LMFDB - Embedded newform 67.2.e.a.14.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [67,2,Mod(9,67)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(67, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("67.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	67.e (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.534997693543$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			14.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	67.14
Dual form			67.2.e.a.24.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0366213 + 0.0801894i) q^{2} +(-0.239446 - 0.153882i) q^{3} +(1.30463 - 1.50563i) q^{4} +(0.260554 + 1.81219i) q^{5} +(0.00357093 - 0.0248364i) q^{6} +(-0.253098 - 0.554206i) q^{7} +(0.337683 + 0.0991526i) q^{8} +(-1.21259 - 2.65520i) q^{9} +(-0.135777 + 0.0872586i) q^{10} +(0.769529 + 5.35219i) q^{11} +(-0.544078 + 0.159756i) q^{12} +(-5.48325 + 1.61003i) q^{13} +(0.0351727 - 0.0405915i) q^{14} +(0.216476 - 0.474017i) q^{15} +(-0.562632 - 3.91319i) q^{16} +(-3.76413 - 4.34403i) q^{17} +(0.168513 - 0.194474i) q^{18} +(-0.821251 + 1.79829i) q^{19} +(3.06841 + 1.97195i) q^{20} +(-0.0246795 + 0.171650i) q^{21} +(-0.401008 + 0.257712i) q^{22} +(2.95918 + 1.90175i) q^{23} +(-0.0655988 - 0.0757051i) q^{24} +(1.58130 - 0.464313i) q^{25} +(-0.329911 - 0.380738i) q^{26} +(-0.239761 + 1.66757i) q^{27} +(-1.16463 - 0.341965i) q^{28} +4.50909 q^{29} +0.0459388 q^{30} +(3.92487 + 1.15244i) q^{31} +(0.885331 - 0.568968i) q^{32} +(0.639348 - 1.39998i) q^{33} +(0.210498 - 0.460927i) q^{34} +(0.938384 - 0.603063i) q^{35} +(-5.57973 - 1.63836i) q^{36} +3.02889 q^{37} -0.174279 q^{38} +(1.56070 + 0.458262i) q^{39} +(-0.0916991 + 0.637781i) q^{40} +(-1.80542 - 2.08357i) q^{41} +(-0.0146683 + 0.00430700i) q^{42} +(-4.28868 - 4.94940i) q^{43} +(9.06235 + 5.82402i) q^{44} +(4.49580 - 2.88927i) q^{45} +(-0.0441312 + 0.306939i) q^{46} +(-1.86582 - 1.19909i) q^{47} +(-0.467452 + 1.02358i) q^{48} +(4.34094 - 5.00971i) q^{49} +(0.0951423 + 0.109800i) q^{50} +(0.232834 + 1.61939i) q^{51} +(-4.72953 + 10.3562i) q^{52} +(-5.19664 + 5.99724i) q^{53} +(-0.142502 + 0.0418423i) q^{54} +(-9.49871 + 2.78907i) q^{55} +(-0.0305157 - 0.212241i) q^{56} +(0.473370 - 0.304216i) q^{57} +(0.165129 + 0.361582i) q^{58} +(0.733886 + 0.215488i) q^{59} +(-0.431270 - 0.944350i) q^{60} +(1.49662 - 10.4092i) q^{61} +(0.0513198 + 0.356937i) q^{62} +(-1.16463 + 1.34405i) q^{63} +(-6.57363 - 4.22462i) q^{64} +(-4.34637 - 9.51722i) q^{65} +0.135677 q^{66} +(8.14151 - 0.846014i) q^{67} -11.4513 q^{68} +(-0.415917 - 0.910731i) q^{69} +(0.0827241 + 0.0531636i) q^{70} +(-8.46440 + 9.76844i) q^{71} +(-0.146201 - 1.01685i) q^{72} +(-1.52925 + 10.6362i) q^{73} +(0.110922 + 0.242885i) q^{74} +(-0.450086 - 0.132157i) q^{75} +(1.63612 + 3.58260i) q^{76} +(2.77145 - 1.78111i) q^{77} +(0.0204070 + 0.141934i) q^{78} +(11.3848 - 3.34289i) q^{79} +(6.94487 - 2.03920i) q^{80} +(-5.42057 + 6.25567i) q^{81} +(0.100963 - 0.221079i) q^{82} +(0.467569 + 3.25201i) q^{83} +(0.226242 + 0.261098i) q^{84} +(6.89147 - 7.95318i) q^{85} +(0.239833 - 0.525160i) q^{86} +(-1.07968 - 0.693870i) q^{87} +(-0.270827 + 1.88364i) q^{88} +(4.42253 - 2.84219i) q^{89} +(0.396331 + 0.254707i) q^{90} +(2.28009 + 2.63136i) q^{91} +(6.72396 - 1.97433i) q^{92} +(-0.762451 - 0.879916i) q^{93} +(0.0278255 - 0.193531i) q^{94} +(-3.47283 - 1.01971i) q^{95} -0.299543 q^{96} -9.24945 q^{97} +(0.560697 + 0.164635i) q^{98} +(13.2780 - 8.53328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 6 q^{2} - 2 q^{3} + 10 q^{4} + 3 q^{5} - 12 q^{6} + 6 q^{8} - q^{9} - 15 q^{10} + 15 q^{11} - 2 q^{12} - 18 q^{13} + 6 q^{15} - 6 q^{16} - 26 q^{17} - 6 q^{18} - q^{19} + 25 q^{20} + 11 q^{21}+ \cdots + 15 q^{99}+O(q^{100}) $ 10 * q - 6 * q^2 - 2 * q^3 + 10 * q^4 + 3 * q^5 - 12 * q^6 + 6 * q^8 - q^9 - 15 * q^10 + 15 * q^11 - 2 * q^12 - 18 * q^13 + 6 * q^15 - 6 * q^16 - 26 * q^17 - 6 * q^18 - q^19 + 25 * q^20 + 11 * q^21 - 9 * q^22 - 6 * q^23 + q^24 - 4 * q^25 + 24 * q^26 - 29 * q^27 + 11 * q^28 + 28 * q^29 - 8 * q^30 - 10 * q^31 - 4 * q^32 + 8 * q^33 + 64 * q^34 - q^36 - 22 * q^37 - 6 * q^38 + 8 * q^39 - 18 * q^40 + 9 * q^41 + 11 * q^42 + 21 * q^43 + 48 * q^44 + 3 * q^45 - 25 * q^46 - 22 * q^47 - 12 * q^48 + 7 * q^49 - 35 * q^50 + 3 * q^51 - 62 * q^52 + 20 * q^53 + 13 * q^54 - 23 * q^55 - 11 * q^56 + 9 * q^57 - 8 * q^58 - 17 * q^59 + 17 * q^60 + 13 * q^61 + 50 * q^62 + 11 * q^63 + 10 * q^64 + 10 * q^65 - 62 * q^66 + 23 * q^67 - 114 * q^68 - 12 * q^69 + 11 * q^70 + q^71 - 16 * q^72 - 18 * q^73 + 22 * q^74 + 14 * q^75 + 21 * q^76 - 22 * q^77 + 37 * q^78 + 5 * q^79 + 18 * q^80 + 11 * q^81 - 12 * q^82 - 12 * q^83 - 11 * q^84 + 23 * q^85 - 61 * q^86 - 10 * q^87 - 2 * q^88 + 51 * q^89 + 18 * q^90 - 11 * q^91 + 38 * q^92 + 13 * q^93 + 11 * q^94 + 3 * q^95 - 8 * q^96 - 10 * q^97 - 2 * q^98 + 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.0366213	+	0.0801894i	0.0258952	+	0.0567025i	0.922138	−	0.386862i	$-0.126441\pi$
$2$	0.0366213	+	0.0801894i	0.0258952	+	0.0567025i	−0.896242	+	0.443564i	$0.853714\pi$
$3$	−0.239446	−	0.153882i	−0.138244	−	0.0888441i	0.469691	−	0.882831i	$-0.344365\pi$
$3$	−0.239446	−	0.153882i	−0.138244	−	0.0888441i	−0.607935	+	0.793987i	$0.708002\pi$
