.7448i	0.470185	−	0.823231i
$636$	2.43303	−	1.58050i	0.0964760	−	0.0626710i
$637$	0.460361	−	4.38004i	0.0182402	−	0.173543i
$638$	−24.3179	−	17.6680i	−0.962755	−	0.699483i
$639$	0.0135171	+	49.4245i	0.000534727	+	1.95520i
$640$	1.13616	−	0.833592i	0.0449105	−	0.0329506i
$641$	1.91800	−	18.2485i	0.0757564	−	0.720774i	−0.889050	−	0.457811i	$-0.848634\pi$
$641$	1.91800	−	18.2485i	0.0757564	−	0.720774i	0.964806	−	0.262963i	$-0.0846997\pi$
$642$	35.5751	+	9.52711i	1.40404	+	0.376005i
$643$	6.43258	−	11.1415i	0.253676	−	0.439380i	−0.710859	−	0.703334i	$-0.751694\pi$
$643$	6.43258	−	11.1415i	0.253676	−	0.439380i	0.964535	+	0.263955i	$0.0850270\pi$
$644$	−7.72202	−	1.64137i	−0.304290	−	0.0646789i
$645$	26.3214	+	13.2526i	1.03640	+	0.521821i
$646$	0.474401	−	0.100837i	0.0186650	−	0.00396738i
$647$	5.33164	−	16.4091i	0.209608	−	0.645108i	−0.789884	−	0.613256i	$-0.789859\pi$
$647$	5.33164	−	16.4091i	0.209608	−	0.645108i	0.999493	−	0.0318523i	$-0.0101406\pi$
$648$	22.2335	+	16.1350i	0.873414	+	0.633842i
$649$	27.7238			1.08825
$650$	−3.49134	+	3.95105i	−0.136942	+	0.154973i
$651$	3.42908	+	6.72768i	0.134396	+	0.263679i
$652$	−0.249958	−	2.37819i	−0.00978909	−	0.0931370i
$653$	−18.9109	−	21.0027i	−0.740041	−	0.821899i	0.249160	−	0.968462i	$-0.419845\pi$
$653$	−18.9109	−	21.0027i	−0.740041	−	0.821899i	−0.989201	+	0.146563i	$0.953179\pi$
$654$	9.39078	+	11.5934i	0.367208	+	0.453338i
$655$	38.7468	−	8.42502i	1.51396	−	0.329193i
$656$	5.30386	+	16.3236i	0.207081	+	0.637329i
$657$	16.1829	−	22.2867i	0.631356	−	0.869487i
$658$	−3.06368	−	9.42904i	−0.119435	−	0.367582i
$659$	2.21265	−	21.0520i	0.0861928	−	0.820069i	−0.862964	−	0.505266i	$-0.831395\pi$
$659$	2.21265	−	21.0520i	0.0861928	−	0.820069i	0.949157	−	0.314804i	$-0.101939\pi$
$660$	−12.4531	−	9.98565i	−0.484734	−	0.388691i
$661$	4.60125	+	43.7780i	0.178968	+	1.70277i	0.603508	+	0.797357i	$0.293769\pi$
$661$	4.60125	+	43.7780i	0.178968	+	1.70277i	−0.424540	+	0.905409i	$0.639564\pi$
$662$	20.9054	−	9.30769i	0.812512	−	0.361754i
$663$	−0.399900	−	0.323742i	−0.0155308	−	0.0125731i
$664$	16.5961	+	7.38906i	0.644053	+	0.286751i
$665$	−1.64925	+	5.15763i	−0.0639553	+	0.200004i
$666$	−5.65546	−	5.08940i	−0.219145	−	0.197210i
$667$	10.4570	+	32.1835i	0.404898	+	1.24615i
$668$	1.28323	+	2.22263i	0.0496498	+	0.0859960i
$669$	19.9316	+	5.33773i	0.770600	+	0.206369i
$670$	2.44259	+	0.507289i	0.0943654	+	0.0195983i
$671$	42.4311	+	47.1245i	1.63803	+	1.81922i
$672$	12.2436	−	1.94091i	0.472308	−	0.0748724i
$673$	8.38851	+	3.73480i	0.323353	+	0.143966i	0.561993	−	0.827142i	$-0.310035\pi$
$673$	8.38851	+	3.73480i	0.323353	+	0.143966i	−0.238640	+	0.971108i	$0.576702\pi$
$674$	18.2961			0.704740
$675$	−6.47955	+	25.1598i	−0.249398	+	0.968401i
$676$	10.3941			0.399771
$677$	19.9666	+	8.88970i	0.767379	+	0.341659i	0.752813	−	0.658235i	$-0.228697\pi$
$677$	19.9666	+	8.88970i	0.767379	+	0.341659i	0.0145662	+	0.999894i	$0.495363\pi$
$678$	23.7523	−	3.76532i	0.912201	−	0.144606i
$679$	−2.04951	−	2.27621i	−0.0786530	−	0.0873530i
$680$	1.01602	−	1.77892i	0.0389628	−	0.0682185i
$681$	37.0606	+	9.92493i	1.42017	+	0.380324i
$682$	−6.93269	−	12.0078i	−0.265466	−	0.459801i
$683$	−1.01224	−	3.11535i	−0.0387322	−	0.119206i	0.929821	−	0.368012i	$-0.119962\pi$
$683$	−1.01224	−	3.11535i	−0.0387322	−	0.119206i	−0.968553	+	0.248807i	$0.919962\pi$
$684$	0.816853	−	3.84817i	0.0312332	−	0.147138i
$685$	12.0671	+	36.5575i	0.461060	+	1.39679i
