LMFDB - Embedded newform 512.2.o.a.109.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

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

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			109.40
Character	$\chi$	$=$	512.109
Dual form			512.2.o.a.357.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.437017 + 1.34500i) q^{2} +(0.0973246 - 0.789087i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-1.66159 + 0.373123i) q^{5} +(1.10385 - 0.213943i) q^{6} +(-1.54386 + 1.14501i) q^{7} +(-2.28825 - 1.66250i) q^{8} +(2.29691 + 0.575346i) q^{9} +O(q^{10})$	\(q+(0.437017 + 1.34500i) q^{2} +(0.0973246 - 0.789087i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-1.66159 + 0.373123i) q^{5} +(1.10385 - 0.213943i) q^{6} +(-1.54386 + 1.14501i) q^{7} +(-2.28825 - 1.66250i) q^{8} +(2.29691 + 0.575346i) q^{9} +(-1.22799 - 2.07177i) q^{10} +(-2.11335 - 0.155890i) q^{11} +(0.770155 + 1.39118i) q^{12} +(-5.70658 - 4.01903i) q^{13} +(-2.21472 - 1.57610i) q^{14} +(0.132713 + 1.34745i) q^{15} +(1.23606 - 3.80423i) q^{16} +(-0.879496 - 0.0866228i) q^{17} +(0.229950 + 3.34077i) q^{18} +(1.03379 + 2.67999i) q^{19} +(2.24988 - 2.55705i) q^{20} +(0.753253 + 1.32968i) q^{21} +(-0.713897 - 2.91057i) q^{22} +(-4.76796 - 0.234235i) q^{23} +(-1.53456 + 1.64383i) q^{24} +(-1.89828 + 0.897819i) q^{25} +(2.91170 - 9.43171i) q^{26} +(1.53596 - 3.98184i) q^{27} +(1.15198 - 3.66758i) q^{28} +(-1.64693 - 3.27188i) q^{29} +(-1.75432 + 0.767359i) q^{30} +(1.04495 + 5.25329i) q^{31} +(5.65685 - 2.37634e-5i) q^{32} +(-0.328691 + 1.65244i) q^{33} +(-0.267848 - 1.22078i) q^{34} +(2.13804 - 2.47858i) q^{35} +(-4.39283 + 1.76926i) q^{36} +(-5.30693 - 5.05262i) q^{37} +(-3.15280 + 2.56164i) q^{38} +(-3.72675 + 4.11183i) q^{39} +(4.42246 + 1.90860i) q^{40} +(0.919160 + 0.434731i) q^{41} +(-1.45923 + 1.59422i) q^{42} +(-3.05794 + 3.91839i) q^{43} +(3.60272 - 2.23216i) q^{44} +(-4.03120 - 0.0989604i) q^{45} +(-1.76864 - 6.51526i) q^{46} +(1.77455 - 0.538304i) q^{47} +(-2.88157 - 1.34560i) q^{48} +(-0.959521 + 3.16312i) q^{49} +(-2.03714 - 2.16082i) q^{50} +(-0.153949 + 0.685568i) q^{51} +(13.9581 - 0.205588i) q^{52} +(0.0417411 - 0.0829253i) q^{53} +(6.02680 + 0.325735i) q^{54} +(3.56968 - 0.529513i) q^{55} +(5.43632 - 0.0533863i) q^{56} +(2.21536 - 0.554919i) q^{57} +(3.68093 - 3.64498i) q^{58} +(7.07164 + 10.0410i) q^{59} +(-1.79876 - 2.02421i) q^{60} +(2.40698 + 1.36354i) q^{61} +(-6.60900 + 3.70123i) q^{62} +(-4.20488 + 1.74172i) q^{63} +(2.47217 + 7.60844i) q^{64} +(10.9816 + 4.54873i) q^{65} +(-2.36617 + 0.280057i) q^{66} +(-3.10141 + 0.858277i) q^{67} +(1.52488 - 0.893754i) q^{68} +(-0.648871 + 3.73954i) q^{69} +(4.26805 + 1.79247i) q^{70} +(1.79850 - 3.00062i) q^{71} +(-4.29939 - 5.13515i) q^{72} +(1.20453 + 0.893343i) q^{73} +(4.47654 - 9.34589i) q^{74} +(0.523708 + 1.58529i) q^{75} +(-4.82323 - 3.12102i) q^{76} +(3.44121 - 2.17912i) q^{77} +(-7.15906 - 3.21552i) q^{78} +(1.78315 + 3.33603i) q^{79} +(-0.634374 + 6.78228i) q^{80} +(3.27230 + 1.74908i) q^{81} +(-0.183022 + 1.42625i) q^{82} +(-8.62875 + 8.21525i) q^{83} +(-2.78192 - 1.26596i) q^{84} +(1.49368 - 0.184228i) q^{85} +(-6.60660 - 2.40052i) q^{86} +(-2.74208 + 0.981133i) q^{87} +(4.57670 + 3.87016i) q^{88} +(-8.59731 + 0.422359i) q^{89} +(-1.62860 - 5.46520i) q^{90} +(13.4120 - 0.329246i) q^{91} +(7.99007 - 5.22609i) q^{92} +(4.24700 - 0.313278i) q^{93} +(1.49953 + 2.15152i) q^{94} +(-2.71770 - 4.06732i) q^{95} +(0.550532 - 4.46375i) q^{96} +(8.03914 - 12.0314i) q^{97} +(-4.67371 + 0.0917838i) q^{98} +(-4.76447 - 1.57397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{119}{128}\right)$	$1$

Coefficient data

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

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

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

$2$	0.437017	+	1.34500i	0.309018	+	0.951056i
$2$	0.437017	+	1.34500i	0.309018	+	0.951056i
$3$	0.0973246	−	0.789087i	0.0561904	−	0.455579i	−0.937890	−	0.346933i	$-0.887223\pi$
$3$	0.0973246	−	0.789087i	0.0561904	−	0.455579i	0.994080	−	0.108647i	$-0.0346517\pi$
$4$	−1.61803	+	1.17557i	−0.809016	+	0.587787i
$5$	−1.66159	+	0.373123i	−0.743087	+	0.166866i	−0.574137	−	0.818759i	$-0.694662\pi$
$5$	−1.66159	+	0.373123i	−0.743087	+	0.166866i	−0.168949	+	0.985625i	$0.554037\pi$
$6$	1.10385	−	0.213943i	0.450645	−	0.0873419i
$7$	−1.54386	+	1.14501i	−0.583525	+	0.432772i	−0.846771	−	0.531957i	$-0.821457\pi$
$7$	−1.54386	+	1.14501i	−0.583525	+	0.432772i	0.263246	+	0.964729i	$0.415207\pi$
$8$	−2.28825	−	1.66250i	−0.809018	−	0.587783i
$9$	2.29691	+	0.575346i	0.765636	+	0.191782i
$10$	−1.22799	−	2.07177i	−0.388326	−	0.655153i
$11$	−2.11335	−	0.155890i	−0.637198	−	0.0470025i	−0.248889	−	0.968532i	$-0.580066\pi$
$11$	−2.11335	−	0.155890i	−0.637198	−	0.0470025i	−0.388309	+	0.921529i	$0.626941\pi$
$12$	0.770155	+	1.39118i	0.222325	+	0.401599i
$13$	−5.70658	−	4.01903i	−1.58272	−	1.11468i	−0.936028	−	0.351926i	$-0.885527\pi$
$13$	−5.70658	−	4.01903i	−1.58272	−	1.11468i	−0.646692	−	0.762751i	$-0.723848\pi$
$14$	−2.21472	−	1.57610i	−0.591910	−	0.421231i
$15$	0.132713	+	1.34745i	0.0342663	+	0.347911i
$16$	1.23606	−	3.80423i	0.309014	−	0.951058i
$17$	−0.879496	−	0.0866228i	−0.213309	−	0.0210091i	−0.00920196	−	0.999958i	$-0.502929\pi$
$17$	−0.879496	−	0.0866228i	−0.213309	−	0.0210091i	−0.204107	+	0.978949i	$0.565429\pi$
$18$	0.229950	+	3.34077i	0.0541998	+	0.787427i
$19$	1.03379	+	2.67999i	0.237167	+	0.614833i	0.999476	−	0.0323813i	$-0.0103091\pi$
$19$	1.03379	+	2.67999i	0.237167	+	0.614833i	−0.762309	+	0.647214i	$0.775934\pi$
$20$	2.24988	−	2.55705i	0.503087	−	0.571773i
$21$	0.753253	+	1.32968i	0.164373	+	0.290160i
$22$	−0.713897	−	2.91057i	−0.152203	−	0.620536i
$23$	−4.76796	−	0.234235i	−0.994189	−	0.0488414i	−0.454535	−	0.890729i	$-0.650195\pi$
$23$	−4.76796	−	0.234235i	−0.994189	−	0.0488414i	−0.539653	+	0.841887i	$0.681445\pi$
$24$	−1.53456	+	1.64383i	−0.313241	+	0.335544i
$25$	−1.89828	+	0.897819i	−0.379656	+	0.179564i
$26$	2.91170	−	9.43171i	0.571032	−	1.84971i
$27$	1.53596	−	3.98184i	0.295596	−	0.766305i
$28$	1.15198	−	3.66758i	0.217704	−	0.693107i
$29$	−1.64693	−	3.27188i	−0.305826	−	0.607573i	0.687065	−	0.726596i	$-0.258899\pi$
$29$	−1.64693	−	3.27188i	−0.305826	−	0.607573i	−0.992891	+	0.119023i	$0.962024\pi$
$30$	−1.75432	+	0.767359i	−0.320294	+	0.140100i
$31$	1.04495	+	5.25329i	0.187678	+	0.943519i	0.953712	+	0.300720i	$0.0972270\pi$
$31$	1.04495	+	5.25329i	0.187678	+	0.943519i	−0.766035	+	0.642799i	$0.777773\pi$
$32$	5.65685		2.37634e-5i	1.00000		4.20081e-6i
$33$	−0.328691	+	1.65244i	−0.0572178	+	0.287653i
$34$	−0.267848	−	1.22078i	−0.0459355	−	0.209361i
$35$	2.13804	−	2.47858i	0.361395	−	0.418957i
$36$	−4.39283	+	1.76926i	−0.732139	+	0.294876i
$37$	−5.30693	−	5.05262i	−0.872454	−	0.830646i	0.114203	−	0.993457i	$-0.463569\pi$
$37$	−5.30693	−	5.05262i	−0.872454	−	0.830646i	−0.986657	+	0.162812i	$0.947944\pi$
$38$	−3.15280	+	2.56164i	−0.511451	+	0.415553i
$39$	−3.72675	+	4.11183i	−0.596757	+	0.658420i
$40$	4.42246	+	1.90860i	0.699252	+	0.301776i
$41$	0.919160	+	0.434731i	0.143549	+	0.0678935i	0.497980	−	0.867189i	$-0.334075\pi$
$41$	0.919160	+	0.434731i	0.143549	+	0.0678935i	−0.354431	+	0.935082i	$0.615325\pi$
$42$	−1.45923	+	1.59422i	−0.225164	+	0.245993i
$43$	−3.05794	+	3.91839i	−0.466332	+	0.597550i	−0.962703	−	0.270561i	$-0.912791\pi$
$43$	−3.05794	+	3.91839i	−0.466332	+	0.597550i	0.496371	+	0.868111i	$0.334666\pi$
$44$	3.60272	−	2.23216i	0.543131	−	0.336511i
$45$	−4.03120	−	0.0989604i	−0.600936	−	0.0147521i
$46$	−1.76864	−	6.51526i	−0.260771	−	0.960622i
$47$	1.77455	−	0.538304i	0.258845	−	0.0785197i	−0.158195	−	0.987408i	$-0.550568\pi$
$47$	1.77455	−	0.538304i	0.258845	−	0.0785197i	0.417040	+	0.908888i	$0.363068\pi$
$48$	−2.88157	−	1.34560i	−0.415919	−	0.194221i
$49$	−0.959521	+	3.16312i	−0.137074	+	0.451874i
$50$	−2.03714	−	2.16082i	−0.288096	−	0.305586i
$51$	−0.153949	+	0.685568i	−0.0215572	+	0.0959987i
$52$	13.9581	−	0.205588i	1.93564	−	0.0285099i
$53$	0.0417411	−	0.0829253i	0.00573358	−	0.0113907i	−0.890339	−	0.455298i	$-0.849533\pi$
$53$	0.0417411	−	0.0829253i	0.00573358	−	0.0113907i	0.896073	+	0.443907i	$0.146408\pi$
$54$	6.02680	+	0.325735i	0.820143	+	0.0443270i
$55$	3.56968	−	0.529513i	0.481336	−	0.0713995i
$56$	5.43632	−	0.0533863i	0.726459	−	0.00713405i
$57$	2.21536	−	0.554919i	0.293432	−	0.0735008i
$58$	3.68093	−	3.64498i	0.483330	−	0.478609i
$59$	7.07164	+	10.0410i	0.920649	+	1.30722i	0.951485	+	0.307697i	$0.0995582\pi$
$59$	7.07164	+	10.0410i	0.920649	+	1.30722i	−0.0308356	+	0.999524i	$0.509817\pi$
$60$	−1.79876	−	2.02421i	−0.232219	−	0.261324i
$61$	2.40698	+	1.36354i	0.308182	+	0.174583i	0.639198	−	0.769042i	$-0.279266\pi$
$61$	2.40698	+	1.36354i	0.308182	+	0.174583i	−0.331016	+	0.943625i	$0.607391\pi$
$62$	−6.60900	+	3.70123i	−0.839344	+	0.470056i
$63$	−4.20488	+	1.74172i	−0.529766	+	0.219436i
$64$	2.47217	+	7.60844i	0.309022	+	0.951055i
$65$	10.9816	+	4.54873i	1.36210	+	0.564200i
$66$	−2.36617	+	0.280057i	−0.291256	+	0.0344726i
$67$	−3.10141	+	0.858277i	−0.378898	+	0.104855i	−0.450958	−	0.892545i	$-0.648918\pi$
$67$	−3.10141	+	0.858277i	−0.378898	+	0.104855i	0.0720602	+	0.997400i	$0.477043\pi$
$68$	1.52488	−	0.893754i	0.184919	−	0.108384i
$69$	−0.648871	+	3.73954i	−0.0781149	+	0.450187i
$70$	4.26805	+	1.79247i	0.510129	+	0.214242i
$71$	1.79850	−	3.00062i	0.213443	−	0.356109i	−0.732323	−	0.680958i	$-0.761564\pi$