$4$	1.30463	−	1.50563i	0.652316	−	0.752813i
$5$	0.260554	+	1.81219i	0.116523	+	0.810438i	0.961336	+	0.275377i	$0.0888025\pi$
$5$	0.260554	+	1.81219i	0.116523	+	0.810438i	−0.844813	+	0.535062i	$0.820288\pi$
$6$	0.00357093	−	0.0248364i	0.00145783	−	0.0101394i
$7$	−0.253098	−	0.554206i	−0.0956619	−	0.209470i	0.855751	−	0.517387i	$-0.173095\pi$
$7$	−0.253098	−	0.554206i	−0.0956619	−	0.209470i	−0.951413	+	0.307917i	$0.900368\pi$
$8$	0.337683	+	0.0991526i	0.119389	+	0.0350557i
$9$	−1.21259	−	2.65520i	−0.404197	−	0.885068i
$10$	−0.135777	+	0.0872586i	−0.0429365	+	0.0275936i
$11$	0.769529	+	5.35219i	0.232022	+	1.61375i	0.689336	+	0.724442i	$0.257902\pi$
$11$	0.769529	+	5.35219i	0.232022	+	1.61375i	−0.457314	+	0.889305i	$0.651188\pi$
$12$	−0.544078	+	0.159756i	−0.157062	+	0.0461175i
$13$	−5.48325	+	1.61003i	−1.52078	+	0.446542i	−0.932214	−	0.361907i	$-0.882126\pi$
$13$	−5.48325	+	1.61003i	−1.52078	+	0.446542i	−0.588567	+	0.808449i	$0.700308\pi$
$14$	0.0351727	−	0.0405915i	0.00940031	−	0.0108485i
$15$	0.216476	−	0.474017i	0.0558939	−	0.122391i
$16$	−0.562632	−	3.91319i	−0.140658	−	0.978298i
$17$	−3.76413	−	4.34403i	−0.912934	−	1.05358i	−0.998361	−	0.0572380i	$-0.981771\pi$
$17$	−3.76413	−	4.34403i	−0.912934	−	1.05358i	0.0854261	−	0.996345i	$-0.472775\pi$
$18$	0.168513	−	0.194474i	0.0397188	−	0.0458379i
$19$	−0.821251	+	1.79829i	−0.188408	+	0.412556i	−0.980138	−	0.198315i	$-0.936453\pi$
$19$	−0.821251	+	1.79829i	−0.188408	+	0.412556i	0.791730	+	0.610871i	$0.209180\pi$
$20$	3.06841	+	1.97195i	0.686118	+	0.440942i
$21$	−0.0246795	+	0.171650i	−0.00538551	+	0.0374570i
$22$	−0.401008	+	0.257712i	−0.0854953	+	0.0549445i
$23$	2.95918	+	1.90175i	0.617031	+	0.396542i	0.811488	−	0.584369i	$-0.198658\pi$
$23$	2.95918	+	1.90175i	0.617031	+	0.396542i	−0.194457	+	0.980911i	$0.562294\pi$
$24$	−0.0655988	−	0.0757051i	−0.0133903	−	0.0154532i
$25$	1.58130	−	0.464313i	0.316261	−	0.0928625i
$26$	−0.329911	−	0.380738i	−0.0647009	−	0.0746688i
$27$	−0.239761	+	1.66757i	−0.0461419	+	0.320924i
$28$	−1.16463	−	0.341965i	−0.220094	−	0.0646254i
$29$	4.50909			0.837317			0.418659	−	0.908144i	$-0.362500\pi$
$29$	4.50909			0.837317			0.418659	+	0.908144i	$0.362500\pi$
$30$	0.0459388			0.00838724
$31$	3.92487	+	1.15244i	0.704927	+	0.206985i	0.614499	−	0.788918i	$-0.289358\pi$
$31$	3.92487	+	1.15244i	0.704927	+	0.206985i	0.0904281	+	0.995903i	$0.471176\pi$
$32$	0.885331	−	0.568968i	0.156506	−	0.100580i
$33$	0.639348	−	1.39998i	0.111296	−	0.243705i
$34$	0.210498	−	0.460927i	0.0361002	−	0.0790484i
$35$	0.938384	−	0.603063i	0.158616	−	0.101936i
$36$	−5.57973	−	1.63836i	−0.929955	−	0.273059i