$686$	17.7975	+	7.92397i	0.679513	+	0.302539i
$687$	20.4709	+	16.5724i	0.781013	+	0.632275i
$688$	10.5861	−	4.71322i	0.403590	−	0.179690i
$689$	−0.200403	−	1.90671i	−0.00763476	−	0.0726399i
$690$	−6.21596	−	22.7605i	−0.236638	−	0.866478i
$691$	−1.98375	+	18.8741i	−0.0754655	+	0.718006i	0.889732	+	0.456484i	$0.150891\pi$
$691$	−1.98375	+	18.8741i	−0.0754655	+	0.718006i	−0.965197	+	0.261523i	$0.915775\pi$
$692$	3.34682	+	10.3004i	0.127227	+	0.391564i
$693$	−9.29290	−	20.8568i	−0.353008	−	0.792286i
$694$	−6.13151	−	18.8708i	−0.232749	−	0.716327i
$695$	−9.70135	−	16.6236i	−0.367993	−	0.630571i
$696$	−19.6955	−	24.3151i	−0.746556	−	0.921662i
$697$	−2.26352	−	2.51390i	−0.0857371	−	0.0952207i
$698$	1.90490	+	18.1239i	0.0721014	+	0.685999i
$699$	11.6359	+	22.8290i	0.440111	+	0.863474i
$700$	3.50760	+	5.94651i	0.132575	+	0.224757i
$701$	26.6440			1.00633			0.503164	−	0.864191i	$-0.332169\pi$
$701$	26.6440			1.00633			0.503164	+	0.864191i	$0.332169\pi$
$702$	4.88120	−	2.48962i	0.184229	−	0.0939645i
$703$	−1.11541	+	3.43287i	−0.0420684	+	0.129473i
$704$	−36.4652	+	7.75091i	−1.37433	+	0.292124i
$705$	−15.8809	+	16.0342i	−0.598109	+	0.603881i
$706$	−20.9345	−	4.44976i	−0.787879	−	0.167469i
$707$	−4.70380	+	8.14722i	−0.176905	+	0.306408i
$708$	8.41489	+	2.25353i	0.316251	+	0.0846929i
$709$	1.72168	−	16.3807i	0.0646592	−	0.615191i	−0.913429	−	0.406999i	$-0.866575\pi$
$709$	1.72168	−	16.3807i	0.0646592	−	0.615191i	0.978088	−	0.208192i	$-0.0667580\pi$
$710$	−11.9553	+	37.3871i	−0.448673	+	1.40311i
$711$	−29.0720	+	16.7953i	−1.09029	+	0.629874i
$712$	3.11223	+	2.26117i	0.116636	+	0.0847408i
$713$	−1.63164	+	15.5240i	−0.0611054	+	0.581379i
$714$	0.741785	−	0.481865i	0.0277606	−	0.0180333i
$715$	−9.61591	+	4.33515i	−0.359615	+	0.162125i
$716$	9.20309	−	4.09748i	0.343935	−	0.153130i
$717$	−2.27731	−	8.49437i	−0.0850475	−	0.317228i
$718$	2.44894	+	4.24168i	0.0913935	+	0.158298i
$719$	−8.80843	−	27.1096i	−0.328499	−	1.01102i	−0.969836	−	0.243757i	$-0.921620\pi$
$719$	−8.80843	−	27.1096i	−0.328499	−	1.01102i	0.641337	−	0.767259i	$-0.278380\pi$
$720$	6.04561	+	8.23522i	0.225306	+	0.306909i
$721$	6.33479	−	19.4965i	0.235920	−	0.726087i
$722$	−17.4054	+	3.69963i	−0.647762	+	0.137686i
$723$	−1.21780	−	23.1763i	−0.0452903	−	0.861936i
$724$	−9.57056	+	16.5767i	−0.355687	+	0.616068i
$725$	14.5570	−	25.7657i	0.540632	−	0.956913i
$726$	9.82054	+	19.2674i	0.364475	+	0.715080i
$727$	−21.9994	−	9.79479i	−0.815914	−	0.363269i	−0.0440291	−	0.999030i	$-0.514019\pi$
$727$	−21.9994	−	9.79479i	−0.815914	−	0.363269i	−0.771885	+	0.635762i	$0.780686\pi$
$728$	1.49066	−	4.58779i	0.0552476	−	0.170035i
$729$	15.8523	−	21.8565i	0.587121	−	0.809499i
$730$	17.6360	−	12.9395i	0.652738	−	0.478911i
$731$	−1.52820	+	1.69724i	−0.0565225	+	0.0627746i
$732$	9.04843	+	17.7525i	0.334440	+	0.656153i
$733$	−1.98030	−	0.420926i	−0.0731441	−	0.0155473i	0.171194	−	0.985237i	$-0.445237\pi$
$733$	−1.98030	−	0.420926i	−0.0731441	−	0.0155473i	−0.244338	+	0.969690i	$0.578571\pi$
$734$	−17.1478	+	7.63470i	−0.632937	+	0.281802i
$735$	−0.984652	−	17.2069i	−0.0363194	−	0.634685i
$736$	23.4101	+	10.4229i	0.862909	+	0.384192i
$737$	4.03758	+	2.93347i	0.148726	+	0.108056i
$738$	34.2592	−	11.1419i	1.26110	−	0.410137i
$739$	−32.8526	+	23.8688i	−1.20850	+	0.878028i	−0.995094	−	0.0989355i	$-0.968456\pi$
$739$	−32.8526	+	23.8688i	−1.20850	+	0.878028i	−0.213408	+	0.976963i	$0.568456\pi$
$740$	2.31962	+	3.97476i	0.0852709	+	0.146115i