$71$	1.79850	−	3.00062i	0.213443	−	0.356109i	0.945766	+	0.324849i	$0.105314\pi$
$72$	−4.29939	−	5.13515i	−0.506688	−	0.605183i
$73$	1.20453	+	0.893343i	0.140980	+	0.104558i	0.663891	−	0.747829i	$-0.268904\pi$
$73$	1.20453	+	0.893343i	0.140980	+	0.104558i	−0.522911	+	0.852387i	$0.675154\pi$
$74$	4.47654	−	9.34589i	0.520387	−	1.08644i
$75$	0.523708	+	1.58529i	0.0604726	+	0.183053i
$76$	−4.82323	−	3.12102i	−0.553262	−	0.358006i
$77$	3.44121	−	2.17912i	0.392162	−	0.248334i
$78$	−7.15906	−	3.21552i	−0.810603	−	0.364086i
$79$	1.78315	+	3.33603i	0.200620	+	0.375333i	0.962033	−	0.272934i	$-0.0879941\pi$
$79$	1.78315	+	3.33603i	0.200620	+	0.375333i	−0.761413	+	0.648267i	$0.775494\pi$
$80$	−0.634374	+	6.78228i	−0.0709251	+	0.758282i
$81$	3.27230	+	1.74908i	0.363589	+	0.194342i
$82$	−0.183022	+	1.42625i	−0.0202114	+	0.157503i
$83$	−8.62875	+	8.21525i	−0.947128	+	0.901741i	−0.995275	−	0.0970996i	$-0.969043\pi$
$83$	−8.62875	+	8.21525i	−0.947128	+	0.901741i	0.0481468	+	0.998840i	$0.484668\pi$
$84$	−2.78192	−	1.26596i	−0.303533	−	0.138127i
$85$	1.49368	−	0.184228i	0.162013	−	0.0199824i
$86$	−6.60660	−	2.40052i	−0.712408	−	0.258855i
$87$	−2.74208	+	0.981133i	−0.293982	+	0.105188i
$88$	4.57670	+	3.87016i	0.487877	+	0.412560i
$89$	−8.59731	+	0.422359i	−0.911313	+	0.0447699i	−0.499320	−	0.866417i	$-0.666417\pi$
$89$	−8.59731	+	0.422359i	−0.911313	+	0.0447699i	−0.411992	+	0.911187i	$0.635167\pi$
$90$	−1.62860	−	5.46520i	−0.171670	−	0.576082i
$91$	13.4120	−	0.329246i	1.40596	−	0.0345143i
$92$	7.99007	−	5.22609i	0.833023	−	0.544857i
$93$	4.24700	−	0.313278i	0.440394	−	0.0324854i
$94$	1.49953	+	2.15152i	0.154664	+	0.221912i
$95$	−2.71770	−	4.06732i	−0.278830	−	0.417299i
$96$	0.550532	−	4.46375i	0.0561884	−	0.455580i
$97$	8.03914	−	12.0314i	0.816251	−	1.22161i	−0.156022	−	0.987754i	$-0.549867\pi$
$97$	8.03914	−	12.0314i	0.816251	−	1.22161i	0.972272	−	0.233852i	$-0.0751330\pi$
$98$	−4.67371	+	0.0917838i	−0.472116	+	0.00927157i
$99$	−4.76447	−	1.57397i	−0.478847	−	0.158190i
$100$	2.01602	−	3.68427i	0.201602	−	0.368427i
$101$	10.6357	−	4.71448i	1.05829	−	0.469108i	0.198684	−	0.980064i	$-0.436333\pi$
$101$	10.6357	−	4.71448i	1.05829	−	0.469108i	0.859607	+	0.510956i	$0.170708\pi$
$102$	−0.989365	+	0.0925435i	−0.0979618	+	0.00916317i
$103$	−3.47461	+	9.71088i	−0.342364	+	0.956842i	0.639755	+	0.768579i	$0.279036\pi$
$103$	−3.47461	+	9.71088i	−0.342364	+	0.956842i	−0.982119	+	0.188263i	$0.939714\pi$
$104$	6.37644	+	18.6837i	0.625261	+	1.83209i
$105$	−1.74773	−	1.92833i	−0.170561	−	0.188185i
$106$	0.129776	+	0.0199019i	0.0126049	+	0.00193304i
$107$	4.16015	+	1.15127i	0.402177	+	0.111297i	0.461931	−	0.886916i	$-0.347157\pi$
$107$	4.16015	+	1.15127i	0.402177	+	0.111297i	−0.0597540	+	0.998213i	$0.519032\pi$
$108$	2.19570	+	8.24838i	0.211281	+	0.793700i
$109$	−1.90220	+	4.29129i	−0.182197	+	0.411031i	−0.981909	−	0.189354i	$-0.939361\pi$
$109$	−1.90220	+	4.29129i	−0.182197	+	0.411031i	0.799712	+	0.600384i	$0.204986\pi$
$110$	2.27221	+	4.56981i	0.216646	+	0.435714i
$111$	−4.50345	+	3.69589i	−0.427449	+	0.350798i
$112$	2.44757	+	7.28850i	0.231273	+	0.688698i
$113$	3.86513	−	4.70968i	0.363601	−	0.443049i	−0.558788	−	0.829310i	$-0.688734\pi$
$113$	3.86513	−	4.70968i	0.363601	−	0.443049i	0.922390	+	0.386261i	$0.126234\pi$
$114$	1.71451	+	2.73714i	0.160579	+	0.256357i
$115$	8.00981	−	1.38983i	0.746918	−	0.129603i
$116$	6.51111	+	3.35792i	0.604541	+	0.311775i
$117$	−10.7952	−	12.5146i	−0.998012	−	1.15697i
$118$	−10.4146	+	13.8994i	−0.958744	+	1.27954i
$119$	1.45700	−	0.873295i	0.133563	−	0.0800548i
$120$	1.93647	−	3.30395i	0.176774	−	0.301608i
$121$	−6.43901	−	0.955137i	−0.585365	−	0.0868307i
$122$	−0.782061	+	3.83327i	−0.0708045	+	0.347048i
$123$	0.432497	−	0.682987i	0.0389969	−	0.0615829i
$124$	−7.86639	−	7.27159i	−0.706422	−	0.653008i
$125$	9.53182	−	7.43871i	0.852552	−	0.665338i
$126$	−4.18021	−	4.89439i	−0.372403	−	0.436027i
$127$	−2.14207	+	2.14207i	−0.190078	+	0.190078i	−0.795730	−	0.605652i	$-0.792912\pi$
$127$	−2.14207	+	2.14207i	−0.190078	+	0.190078i	0.605652	+	0.795730i	$0.292912\pi$
$128$	−9.15294	+	6.65008i	−0.809014	+	0.587790i
$129$	2.79434	+	2.79434i	0.246028	+	0.246028i
$130$	−1.31888	+	16.7581i	−0.115673	+	1.46978i
$131$	−3.74237	−	4.79541i	−0.326973	−	0.418977i	0.596517	−	0.802601i	$-0.296551\pi$
$131$	−3.74237	−	4.79541i	−0.326973	−	0.418977i	−0.923489	+	0.383624i	$0.874676\pi$
$132$	−1.41073	−	3.06010i	−0.122789	−	0.266348i
$133$	−4.66463	−	2.95385i	−0.404475	−	0.256131i
$134$	−2.50975	−	3.79631i	−0.216809	−	0.327951i
$135$	−1.06643	+	7.18929i	−0.0917837	+	0.618756i
$136$	1.86850	+	1.66038i	0.160222	+	0.142376i
$137$	−9.57902	−	15.9816i	−0.818391	−	1.36540i	−0.928442	−	0.371477i	$-0.878851\pi$
$137$	−9.57902	−	15.9816i	−0.818391	−	1.36540i	0.110051	−	0.993926i	$-0.464899\pi$
$138$	−5.31323	+	0.761512i	−0.452293	+	0.0648242i
$139$	−11.1141	+	9.58705i	−0.942682	+	0.813163i	−0.982542	−	0.186042i	$-0.940434\pi$
$139$	−11.1141	+	9.58705i	−0.942682	+	0.813163i	0.0398595	+	0.999205i	$0.487309\pi$
$140$	−0.545662	+	6.52385i	−0.0461169	+	0.551366i
$141$	−0.252061	−	1.45266i	−0.0212274	−	0.122336i
$142$	4.82181	+	1.10766i	0.404637	+	0.0929526i
$143$	11.4334	+	9.38319i	0.956113	+	0.784662i
$144$	5.02785	−	8.02681i	0.418988	−	0.668901i
$145$	3.95733	+	4.82202i	0.328638	+	0.400447i
$146$	−0.675141	+	2.01050i	−0.0558751	+	0.166390i
$147$	2.40259	+	1.06499i	0.198162	+	0.0878393i
$148$	14.5265	+	1.93661i	1.19407	+	0.159189i
$149$	3.91938	−	14.1628i	0.321088	−	1.16026i	−0.609074	−	0.793113i	$-0.708459\pi$
$149$	3.91938	−	14.1628i	0.321088	−	1.16026i	0.930162	−	0.367149i	$-0.119666\pi$
$150$	−1.90334	+	1.39718i	−0.155407	+	0.114080i
$151$	−14.8946	+	13.4997i	−1.21211	+	1.09859i	−0.219704	+	0.975567i	$0.570509\pi$
$151$	−14.8946	+	13.4997i	−1.21211	+	1.09859i	−0.992404	+	0.123024i	$0.960741\pi$
$152$	2.08993	−	7.85117i	0.169516	−	0.636814i
$153$	−1.97028	−	0.704979i	−0.159288	−	0.0569942i
$154$	4.43478	+	3.67610i	0.357365	+	0.296229i
$155$	−3.69640	−	8.33894i	−0.296902	−	0.669800i
$156$	1.19624	−	11.0341i	0.0957756	−	0.883439i
$157$	−3.63568	+	11.0053i	−0.290159	+	0.878322i	0.696788	+	0.717277i	$0.254612\pi$
$157$	−3.63568	+	11.0053i	−0.290159	+	0.878322i	−0.986947	+	0.161046i	$0.948513\pi$
$158$	−3.70769	+	3.85623i	−0.294968	+	0.306785i
$159$	−0.0613728	−	0.0410080i	−0.00486718	−	0.00325215i
$160$	−9.39937	+	2.11074i	−0.743086	+	0.166869i
$161$	7.62928	−	5.09772i	0.601271	−	0.401757i
$162$	−0.922456	+	5.16561i	−0.0724750	+	0.405849i
$163$	−0.989488	−	13.4142i	−0.0775026	−	1.05068i	−0.886458	−	0.462808i	$-0.846842\pi$
$163$	−0.989488	−	13.4142i	−0.0775026	−	1.05068i	0.808956	−	0.587869i	$-0.200033\pi$
$164$	−1.99829	+	0.377133i	−0.156040	+	0.0294491i
$165$	−0.0704134	−	2.86832i	−0.00548168	−	0.223299i
$166$	−14.8204	−	8.01543i	−1.15029	−	0.622118i
$167$	1.18387	+	24.0982i	0.0916107	+	1.86478i	0.403915	+	0.914796i	$0.367649\pi$
$167$	1.18387	+	24.0982i	0.0916107	+	1.86478i	−0.312304	+	0.949982i	$0.601101\pi$
$168$	0.486961	−	4.29492i	0.0375698	−	0.331360i
$169$	12.0329	+	33.6297i	0.925607	+	2.58690i
$170$	0.900553	+	1.92849i	0.0690692	+	0.147908i
$171$	0.832593	+	6.75048i	0.0636699	+	0.516222i
$172$	0.341493	−	9.93493i	0.0260386	−	0.757531i
$173$	−5.34003	−	5.60881i	−0.405995	−	0.426430i	0.489154	−	0.872198i	$-0.337306\pi$
$173$	−5.34003	−	5.60881i	−0.405995	−	0.426430i	−0.895149	+	0.445768i	$0.852931\pi$
$174$	−2.51796	−	3.25932i	−0.190886	−	0.247088i
$175$	1.90267	−	3.55965i	0.143829	−	0.269084i
$176$	−3.20525	+	7.84697i	−0.241605	+	0.591487i
$177$	8.61143	−	4.60290i	0.647275	−	0.345975i
$178$	−4.32524	−	11.3788i	−0.324191	−	0.852875i
$179$	−9.55446	−	15.0881i	−0.714134	−	1.12774i	−0.986215	−	0.165466i	$-0.947087\pi$
$179$	−9.55446	−	15.0881i	−0.714134	−	1.12774i	0.272082	−	0.962274i	$-0.412288\pi$
$180$	6.63894	−	4.57885i	0.494838	−	0.341287i
$181$	−24.8442	+	8.20742i	−1.84666	+	0.610053i	−0.850150	+	0.526541i	$0.823489\pi$
$181$	−24.8442	+	8.20742i	−1.84666	+	0.610053i	−0.996507	+	0.0835117i	$0.973386\pi$
$182$	6.30410	+	17.8952i	0.467291	+	1.32648i
$183$	1.31021	−	1.76661i	0.0968532	−	0.130591i
$184$	10.5209	+	8.46273i	0.775609	+	0.623881i
$185$	10.7032	+	6.41526i	0.786915	+	0.471659i
$186$	2.27737	+	5.57530i	0.166985	+	0.408801i
$187$	1.84518	+	0.320168i	0.134933	+	0.0234130i
$188$	−2.23846	+	2.95711i	−0.163257	+	0.215669i
$189$	2.18791	+	7.90610i	0.159147	+	0.575084i
$190$	4.28286	−	5.43279i	0.310711	−	0.394136i
$191$	3.37412	−	8.14585i	0.244143	−	0.589413i	−0.753544	−	0.657398i	$-0.771657\pi$
$191$	3.37412	−	8.14585i	0.244143	−	0.589413i	0.997686	+	0.0679852i	$0.0216571\pi$
$192$	6.24432	−	1.21027i	0.450645	−	0.0873438i
$193$	3.41521	+	8.24505i	0.245832	+	0.593492i	0.997842	−	0.0656603i	$-0.0209154\pi$
$193$	3.41521	+	8.24505i	0.245832	+	0.593492i	−0.752010	+	0.659152i	$0.770915\pi$
$194$	19.6955	+	5.55467i	1.41405	+	0.398802i
$195$	4.65812	−	8.22273i	0.333575	−	0.588842i
$196$	−2.16594	−	6.24601i	−0.154710	−	0.446144i
$197$	9.75457	−	6.86995i	0.694985	−	0.489463i	−0.173719	−	0.984795i	$-0.555579\pi$
$197$	9.75457	−	6.86995i	0.694985	−	0.489463i	0.868704	+	0.495332i	$0.164954\pi$
$198$	0.0348270	−	7.09605i	0.00247504	−	0.504294i
$199$	−4.26243	−	17.0166i	−0.302156	−	1.20627i	−0.910806	−	0.412834i	$-0.864539\pi$
$199$	−4.26243	−	17.0166i	−0.302156	−	1.20627i	0.608651	−	0.793438i	$-0.291711\pi$
$200$	5.83636	+	1.10146i	0.412693	+	0.0778849i
$201$	0.375411	+	2.53082i	0.0264795	+	0.178510i