$37$	3.02889			0.497946			0.248973	−	0.968510i	$-0.419907\pi$
$37$	3.02889			0.497946			0.248973	+	0.968510i	$0.419907\pi$
$38$	−0.174279			−0.0282718
$39$	1.56070	+	0.458262i	0.249911	+	0.0733806i
$40$	−0.0916991	+	0.637781i	−0.0144989	+	0.100842i
$41$	−1.80542	−	2.08357i	−0.281960	−	0.325399i	0.597049	−	0.802205i	$-0.296340\pi$
$41$	−1.80542	−	2.08357i	−0.281960	−	0.325399i	−0.879009	+	0.476806i	$0.841794\pi$
$42$	−0.0146683	+	0.00430700i	−0.00226337	+	0.000664584i
$43$	−4.28868	−	4.94940i	−0.654017	−	0.754776i	0.327771	−	0.944757i	$-0.393703\pi$
$43$	−4.28868	−	4.94940i	−0.654017	−	0.754776i	−0.981788	+	0.189981i	$0.939157\pi$
$44$	9.06235	+	5.82402i	1.36620	+	0.878004i
$45$	4.49580	−	2.88927i	0.670194	−	0.430708i
$46$	−0.0441312	+	0.306939i	−0.00650679	+	0.0452557i
$47$	−1.86582	−	1.19909i	−0.272157	−	0.174905i	0.397442	−	0.917627i	$-0.369898\pi$
$47$	−1.86582	−	1.19909i	−0.272157	−	0.174905i	−0.669600	+	0.742722i	$0.733534\pi$
$48$	−0.467452	+	1.02358i	−0.0674708	+	0.147740i
$49$	4.34094	−	5.00971i	0.620134	−	0.715673i
$50$	0.0951423	+	0.109800i	0.0134552	+	0.0155281i
$51$	0.232834	+	1.61939i	0.0326032	+	0.226760i
$52$	−4.72953	+	10.3562i	−0.655868	+	1.43615i
$53$	−5.19664	+	5.99724i	−0.713813	+	0.823784i	−0.990549	−	0.137162i	$-0.956202\pi$
$53$	−5.19664	+	5.99724i	−0.713813	+	0.823784i	0.276736	+	0.960946i	$0.410747\pi$
$54$	−0.142502	+	0.0418423i	−0.0193921	+	0.00569402i
$55$	−9.49871	+	2.78907i	−1.28081	+	0.376079i
$56$	−0.0305157	−	0.212241i	−0.00407783	−	0.0283619i
$57$	0.473370	−	0.304216i	0.0626994	−	0.0402945i
$58$	0.165129	+	0.361582i	0.0216825	+	0.0474780i
$59$	0.733886	+	0.215488i	0.0955439	+	0.0280542i	0.329155	−	0.944276i	$-0.393236\pi$
$59$	0.733886	+	0.215488i	0.0955439	+	0.0280542i	−0.233611	+	0.972330i	$0.575054\pi$
$60$	−0.431270	−	0.944350i	−0.0556768	−	0.121915i
$61$	1.49662	−	10.4092i	0.191622	−	1.33276i	−0.636093	−	0.771612i	$-0.719451\pi$
$61$	1.49662	−	10.4092i	0.191622	−	1.33276i	0.827715	−	0.561148i	$-0.189640\pi$
$62$	0.0513198	+	0.356937i	0.00651762	+	0.0453310i
$63$	−1.16463	+	1.34405i	−0.146729	+	0.169335i
$64$	−6.57363	−	4.22462i	−0.821704	−	0.528077i
$65$	−4.34637	−	9.51722i	−0.539101	−	1.18047i
$66$	0.135677			0.0167007
$67$	8.14151	−	0.846014i	0.994644	−	0.103357i
$67$	8.14151	−	0.846014i	0.994644	−	0.103357i
$68$	−11.4513			−1.38867
$69$	−0.415917	−	0.910731i	−0.0500705	−	0.109639i
$70$	0.0827241	+	0.0531636i	0.00988743	+	0.00635426i
$71$	−8.46440	+	9.76844i	−1.00454	+	1.15930i	−0.0173337	+	0.999850i	$0.505518\pi$
$71$	−8.46440	+	9.76844i	−1.00454	+	1.15930i	−0.987206	+	0.159451i	$0.949028\pi$
$72$	−0.146201	−	1.01685i	−0.0172299	−	0.119837i