$741$	−2.02046	−	1.63568i	−0.0742234	−	0.0600882i
$742$	3.22403	+	0.685288i	0.118358	+	0.0251577i
$743$	4.58729	−	7.94543i	0.168292	−	0.291489i	−0.769528	−	0.638613i	$-0.779508\pi$
$743$	4.58729	−	7.94543i	0.168292	−	0.291489i	0.937819	+	0.347124i	$0.112842\pi$
$744$	−3.73769	−	13.9416i	−0.137030	−	0.511124i
$745$	2.14221	−	21.3389i	0.0784843	−	0.781797i
$746$	−3.32647	+	10.2378i	−0.121791	+	0.374833i
$747$	7.25786	−	16.3134i	0.265551	−	0.596877i
$748$	1.00080	−	0.727124i	0.0365929	−	0.0265863i
$749$	−15.9332	−	27.5972i	−0.582188	−	1.00838i
$750$	−10.9921	+	17.4618i	−0.401375	+	0.637614i
$751$	−7.16746	+	12.4144i	−0.261544	+	0.453008i	−0.966652	−	0.256092i	$-0.917565\pi$
$751$	−7.16746	+	12.4144i	−0.261544	+	0.453008i	0.705108	+	0.709100i	$0.250898\pi$
$752$	0.927582	+	8.82535i	0.0338254	+	0.321827i
$753$	−43.9443	+	6.96626i	−1.60142	+	0.253865i
$754$	−6.10499	+	1.29766i	−0.222331	+	0.0472578i
$755$	26.7573	+	19.2502i	0.973798	+	0.700588i
$756$	−1.12529	−	7.08598i	−0.0409264	−	0.257715i
$757$	−7.98963			−0.290388			−0.145194	−	0.989403i	$-0.546381\pi$
$757$	−7.98963			−0.290388			−0.145194	+	0.989403i	$0.546381\pi$
$758$	−15.7537	+	17.4963i	−0.572202	+	0.635494i
$759$	7.37740	−	46.6204i	0.267783	−	1.69221i
$760$	5.13337	−	8.98784i	0.186207	−	0.326023i
$761$	0.0356082	+	0.338790i	0.00129080	+	0.0122811i	0.995148	−	0.0983859i	$-0.0313680\pi$
$761$	0.0356082	+	0.338790i	0.00129080	+	0.0122811i	−0.993858	+	0.110667i	$0.964701\pi$
$762$	−18.4067	+	7.06855i	−0.666804	+	0.256067i
$763$	1.34939	−	12.8386i	0.0488513	−	0.464789i
$764$	7.98897	−	5.80433i	0.289031	−	0.209993i
$765$	−1.74868	−	0.998120i	−0.0632238	−	0.0360871i
$766$	6.69945	+	4.86744i	0.242061	+	0.175868i
$767$	3.85190	−	4.27797i	0.139084	−	0.154469i
$768$	−28.2189	−	1.47502i	−1.01826	−	0.0532252i
$769$	1.75737	+	0.373540i	0.0633723	+	0.0134702i	0.239489	−	0.970899i	$-0.423020\pi$
$769$	1.75737	+	0.373540i	0.0633723	+	0.0134702i	−0.176116	+	0.984369i	$0.556354\pi$
$770$	−1.97963	−	18.0256i	−0.0713409	−	0.649596i
$771$	12.1436	−	31.6482i	0.437343	−	1.13978i
$772$	−15.0083	+	3.19012i	−0.540161	+	0.114815i
$773$	−34.6828	+	25.1985i	−1.24745	+	0.906328i	−0.998071	−	0.0620773i	$-0.980227\pi$
$773$	−34.6828	+	25.1985i	−1.24745	+	0.906328i	−0.249382	+	0.968405i	$0.580227\pi$
$774$	−9.89884	−	22.2168i	−0.355807	−	0.798567i
$775$	10.9684	−	8.12646i	0.393997	−	0.291911i
$776$	2.92738	+	5.07038i	0.105087	+	0.182016i
$777$	0.345435	+	6.57410i	0.0123924	+	0.235844i
$778$	8.93009	+	9.91787i	0.320159	+	0.355573i
$779$	−11.4363	−	12.7012i	−0.409746	−	0.455069i
$780$	−3.27107	+	0.534200i	−0.117123	+	0.0191274i
$781$	−52.5433	+	58.3552i	−1.88015	+	2.08811i
$782$	1.82852			0.0653878
$783$	−23.8928	+	19.3642i	−0.853858	+	0.692021i
$784$	−5.48279	−	3.98348i	−0.195814	−	0.142267i
$785$	3.02404	−	30.1230i	0.107933	−	1.07514i
$786$	−29.1616	−	14.8535i	−1.04016	−	0.529808i
$787$	10.0343	−	4.46758i	0.357686	−	0.159252i	−0.220024	−	0.975495i	$-0.570613\pi$
$787$	10.0343	−	4.46758i	0.357686	−	0.159252i	0.577709	+	0.816243i	$0.303947\pi$
$788$	7.61198	−	3.38907i	0.271165	−	0.120731i
$789$	0.677587	+	12.8954i	0.0241227	+	0.459088i
$790$	−26.0557	+	5.66548i	−0.927019	+	0.201569i
$791$	−16.8345	−	12.2310i	−0.598565	−	0.434883i
$792$	9.08613	+	42.6894i	0.322861	+	1.51690i
$793$	13.1670			0.467572
$794$	20.3126	−	22.5594i	0.720866	−	0.800603i
$795$	−1.97662	−	7.23766i	−0.0701036	−	0.256693i
$796$	−1.80054	−	1.99970i	−0.0638184	−	0.0708775i