$202$	10.9889	+	12.2447i	0.773179	+	0.861531i
$203$	6.28895	+	3.16559i	0.441398	+	0.222181i
$204$	−0.556840	−	1.29025i	−0.0389866	−	0.0903356i
$205$	−1.68948	−	0.379385i	−0.117998	−	0.0264974i
$206$	−14.5796	−	0.429516i	−1.01581	−	0.0299258i
$207$	−10.8168	−	3.28124i	−0.751820	−	0.228062i
$208$	−22.3429	+	16.7414i	−1.54920	+	1.16081i
$209$	−1.76697	−	5.82491i	−0.122224	−	0.402917i
$210$	1.82980	−	3.19341i	0.126268	−	0.220366i
$211$	0.469600	−	19.1294i	0.0323286	−	1.31692i	−0.736051	−	0.676926i	$-0.763312\pi$
$211$	0.469600	−	19.1294i	0.0323286	−	1.31692i	0.768379	−	0.639995i	$-0.221063\pi$
$212$	0.0299464	+	0.183246i	0.00205672	+	0.0125854i
$213$	−2.19271	−	1.71121i	−0.150242	−	0.117250i
$214$	0.269605	+	6.09852i	0.0184298	+	0.416886i
$215$	3.61901	−	7.65176i	0.246815	−	0.521846i
$216$	−10.1345	+	6.55789i	−0.689564	+	0.446208i
$217$	−7.62831	−	6.91389i	−0.517843	−	0.469346i
$218$	−6.60306	−	0.683082i	−0.447216	−	0.0462642i
$219$	0.822156	−	0.863537i	0.0555561	−	0.0583524i
$220$	−5.15338	+	5.05319i	−0.347441	+	0.340686i
$221$	4.67077	+	4.02904i	0.314190	+	0.271022i
$222$	−6.93904	−	4.44196i	−0.465718	−	0.298125i
$223$	15.8213	+	3.14704i	1.05947	+	0.210742i	0.693921	−	0.720051i	$-0.255882\pi$
$223$	15.8213	+	3.14704i	1.05947	+	0.210742i	0.365548	+	0.930792i	$0.380882\pi$
$224$	−8.73338	+	6.47717i	−0.583523	+	0.432774i
$225$	−4.87673	+	0.970042i	−0.325115	+	0.0646695i
$226$	8.02363	+	3.14038i	0.533724	+	0.208895i
$227$	5.56435	−	2.80086i	0.369319	−	0.185899i	−0.255239	−	0.966878i	$-0.582154\pi$
$227$	5.56435	−	2.80086i	0.369319	−	0.185899i	0.624558	+	0.780978i	$0.285279\pi$
$228$	−2.93217	+	3.50219i	−0.194188	+	0.231938i
$229$	−5.79009	−	2.23348i	−0.382620	−	0.147593i	0.160938	−	0.986965i	$-0.448548\pi$
$229$	−5.79009	−	2.23348i	−0.382620	−	0.147593i	−0.543558	+	0.839372i	$0.682923\pi$
$230$	5.36974	+	10.1658i	0.354070	+	0.670312i
$231$	−1.38460	−	2.92749i	−0.0911001	−	0.192615i
$232$	−1.67093	+	10.2249i	−0.109702	+	0.671297i
$233$	0.228150	−	4.64411i	0.0149466	−	0.304245i	−0.979670	−	0.200618i	$-0.935705\pi$
$233$	0.228150	−	4.64411i	0.0149466	−	0.304245i	0.994616	−	0.103628i	$-0.0330450\pi$
$234$	12.1144	−	19.9885i	0.791944	−	1.30669i
$235$	−2.74773	+	1.55657i	−0.179242	+	0.101539i
$236$	−23.2460	−	7.93336i	−1.51319	−	0.516418i
$237$	2.80596	−	1.08238i	0.182267	−	0.0703081i
$238$	1.81131	+	1.57802i	0.117410	+	0.102288i
$239$	−0.593186	+	6.02272i	−0.0383700	+	0.389577i	0.956750	+	0.290910i	$0.0939580\pi$
$239$	−0.593186	+	6.02272i	−0.0383700	+	0.389577i	−0.995120	+	0.0986673i	$0.968542\pi$
$240$	5.29007	+	1.16066i	0.341472	+	0.0749202i
$241$	3.99426	−	0.393400i	0.257293	−	0.0253411i	0.0314516	−	0.999505i	$-0.489987\pi$
$241$	3.99426	−	0.393400i	0.257293	−	0.0253411i	0.225841	+	0.974164i	$0.427487\pi$
$242$	−1.52930	−	9.07786i	−0.0983073	−	0.583547i
$243$	9.07097	−	12.8798i	0.581903	−	0.826239i
$244$	−5.49750	+	0.623334i	−0.351942	+	0.0399048i
$245$	0.414101	−	5.61383i	0.0264559	−	0.358655i
$246$	1.10762	+	0.283230i	0.0706195	+	0.0180581i
$247$	4.87157	−	19.4484i	0.309971	−	1.23747i
$248$	6.34252	−	13.7581i	0.402750	−	0.873638i
$249$	5.64275	+	7.60837i	0.357595	+	0.482161i
$250$	14.1706	+	9.56943i	0.896228	+	0.605224i
$251$	−6.84090	−	30.4639i	−0.431794	−	1.92287i	−0.382154	−	0.924099i	$-0.624817\pi$
$251$	−6.84090	−	30.4639i	−0.431794	−	1.92287i	−0.0496404	−	0.998767i	$-0.515808\pi$
$252$	4.75612	−	7.76131i	0.299607	−	0.488916i
$253$	10.0398	+	1.23830i	0.631199	+	0.0778510i
$254$	−3.81720	−	1.94495i	−0.239512	−	0.122037i
$255$		−	1.19658i		−	0.0749325i
$256$	−12.9443	−	9.40448i	−0.809021	−	0.587780i
$257$		−	19.2130i		−	1.19847i	−0.800572	−	0.599236i	$-0.795471\pi$
$257$		−	19.2130i		−	1.19847i	0.800572	−	0.599236i	$-0.204529\pi$
$258$	−2.53720	+	4.97955i	−0.157959	+	0.310013i
$259$	13.9785	+	1.72408i	0.868579	+	0.107129i
$260$	−23.1159	+	5.54968i	−1.43359	+	0.344177i
$261$	−1.90038	−	8.46276i	−0.117630	−	0.523831i
$262$	4.81433	−	7.12915i	0.297430	−	0.440441i
$263$	−16.3946	−	22.1056i	−1.01094	−	1.36309i	−0.930484	−	0.366331i	$-0.880614\pi$
$263$	−16.3946	−	22.1056i	−1.01094	−	1.36309i	−0.0804519	−	0.996758i	$-0.525636\pi$
$264$	3.49931	−	3.23475i	0.215368	−	0.199085i
$265$	−0.0384153	+	0.153363i	−0.00235984	+	0.00942099i
$266$	1.93439	−	7.56480i	0.118605	−	0.463828i
$267$	−0.503451	+	6.82512i	−0.0308107	+	0.417691i
$268$	4.00922	−	5.03466i	0.244902	−	0.307541i
$269$	12.4786	−	17.7183i	0.760836	−	1.08030i	−0.233325	−	0.972399i	$-0.574961\pi$
$269$	12.4786	−	17.7183i	0.760836	−	1.08030i	0.994161	−	0.107906i	$-0.0344145\pi$
$270$	−10.1356	+	1.70750i	−0.616834	+	0.103915i
$271$	8.01172	−	0.789086i	0.486678	−	0.0479336i	0.148297	−	0.988943i	$-0.452621\pi$
$271$	8.01172	−	0.789086i	0.486678	−	0.0479336i	0.338381	+	0.941009i	$0.390121\pi$
$272$	−1.41664	+	3.23874i	−0.0858964	+	0.196377i
$273$	1.04551	−	10.6153i	0.0632772	−	0.642465i
$274$	17.3090	−	19.8680i	1.04568	−	1.20027i
$275$	4.15168	−	1.60148i	0.250356	−	0.0965729i
$276$	−3.34621	−	6.81349i	−0.201418	−	0.410124i
$277$	−14.9605	+	8.47502i	−0.898889	+	0.509214i	−0.871492	−	0.490410i	$-0.836847\pi$
$277$	−14.9605	+	8.47502i	−0.898889	+	0.509214i	−0.0273975	+	0.999625i	$0.508722\pi$
$278$	−17.7516	−	10.7587i	−1.06467	−	0.645262i
$279$	−0.622316	+	12.6675i	−0.0372571	+	0.758386i
$280$	−9.01302	+	2.11712i	−0.538631	+	0.126522i
$281$	−1.63230	−	3.45122i	−0.0973751	−	0.205882i	0.849421	−	0.527715i	$-0.176951\pi$
$281$	−1.63230	−	3.45122i	−0.0973751	−	0.205882i	−0.946797	+	0.321833i	$0.895701\pi$
$282$	1.84367	−	0.973861i	0.109789	−	0.0579926i
$283$	3.30349	+	1.27430i	0.196372	+	0.0757491i	0.456083	−	0.889937i	$-0.349252\pi$
$283$	3.30349	+	1.27430i	0.196372	+	0.0757491i	−0.259711	+	0.965687i	$0.583627\pi$
$284$	0.617415	+	6.96938i	0.0366368	+	0.413557i
$285$	−3.47397	+	1.74865i	−0.205780	+	0.103581i
$286$	−7.62374	+	19.4786i	−0.450801	+	1.15179i
$287$	−1.91683	+	0.381280i	−0.113147	+	0.0225063i
$288$	12.9933	+	3.25459i	0.765637	+	0.191779i
$289$	−15.9073	−	3.16417i	−0.935726	−	0.186127i
$290$	−4.75618	+	7.42990i	−0.279293	+	0.436299i
$291$	−8.71142	−	7.51453i	−0.510673	−	0.440509i
$292$	−2.99916	−	0.0294401i	−0.175513	−	0.00172285i
$293$	−4.42789	+	4.65076i	−0.258680	+	0.271700i	−0.840732	−	0.541451i	$-0.817875\pi$
$293$	−4.42789	+	4.65076i	−0.258680	+	0.271700i	0.582052	+	0.813152i	$0.302250\pi$
$294$	−0.382441	+	3.69690i	−0.0223044	+	0.215607i
$295$	−15.4967	−	14.0454i	−0.902252	−	0.817754i
$296$	3.74360	+	20.3844i	0.217592	+	1.18482i
$297$	−3.86675	+	8.17556i	−0.224372	+	0.474394i
$298$	20.7618	−	0.917841i	1.20270	−	0.0531691i
$299$	26.2673	+	20.4992i	1.51908	+	1.18550i
$300$	−2.71100	−	1.94939i	−0.156519	−	0.112548i
$301$	0.234460	−	9.55083i	0.0135140	−	0.550501i
$302$	−24.6663	−	14.1336i	−1.41938	−	0.813299i
$303$	−2.68502	−	8.85132i	−0.154250	−	0.508495i
$304$	11.4731	−	0.620146i	0.658029	−	0.0355678i
$305$	−4.50818	−	1.36754i	−0.258138	−	0.0783052i
$306$	0.0871463	−	2.95811i	0.00498182	−	0.169104i
$307$	24.5035	+	5.50246i	1.39849	+	0.314042i	0.852052	−	0.523457i	$-0.175358\pi$
$307$	24.5035	+	5.50246i	1.39849	+	0.314042i	0.546439	+	0.837499i	$0.315983\pi$
$308$	−3.00627	+	7.57128i	−0.171298	+	0.431414i
$309$	7.32456	+	3.68688i	0.416680	+	0.209739i
$310$	9.60045	−	8.61590i	0.545269	−	0.489350i
$311$	3.27220	+	22.0594i	0.185549	+	1.25087i	0.859130	+	0.511758i	$0.171005\pi$
$311$	3.27220	+	22.0594i	0.185549	+	1.25087i	−0.673581	+	0.739114i	$0.735245\pi$
$312$	15.3637	−	3.21318i	0.869796	−	0.181910i
$313$	4.78306	+	19.0950i	0.270355	+	1.07932i	0.941236	+	0.337751i	$0.109666\pi$
$313$	4.78306	+	19.0950i	0.270355	+	1.07932i	−0.670881	+	0.741565i	$0.734084\pi$
$314$	−16.3910	−	0.0804461i	−0.924998	−	0.00453983i
$315$	6.33693	−	4.46297i	0.357045	−	0.251460i
$316$	−6.80694	−	3.30159i	−0.382920	−	0.185729i
$317$	−11.9509	+	21.0963i	−0.671230	+	1.18489i	0.301615	+	0.953430i	$0.402474\pi$
$317$	−11.9509	+	21.0963i	−0.671230	+	1.18489i	−0.972845	+	0.231457i	$0.925651\pi$
$318$	0.0283347	−	0.100467i	0.00158893	−	0.00563394i
$319$	2.97047	+	7.17135i	0.166314	+	0.401518i
$320$	−6.94663	−	11.7197i	−0.388328	−	0.655151i
$321$	1.31334	−	3.17068i	0.0733033	−	0.176970i
$322$	10.1905	+	8.03356i	0.567897	+	0.447693i
$323$	−0.677063	−	2.44659i	−0.0376728	−	0.136132i
$324$	−7.35086	+	1.01676i	−0.408381	+	0.0564866i
$325$	14.4410	+	2.50576i	0.801044	+	0.138994i
$326$	17.6096	−	7.19307i	0.975304	−	0.398387i
$327$	3.20107	+	1.91865i	0.177019	+	0.106101i
$328$	−1.38053	−	2.52288i	−0.0762269	−	0.139303i
$329$	−2.12330	+	2.86294i	−0.117061	+	0.157839i
$330$	3.82712	−	1.34821i	0.210676	−	0.0742167i
$331$	−4.28835	+	1.41668i	−0.235709	+	0.0778678i	−0.429111	−	0.903252i	$-0.641173\pi$
$331$	−4.28835	+	1.41668i	−0.235709	+	0.0778678i	0.193402	+	0.981120i	$0.438048\pi$
$332$	4.30396	−	23.4363i	0.236210	−	1.28623i
$333$	−9.28254	−	14.6587i	−0.508680	−	0.803293i
$334$	−31.8947	+	12.1237i	−1.74520	+	0.663377i
$335$	4.83304	−	2.58331i	0.264057	−	0.141142i
$336$	5.98947	−	1.22199i	0.326752	−	0.0666652i
$337$	5.16340	−	9.66005i	0.281268	−	0.526216i	−0.701125	−	0.713038i	$-0.747319\pi$
$337$	5.16340	−	9.66005i	0.281268	−	0.526216i	0.982394	+	0.186822i	$0.0598187\pi$
$338$	−39.9732	+	30.8809i	−2.17426	+	1.67970i
$339$	−3.34017	−	3.50829i	−0.181413	−	0.190544i
$340$	−2.20026	+	2.05402i	−0.119326	+	0.111395i
$341$	−1.38940	−	11.2649i	−0.0752400	−	0.610030i
$342$	−8.71552	+	4.06991i	−0.471281	+	0.220076i
$343$	−6.67322	−	18.6504i	−0.360320	−	1.00703i