$73$	−1.52925	+	10.6362i	−0.178986	+	1.24487i	0.680130	+	0.733091i	$0.261923\pi$
$73$	−1.52925	+	10.6362i	−0.178986	+	1.24487i	−0.859116	+	0.511781i	$0.828986\pi$
$74$	0.110922	+	0.242885i	0.0128944	+	0.0282348i
$75$	−0.450086	−	0.132157i	−0.0519714	−	0.0152602i
$76$	1.63612	+	3.58260i	0.187676	+	0.410953i
$77$	2.77145	−	1.78111i	0.315837	−	0.202976i
$78$	0.0204070	+	0.141934i	0.00231063	+	0.0160708i
$79$	11.3848	−	3.34289i	1.28089	−	0.376104i	0.430662	−	0.902513i	$-0.358280\pi$
$79$	11.3848	−	3.34289i	1.28089	−	0.376104i	0.850232	+	0.526409i	$0.176462\pi$
$80$	6.94487	−	2.03920i	0.776460	−	0.227989i
$81$	−5.42057	+	6.25567i	−0.602285	+	0.695074i
$82$	0.100963	−	0.221079i	0.0111495	−	0.0244141i
$83$	0.467569	+	3.25201i	0.0513224	+	0.356955i	0.999259	+	0.0384952i	$0.0122564\pi$
$83$	0.467569	+	3.25201i	0.0513224	+	0.356955i	−0.947936	+	0.318460i	$0.896834\pi$
$84$	0.226242	+	0.261098i	0.0246851	+	0.0284881i
$85$	6.89147	−	7.95318i	0.747485	−	0.862644i
$86$	0.239833	−	0.525160i	0.0258618	−	0.0566295i
$87$	−1.07968	−	0.693870i	−0.115754	−	0.0743907i
$88$	−0.270827	+	1.88364i	−0.0288703	+	0.200797i
$89$	4.42253	−	2.84219i	0.468787	−	0.301271i	−0.284838	−	0.958576i	$-0.591940\pi$
$89$	4.42253	−	2.84219i	0.468787	−	0.301271i	0.753625	+	0.657304i	$0.228303\pi$
$90$	0.396331	+	0.254707i	0.0417770	+	0.0268484i
$91$	2.28009	+	2.63136i	0.239018	+	0.275841i
$92$	6.72396	−	1.97433i	0.701021	−	0.205838i
$93$	−0.762451	−	0.879916i	−0.0790625	−	0.0912430i
$94$	0.0278255	−	0.193531i	0.00286998	−	0.0199612i
$95$	−3.47283	−	1.01971i	−0.356305	−	0.104621i
$96$	−0.299543			−0.0305720
$97$	−9.24945			−0.939139			−0.469570	−	0.882895i	$-0.655591\pi$
$97$	−9.24945			−0.939139			−0.469570	+	0.882895i	$0.655591\pi$
$98$	0.560697	+	0.164635i	0.0566389	+	0.0166307i
$99$	13.2780	−	8.53328i	1.33449	−	0.857626i
$100$	1.36394	−	2.98661i	0.136394	−	0.298661i
$101$	−2.15093	+	4.70988i	−0.214026	+	0.468651i	−0.985945	−	0.167070i	$-0.946570\pi$
$101$	−2.15093	+	4.70988i	−0.214026	+	0.468651i	0.771919	+	0.635720i	$0.219297\pi$
$102$	−0.121332	+	0.0779750i	−0.0120136	+	0.00772068i
$103$	9.60270	+	2.81961i	0.946182	+	0.277824i	0.718196	−	0.695840i	$-0.244968\pi$
$103$	9.60270	+	2.81961i	0.946182	+	0.277824i	0.227985	+	0.973665i	$0.426786\pi$
$104$	−2.01124			−0.197218
$105$	−0.317493			−0.0309841
$106$	−0.671223	−	0.197089i	−0.0651949	−	0.0191430i
$107$	1.21428	−	8.44550i	0.117389	−	0.816457i	−0.843024	−	0.537876i	$-0.819227\pi$
$107$	1.21428	−	8.44550i	0.117389	−	0.816457i	0.960413	−	0.278581i	$-0.0898641\pi$
$108$	2.19794	+	2.53656i	0.211497	+	0.244080i