$797$	−22.8733	−	25.4033i	−0.810213	−	0.899832i	0.186366	−	0.982480i	$-0.440329\pi$
$797$	−22.8733	−	25.4033i	−0.810213	−	0.899832i	−0.996579	+	0.0826482i	$0.973662\pi$
$798$	3.74780	−	2.43458i	0.132671	−	0.0861831i
$799$	−0.874486	−	1.51465i	−0.0309371	−	0.0535846i
$800$	−7.12367	−	21.2477i	−0.251860	−	0.751221i
$801$	2.22155	−	3.05946i	0.0784945	−	0.108101i
$802$	−7.55966	+	5.49242i	−0.266941	+	0.193944i
$803$	42.8026	−	9.09798i	1.51047	−	0.321061i
$804$	0.987065	+	1.21858i	0.0348111	+	0.0429761i
$805$	−10.1249	+	17.7274i	−0.356857	+	0.624807i
$806$	−2.81610	−	0.598581i	−0.0991929	−	0.0210841i
$807$	3.15865	+	6.19711i	0.111190	+	0.218149i
$808$	12.0326	−	13.3636i	0.423306	−	0.470128i
$809$	−6.42510	−	4.66811i	−0.225894	−	0.164122i	0.469082	−	0.883155i	$-0.344585\pi$
$809$	−6.42510	−	4.66811i	−0.225894	−	0.164122i	−0.694976	+	0.719033i	$0.744585\pi$
$810$	17.2818	−	12.6941i	0.607220	−	0.446025i
$811$	−6.94724	+	5.04746i	−0.243951	+	0.177240i	−0.703041	−	0.711149i	$-0.748175\pi$
$811$	−6.94724	+	5.04746i	−0.243951	+	0.177240i	0.459091	+	0.888389i	$0.348175\pi$
$812$	−0.854254	+	8.12769i	−0.0299785	+	0.285226i
$813$	−6.51935	+	41.1980i	−0.228644	+	1.44488i
$814$	−1.26353	−	12.0217i	−0.0442868	−	0.421360i
$815$	−6.05460	−	1.25745i	−0.212083	−	0.0440466i
$816$	−0.739112	+	0.283834i	−0.0258741	+	0.00993619i
$817$	−7.72109	+	8.57514i	−0.270127	+	0.300006i
$818$	12.3550			0.431982
$819$	−4.50950	−	1.46386i	−0.157575	−	0.0511515i
$820$	−21.7908	+	0.101663i	−0.760968	+	0.00355022i
$821$	−1.65706	+	0.352220i	−0.0578319	+	0.0122926i	−0.236737	−	0.971574i	$-0.576078\pi$
$821$	−1.65706	+	0.352220i	−0.0578319	+	0.0122926i	0.178905	+	0.983866i	$0.442745\pi$
$822$	11.3826	−	29.6647i	0.397013	−	1.03468i
$823$	0.455648	+	4.33520i	0.0158829	+	0.151116i	0.999589	−	0.0286686i	$-0.00912674\pi$
$823$	0.455648	+	4.33520i	0.0158829	+	0.151116i	−0.983706	+	0.179784i	$0.942460\pi$
$824$	−19.5925	+	33.9352i	−0.682538	+	1.18219i
$825$	−34.4040	+	22.8082i	−1.19780	+	0.794080i
$826$	4.94833	+	8.57075i	0.172174	+	0.298215i
$827$	21.8549	−	15.8785i	0.759968	−	0.552149i	−0.138933	−	0.990302i	$-0.544367\pi$
$827$	21.8549	−	15.8785i	0.759968	−	0.552149i	0.898901	+	0.438153i	$0.144367\pi$
$828$	6.02878	−	13.5508i	0.209515	−	0.470924i
$829$	16.9452	−	52.1521i	0.588533	−	1.81132i	0.00393824	−	0.999992i	$-0.498746\pi$
$829$	16.9452	−	52.1521i	0.588533	−	1.81132i	0.584595	−	0.811326i	$-0.301254\pi$
$830$	9.43915	−	10.5821i	0.327638	−	0.367310i
$831$	−30.8989	−	8.27480i	−1.07187	−	0.287050i
$832$	−3.87040	+	6.70373i	−0.134182	+	0.232410i
$833$	1.30651	+	0.277708i	0.0452680	+	0.00962200i
$834$	−2.48291	+	15.6904i	−0.0859762	+	0.543313i
$835$	6.48527	−	1.41014i	0.224432	−	0.0487999i
$836$	5.05645	−	3.67373i	0.174881	−	0.127059i
$837$	−13.7015	+	3.67732i	−0.473592	+	0.127107i
$838$	−24.6786	−	17.9301i	−0.852508	−	0.619384i
$839$	−19.4076	−	8.64084i	−0.670026	−	0.298315i	0.0433873	−	0.999058i	$-0.486185\pi$
$839$	−19.4076	−	8.64084i	−0.670026	−	0.298315i	−0.713413	+	0.700744i	$0.752852\pi$
$840$	2.86353	−	18.6591i	0.0988011	−	0.643800i
$841$	5.50960	−	2.45303i	0.189986	−	0.0845873i
$842$	−14.5088	−	3.08393i	−0.500005	−	0.106279i
$843$	6.16040	−	9.48903i	0.212176	−	0.326820i
$844$	−4.96438	+	5.51350i	−0.170881	+	0.189782i
$845$	8.18662	−	25.6016i	0.281628	−	0.880723i
$846$	18.5234	−	1.95201i	0.636846	−	0.0671113i
$847$	5.78232	−	17.7961i	0.198683	−	0.611483i
$848$	−2.69514	−	1.19995i	−0.0925514	−	0.0412065i