$344$	13.5117	−	3.88243i	0.728501	−	0.209326i
$345$	−0.317148	−	6.45570i	−0.0170747	−	0.347563i
$346$	5.21014	−	9.63347i	0.280099	−	0.517898i
$347$	0.593920	+	24.1936i	0.0318833	+	1.29878i	0.776001	+	0.630732i	$0.217245\pi$
$347$	0.593920	+	24.1936i	0.0318833	+	1.29878i	−0.744117	+	0.668049i	$0.767130\pi$
$348$	3.28338	−	4.81102i	0.176008	−	0.257898i
$349$	2.22116	+	30.1115i	0.118896	+	1.61183i	0.646889	+	0.762584i	$0.276070\pi$
$349$	2.22116	+	30.1115i	0.118896	+	1.61183i	−0.527993	+	0.849249i	$0.677055\pi$
$350$	5.61922	+	1.00346i	0.300360	+	0.0536372i
$351$	−24.7682	+	16.5496i	−1.32203	+	0.883351i
$352$	−11.9549	−	0.881795i	−0.637198	−	0.0469999i
$353$	−1.57038	−	1.04929i	−0.0835827	−	0.0558482i	0.513077	−	0.858343i	$-0.328506\pi$
$353$	−1.57038	−	1.04929i	−0.0835827	−	0.0558482i	−0.596659	+	0.802495i	$0.703506\pi$
$354$	9.95423	+	9.57079i	0.529061	+	0.508682i
$355$	−1.86878	+	5.65688i	−0.0991845	+	0.300236i
$356$	13.4142	−	10.7902i	0.710951	−	0.571877i
$357$	−0.547303	−	1.23470i	−0.0289664	−	0.0653470i
$358$	16.1180	−	19.4445i	0.851864	−	1.02767i
$359$	−7.51287	−	2.68815i	−0.396514	−	0.141875i	0.131080	−	0.991372i	$-0.458156\pi$
$359$	−7.51287	−	2.68815i	−0.396514	−	0.141875i	−0.527594	+	0.849497i	$0.676906\pi$
$360$	9.05987	+	6.92832i	0.477497	+	0.365155i
$361$	7.96443	−	7.21854i	0.419180	−	0.379923i
$362$	−21.8963	−	29.8286i	−1.15084	−	1.56776i
$363$	−1.38036	+	4.98798i	−0.0724501	+	0.261801i
$364$	−21.3140	+	16.2995i	−1.11715	+	0.854326i
$365$	−2.33477	−	1.03493i	−0.122207	−	0.0541708i
$366$	2.94867	+	0.990185i	0.154129	+	0.0517578i
$367$	23.4555	+	28.5806i	1.22437	+	1.49189i	0.814935	+	0.579552i	$0.196773\pi$
$367$	23.4555	+	28.5806i	1.22437	+	1.49189i	0.409430	+	0.912341i	$0.365727\pi$
$368$	−6.78455	+	17.8489i	−0.353669	+	0.930438i
$369$	1.86111	+	1.52737i	0.0968854	+	0.0795118i
$370$	−3.95101	+	17.1994i	−0.205403	+	0.894152i
$371$	0.0305075	+	0.175819i	0.00158387	+	0.00912807i
$372$	−6.50351	+	5.49956i	−0.337191	+	0.285139i
$373$	−27.4448	+	23.6741i	−1.42104	+	1.22580i	−0.484709	+	0.874676i	$0.661074\pi$
$373$	−27.4448	+	23.6741i	−1.42104	+	1.22580i	−0.936330	+	0.351121i	$0.885801\pi$
$374$	0.375748	+	2.62167i	0.0194295	+	0.135564i
$375$	−4.94210	−	8.24540i	−0.255209	−	0.425791i
$376$	−4.95555	−	1.71842i	−0.255563	−	0.0886207i
$377$	−3.75146	+	25.2903i	−0.193210	+	1.30251i
$378$	−9.67752	+	6.39783i	−0.497758	+	0.329069i
$379$	−12.4510	−	7.88450i	−0.639564	−	0.405000i	0.175411	−	0.984495i	$-0.443875\pi$
$379$	−12.4510	−	7.88450i	−0.639564	−	0.405000i	−0.814975	+	0.579496i	$0.803250\pi$
$380$	9.17876	+	3.38621i	0.470861	+	0.173709i
$381$	1.48180	+	1.89875i	0.0759150	+	0.0972761i
$382$	12.4307	+	0.978305i	0.636009	+	0.0500545i
$383$	−10.3999	−	10.3999i	−0.531413	−	0.531413i	0.389580	−	0.920993i	$-0.372620\pi$
$383$	−10.3999	−	10.3999i	−0.531413	−	0.531413i	−0.920993	+	0.389580i	$0.872620\pi$
$384$	4.35669	+	7.86968i	0.222326	+	0.401598i
$385$	−4.90481	+	4.90481i	−0.249972	+	0.249972i
$386$	−9.59706	+	8.19668i	−0.488477	+	0.417200i
$387$	−9.27825	+	7.24082i	−0.471640	+	0.368071i
$388$	1.13623	+	28.9178i	0.0576835	+	1.46808i
$389$	6.54523	−	10.3361i	0.331856	−	0.524059i	−0.637264	−	0.770645i	$-0.719934\pi$
$389$	6.54523	−	10.3361i	0.331856	−	0.524059i	0.969121	+	0.246587i	$0.0793090\pi$
$390$	13.0952	+	2.67168i	0.663102	+	0.135286i
$391$	4.17311	+	0.619023i	0.211043	+	0.0313053i
$392$	7.45431	−	5.64280i	0.376500	−	0.285004i
$393$	−4.14822	+	2.48635i	−0.209250	+	0.125420i
$394$	13.5030	+	10.1176i	0.680270	+	0.509717i
$395$	−4.20761	−	4.87779i	−0.211708	−	0.245428i
$396$	9.55938	−	3.05425i	0.480377	−	0.153482i
$397$	22.0563	−	3.82713i	1.10697	−	0.192078i	0.412050	−	0.911161i	$-0.364813\pi$
$397$	22.0563	−	3.82713i	1.10697	−	0.192078i	0.694924	+	0.719083i	$0.255438\pi$
$398$	21.0245	−	13.1695i	1.05386	−	0.660127i
$399$	−2.78482	+	3.39332i	−0.139416	+	0.169878i
$400$	1.06913	+	8.33125i	0.0534567	+	0.416562i
$401$	−10.3548	+	8.49794i	−0.517093	+	0.424367i	−0.856403	−	0.516307i	$-0.827306\pi$
$401$	−10.3548	+	8.49794i	−0.517093	+	0.424367i	0.339311	+	0.940674i	$0.389806\pi$
$402$	−3.23988	+	1.61094i	−0.161590	+	0.0803462i
$403$	15.1501	−	34.1780i	0.754678	−	1.70253i
$404$	−11.6667	+	20.1312i	−0.580439	+	1.00157i
$405$	−6.08985	−	1.68529i	−0.302607	−	0.0837426i
$406$	−1.50933	+	9.84203i	−0.0749068	+	0.488452i
$407$	10.4277	+	11.5052i	0.516884	+	0.570293i
$408$	1.49203	−	1.31281i	0.0738667	−	0.0649938i
$409$	−8.82634	+	24.6680i	−0.436434	+	1.21975i	0.499109	+	0.866539i	$0.333661\pi$
$409$	−8.82634	+	24.6680i	−0.436434	+	1.21975i	−0.935543	+	0.353213i	$0.885089\pi$
$410$	−0.228059	−	2.43814i	−0.0112630	−	0.120411i
$411$	−13.5432	+	6.00327i	−0.668035	+	0.296120i
$412$	−5.79383	−	19.7972i	−0.285441	−	0.975337i
$413$	−22.4146	−	7.40478i	−1.10295	−	0.364365i
$414$	−0.313870	−	15.9825i	−0.0154259	−	0.785498i
$415$	11.2722	−	16.8700i	0.553328	−	0.828114i
$416$	−32.2814	−	22.7349i	−1.58272	−	1.11467i
$417$	6.48335	+	9.70301i	0.317491	+	0.475159i
$418$	7.06229	−	4.92215i	0.345428	−	0.240750i
$419$	−3.40031	+	0.250822i	−0.166116	+	0.0122535i	−0.156367	−	0.987699i	$-0.549978\pi$
$419$	−3.40031	+	0.250822i	−0.166116	+	0.0122535i	−0.00974906	+	0.999952i	$0.503103\pi$
$420$	5.09478	+	1.06551i	0.248600	+	0.0519914i
$421$	−21.2123	+	0.520732i	−1.03382	+	0.0253789i	−0.537918	−	0.842997i	$-0.680789\pi$
$421$	−21.2123	+	0.520732i	−1.03382	+	0.0253789i	−0.495906	+	0.868376i	$0.665164\pi$
$422$	25.9342	−	7.72826i	1.26246	−	0.376206i
$423$	4.38569	−	0.215455i	0.213240	−	0.0104758i
$424$	−0.233378	+	0.120359i	−0.0113338	+	0.00584516i
$425$	1.74730	−	0.625194i	0.0847566	−	0.0303264i
$426$	1.34332	−	3.69702i	0.0650840	−	0.179121i
$427$	−5.27730	+	0.650893i	−0.255386	+	0.0314989i
$428$	−8.08467	+	3.02778i	−0.390787	+	0.146353i
$429$	8.51690	−	8.10877i	0.411200	−	0.391495i
$430$	11.8732	+	1.52361i	0.572575	+	0.0734750i
$431$	22.6103	+	12.0855i	1.08910	+	0.582137i	0.915353	−	0.402653i	$-0.131912\pi$
$431$	22.6103	+	12.0855i	1.08910	+	0.582137i	0.173749	+	0.984790i	$0.444412\pi$
$432$	−13.2493	−	10.7649i	−0.637457	−	0.517928i
$433$	−8.14078	−	15.2303i	−0.391221	−	0.731923i	0.606797	−	0.794857i	$-0.292454\pi$
$433$	−8.14078	−	15.2303i	−0.391221	−	0.731923i	−0.998018	+	0.0629342i	$0.979954\pi$
$434$	5.96546	−	13.2815i	0.286351	−	0.637534i
$435$	4.19014	−	2.65338i	0.200902	−	0.127220i
$436$	−1.96691	−	9.17961i	−0.0941978	−	0.439624i
$437$	−4.30131	−	13.0203i	−0.205760	−	0.622843i
$438$	1.52075	+	0.728416i	0.0726643	+	0.0348051i
$439$	−4.83153	−	3.58331i	−0.230597	−	0.171022i	0.474232	−	0.880400i	$-0.342726\pi$
$439$	−4.83153	−	3.58331i	−0.230597	−	0.171022i	−0.704828	+	0.709378i	$0.748976\pi$
$440$	−9.04865	−	4.72295i	−0.431377	−	0.225158i
$441$	−4.02382	+	6.71334i	−0.191610	+	0.319683i
$442$	−3.37783	+	8.04293i	−0.160667	+	0.382563i
$443$	0.117548	−	0.677448i	0.00558489	−	0.0321865i	−0.982354	−	0.187032i	$-0.940113\pi$
$443$	0.117548	−	0.677448i	0.00558489	−	0.0321865i	0.987939	+	0.154846i	$0.0494881\pi$
$444$	2.94194	−	11.2742i	0.139618	−	0.535050i
$445$	14.1276	−	3.90964i	0.669714	−	0.185335i
$446$	2.68140	+	22.6548i	0.126968	+	1.07274i
$447$	−10.7942	−	4.47112i	−0.510550	−	0.211477i
$448$	−12.5284	−	8.91573i	−0.591912	−	0.421229i
$449$	14.8605	−	6.15540i	0.701308	−	0.290491i	−0.00339442	−	0.999994i	$-0.501080\pi$
$449$	14.8605	−	6.15540i	0.701308	−	0.290491i	0.704702	+	0.709503i	$0.251080\pi$
$450$	−3.43592	−	6.13526i	−0.161971	−	0.289219i
$451$	−1.87473	−	1.06202i	−0.0882778	−	0.0500087i
$452$	−0.717337	+	12.1642i	−0.0337407	+	0.572154i
$453$	9.20282	+	13.0670i	0.432386	+	0.613941i
$454$	6.19886	+	6.26001i	0.290927	+	0.293797i
$455$	−22.1624	+	5.55139i	−1.03899	+	0.260253i
$456$	−5.99185	−	2.41325i	−0.280594	−	0.113011i
$457$	32.6082	−	4.83697i	1.52535	−	0.226264i	0.669234	−	0.743052i	$-0.266622\pi$
$457$	32.6082	−	4.83697i	1.52535	−	0.226264i	0.856114	+	0.516788i	$0.172872\pi$
$458$	0.473660	−	8.76372i	0.0221327	−	0.409502i
$459$	−1.69579	+	3.36896i	−0.0791528	+	0.157250i
$460$	−11.3263	+	11.6649i	−0.528090	+	0.543879i
$461$	−8.25864	+	36.7774i	−0.384643	+	1.71289i	0.275112	+	0.961412i	$0.411285\pi$
$461$	−8.25864	+	36.7774i	−0.384643	+	1.71289i	−0.659755	+	0.751481i	$0.729340\pi$
$462$	3.33238	−	3.14165i	0.155036	−	0.146163i
$463$	0.258532	−	0.852266i	0.0120150	−	0.0396082i	−0.950728	−	0.310027i	$-0.899662\pi$
$463$	0.258532	−	0.852266i	0.0120150	−	0.0396082i	0.962743	+	0.270418i	$0.0871620\pi$
$464$	−14.4827	+	2.22106i	−0.672341	+	0.103110i
$465$	−6.93989	+	2.10519i	−0.321830	+	0.0976260i
$466$	6.34601	−	1.72269i	0.293973	−	0.0798022i
$467$	5.60595	+	0.137618i	0.259413	+	0.00636822i	0.154040	−	0.988065i	$-0.450771\pi$
$467$	5.60595	+	0.137618i	0.259413	+	0.00636822i	0.105373	+	0.994433i	$0.466396\pi$
$468$	32.1787	+	7.55850i	1.48746	+	0.349392i
$469$	3.80542	−	4.87620i	0.175718	−	0.225162i
$470$	−3.29438	−	3.01544i	−0.151958	−	0.139092i
$471$	8.33033	+	3.93995i	0.383841	+	0.181543i
$472$	0.511433	−	34.7328i	0.0235406	−	1.59871i
$473$	7.07333	−	7.80422i	0.325232	−	0.358838i
$474$	2.68205	+	3.30099i	0.123191	+	0.151620i
$475$	−4.36857	−	4.15922i	−0.200444	−	0.190838i
$476$	−1.33086	+	3.12584i	−0.0609998	+	0.143272i
$477$	0.143586	−	0.166456i	0.00657436	−	0.00762151i
$478$	−8.35977	+	1.83420i	−0.382367	+	0.0838942i
$479$	2.53458	−	12.7422i	0.115808	−	0.582205i	−0.878685	−	0.477402i	$-0.841579\pi$
$479$	2.53458	−	12.7422i	0.115808	−	0.582205i	0.994493	−	0.104803i	$-0.0334213\pi$