$109$	−5.34446	+	1.56927i	−0.511906	+	0.150309i	−0.527477	−	0.849570i	$-0.676862\pi$
$109$	−5.34446	+	1.56927i	−0.511906	+	0.150309i	0.0155705	+	0.999879i	$0.495044\pi$
$110$	−0.571509	−	0.659557i	−0.0544913	−	0.0628863i
$111$	−0.725254	−	0.466092i	−0.0688380	−	0.0442395i
$112$	−2.02632	+	1.30223i	−0.191469	+	0.123050i
$113$	1.48006	−	10.2941i	0.139232	−	0.968383i	−0.793694	−	0.608317i	$-0.791845\pi$
$113$	1.48006	−	10.2941i	0.139232	−	0.968383i	0.932927	−	0.360066i	$-0.117246\pi$
$114$	0.0417304	+	0.0268185i	0.00390841	+	0.00251178i
$115$	−2.67531	+	5.85812i	−0.249474	+	0.546272i
$116$	5.88271	−	6.78901i	0.546196	−	0.630343i
$117$	10.9239	+	12.6068i	1.00991	+	1.16550i
$118$	0.00959596	+	0.0667414i	0.000883380	+	0.00614404i
$119$	−1.45480	+	3.18557i	−0.133361	+	0.292020i
$120$	0.120100	−	0.138603i	0.0109636	−	0.0126527i
$121$	−17.4994	+	5.13828i	−1.59085	+	0.467116i
$122$	0.889516	−	0.261185i	0.0805330	−	0.0236466i
$123$	0.111676	+	0.776725i	0.0100695	+	0.0700349i
$124$	6.85566	−	4.40586i	0.615656	−	0.395658i
$125$	5.05621	+	11.0716i	0.452241	+	0.990270i
$126$	−0.150429	−	0.0441699i	−0.0134013	−	0.00393497i
$127$	5.32196	+	11.6535i	0.472247	+	1.03408i	0.984523	+	0.175256i	$0.0560754\pi$
$127$	5.32196	+	11.6535i	0.472247	+	1.03408i	−0.512276	+	0.858821i	$0.671197\pi$
$128$	0.397578	−	2.76521i	0.0351412	−	0.244413i
$129$	0.265280	+	1.84506i	0.0233566	+	0.162449i
$130$	0.604011	−	0.697066i	0.0529753	−	0.0611367i
$131$	−13.9362	−	8.95624i	−1.21761	−	0.782510i	−0.235694	−	0.971827i	$-0.575736\pi$
$131$	−13.9362	−	8.95624i	−1.21761	−	0.782510i	−0.981916	+	0.189317i	$0.939373\pi$
$132$	−1.27373	−	2.78907i	−0.110864	−	0.242758i
$133$	1.20448			0.104442
$134$	0.365994	+	0.621881i	0.0316171	+	0.0537224i
$135$	−3.08443			−0.265466
$136$	−0.840358	−	1.84013i	−0.0720601	−	0.157790i
$137$	−14.1127	−	9.06967i	−1.20573	−	0.774874i	−0.225789	−	0.974176i	$-0.572496\pi$
$137$	−14.1127	−	9.06967i	−1.20573	−	0.774874i	−0.979938	+	0.199302i	$0.936132\pi$
$138$	0.0577996	−	0.0667043i	0.00492023	−	0.00567825i
$139$	1.70167	+	11.8353i	0.144333	+	1.00386i	0.925286	+	0.379270i	$0.123825\pi$
$139$	1.70167	+	11.8353i	0.144333	+	1.00386i	−0.780953	+	0.624590i	$0.785266\pi$
$140$	0.316259	−	2.19963i	0.0267288	−	0.185903i
$141$	0.262243	+	0.574232i	0.0220849	+	0.0483591i
$142$	−1.09330	−	0.321023i	−0.0917480	−	0.0269396i
$143$	−12.8367	−	28.1085i	−1.07346	−	2.35055i
$144$	−9.70808	+	6.23900i	−0.809006	+	0.519917i
$145$	1.17486	+	8.17135i	0.0975671	+	0.678594i
$146$	−0.908914	+	0.266881i	−0.0752223	+	0.0220872i
$147$	−1.81033	+	0.531560i	−0.149313	+	0.0438423i
$148$	3.95158	−	4.56037i	0.324818	−	0.374860i