$849$	−43.0214	−	2.24876i	−1.47649	−	0.0771771i
$850$	−1.08103	−	1.17831i	−0.0370791	−	0.0404157i
$851$	−6.80424	+	11.7853i	−0.233246	+	0.403995i
$852$	−20.6917	+	13.4414i	−0.708886	+	0.460493i
$853$	−14.2031	+	3.01897i	−0.486306	+	0.103368i	−0.444539	−	0.895760i	$-0.646632\pi$
$853$	−14.2031	+	3.01897i	−0.486306	+	0.103368i	−0.0417679	+	0.999127i	$0.513299\pi$
$854$	−6.99506	+	21.5286i	−0.239366	+	0.736693i
$855$	−8.83506	−	5.04291i	−0.302153	−	0.172464i
$856$	18.8229	+	57.9309i	0.643353	+	1.98004i
$857$	27.2809	+	47.2519i	0.931897	+	1.61409i	0.780075	+	0.625686i	$0.215181\pi$
$857$	27.2809	+	47.2519i	0.931897	+	1.61409i	0.151822	+	0.988408i	$0.451486\pi$
$858$	8.40930	+	2.25203i	0.287089	+	0.0768832i
$859$	20.8211	−	9.27017i	0.710408	−	0.316294i	−0.0195281	−	0.999809i	$-0.506216\pi$
$859$	20.8211	−	9.27017i	0.710408	−	0.316294i	0.729936	+	0.683515i	$0.239550\pi$
$860$	1.60607	+	14.6241i	0.0547666	+	0.498678i
$861$	−27.7759	−	14.1477i	−0.946600	−	0.482154i
$862$	−1.19995	+	11.4167i	−0.0408704	+	0.388856i
$863$	−35.8456	−	26.0434i	−1.22020	−	0.886526i	−0.224082	−	0.974570i	$-0.571938\pi$
$863$	−35.8456	−	26.0434i	−1.22020	−	0.886526i	−0.996117	+	0.0880440i	$0.971938\pi$
$864$	−1.20932	+	23.2578i	−0.0411421	+	0.791248i
$865$	28.0071	−	0.130664i	0.952270	−	0.00444272i
$866$	−1.16322	+	11.0673i	−0.0395279	+	0.376083i
$867$	−20.7075	+	20.7132i	−0.703263	+	0.703456i
$868$	−1.88489	+	3.26472i	−0.0639773	+	0.110812i
$869$	−52.1773	−	11.0906i	−1.76999	−	0.376224i
$870$	−22.7601	+	8.86242i	−0.771640	+	0.300464i
$871$	1.01363	−	0.215454i	0.0343456	−	0.00730038i
$872$	−7.62529	+	23.4682i	−0.258225	+	0.794734i
$873$	4.98262	−	2.87854i	0.168636	−	0.0974237i
$874$	9.23843			0.312495
$875$	17.4096	−	3.95597i	0.588550	−	0.133736i
$876$	13.7313	+	0.717742i	0.463936	+	0.0242502i
$877$	1.99617	+	18.9923i	0.0674060	+	0.641325i	0.975111	+	0.221717i	$0.0711660\pi$
$877$	1.99617	+	18.9923i	0.0674060	+	0.641325i	−0.907705	+	0.419609i	$0.862167\pi$
$878$	−18.7634	−	20.8389i	−0.633235	−	0.703278i
$879$	−4.35827	+	11.3583i	−0.147001	+	0.383107i
$880$	−1.62129	+	16.1499i	−0.0546535	+	0.544414i
$881$	−8.53041	−	26.2539i	−0.287397	−	0.884517i	−0.985670	−	0.168685i	$-0.946048\pi$
$881$	−8.53041	−	26.2539i	−0.287397	−	0.884517i	0.698273	−	0.715832i	$-0.253952\pi$
$882$	−8.35794	+	11.5103i	−0.281427	+	0.387573i
$883$	−15.3512	−	47.2463i	−0.516610	−	1.58996i	−0.780333	−	0.625365i	$-0.784950\pi$
$883$	−15.3512	−	47.2463i	−0.516610	−	1.58996i	0.263722	−	0.964599i	$-0.415050\pi$
$884$	0.0268495	−	0.255456i	0.000903047	−	0.00859192i
$885$	12.1785	−	18.9518i	0.409375	−	0.637058i
$886$	0.243160	+	2.31351i	0.00816911	+	0.0777239i
$887$	−6.42792	+	2.86190i	−0.215829	+	0.0960931i	−0.511803	−	0.859103i	$-0.671022\pi$
$887$	−6.42792	+	2.86190i	−0.215829	+	0.0960931i	0.295975	+	0.955196i	$0.404356\pi$
$888$	1.96681	−	12.4289i	0.0660018	−	0.417088i
$889$	15.5856	+	6.93917i	0.522725	+	0.232732i
$890$	2.42103	−	1.77629i	0.0811530	−	0.0595415i
$891$	41.9548	−	8.94176i	1.40554	−	0.299560i
$892$	3.18321	+	9.79692i	0.106582	+	0.328025i
$893$	−4.41826	−	7.65265i	−0.147851	−	0.256086i
$894$	−12.5143	+	12.5178i	−0.418542	+	0.418657i
$895$	−2.84393	−	25.8954i	−0.0950620	−	0.865589i
$896$	0.673365	+	0.747847i	0.0224955	+	0.0249838i
$897$	−6.16884	−	7.61575i	−0.205972	−	0.254283i
$898$	31.6706	+	14.1006i	1.05686	+	0.470545i
$899$	16.1590			0.538934
$900$	−12.2965	+	4.12636i	−0.409884	+	0.137545i
$901$	0.581454			0.0193711