$480$	0.750768	+	7.62235i	0.0342677	+	0.347911i
$481$	9.97782	+	50.1619i	0.454949	+	2.28718i
$482$	2.27468	+	5.20034i	0.103609	+	0.236869i
$483$	−3.28003	−	6.51629i	−0.149246	−	0.296502i
$484$	11.5414	−	6.02409i	0.524607	−	0.273822i
$485$	−8.86857	+	22.9909i	−0.402701	+	1.04396i
$486$	21.2874	+	6.57174i	0.965618	+	0.298100i
$487$	−24.2946	+	11.4905i	−1.10089	+	0.520683i	−0.889600	−	0.456740i	$-0.849017\pi$
$487$	−24.2946	+	11.4905i	−1.10089	+	0.520683i	−0.211292	+	0.977423i	$0.567767\pi$
$488$	−3.24089	−	7.12172i	−0.146708	−	0.322385i
$489$	−10.6812	−	0.524735i	−0.483022	−	0.0237293i
$490$	7.73155	−	1.89638i	0.349276	−	0.0856695i
$491$	−8.48986	−	14.9867i	−0.383142	−	0.676340i	0.610110	−	0.792317i	$-0.291125\pi$
$491$	−8.48986	−	14.9867i	−0.383142	−	0.676340i	−0.993252	+	0.115976i	$0.963000\pi$
$492$	0.103108	+	1.61353i	0.00464845	+	0.0727434i
$493$	1.16505	+	3.02027i	0.0524710	+	0.136026i
$494$	28.2870	−	1.94704i	1.27269	−	0.0876014i
$495$	8.50389	+	0.837560i	0.382221	+	0.0376455i
$496$	21.2763	+	2.51815i	0.955336	+	0.113068i
$497$	0.659090	+	6.69185i	0.0295642	+	0.300170i
$498$	−7.76726	+	10.9145i	−0.348059	+	0.489089i
$499$	8.07507	+	5.68711i	0.361490	+	0.254590i	0.742306	−	0.670061i	$-0.233732\pi$
$499$	8.07507	+	5.68711i	0.361490	+	0.254590i	−0.380816	+	0.924651i	$0.624357\pi$
$500$	−6.67805	+	23.2414i	−0.298651	+	1.03939i
$501$	19.1308	+	1.41117i	0.854702	+	0.0630466i
$502$	37.9843	−	22.5143i	1.69532	−	1.00486i
$503$	8.95672	+	2.24354i	0.399360	+	0.100035i	0.437457	−	0.899240i	$-0.355879\pi$
$503$	8.95672	+	2.24354i	0.399360	+	0.100035i	−0.0380964	+	0.999274i	$0.512129\pi$
$504$	12.5174	+	3.00514i	0.557571	+	0.133859i
$505$	−15.9131	+	11.8020i	−0.708124	+	0.525180i
$506$	2.72208	+	14.0447i	0.121011	+	0.624363i
$507$	27.7078	−	6.22200i	1.23055	−	0.276329i
$508$	0.947777	−	5.98409i	0.0420508	−	0.265501i
$509$	−2.98401	+	24.1937i	−0.132264	+	1.07237i	0.769047	+	0.639193i	$0.220731\pi$
$509$	−2.98401	+	24.1937i	−0.132264	+	1.07237i	−0.901310	+	0.433174i	$0.857394\pi$
$510$	1.60939	−	0.522925i	0.0712651	−	0.0231555i
$511$	−2.88252			−0.127515
$512$	6.99209	−	21.5200i	0.309010	−	0.951059i
$513$	12.2592			0.541255
$514$	25.8414	−	8.39640i	1.13981	−	0.370349i
$515$	2.15003	−	17.4320i	0.0947417	−	0.768145i
$516$	−7.80628	−	1.23638i	−0.343652	−	0.0544286i
$517$	−3.83416	+	0.860988i	−0.168626	+	0.0378662i
$518$	3.78995	+	19.5544i	0.166521	+	0.859172i
$519$	−4.94555	+	3.66787i	−0.217086	+	0.161002i
$520$	−17.5664	−	28.6655i	−0.770336	−	1.25707i
$521$	15.2081	+	3.80944i	0.666280	+	0.166894i	0.561342	−	0.827584i	$-0.310285\pi$
$521$	15.2081	+	3.80944i	0.666280	+	0.166894i	0.104938	+	0.994479i	$0.466535\pi$
$522$	10.5519	−	6.25437i	0.461843	−	0.273746i
$523$	−23.9784	−	1.76875i	−1.04850	−	0.0773421i	−0.461670	−	0.887052i	$-0.652750\pi$
$523$	−23.9784	−	1.76875i	−1.04850	−	0.0773421i	−0.586831	+	0.809710i	$0.699625\pi$
$524$	11.6926	+	3.35969i	0.510795	+	0.146769i
$525$	−2.62370	−	1.84782i	−0.114507	−	0.0806453i
$526$	22.5672	−	31.7113i	0.983978	−	1.38268i
$527$	−0.463970	−	4.71077i	−0.0202109	−	0.205204i
$528$	5.87999	+	3.29292i	0.255894	+	0.143306i
$529$	−0.210657	−	0.0207479i	−0.00915898	−	0.000902081i
$530$	−0.223060	+	0.0153536i	−0.00968912	+	0.000666918i
$531$	10.4659	+	27.1318i	0.454181	+	1.17742i
$532$	11.0200	−	0.704200i	0.477777	−	0.0305309i
$533$	−3.49807	−	6.17495i	−0.151518	−	0.267467i
$534$	−9.39979	+	2.30556i	−0.406769	+	0.0997712i
$535$	−7.34205	−	0.360692i	−0.317424	−	0.0155941i
$536$	8.52370	+	3.19216i	0.368168	+	0.137880i
$537$	−12.8357	+	6.07085i	−0.553903	+	0.261976i
$538$	29.2845	+	9.04053i	1.26254	+	0.389765i
$539$	2.52090	−	6.53518i	0.108583	−	0.281490i
$540$	−6.72602	−	12.8862i	−0.289442	−	0.554532i
$541$	6.65116	+	13.2136i	0.285956	+	0.568096i	0.989835	−	0.142224i	$-0.0454252\pi$
$541$	6.65116	+	13.2136i	0.285956	+	0.568096i	−0.703879	+	0.710320i	$0.748550\pi$
$542$	4.56258	+	10.4309i	0.195980	+	0.448045i
$543$	4.05841	+	20.4030i	0.174163	+	0.875578i
$544$	−4.97518	−	0.489992i	−0.213309	−	0.0210082i
$545$	1.55950	−	7.84012i	0.0668015	−	0.335834i
$546$	14.7344	−	3.23284i	0.630574	−	0.138353i
$547$	−14.6702	+	17.0069i	−0.627254	+	0.727161i	−0.977836	−	0.209371i	$-0.932859\pi$
$547$	−14.6702	+	17.0069i	−0.627254	+	0.727161i	0.350583	+	0.936532i	$0.385984\pi$
$548$	34.2867	+	14.5980i	1.46466	+	0.623594i
$549$	4.74410	+	4.51676i	0.202473	+	0.192771i
$550$	3.96834	+	4.88412i	0.169211	+	0.208260i
$551$	7.06604	−	7.79617i	0.301023	−	0.332128i
$552$	7.70177	−	7.47825i	0.327809	−	0.318295i
$553$	−6.57271	−	3.10866i	−0.279500	−	0.132194i
$554$	−17.9369	−	16.4181i	−0.762064	−	0.697538i
$555$	6.10388	−	7.82140i	0.259095	−	0.332000i
$556$	6.71262	−	28.5776i	0.284679	−	1.21196i
$557$	29.7575	+	0.730506i	1.26087	+	0.0309525i	0.649479	−	0.760379i	$-0.274987\pi$
$557$	29.7575	+	0.730506i	1.26087	+	0.0309525i	0.611387	+	0.791332i	$0.290612\pi$
$558$	−17.3098	+	4.69892i	−0.732780	+	0.198921i
$559$	33.1985	−	10.0707i	1.40415	−	0.425944i
$560$	−6.78637	−	11.1973i	−0.286776	−	0.473171i
$561$	0.432222	−	1.42484i	0.0182484	−	0.0601569i
$562$	3.92853	−	3.70368i	0.165715	−	0.156231i
$563$	−5.61353	+	24.9982i	−0.236582	+	1.05355i	0.702991	+	0.711199i	$0.251847\pi$
$563$	−5.61353	+	24.9982i	−0.236582	+	1.05355i	−0.939573	+	0.342349i	$0.888778\pi$
$564$	2.11556	+	2.05414i	0.0890810	+	0.0864950i
$565$	−4.66498	+	9.26773i	−0.196257	+	0.389896i
$566$	−0.270243	+	5.00007i	−0.0113592	+	0.210169i
$567$	−7.05469	+	1.04646i	−0.296269	+	0.0439473i
$568$	−9.10397	+	3.87616i	−0.381994	+	0.162640i
$569$	−27.2858	+	6.83474i	−1.14388	+	0.286527i	−0.768193	−	0.640219i	$-0.778844\pi$
$569$	−27.2858	+	6.83474i	−1.14388	+	0.286527i	−0.375689	+	0.926746i	$0.622594\pi$
$570$	−3.87011	−	3.90829i	−0.162101	−	0.163700i
$571$	−8.50011	−	12.0692i	−0.355718	−	0.505081i	0.599745	−	0.800191i	$-0.295269\pi$
$571$	−8.50011	−	12.0692i	−0.355718	−	0.505081i	−0.955463	+	0.295110i	$0.904644\pi$
$572$	−29.5303	−	1.74144i	−1.23472	−	0.0728134i
$573$	−6.09939	−	3.45526i	−0.254806	−	0.144346i
$574$	−1.35051	−	2.41150i	−0.0563691	−	0.100654i
$575$	9.26122	−	3.83612i	0.386220	−	0.159977i
$576$	1.30088	+	18.8982i	0.0542031	+	0.787427i
$577$	2.78174	+	1.15223i	0.115805	+	0.0479681i	0.439834	−	0.898079i	$-0.355037\pi$
$577$	2.78174	+	1.15223i	0.115805	+	0.0479681i	−0.324029	+	0.946047i	$0.605037\pi$
$578$	−2.69599	−	22.7781i	−0.112138	−	0.947445i
$579$	6.83844	−	1.89245i	0.284196	−	0.0786476i
$580$	−12.0717	−	3.15005i	−0.501251	−	0.130799i
$581$	3.91508	−	22.5632i	0.162425	−	0.936078i
$582$	6.29997	−	15.0008i	0.261142	−	0.621804i
$583$	−0.101141	+	0.168743i	−0.00418882	+	0.00698862i
$584$	−1.27109	−	4.04673i	−0.0525980	−	0.167455i
$585$	22.6066	+	16.7662i	0.934669	+	0.693198i
$586$	−8.19032	−	3.92304i	−0.338339	−	0.162059i
$587$	−2.84756	−	8.61969i	−0.117531	−	0.355773i	0.873951	−	0.486014i	$-0.161550\pi$
$587$	−2.84756	−	8.61969i	−0.117531	−	0.355773i	−0.991482	+	0.130242i	$0.958425\pi$
$588$	−5.13945	+	1.10122i	−0.211947	+	0.0454137i
$589$	−12.9985	+	8.23123i	−0.535595	+	0.339162i
$590$	12.1187	−	26.9811i	0.498918	−	1.11079i
$591$	−4.47162	−	8.36582i	−0.183938	−	0.344124i
$592$	−25.7810	+	13.9435i	−1.05959	+	0.573073i
$593$	−20.7011	−	11.0650i	−0.850092	−	0.454383i	−0.0120097	−	0.999928i	$-0.503823\pi$
$593$	−20.7011	−	11.0650i	−0.850092	−	0.454383i	−0.838082	+	0.545544i	$0.816323\pi$
$594$	−12.6859	−	1.62791i	−0.520510	−	0.0667939i
$595$	−2.09510	+	1.99470i	−0.0858908	+	0.0817748i
$596$	10.3077	+	27.5234i	0.422222	+	1.12740i
$597$	−13.8424	+	1.70730i	−0.566531	+	0.0698750i
$598$	−16.0921	+	44.2880i	−0.658056	+	1.81107i
$599$	0.232306	−	0.0831203i	0.00949176	−	0.00339620i	−0.332140	−	0.943230i	$-0.607771\pi$
$599$	0.232306	−	0.0831203i	0.00949176	−	0.00339620i	0.341631	+	0.939834i	$0.389021\pi$
$600$	1.43717	−	4.49820i	0.0586721	−	0.183638i
$601$	−35.7812	+	1.75782i	−1.45955	+	0.0717029i	−0.763274	−	0.646075i	$-0.776409\pi$
$601$	−35.7812	+	1.75782i	−1.45955	+	0.0717029i	−0.696273	+	0.717778i	$0.745159\pi$
$602$	12.9483	−	3.85853i	0.527733	−	0.157262i
$603$	−7.61747	+	0.186998i	−0.310207	+	0.00761516i
$604$	8.23010	−	39.3527i	0.334878	−	1.60124i
$605$	11.0554	−	0.815495i	0.449466	−	0.0331546i
$606$	10.7316	−	7.47952i	0.435941	−	0.303835i
$607$	−14.9460	−	22.3683i	−0.606641	−	0.907902i	0.393293	−	0.919413i	$-0.371336\pi$
$607$	−14.9460	−	22.3683i	−0.606641	−	0.907902i	−0.999934	+	0.0115111i	$0.996336\pi$
$608$	5.84805	+	15.1603i	0.237170	+	0.614832i
$609$	3.10999	−	4.65443i	0.126023	−	0.188607i
$610$	−0.130813	−	6.66113i	−0.00529648	−	0.269701i
$611$	−12.2901	−	4.06009i	−0.497203	−	0.164254i
$612$	4.01674	−	1.17553i	0.162367	−	0.0475182i
$613$	−10.0817	+	4.46893i	−0.407198	+	0.180498i	−0.598663	−	0.801001i	$-0.704301\pi$
$613$	−10.0817	+	4.46893i	−0.407198	+	0.180498i	0.191465	+	0.981499i	$0.438676\pi$
$614$	3.30769	+	35.3619i	0.133487	+	1.42709i
$615$	−0.463795	+	1.29622i	−0.0187020	+	0.0522687i
$616$	−11.4971	−	0.734642i	−0.463233	−	0.0295996i
$617$	−31.9956	−	35.3017i	−1.28809	−	1.42119i	−0.853956	−	0.520345i	$-0.825803\pi$
$617$	−31.9956	−	35.3017i	−1.28809	−	1.42119i	−0.434137	−	0.900847i	$-0.642947\pi$
$618$	−1.75788	+	11.4627i	−0.0707121	+	0.461099i
$619$	33.6647	+	9.31627i	1.35310	+	0.374452i	0.866501	−	0.499175i	$-0.166363\pi$
$619$	33.6647	+	9.31627i	1.35310	+	0.374452i	0.486596	+	0.873627i	$0.338238\pi$
$620$	15.7839	+	9.14728i	0.633897	+	0.367364i
$621$	−8.25610	+	18.6255i	−0.331306	+	0.747414i