$149$	3.05447	−	6.68836i	0.250232	−	0.547932i	−0.742278	−	0.670092i	$-0.766255\pi$
$149$	3.05447	−	6.68836i	0.250232	−	0.547932i	0.992510	+	0.122160i	$0.0389821\pi$
$150$	−0.00588512	−	0.0409319i	−0.000480518	−	0.00334208i
$151$	−3.02720	−	3.49357i	−0.246350	−	0.284303i	0.619085	−	0.785324i	$-0.287503\pi$
$151$	−3.02720	−	3.49357i	−0.246350	−	0.284303i	−0.865435	+	0.501021i	$0.832958\pi$
$152$	−0.455627	+	0.525822i	−0.0369562	+	0.0426498i
$153$	−6.96994	+	15.2620i	−0.563487	+	1.23386i
$154$	0.244320	+	0.157015i	0.0196879	+	0.0126526i
$155$	−1.06581	+	7.41290i	−0.0856082	+	0.595418i
$156$	2.72611	−	1.75196i	0.218263	−	0.140269i
$157$	1.91636	+	1.23157i	0.152942	+	0.0982898i	0.614873	−	0.788626i	$-0.289207\pi$
$157$	1.91636	+	1.23157i	0.152942	+	0.0982898i	−0.461932	+	0.886916i	$0.652843\pi$
$158$	0.684992	+	0.790523i	0.0544950	+	0.0628906i
$159$	2.16718	−	0.636342i	0.171869	−	0.0504652i
$160$	1.26176	+	1.45615i	0.0997507	+	0.115118i
$161$	0.305000	−	2.12132i	0.0240374	−	0.167184i
$162$	−0.700147	−	0.205582i	−0.0550087	−	0.0161520i
$163$	−11.9173			−0.933433			−0.466717	−	0.884407i	$-0.654563\pi$
$163$	−11.9173			−0.933433			−0.466717	+	0.884407i	$0.654563\pi$
$164$	−5.49249			−0.428891
$165$	2.70362	+	0.793853i	0.210476	+	0.0618014i
$166$	−0.243654	+	0.156587i	−0.0189112	+	0.0121535i
$167$	−7.73872	+	16.9454i	−0.598840	+	1.31128i	0.331110	+	0.943592i	$0.392577\pi$
$167$	−7.73872	+	16.9454i	−0.598840	+	1.31128i	−0.929950	+	0.367685i	$0.880151\pi$
$168$	−0.0253533	+	0.0555161i	−0.00195605	+	0.00428316i
$169$	16.5376	−	10.6281i	1.27212	−	0.817543i
$170$	0.890136	+	0.261368i	0.0682703	+	0.0200460i
$171$	5.77066			0.441294
$172$	−13.0471			−0.994831
$173$	8.82447	+	2.59110i	0.670912	+	0.196998i	0.599409	−	0.800443i	$-0.295402\pi$
$173$	8.82447	+	2.59110i	0.670912	+	0.196998i	0.0715029	+	0.997440i	$0.477220\pi$
$174$	0.0161017	−	0.111990i	0.00122066	−	0.00848991i
$175$	−0.657549	−	0.758852i	−0.0497060	−	0.0573638i
$176$	20.5112	−	6.02263i	1.54609	−	0.453973i
$177$	−0.142566	−	0.164530i	−0.0107159	−	0.0123668i
$178$	0.389872	+	0.250556i	0.0292222	+	0.0187799i
$179$	−14.7436	+	9.47515i	−1.10199	+	0.708206i	−0.959533	−	0.281595i	$-0.909137\pi$
$179$	−14.7436	+	9.47515i	−1.10199	+	0.708206i	−0.142457	+	0.989801i	$0.545500\pi$
$180$	1.51520	−	10.5384i	0.112936	−	0.785488i
$181$	16.3259	+	10.4920i	1.21349	+	0.779864i	0.981240	−	0.192791i	$-0.0617540\pi$
$181$	16.3259	+	10.4920i	1.21349	+	0.779864i	0.232253	+	0.972655i	$0.425390\pi$
$182$	−0.127508	+	0.279203i	−0.00945149	+	0.0206959i
$183$	−1.96015	+	2.26213i	−0.144898	+	0.167222i