$902$	52.2882	+	23.2802i	1.74101	+	0.775146i
$903$	−7.53922	+	19.6484i	−0.250889	+	0.653857i
$904$	26.6148	+	29.5587i	0.885195	+	0.983108i
$905$	33.2921	+	36.6295i	1.10667	+	1.21761i
$906$	−7.04482	−	26.2773i	−0.234049	−	0.873004i
$907$	−24.0868	−	41.7196i	−0.799789	−	1.38528i	−0.919753	−	0.392497i	$-0.871611\pi$
$907$	−24.0868	−	41.7196i	−0.799789	−	1.38528i	0.119964	−	0.992778i	$-0.461722\pi$
$908$	5.91884	+	18.2163i	0.196424	+	0.604529i
$909$	−13.1376	−	11.8226i	−0.435746	−	0.392132i
$910$	−3.05652	−	2.19898i	−0.101323	−	0.0728953i
$911$	−48.2662	−	21.4895i	−1.59913	−	0.711979i	−0.602827	−	0.797872i	$-0.705959\pi$
$911$	−48.2662	−	21.4895i	−1.59913	−	0.711979i	−0.996304	+	0.0858924i	$0.972626\pi$
$912$	−3.73430	+	1.43405i	−0.123655	+	0.0474861i
$913$	25.9153	−	11.5382i	0.857672	−	0.381860i
$914$	2.33504	+	22.2164i	0.0772362	+	0.734854i
$915$	50.8532	−	8.30487i	1.68115	−	0.274551i
$916$	−1.37443	+	13.0768i	−0.0454123	+	0.432069i
$917$	8.75044	+	26.9311i	0.288965	+	0.889342i
$918$	0.596176	+	1.55119i	0.0196767	+	0.0511969i
$919$	−5.29882	−	16.3081i	−0.174792	−	0.537954i	0.824832	−	0.565378i	$-0.191270\pi$
$919$	−5.29882	−	16.3081i	−0.174792	−	0.537954i	−0.999624	+	0.0274237i	$0.991270\pi$
$920$	25.9759	−	29.1212i	0.856399	−	0.960097i
$921$	−35.6119	+	5.64536i	−1.17345	+	0.186021i
$922$	−10.4331	−	11.5872i	−0.343597	−	0.381604i
$923$	1.70433	+	16.2156i	0.0560986	+	0.533743i
$924$	6.20711	−	9.56098i	0.204199	−	0.314533i
$925$	11.6172	−	2.58284i	0.381972	−	0.0849233i
$926$	28.2265			0.927582
$927$	33.3584	+	19.2473i	1.09564	+	0.632166i
$928$	8.19752	−	25.2294i	0.269097	−	0.828195i
$929$	38.9315	−	8.27514i	1.27730	−	0.271499i	0.481172	−	0.876626i	$-0.340211\pi$
$929$	38.9315	−	8.27514i	1.27730	−	0.271499i	0.796129	+	0.605127i	$0.206878\pi$
$930$	−11.2538	−	0.535611i	−0.369028	−	0.0175634i
$931$	6.60103	+	1.40309i	0.216340	+	0.0459845i
$932$	−6.39599	+	11.0782i	−0.209508	+	0.362878i
$933$	−3.06473	−	11.4315i	−0.100335	−	0.374250i
$934$	−2.42585	+	23.0804i	−0.0793762	+	0.755214i
$935$	−1.00273	−	3.03778i	−0.0327927	−	0.0993460i
$936$	7.84969	+	4.52916i	0.256575	+	0.148040i
$937$	−18.7168	−	13.5986i	−0.611453	−	0.444246i	0.238473	−	0.971149i	$-0.423353\pi$
$937$	−18.7168	−	13.5986i	−0.611453	−	0.444246i	−0.849926	+	0.526903i	$0.823353\pi$
$938$	−0.186223	+	1.77180i	−0.00608041	+	0.0578513i
$939$	−2.88270	−	54.8616i	−0.0940733	−	1.79034i
$940$	−11.0310	−	2.29098i	−0.359793	−	0.0747237i
$941$	−30.7723	+	13.7007i	−1.00315	+	0.446630i	−0.841523	−	0.540222i	$-0.818340\pi$
$941$	−30.7723	+	13.7007i	−1.00315	+	0.446630i	−0.161625	+	0.986852i	$0.551674\pi$
$942$	−17.6658	+	17.6707i	−0.575584	+	0.575741i
$943$	−32.2182	−	55.8036i	−1.04917	−	1.81722i
$944$	−2.73733	−	8.42463i	−0.0890924	−	0.274198i
$945$	−18.3398	−	2.80940i	−0.596594	−	0.0913897i
$946$	11.9413	−	36.7515i	0.388245	−	1.19489i
$947$	40.1494	−	8.53401i	1.30468	−	0.277318i	0.497417	−	0.867512i	$-0.334282\pi$
$947$	40.1494	−	8.53401i	1.30468	−	0.277318i	0.807262	+	0.590194i	$0.200949\pi$
$948$	−14.9357	−	7.60754i	−0.485088	−	0.247081i
$949$	4.54306	−	7.86880i	0.147474	−	0.255432i
$950$	−5.46182	−	5.95331i	−0.177205	−	0.193151i
$951$	−7.36781	+	11.3488i	−0.238918	+	0.368011i
$952$	1.33651	+	0.595053i	0.0433166	+	0.0192858i
$953$	−18.3625	+	56.5138i	−0.594818	+	1.83066i	−0.0391893	+	0.999232i	$0.512478\pi$
$953$	−18.3625	+	56.5138i	−0.594818	+	1.83066i	−0.555629	+	0.831430i	$0.687522\pi$
$954$	−2.51708	+	5.65762i	−0.0814935	+	0.183172i