$622$	−28.2398	+	14.0414i	−1.13231	+	0.563009i
$623$	12.7895	−	10.4960i	0.512399	−	0.420515i
$624$	11.0359	+	19.2599i	0.441789	+	0.771012i
$625$	−6.40166	+	7.80045i	−0.256067	+	0.312018i
$626$	−23.5925	+	14.7781i	−0.942946	+	0.590650i
$627$	−4.76833	+	0.827383i	−0.190429	+	0.0330425i
$628$	−7.05495	−	22.0810i	−0.281523	−	0.881128i
$629$	4.22976	+	4.90346i	0.168651	+	0.195514i
$630$	8.77202	+	6.57275i	0.349486	+	0.261865i
$631$	11.7419	−	7.03784i	0.467439	−	0.280172i	−0.260929	−	0.965358i	$-0.584029\pi$
$631$	11.7419	−	7.03784i	0.467439	−	0.280172i	0.728368	+	0.685186i	$0.240279\pi$
$632$	1.46588	−	10.5982i	0.0583094	−	0.421572i
$633$	−15.0490	−	2.23231i	−0.598145	−	0.0887265i
$634$	−33.5972	−	6.85449i	−1.33432	−	0.272227i
$635$	2.75999	−	4.35850i	0.109527	−	0.172962i
$636$	0.147511	−	0.00579598i	0.00584920	−	0.000229825i
$637$	18.1882	−	14.1942i	0.720644	−	0.562396i
$638$	−8.34729	+	7.12928i	−0.330473	+	0.282251i
$639$	5.85740	−	5.85740i	0.231715	−	0.231715i
$640$	12.7272	−	14.4649i	0.503085	−	0.571775i
$641$	27.0008	+	27.0008i	1.06647	+	1.06647i	0.997628	+	0.0688391i	$0.0219295\pi$
$641$	27.0008	+	27.0008i	1.06647	+	1.06647i	0.0688391	+	0.997628i	$0.478070\pi$
$642$	4.83850	+	0.380794i	0.190960	+	0.0150287i
$643$	−11.1145	−	14.2420i	−0.438315	−	0.561648i	0.517476	−	0.855698i	$-0.326872\pi$
$643$	−11.1145	−	14.2420i	−0.438315	−	0.561648i	−0.955790	+	0.294050i	$0.904997\pi$
$644$	−6.35167	+	17.2170i	−0.250291	+	0.678447i
$645$	−5.68568	−	3.60042i	−0.223874	−	0.141766i
$646$	2.99477	−	1.97985i	0.117828	−	0.0778962i
$647$	−1.85713	+	12.5198i	−0.0730115	+	0.492203i	0.921567	+	0.388218i	$0.126909\pi$
$647$	−1.85713	+	12.5198i	−0.0730115	+	0.492203i	−0.994579	+	0.103985i	$0.966841\pi$
$648$	−4.57999	−	9.44253i	−0.179919	−	0.370938i
$649$	−13.3795	−	22.3224i	−0.525193	−	0.876231i
$650$	2.94074	+	20.5182i	0.115346	+	0.804790i
$651$	−6.19808	+	5.34650i	−0.242922	+	0.209546i
$652$	17.3703	+	20.5413i	0.680275	+	0.804460i
$653$	−0.436543	−	2.51586i	−0.0170832	−	0.0984531i	0.975506	−	0.219975i	$-0.0705976\pi$
$653$	−0.436543	−	2.51586i	−0.0170832	−	0.0984531i	−0.992589	+	0.121522i	$0.961223\pi$
$654$	−1.18165	+	5.14391i	−0.0462062	+	0.201143i
$655$	8.00757	+	6.57165i	0.312882	+	0.256775i
$656$	2.78995	−	2.95935i	0.108929	−	0.115543i
$657$	2.25272	+	2.74495i	0.0878870	+	0.107091i
$658$	−4.77856	−	1.60468i	−0.186288	−	0.0625569i
$659$	−40.1604	−	17.8019i	−1.56443	−	0.693463i	−0.572457	−	0.819935i	$-0.694010\pi$
$659$	−40.1604	−	17.8019i	−1.56443	−	0.693463i	−0.991970	+	0.126471i	$0.959635\pi$
$660$	3.48586	+	4.55827i	0.135687	+	0.177430i
$661$	6.89277	−	24.9073i	0.268098	−	0.968780i	−0.699156	−	0.714969i	$-0.746441\pi$
$661$	6.89277	−	24.9073i	0.268098	−	0.968780i	0.967254	−	0.253811i	$-0.0816842\pi$
$662$	−3.77951	−	5.14871i	−0.146895	−	0.200110i
$663$	3.63384	−	3.29352i	0.141127	−	0.127910i
$664$	33.4026	−	4.45323i	1.29627	−	0.172819i
$665$	8.85287	+	3.16761i	0.343299	+	0.122835i
$666$	15.6593	−	18.8911i	0.606786	−	0.732015i
$667$	7.08609	+	15.9860i	0.274374	+	0.618979i
$668$	−30.2448	−	37.6000i	−1.17021	−	1.45479i
$669$	4.02309	−	12.1781i	0.155541	−	0.470831i
$670$	5.58667	+	5.37147i	0.215832	+	0.207518i
$671$	−4.87422	−	3.25685i	−0.188167	−	0.125729i
$672$	4.26108	+	7.52178i	0.164375	+	0.290159i
$673$	1.34175	−	0.896529i	0.0517207	−	0.0345586i	−0.529441	−	0.848347i	$-0.677598\pi$
$673$	1.34175	−	0.896529i	0.0517207	−	0.0345586i	0.581162	+	0.813788i	$0.302598\pi$
$674$	15.2492	+	2.72315i	0.587378	+	0.104892i
$675$	0.659281	+	8.93766i	0.0253757	+	0.344011i
$676$	−59.0038	−	40.2684i	−2.26938	−	1.54878i
$677$	0.0628639	+	2.56079i	0.00241605	+	0.0984191i	0.999695	+	0.0246981i	$0.00786245\pi$
$677$	0.0628639	+	2.56079i	0.00241605	+	0.0984191i	−0.997279	+	0.0737211i	$0.976513\pi$
$678$	3.25893	−	6.02570i	0.125158	−	0.231416i
$679$	1.36473	+	27.7797i	0.0523735	+	1.06609i
$680$	−3.72420	−	2.06169i	−0.142817	−	0.0790623i
$681$	−1.66857	−	4.66335i	−0.0639398	−	0.178700i
$682$	14.5441	−	6.79170i	0.556922	−	0.260068i
$683$	5.09668	+	41.3228i	0.195019	+	1.58117i	0.697500	+	0.716585i	$0.254296\pi$
$683$	5.09668	+	41.3228i	0.195019	+	1.58117i	−0.502481	+	0.864588i	$0.667579\pi$
$684$	−9.28285	−	9.94372i	−0.354939	−	0.380208i
$685$	21.8795	+	22.9808i	0.835974	+	0.878051i
$686$	22.1684	−	17.1260i	0.846394	−	0.653874i
$687$	−2.32593	+	4.35151i	−0.0887398	+	0.166020i
$688$	11.1267	+	16.4765i	0.424201	+	0.628160i
$689$	−0.571478	+	0.305461i	−0.0217716	+	0.0116371i
$690$	8.54429	−	3.24781i	0.325276	−	0.123642i
$691$	22.7424	+	35.9142i	0.865162	+	1.36624i	0.929697	+	0.368325i	$0.120068\pi$
$691$	22.7424	+	35.9142i	0.865162	+	1.36624i	−0.0645354	+	0.997915i	$0.520557\pi$
$692$	15.2339	+	2.79764i	0.579106	+	0.106350i
$693$	9.15789	−	3.02536i	0.347880	−	0.114924i
$694$	−32.2808	+	11.3718i	−1.22536	+	0.431669i
$695$	14.8899	−	20.0767i	0.564805	−	0.761552i
$696$	7.90570	+	2.31364i	0.299665	+	0.0876983i
$697$	−0.770741	−	0.461964i	−0.0291939	−	0.0174981i
$698$	−39.5292	+	16.1467i	−1.49620	+	0.611162i
$699$	−3.64240	−	0.632016i	−0.137768	−	0.0239050i
$700$	1.10604	+	7.99636i	0.0418045	+	0.302234i
$701$	12.8320	+	46.3691i	0.484660	+	1.75134i	0.644910	+	0.764259i	$0.276895\pi$
$701$	12.8320	+	46.3691i	0.484660	+	1.75134i	−0.160250	+	0.987076i	$0.551230\pi$
$702$	−33.0833	−	26.0807i	−1.24865	−	0.984352i
$703$	8.05475	−	19.4459i	0.303791	−	0.733415i
$704$	−4.03848	−	16.4647i	−0.152206	−	0.620535i
$705$	0.960845	+	2.31969i	0.0361875	+	0.0873644i
$706$	0.725013	−	2.57071i	0.0272862	−	0.0967500i
$707$	−11.0219	+	19.4564i	−0.414523	+	0.731735i
$708$	−8.52252	+	17.5710i	−0.320296	+	0.660359i
$709$	39.5613	−	27.8622i	1.48576	−	1.04639i	0.502414	−	0.864627i	$-0.332445\pi$
$709$	39.5613	−	27.8622i	1.48576	−	1.04639i	0.983343	−	0.181761i	$-0.0581797\pi$
$710$	−8.42517	−	0.0413502i	−0.316191	−	0.00155185i
$711$	2.17635	+	8.68848i	0.0816196	+	0.325844i
$712$	20.3750	+	13.3266i	0.763584	+	0.499435i
$713$	−3.75175	−	25.2923i	−0.140504	−	0.947203i
$714$	1.42148	−	1.27570i	0.0531976	−	0.0477420i
$715$	−22.4988	−	11.3249i	−0.841408	−	0.423529i
$716$	33.1966	+	13.1811i	1.24062	+	0.492602i
$717$	4.69471	+	1.05423i	0.175327	+	0.0393711i
$718$	0.332297	−	11.2796i	0.0124012	−	0.420949i
$719$	−9.73453	−	2.95294i	−0.363037	−	0.110126i	0.103496	−	0.994630i	$-0.466997\pi$
$719$	−9.73453	−	2.95294i	−0.363037	−	0.110126i	−0.466533	+	0.884504i	$0.654497\pi$
$720$	−5.35925	+	15.2133i	−0.199728	+	0.566966i
$721$	−5.75470	−	18.9707i	−0.214316	−	0.706507i
$722$	13.1895	+	7.55750i	0.490862	+	0.281261i
$723$	0.0783126	−	3.19010i	0.00291248	−	0.118641i
$724$	30.5503	−	42.4861i	1.13539	−	1.57898i
$725$	6.06388	+	4.73230i	0.225207	+	0.175753i
$726$	−7.31206	+	0.323253i	−0.271376	+	0.0119971i
$727$	8.29597	−	17.5404i	0.307680	−	0.650536i	−0.689604	−	0.724187i	$-0.742215\pi$
$727$	8.29597	−	17.5404i	0.307680	−	0.650536i	0.997284	+	0.0736514i	$0.0234652\pi$
$728$	−31.2373	−	21.5440i	−1.15773	−	0.798475i
$729$	−1.03272	−	0.936004i	−0.0382489	−	0.0346668i
$730$	0.371646	−	3.59254i	0.0137552	−	0.132966i
$731$	3.02887	−	3.18133i	0.112027	−	0.117666i
$732$	−0.0431779	+	4.39867i	−0.00159590	+	0.162580i
$733$	−17.3038	−	14.9264i	−0.639132	−	0.551319i	0.272588	−	0.962131i	$-0.412120\pi$
$733$	−17.3038	−	14.9264i	−0.639132	−	0.551319i	−0.911720	+	0.410812i	$0.865245\pi$
$734$	−28.1903	+	44.0377i	−1.04052	+	1.62546i
$735$	−4.38950	−	0.873125i	−0.161909	−	0.0322057i
$736$	−26.9717	−	1.32492i	−0.994189	−	0.0488372i
$737$	6.68816	−	1.33036i	0.246361	−	0.0490043i
$738$	−1.24097	+	3.17067i	−0.0456809	+	0.116714i
$739$	−14.5175	+	7.30749i	−0.534035	+	0.268810i	−0.696069	−	0.717975i	$-0.745069\pi$
$739$	−14.5175	+	7.30749i	−0.534035	+	0.268810i	0.162035	+	0.986785i	$0.448194\pi$
$740$	−24.8597	+	2.20231i	−0.913862	+	0.0809587i
$741$	−14.8724	−	5.73690i	−0.546349	−	0.210750i
$742$	−0.223144	+	0.117868i	−0.00819187	+	0.00432709i
$743$	4.66499	+	9.86329i	0.171142	+	0.361849i	0.971270	−	0.237980i	$-0.0764853\pi$
$743$	4.66499	+	9.86329i	0.171142	+	0.361849i	−0.800128	+	0.599829i	$0.795235\pi$
$744$	−10.2390	−	6.34379i	−0.375381	−	0.232575i
$745$	−1.22794	+	24.9952i	−0.0449881	+	0.915754i
$746$	−43.8354	−	26.5672i	−1.60493	−	0.972695i
$747$	−24.5460	+	13.9052i	−0.898093	+	0.508763i
$748$	−3.36194	+	1.65110i	−0.122925	+	0.0603701i
$749$	−7.74092	+	2.98600i	−0.282847	+	0.109106i
$750$	8.93025	−	10.2505i	0.326087	−	0.374295i
$751$	1.10395	−	11.2086i	0.0402838	−	0.409009i	−0.953804	−	0.300430i	$-0.902870\pi$
$751$	1.10395	−	11.2086i	0.0402838	−	0.409009i	0.994088	−	0.108579i	$-0.0346300\pi$
$752$	0.145610	−	7.41617i	0.00530985	−	0.270440i
$753$	−24.7045	+	2.43318i	−0.900281	+	0.0886699i
$754$	−35.6548	+	6.00658i	−1.29847	+	0.218747i
$755$	19.7117	−	27.9885i	0.717384	−	1.01861i
$756$	−12.8343	−	10.2203i	−0.466779	−	0.371707i
$757$	−1.65242	+	22.4013i	−0.0600581	+	0.814188i	0.880390	+	0.474250i	$0.157281\pi$
$757$	−1.65242	+	22.4013i	−0.0600581	+	0.814188i	−0.940448	+	0.339937i	$0.889594\pi$
$758$	5.16333	−	20.1922i	0.187541	−	0.733414i
$759$	1.95425	−	7.80178i	0.0709346	−	0.283187i
$760$	−0.543160	+	13.8252i	−0.0197025	+	0.501494i
$761$	28.7844	+	38.8113i	1.04343	+	1.40691i	0.909396	+	0.415931i	$0.136544\pi$
$761$	28.7844	+	38.8113i	1.04343	+	1.40691i	0.134037	+	0.990976i	$0.457206\pi$
$762$	−1.90624	+	2.82281i	−0.0690559	+	0.102259i
$763$	−1.97682	−	8.80319i	−0.0715657	−	0.318697i
$764$	4.11660	+	17.1468i	0.148934	+	0.620348i
$765$	3.53685	+	0.436229i	0.127875	+	0.0157719i
$766$	9.44294	−	18.5329i	0.341187	−	0.669619i
$767$		−	85.7206i		−	3.09519i
$768$	−8.68075	+	9.29892i	−0.313240	+	0.335546i
$769$		−	20.8467i		−	0.751750i	−0.926670	−	0.375875i	$-0.877342\pi$
$769$		−	20.8467i		−	0.751750i	0.926670	−	0.375875i	$-0.122658\pi$
$770$	−8.74043	−	4.45346i	−0.314983	−	0.160492i
$771$	−15.1607	−	1.86989i	−0.545999	−	0.0673426i
$772$	−15.2186	−	9.32592i	−0.547729	−	0.335647i
$773$	3.98092	+	17.7279i	0.143184	+	0.637627i	0.993738	+	0.111739i	$0.0356420\pi$
$773$	3.98092	+	17.7279i	0.143184	+	0.637627i	−0.850554	+	0.525888i	$0.823733\pi$
$774$	−13.7936	−	9.31485i	−0.495802	−	0.334815i
$775$	−6.70011	−	9.03405i	−0.240675	−	0.324513i
$776$	−38.3978	+	14.1658i	−1.37840	+	0.508523i
$777$	2.72089	−	10.8624i	0.0976115	−	0.389687i
$778$	16.7623	+	4.28628i	0.600959	+	0.153671i
$779$	−0.214858	+	2.91276i	−0.00769810	+	0.104361i
$780$	2.12943	+	18.7806i	0.0762460	+	0.672453i
$781$	−4.26863	+	6.06099i	−0.152744	+	0.216879i
$782$	0.991139	+	5.88335i	0.0354430	+	0.210388i
$783$	−15.5577	+	1.53230i	−0.555987	+	0.0547599i
$784$	10.8472	+	7.56003i	0.387400	+	0.270001i
$785$	1.93466	−	19.6430i	0.0690510	−	0.701087i
$786$	−5.15697	−	4.49276i	−0.183943	−	0.160251i
$787$	−45.2592	+	17.4584i	−1.61332	+	0.622325i	−0.987496	−	0.157643i	$-0.949611\pi$
$787$	−45.2592	+	17.4584i	−1.61332	+	0.622325i	−0.625820	+	0.779967i	$0.715236\pi$
$788$	−7.70709	+	22.5830i	−0.274554	+	0.804486i
$789$	−19.0388	+	10.7854i	−0.677801	+	0.383969i
$790$	4.72181	−	7.79090i	0.167995	−	0.277188i
$791$	−0.574622	+	11.6967i	−0.0204312	+	0.415887i
$792$	8.28557	+	11.5226i	0.294415	+	0.409437i
$793$	−8.25552	−	17.4548i	−0.293162	−	0.619839i
$794$	14.7865	+	27.9931i	0.524752	+	0.993439i
$795$	0.117278	+	0.0452390i	0.00415941	+	0.00160446i
$796$	26.9010	+	22.5226i	0.953480	+	0.798291i
$797$	−16.9107	+	8.51211i	−0.599006	+	0.301514i	−0.723086	−	0.690758i	$-0.757277\pi$
$797$	−16.9107	+	8.51211i	−0.599006	+	0.301514i	0.124080	+	0.992272i	$0.460402\pi$
$798$	−5.78102	−	2.26264i	−0.204646	−	0.0800966i
$799$	−1.60734	+	0.319720i	−0.0568636	+	0.0113109i
$800$	−10.7383	+	5.07888i	−0.379655	+	0.179565i
$801$	−19.9902	−	3.97630i	−0.706320	−	0.140496i
$802$	−15.9549	−	10.2134i	−0.563388	−	0.360647i
$803$	−2.40633	−	2.07572i	−0.0849176	−	0.0732505i
$804$	−3.58259	−	3.65362i	−0.126348	−	0.128853i
$805$	−10.7747	+	11.3170i	−0.379757	+	0.398871i
$806$	52.5901	+	5.44041i	1.85241	+	0.191630i
$807$	−12.7668	−	11.5712i	−0.449413	−	0.407324i
$808$	−32.1749	−	6.89395i	−1.13191	−	0.242528i
$809$	14.3551	−	30.3514i	0.504699	−	1.06710i	−0.477392	−	0.878691i	$-0.658418\pi$
$809$	14.3551	−	30.3514i	0.504699	−	1.06710i	0.982091	−	0.188407i	$-0.0603323\pi$
$810$	−0.394661	−	8.92732i	−0.0138670	−	0.313674i
$811$	9.99600	+	7.80096i	0.351007	+	0.273929i	0.775296	−	0.631598i	$-0.217601\pi$
$811$	9.99600	+	7.80096i	0.351007	+	0.273929i	−0.424289	+	0.905527i	$0.639476\pi$
$812$	−13.8971	+	2.27109i	−0.487693	+	0.0796997i
$813$	0.157080	−	6.39874i	0.00550905	−	0.224414i
$814$	−10.9174	+	19.0533i	−0.382655	+	0.667816i
$815$	6.64925	+	21.9197i	0.232913	+	0.767812i
$816$	2.41777	+	1.43306i	0.0846388	+	0.0501671i
$817$	−13.6625	−	4.14448i	−0.477992	−	0.144997i
$818$	−37.0356	−	1.09107i	−1.29492	−	0.0381485i
$819$	30.9955	+	6.96028i	1.08307	+	0.243212i
$820$	3.17962	−	1.37225i	0.111037	−	0.0479210i
$821$	10.3975	+	5.23366i	0.362875	+	0.182656i	0.621676	−	0.783275i	$-0.286452\pi$
$821$	10.3975	+	5.23366i	0.362875	+	0.182656i	−0.258800	+	0.965931i	$0.583327\pi$
$822$	−13.9930	−	15.5920i	−0.488061	−	0.543833i
$823$	−4.01589	−	27.0729i	−0.139985	−	0.943703i	−0.939375	−	0.342891i	$-0.888594\pi$
$823$	−4.01589	−	27.0729i	−0.139985	−	0.943703i	0.799390	−	0.600812i	$-0.205156\pi$
$824$	24.0951	−	16.4444i	0.839394	−	0.572867i
$825$	−0.859646	−	3.43190i	−0.0299290	−	0.119483i
$826$	0.163844	−	33.3836i	0.00570088	−	1.16156i
$827$	−38.4543	+	27.0826i	−1.33719	+	0.941755i	−0.337189	+	0.941437i	$0.609476\pi$
$827$	−38.4543	+	27.0826i	−1.33719	+	0.941755i	−1.00000		0.000317482i	$0.999899\pi$
$828$	21.3593	−	7.40679i	0.742286	−	0.257404i
$829$	1.58422	−	2.79655i	0.0550224	−	0.0971281i	−0.841219	−	0.540694i	$-0.818162\pi$
$829$	1.58422	−	2.79655i	0.0550224	−	0.0971281i	0.896242	+	0.443566i	$0.146287\pi$
$830$	27.6162	+	7.78854i	0.958572	+	0.270344i
$831$	5.23150	+	12.6300i	0.181479	+	0.438128i
$832$	16.4709	−	53.3539i	0.571024	−	1.84971i
$833$	1.11789	−	2.69883i	0.0387327	−	0.0935091i
$834$	−10.2172	+	12.9605i	−0.353792	+	0.448784i
$835$	−10.9587	−	39.5997i	−0.379242	−	1.37041i
$836$	9.70662	+	7.34769i	0.335710	+	0.254125i
$837$	22.5228	+	3.90807i	0.778500	+	0.135083i
$838$	−1.82335	−	4.46379i	−0.0629866	−	0.154199i
$839$	−15.5303	−	9.30853i	−0.536167	−	0.321366i	0.220263	−	0.975440i	$-0.429308\pi$
$839$	−15.5303	−	9.30853i	−0.536167	−	0.321366i	−0.756430	+	0.654074i	$0.773058\pi$
$840$	0.793404	+	7.31810i	0.0273750	+	0.252499i
$841$	9.28245	−	12.5159i	0.320085	−	0.431584i
$842$	−9.97052	−	28.3029i	−0.343607	−	0.975382i
$843$	−2.88217	+	0.952141i	−0.0992673	+	0.0327935i
$844$	21.7282	+	31.5040i	0.747914	+	1.08441i
$845$	−32.5418	−	51.3891i	−1.11947	−	1.76784i
$846$	2.20641	+	5.80458i	0.0758579	+	0.199566i
$847$	11.0346	−	5.89811i	0.379153	−	0.202661i
$848$	−0.263873	−	0.261293i	−0.00906143	−	0.00897284i
$849$	1.32704	−	2.48272i	0.0455439	−	0.0852067i
$850$	1.60448	+	2.07689i	0.0550334	+	0.0712369i
$851$	24.1198	+	25.3338i	0.826815	+	0.868430i
$852$	5.55953	+	0.191098i	0.190466	+	0.00654691i
$853$	−5.42383	−	43.9753i	−0.185708	−	1.50568i	−0.739572	−	0.673077i	$-0.764972\pi$
$853$	−5.42383	−	43.9753i	−0.185708	−	1.50568i	0.553864	−	0.832607i	$-0.313153\pi$
$854$	−3.18172	−	6.81350i	−0.108876	−	0.233153i
$855$	−3.90219	−	10.9059i	−0.133452	−	0.372973i
$856$	−7.60548	−	9.55066i	−0.259950	−	0.326435i
$857$	0.602264	+	12.2594i	0.0205729	+	0.418772i	0.986888	+	0.161409i	$0.0516037\pi$
$857$	0.602264	+	12.2594i	0.0205729	+	0.418772i	−0.966315	+	0.257363i	$0.917146\pi$
$858$	14.6283	+	7.91154i	0.499402	+	0.270095i
$859$	1.06937	+	43.5612i	0.0364863	+	1.48629i	0.686925	+	0.726729i	$0.258960\pi$
$859$	1.06937	+	43.5612i	0.0364863	+	1.48629i	−0.650438	+	0.759559i	$0.725415\pi$
$860$	3.13953	+	16.6352i	0.107057	+	0.567256i
$861$	0.114309	+	1.54965i	0.00389564	+	0.0528119i
$862$	−6.37382	+	35.6924i	−0.217093	+	1.21569i
$863$	38.9021	−	25.9936i	1.32424	−	0.884831i	0.326076	−	0.945344i	$-0.394274\pi$
$863$	38.9021	−	25.9936i	1.32424	−	0.884831i	0.998167	+	0.0605125i	$0.0192735\pi$
$864$	8.68863	−	22.5247i	0.295593	−	0.766306i
$865$	10.9657	+	7.32706i	0.372846	+	0.249128i
$866$	16.9271	−	17.6052i	0.575206	−	0.598250i
$867$	−4.04498	+	12.2443i	−0.137375	+	0.415839i
$868$	20.4706	+	2.21927i	0.694818	+	0.0753269i
$869$	−3.24835	−	7.32816i	−0.110193	−	0.248591i
$870$	5.39994	+	4.47615i	0.183075	+	0.151756i
$871$	21.1479	+	7.56684i	0.716569	+	0.256393i
$872$	11.4870	−	6.65713i	0.388998	−	0.225439i
$873$	25.3874	−	23.0098i	0.859233	−	0.778763i
$874$	15.6324	−	11.4753i	0.528775	−	0.388159i
$875$	−6.19845	+	22.3983i	−0.209546	+	0.757202i
$876$	−0.315123	+	2.36373i	−0.0106470	+	0.0798632i
$877$	14.1958	+	6.29256i	0.479358	+	0.212485i	0.630746	−	0.775990i	$-0.282749\pi$
$877$	14.1958	+	6.29256i	0.479358	+	0.212485i	−0.151388	+	0.988474i	$0.548374\pi$
$878$	2.70808	−	8.06437i	0.0913932	−	0.272159i
$879$	3.23891	+	3.94662i	0.109246	+	0.133116i
$880$	2.39794	−	14.2344i	0.0808345	−	0.479842i
$881$	−18.5830	−	15.2507i	−0.626078	−	0.513809i	0.267009	−	0.963694i	$-0.413965\pi$
$881$	−18.5830	−	15.2507i	−0.626078	−	0.513809i	−0.893086	+	0.449886i	$0.851465\pi$
$882$	−10.7879	−	2.47818i	−0.363247	−	0.0834446i
$883$	−3.99111	−	23.0013i	−0.134312	−	0.774056i	−0.973236	−	0.229808i	$-0.926190\pi$
$883$	−3.99111	−	23.0013i	−0.134312	−	0.774056i	0.838924	−	0.544248i	$-0.183185\pi$
$884$	−12.2939	−	1.02827i	−0.413488	−	0.0345846i
$885$	−12.5912	+	10.8613i	−0.423250	+	0.365098i
$886$	0.962536	−	0.137954i	0.0323370	−	0.00463466i
$887$	−9.31405	−	15.5396i	−0.312735	−	0.521767i	0.660724	−	0.750629i	$-0.270250\pi$
$887$	−9.31405	−	15.5396i	−0.312735	−	0.521767i	−0.973459	+	0.228862i	$0.926500\pi$
$888$	16.4494	−	0.970116i	0.552007	−	0.0325549i
$889$	0.854377	−	5.75974i	0.0286549	−	0.193176i
$890$	11.4325	+	17.2930i	0.383217	+	0.579664i
$891$	−6.64283	−	4.20653i	−0.222543	−	0.140924i
$892$	−29.2989	+	13.5070i	−0.980999	+	0.452249i
$893$	3.27716	+	4.19929i	0.109666	+	0.140524i
$894$	1.29637	−	16.4722i	0.0433572	−	0.550911i
$895$	21.5053	+	21.5053i	0.718844	+	0.718844i
$896$	6.51650	−	20.7470i	0.217701	−	0.693108i
$897$	18.7321	−	18.7321i	0.625448	−	0.625448i
$898$	14.7733	+	17.2972i	0.492990	+	0.577216i
$899$	15.4672	−	12.0707i	0.515860	−	0.402581i
$900$	6.75035	−	7.30251i	0.225012	−	0.243417i
$901$	−0.0438944	+	0.0693168i	−0.00146233	+	0.00230928i
$902$	0.609127	−	2.98563i	0.0202817	−	0.0994107i
$903$	−7.51361	−	1.11454i	−0.250037	−	0.0370895i
$904$	−16.6742	+	4.35113i	−0.554577	+	0.144716i
$905$	38.2186	−	22.9073i	1.27043	−	0.761466i
$906$	−13.5533	+	18.0883i	−0.450278	+	0.600943i
$907$	6.67280	+	7.73563i	0.221567	+	0.256857i	0.857021	−	0.515281i	$-0.172312\pi$
$907$	6.67280	+	7.73563i	0.221567	+	0.256857i	−0.635455	+	0.772138i	$0.719187\pi$
$908$	−5.71068	+	11.0732i	−0.189516	+	0.367476i
$909$	27.1417	−	4.70952i	0.900232	−	0.156205i
$910$	−17.1519	−	27.3823i	−0.568581	−	0.907714i
$911$	−29.6483	+	36.1266i	−0.982292	+	1.19693i	−0.00187403	+	0.999998i	$0.500597\pi$