$955$	−8.00435	−	24.2493i	−0.259015	−	0.784689i
$956$	2.93775	−	3.26271i	0.0950137	−	0.105523i
$957$	−48.7955	−	2.55057i	−1.57733	−	0.0824483i
$958$	6.59610	+	1.40204i	0.213110	+	0.0452980i
$959$	−25.1156	+	11.1822i	−0.811025	+	0.361092i
$960$	−10.7199	+	28.3322i	−0.345984	+	0.914419i
$961$	−21.5105	−	9.57709i	−0.693887	−	0.308939i
$962$	−2.03059	−	1.47531i	−0.0654687	−	0.0475658i
$963$	56.9322	−	18.5156i	1.83462	−	0.596658i
$964$	9.37349	−	6.81024i	0.301900	−	0.219343i
$965$	−3.96335	+	39.4797i	−0.127585	+	1.27090i
$966$	15.7294	−	6.04041i	0.506084	−	0.194347i
$967$	6.02838	+	1.28137i	0.193860	+	0.0412062i	0.303818	−	0.952730i	$-0.401738\pi$
$967$	6.02838	+	1.28137i	0.193860	+	0.0412062i	−0.109958	+	0.993936i	$0.535072\pi$
$968$	−17.8838	+	30.9756i	−0.574807	+	0.995595i
$969$	0.557404	−	0.557557i	0.0179064	−	0.0179113i
$970$	4.46566	−	0.971002i	0.143384	−	0.0311770i
$971$	−13.0593	+	40.1925i	−0.419094	+	1.28984i	0.489443	+	0.872036i	$0.337200\pi$
$971$	−13.0593	+	40.1925i	−0.419094	+	1.28984i	−0.908537	+	0.417804i	$0.862800\pi$
$972$	13.4612	+	0.696244i	0.431769	+	0.0223320i
$973$	11.1201	−	8.07923i	0.356494	−	0.259008i
$974$	12.3308	+	21.3576i	0.395105	+	0.684341i
$975$	−1.26058	+	8.47773i	−0.0403710	+	0.271505i
$976$	10.1306	−	17.5467i	0.324273	−	0.561657i
$977$	−1.22573	−	11.6621i	−0.0392147	−	0.373103i	−0.996476	−	0.0838785i	$-0.973269\pi$
$977$	−1.22573	−	11.6621i	−0.0392147	−	0.373103i	0.957261	−	0.289225i	$-0.0933974\pi$
$978$	3.21242	+	3.96590i	0.102722	+	0.126816i
$979$	5.87583	−	1.24895i	0.187792	−	0.0399165i
$980$	6.93731	−	5.08987i	0.221604	−	0.162590i
$981$	23.0677	+	7.48819i	0.736496	+	0.239080i
$982$	−10.7959			−0.344510
$983$	3.94352	−	4.37972i	0.125779	−	0.139692i	−0.676966	−	0.736014i	$-0.736706\pi$
$983$	3.94352	−	4.37972i	0.125779	−	0.139692i	0.802745	+	0.596323i	$0.203372\pi$
$984$	46.3103	+	37.4909i	1.47632	+	1.19516i
$985$	−2.35225	−	21.4184i	−0.0749488	−	0.682447i
$986$	−0.197861	−	1.88252i	−0.00630118	−	0.0599517i
$987$	−12.5261	−	10.1406i	−0.398710	−	0.322779i
$988$	0.135655	−	1.29067i	0.00431575	−	0.0410616i
$989$	−35.1953	+	25.5709i	−1.11914	+	0.813106i
$990$	33.8987	+	3.39371i	1.07737	+	0.107859i
$991$	−6.01131	−	4.36747i	−0.190956	−	0.138737i	0.488200	−	0.872732i	$-0.337654\pi$
$991$	−6.01131	−	4.36747i	−0.190956	−	0.138737i	−0.679155	+	0.733995i	$0.737654\pi$
$992$	8.18793	−	9.09362i	0.259967	−	0.288723i
$993$	20.2558	−	31.2006i	0.642799	−	0.990120i
$994$	−27.4187	−	5.82802i	−0.869668	−	0.184854i
$995$	−6.34362	+	2.85990i	−0.201106	+	0.0906649i
$996$	8.80387	−	1.39563i	0.278961	−	0.0442222i
$997$	1.78229	−	0.378837i	0.0564456	−	0.0119979i	−0.179602	−	0.983739i	$-0.557481\pi$
$997$	1.78229	−	0.378837i	0.0564456	−	0.0119979i	0.236048	+	0.971741i	$0.424148\pi$
$998$	−3.51103	+	2.55091i	−0.111140	+	0.0807476i
$999$	−12.2163	−	1.92973i	−0.386506	−	0.0610541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.211.11	yes	224
3.2	odd	2		675.2.r.a.361.18		224
9.2	odd	6		675.2.r.a.586.11		224
9.7	even	3	inner	225.2.q.a.61.18	yes	224
25.16	even	5	inner	225.2.q.a.166.18	yes	224
75.41	odd	10		675.2.r.a.91.11		224
225.16	even	15	inner	225.2.q.a.16.11	✓	224
225.191	odd	30		675.2.r.a.316.18		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.11	✓	224	225.16	even	15	inner
225.2.q.a.61.18	yes	224	9.7	even	3	inner
225.2.q.a.166.18	yes	224	25.16	even	5	inner
225.2.q.a.211.11	yes	224	1.1	even	1	trivial
675.2.r.a.91.11		224	75.41	odd	10