$911$	−29.6483	+	36.1266i	−0.982292	+	1.19693i	−0.980418	+	0.196928i	$0.936903\pi$
$912$	0.627268	−	9.11365i	0.0207709	−	0.301783i
$913$	19.5162	−	16.0165i	0.645892	−	0.530070i
$914$	20.7561	+	41.7441i	0.686549	+	1.38077i
$915$	−1.51787	+	3.42425i	−0.0501791	+	0.113202i
$916$	11.9942	−	3.19283i	0.396299	−	0.105494i
$917$	11.2685	+	3.11841i	0.372118	+	0.102979i
$918$	−5.27233	−	0.808541i	−0.174013	−	0.0266858i
$919$	21.1625	+	23.3492i	0.698085	+	0.770218i	0.982051	−	0.188616i	$-0.0604002\pi$
$919$	21.1625	+	23.3492i	0.698085	+	0.770218i	−0.283966	+	0.958834i	$0.591650\pi$
$920$	−20.6390	−	10.1360i	−0.680449	−	0.334175i
$921$	6.72671	−	18.7999i	0.221653	−	0.619478i
$922$	−53.0746	+	4.96451i	−1.74792	+	0.163497i
$923$	−22.3229	+	9.89506i	−0.734767	+	0.325700i
$924$	5.68181	+	3.10908i	0.186918	+	0.102281i
$925$	14.6104	+	4.82662i	0.480386	+	0.158698i
$926$	1.25928	−	0.0247301i	0.0413825	−	0.000812682i
$927$	−13.5680	+	20.3059i	−0.445631	+	0.666934i
$928$	−9.31649	−	18.5085i	−0.305829	−	0.607571i
$929$	−15.3938	−	23.0385i	−0.505055	−	0.755868i	0.488085	−	0.872796i	$-0.337695\pi$
$929$	−15.3938	−	23.0385i	−0.505055	−	0.755868i	−0.993140	+	0.116928i	$0.962695\pi$
$930$	−5.86433	−	8.41413i	−0.192299	−	0.275910i
$931$	−9.46907	+	0.698481i	−0.310336	+	0.0228918i
$932$	5.09033	+	7.78252i	0.166739	+	0.254925i
$933$	17.7252	−	0.435129i	0.580297	−	0.0142455i
$934$	2.26480	+	7.60013i	0.0741066	+	0.248684i
$935$	−3.18539	+	0.156488i	−0.104173	+	0.00511771i
$936$	3.89649	+	46.5835i	0.127361	+	1.52263i
$937$	−41.8059	+	14.9584i	−1.36574	+	0.488669i	−0.914807	−	0.403890i	$-0.867658\pi$
$937$	−41.8059	+	14.9584i	−1.36574	+	0.488669i	−0.450930	+	0.892559i	$0.648908\pi$
$938$	8.22151	+	2.98730i	0.268442	+	0.0975388i
$939$	15.5332	−	1.91583i	0.506905	−	0.0625208i
$940$	2.61605	−	5.74873i	0.0853261	−	0.187503i
$941$	−8.53123	+	8.12240i	−0.278110	+	0.264783i	−0.815767	−	0.578381i	$-0.803685\pi$
$941$	−8.53123	+	8.12240i	−0.278110	+	0.264783i	0.537657	+	0.843164i	$0.319310\pi$
$942$	−1.65873	+	12.9261i	−0.0540442	+	0.421155i
$943$	−4.28069	−	2.28808i	−0.139399	−	0.0745101i
$944$	46.9390	−	14.4910i	1.52774	−	0.471641i
$945$	−6.58536	−	12.3203i	−0.214222	−	0.400781i
$946$	13.5878	+	6.10303i	0.441778	+	0.198427i
$947$	−17.6946	+	11.2050i	−0.574997	+	0.364113i	−0.790567	−	0.612376i	$-0.790214\pi$
$947$	−17.6946	+	11.2050i	−0.574997	+	0.364113i	0.215570	+	0.976488i	$0.430839\pi$
$948$	−3.26772	+	5.04994i	−0.106131	+	0.164014i
$949$	−3.28340	−	9.93898i	−0.106584	−	0.322633i
$950$	3.68500	−	7.69336i	0.119557	−	0.249605i
$951$	15.4837	+	11.4835i	0.502093	+	0.372378i
$952$	−4.78585	−	0.423956i	−0.155110	−	0.0137405i
$953$	13.1639	−	21.9626i	0.426420	−	0.711438i	−0.567279	−	0.823526i	$-0.692004\pi$
$953$	13.1639	−	21.9626i	0.426420	−	0.711438i	0.993698	+	0.112088i	$0.0357537\pi$
$954$	0.286633	+	0.120379i	0.00928008	+	0.00389740i
$955$	−2.56701	+	14.7940i	−0.0830664	+	0.478724i
$956$	−6.12035	−	10.4423i	−0.197946	−	0.337728i
$957$	5.94792	−	1.64601i	0.192269	−	0.0532079i
$958$	18.2458	−	2.15955i	0.589496	−	0.0697720i
$959$	33.0878	+	13.7054i	1.06846	+	0.442570i
$960$	−9.92393	+	4.34088i	−0.320294	+	0.140101i
$961$	2.13508	−	0.884380i	0.0688736	−	0.0285284i
$962$	−63.1071	+	35.3417i	−2.03465	+	1.13946i
$963$	8.89312	+	5.03789i	0.286577	+	0.162344i
$964$	−6.00036	+	5.33207i	−0.193259	+	0.171735i
$965$	−8.75111	−	12.4256i	−0.281708	−	0.399995i
$966$	7.33097	−	7.25936i	0.235870	−	0.233566i
$967$	−39.9073	+	9.99626i	−1.28333	+	0.321458i	−0.823890	−	0.566750i	$-0.808201\pi$
$967$	−39.9073	+	9.99626i	−1.28333	+	0.321458i	−0.459442	+	0.888208i	$0.651951\pi$
$968$	13.1462	+	12.8905i	0.422533	+	0.414315i
$969$	−1.99647	+	0.296148i	−0.0641358	+	0.00951365i
$970$	−34.7984	−	1.88078i	−1.11731	−	0.0603881i
$971$	−4.79300	+	9.52205i	−0.153815	+	0.305577i	−0.956967	−	0.290196i	$-0.906279\pi$
$971$	−4.79300	+	9.52205i	−0.153815	+	0.305577i	0.803153	+	0.595773i	$0.203154\pi$
$972$	0.464014	+	31.5035i	0.0148833	+	1.01048i
$973$	6.18134	−	27.5268i	0.198165	−	0.882467i
$974$	−26.0718	−	27.6546i	−0.835394	−	0.886110i
$975$	3.38273	−	11.1514i	0.108334	−	0.357129i
$976$	8.16236	−	7.47129i	0.261271	−	0.239150i
$977$	−4.20670	+	1.27609i	−0.134584	+	0.0408257i	−0.356858	−	0.934159i	$-0.616152\pi$
$977$	−4.20670	+	1.27609i	−0.134584	+	0.0408257i	0.222274	+	0.974984i	$0.428652\pi$
$978$	−3.96211	−	14.5955i	−0.126694	−	0.466714i
$979$	18.2349	+	0.447642i	0.582791	+	0.0143067i
$980$	5.92944	+	9.57016i	0.189409	+	0.305708i
$981$	−6.83815	+	8.76227i	−0.218325	+	0.279758i
$982$	16.4468	−	17.9683i	0.524840	−	0.573391i
$983$	15.0053	+	7.09698i	0.478595	+	0.226359i	0.651600	−	0.758562i	$-0.274098\pi$
$983$	15.0053	+	7.09698i	0.478595	+	0.226359i	−0.173006	+	0.984921i	$0.555348\pi$
$984$	−2.12513	+	0.843819i	−0.0677466	+	0.0269000i
$985$	−13.6448	+	15.0547i	−0.434759	+	0.479683i
$986$	−3.55310	+	2.88689i	−0.113154	+	0.0919373i
$987$	2.05246	+	1.95410i	0.0653305	+	0.0621998i
$988$	14.9807	+	37.1950i	0.476598	+	1.18333i
$989$	15.4980	−	17.9665i	0.492807	−	0.571301i
$990$	2.58983	+	11.8037i	0.0823102	+	0.375147i
$991$	11.1399	−	56.0039i	0.353869	−	1.77902i	−0.236236	−	0.971696i	$-0.575914\pi$
$991$	11.1399	−	56.0039i	0.353869	−	1.77902i	0.590106	−	0.807326i	$-0.299086\pi$
$992$	5.91123	+	29.7171i	0.187682	+	0.943519i
$993$	0.700522	+	3.52176i	0.0222304	+	0.111760i
$994$	−8.71248	+	3.81093i	−0.276343	+	0.120875i
$995$	13.4317	+	26.6842i	0.425813	+	0.845946i
$996$	−18.0744	−	5.67712i	−0.572708	−	0.179886i
$997$	9.46733	−	24.5431i	0.299833	−	0.777288i	−0.698276	−	0.715828i	$-0.746049\pi$
$997$	9.46733	−	24.5431i	0.299833	−	0.777288i	0.998110	−	0.0614600i	$-0.0195757\pi$
$998$	−4.12020	+	13.3463i	−0.130423	+	0.422470i
$999$	−28.2700	+	13.3707i	−0.894422	+	0.423030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.109.40	✓	4032
512.357	even	128	inner	512.2.o.a.357.40	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.109.40	✓	4032	1.1	even	1	trivial
512.2.o.a.357.40	yes	4032	512.357	even	128	inner

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(0.437017 + 1.34500i) q^{2} +(0.0973246 - 0.789087i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-1.66159 + 0.373123i) q^{5} +(1.10385 - 0.213943i) q^{6} +(-1.54386 + 1.14501i) q^{7} +(-2.28825 - 1.66250i) q^{8} +(2.29691 + 0.575346i) q^{9} +O(q^{10})\)	\(q+(0.437017 + 1.34500i) q^{2} +(0.0973246 - 0.789087i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-1.66159 + 0.373123i) q^{5} +(1.10385 - 0.213943i) q^{6} +(-1.54386 + 1.14501i) q^{7} +(-2.28825 - 1.66250i) q^{8} +(2.29691 + 0.575346i) q^{9} +(-1.22799 - 2.07177i) q^{10} +(-2.11335 - 0.155890i) q^{11} +(0.770155 + 1.39118i) q^{12} +(-5.70658 - 4.01903i) q^{13} +(-2.21472 - 1.57610i) q^{14} +(0.132713 + 1.34745i) q^{15} +(1.23606 - 3.80423i) q^{16} +(-0.879496 - 0.0866228i) q^{17} +(0.229950 + 3.34077i) q^{18} +(1.03379 + 2.67999i) q^{19} +(2.24988 - 2.55705i) q^{20} +(0.753253 + 1.32968i) q^{21} +(-0.713897 - 2.91057i) q^{22} +(-4.76796 - 0.234235i) q^{23} +(-1.53456 + 1.64383i) q^{24} +(-1.89828 + 0.897819i) q^{25} +(2.91170 - 9.43171i) q^{26} +(1.53596 - 3.98184i) q^{27} +(1.15198 - 3.66758i) q^{28} +(-1.64693 - 3.27188i) q^{29} +(-1.75432 + 0.767359i) q^{30} +(1.04495 + 5.25329i) q^{31} +(5.65685 - 2.37634e-5i) q^{32} +(-0.328691 + 1.65244i) q^{33} +(-0.267848 - 1.22078i) q^{34} +(2.13804 - 2.47858i) q^{35} +(-4.39283 + 1.76926i) q^{36} +(-5.30693 - 5.05262i) q^{37} +(-3.15280 + 2.56164i) q^{38} +(-3.72675 + 4.11183i) q^{39} +(4.42246 + 1.90860i) q^{40} +(0.919160 + 0.434731i) q^{41} +(-1.45923 + 1.59422i) q^{42} +(-3.05794 + 3.91839i) q^{43} +(3.60272 - 2.23216i) q^{44} +(-4.03120 - 0.0989604i) q^{45} +(-1.76864 - 6.51526i) q^{46} +(1.77455 - 0.538304i) q^{47} +(-2.88157 - 1.34560i) q^{48} +(-0.959521 + 3.16312i) q^{49} +(-2.03714 - 2.16082i) q^{50} +(-0.153949 + 0.685568i) q^{51} +(13.9581 - 0.205588i) q^{52} +(0.0417411 - 0.0829253i) q^{53} +(6.02680 + 0.325735i) q^{54} +(3.56968 - 0.529513i) q^{55} +(5.43632 - 0.0533863i) q^{56} +(2.21536 - 0.554919i) q^{57} +(3.68093 - 3.64498i) q^{58} +(7.07164 + 10.0410i) q^{59} +(-1.79876 - 2.02421i) q^{60} +(2.40698 + 1.36354i) q^{61} +(-6.60900 + 3.70123i) q^{62} +(-4.20488 + 1.74172i) q^{63} +(2.47217 + 7.60844i) q^{64} +(10.9816 + 4.54873i) q^{65} +(-2.36617 + 0.280057i) q^{66} +(-3.10141 + 0.858277i) q^{67} +(1.52488 - 0.893754i) q^{68} +(-0.648871 + 3.73954i) q^{69} +(4.26805 + 1.79247i) q^{70} +(1.79850 - 3.00062i) q^{71} +(-4.29939 - 5.13515i) q^{72} +(1.20453 + 0.893343i) q^{73} +(4.47654 - 9.34589i) q^{74} +(0.523708 + 1.58529i) q^{75} +(-4.82323 - 3.12102i) q^{76} +(3.44121 - 2.17912i) q^{77} +(-7.15906 - 3.21552i) q^{78} +(1.78315 + 3.33603i) q^{79} +(-0.634374 + 6.78228i) q^{80} +(3.27230 + 1.74908i) q^{81} +(-0.183022 + 1.42625i) q^{82} +(-8.62875 + 8.21525i) q^{83} +(-2.78192 - 1.26596i) q^{84} +(1.49368 - 0.184228i) q^{85} +(-6.60660 - 2.40052i) q^{86} +(-2.74208 + 0.981133i) q^{87} +(4.57670 + 3.87016i) q^{88} +(-8.59731 + 0.422359i) q^{89} +(-1.62860 - 5.46520i) q^{90} +(13.4120 - 0.329246i) q^{91} +(7.99007 - 5.22609i) q^{92} +(4.24700 - 0.313278i) q^{93} +(1.49953 + 2.15152i) q^{94} +(-2.71770 - 4.06732i) q^{95} +(0.550532 - 4.46375i) q^{96} +(8.03914 - 12.0314i) q^{97} +(-4.67371 + 0.0917838i) q^{98} +(-4.76447 - 1.57397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

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