675.2.r.a.316.18		224	225.191	odd	30
675.2.r.a.361.18		224	3.2	odd	2
675.2.r.a.586.11		224	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.973390 - 0.433381i) q^{2} +(-1.71069 + 0.271186i) q^{3} +(-0.578592 - 0.642592i) q^{4} +(-2.03848 + 0.919011i) q^{5} +(1.78270 + 0.477410i) q^{6} +(-0.798426 - 1.38291i) q^{7} +(0.943229 + 2.90296i) q^{8} +(2.85292 - 0.927831i) q^{9} +O(q^{10})\)	\(q+(-0.973390 - 0.433381i) q^{2} +(-1.71069 + 0.271186i) q^{3} +(-0.578592 - 0.642592i) q^{4} +(-2.03848 + 0.919011i) q^{5} +(1.78270 + 0.477410i) q^{6} +(-0.798426 - 1.38291i) q^{7} +(0.943229 + 2.90296i) q^{8} +(2.85292 - 0.927831i) q^{9} +(2.38252 - 0.0111154i) q^{10} +(4.35427 + 1.93865i) q^{11} +(1.16405 + 0.942368i) q^{12} +(0.904123 - 0.402542i) q^{13} +(0.177851 + 1.69214i) q^{14} +(3.23799 - 2.12495i) q^{15} +(0.159189 - 1.51458i) q^{16} +(0.0927524 + 0.285463i) q^{17} +(-3.17910 - 0.333258i) q^{18} +(0.468623 + 1.44227i) q^{19} +(1.77000 + 0.778180i) q^{20} +(1.74089 + 2.14922i) q^{21} +(-3.39823 - 3.77412i) q^{22} +(0.597633 + 5.68610i) q^{23} +(-2.40082 - 4.71027i) q^{24} +(3.31084 - 3.74678i) q^{25} -1.05452 q^{26} +(-4.62884 + 2.36090i) q^{27} +(-0.426686 + 1.31321i) q^{28} +(5.78936 - 1.23057i) q^{29} +(-4.07274 + 0.665123i) q^{30} +(2.67051 + 0.567634i) q^{31} +(2.24101 - 3.88154i) q^{32} +(-7.97454 - 2.13560i) q^{33} +(0.0334298 - 0.318064i) q^{34} +(2.89849 + 2.08529i) q^{35} +(-2.24689 - 1.29642i) q^{36} +(1.92560 + 1.39903i) q^{37} +(0.168901 - 1.60699i) q^{38} +(-1.43751 + 0.933810i) q^{39} +(-4.59061 - 5.05080i) q^{40} +(-10.2958 + 4.58400i) q^{41} +(-0.763133 - 2.84649i) q^{42} +(3.80449 + 6.58957i) q^{43} +(-1.27359 - 3.91970i) q^{44} +(-4.96294 + 4.51323i) q^{45} +(1.88252 - 5.79380i) q^{46} +(-5.69960 + 1.21149i) q^{47} +(0.138411 + 2.63415i) q^{48} +(2.22503 - 3.85387i) q^{49} +(-4.84652 + 2.21222i) q^{50} +(-0.236084 - 0.463185i) q^{51} +(-0.781789 - 0.348075i) q^{52} +(0.598625 - 1.84238i) q^{53} +(5.52884 - 0.292028i) q^{54} +(-10.6578 + 0.0497227i) q^{55} +(3.26145 - 3.62220i) q^{56} +(-1.19279 - 2.34020i) q^{57} +(-6.16861 - 1.31118i) q^{58} +(5.31370 - 2.36581i) q^{59} +(-3.23895 - 0.851225i) q^{60} +(12.1540 + 5.41129i) q^{61} +(-2.35344 - 1.70988i) q^{62} +(-3.56095 - 3.20453i) q^{63} +(-6.32771 + 4.59735i) q^{64} +(-1.47310 + 1.65147i) q^{65} +(6.83681 + 5.53479i) q^{66} +(1.02420 + 0.217699i) q^{67} +(0.129770 - 0.224768i) q^{68} +(-2.56436 - 9.56508i) q^{69} +(-1.91764 - 3.28595i) q^{70} +(-5.09100 + 15.6685i) q^{71} +(5.38441 + 7.40674i) q^{72} +(7.42742 - 5.39634i) q^{73} +(-1.26805 - 2.19633i) q^{74} +(-4.64774 + 7.30743i) q^{75} +(0.655651 - 1.13562i) q^{76} +(-0.795582 - 7.56945i) q^{77} +(1.80395 - 0.285971i) q^{78} +(-10.9470 + 2.32686i) q^{79} +(1.06741 + 3.23374i) q^{80} +(7.27826 - 5.29405i) q^{81} +12.0085 q^{82} +(3.98246 - 4.42297i) q^{83} +(0.373804 - 2.36220i) q^{84} +(-0.451418 - 0.496671i) q^{85} +(-0.847457 - 8.06302i) q^{86} +(-9.57009 + 3.67511i) q^{87} +(-1.52074 + 14.4689i) q^{88} +(1.01962 - 0.740795i) q^{89} +(6.78682 - 2.24229i) q^{90} +(-1.27856 - 0.928926i) q^{91} +(3.30805 - 3.67397i) q^{92} +(-4.72234 - 0.246840i) q^{93} +(6.07297 + 1.29085i) q^{94} +(-2.28075 - 2.50938i) q^{95} +(-2.78105 + 7.24785i) q^{96} +(1.87620 - 0.398799i) q^{97} +(-3.83602 + 2.78703i) q^{98} +(14.2211 + 1.49077i) 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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