$184$	0.810700	+	0.935597i	0.0597656	+	0.0689732i
$185$	0.789189	+	5.48893i	0.0580223	+	0.403554i
$186$	0.0426380	−	0.0933642i	0.00312637	−	0.00684580i
$187$	20.3535	−	23.4892i	1.48839	−	1.71770i
$188$	−4.23958	+	1.24485i	−0.309203	+	0.0907902i
$189$	0.984861	−	0.289181i	0.0716381	−	0.0210349i
$190$	−0.0454092	−	0.315828i	−0.00329433	−	0.0229125i
$191$	12.4377	−	7.99323i	0.899960	−	0.578369i	−0.00681804	−	0.999977i	$-0.502170\pi$
$191$	12.4377	−	7.99323i	0.899960	−	0.578369i	0.906779	+	0.421607i	$0.138534\pi$
$192$	0.923933	+	2.02313i	0.0666792	+	0.146007i
$193$	−8.21738	−	2.41284i	−0.591500	−	0.173680i	−0.0277350	−	0.999615i	$-0.508829\pi$
$193$	−8.21738	−	2.41284i	−0.591500	−	0.173680i	−0.563765	+	0.825935i	$0.690648\pi$
$194$	−0.338727	−	0.741708i	−0.0243192	−	0.0532515i
$195$	−0.423814	+	2.94769i	−0.0303499	+	0.211088i
$196$	−1.87942	−	13.0717i	−0.134244	−	0.933690i
$197$	0.886535	−	1.02312i	0.0631630	−	0.0728940i	−0.723289	−	0.690546i	$-0.757370\pi$
$197$	0.886535	−	1.02312i	0.0631630	−	0.0728940i	0.786452	+	0.617652i	$0.211916\pi$
$198$	1.17054	+	0.752259i	0.0831865	+	0.0534607i
$199$	0.637120	+	1.39510i	0.0451642	+	0.0988958i	0.930869	−	0.365353i	$-0.119052\pi$
$199$	0.637120	+	1.39510i	0.0451642	+	0.0988958i	−0.885705	+	0.464249i	$0.846324\pi$
$200$	0.580016			0.0410134
$201$	−2.07964	−	1.05026i	−0.146686	−	0.0740797i
$202$	−0.456453			−0.0321159
$203$	−1.14124	−	2.49897i	−0.0800994	−	0.175393i
$204$	2.74196	+	1.76215i	0.191976	+	0.123375i
$205$	3.30542	−	3.81466i	0.230861	−	0.266428i
$206$	0.125561	+	0.873293i	0.00874822	+	0.0608452i
$207$	1.46126	−	10.1633i	0.101564	−	0.706395i
$208$	9.38540	+	20.5512i	0.650761	+	1.42497i
$209$	−10.2568	−	3.01166i	−0.709475	−	0.208321i
$210$	−0.0116270	−	0.0254596i	−0.000802339	−	0.00175688i
$211$	−15.4357	+	9.91993i	−1.06264	+	0.682916i	−0.950484	−	0.310775i	$-0.899412\pi$
$211$	−15.4357	+	9.91993i	−1.06264	+	0.682916i	−0.112155	+	0.993691i	$0.535775\pi$
$212$	2.24990	+	15.6484i	0.154524	+	1.07473i
$213$	3.52996	−	1.03649i	0.241869	−	0.0710190i
$214$	0.721708	−	0.211913i	0.0493350	−	0.0144861i
$215$	7.85184	−	9.06150i	0.535491	−	0.617990i
$216$	−0.246307	+	0.539337i	−0.0167591	+	0.0366972i
$217$	−0.354682	−	2.46687i	−0.0240774	−	0.167462i
$218$	−0.321560	−	0.371100i	−0.0217788	−	0.0251341i
$219$	2.00290	−	2.31147i	0.135343	−	0.156194i
$220$	−8.19303	+	17.9402i	−0.552374	+	1.20953i
$221$	27.6337	+	17.7591i	1.85884	+	1.19461i
$222$	0.0108160	−	0.0752266i	0.000725919	−	0.00504888i
$223$	23.8768	−	15.3447i	1.59891	−	1.02756i	0.631160	−	0.775653i	$-0.282579\pi$
$223$	23.8768	−	15.3447i	1.59891	−	1.02756i	0.967752	−	0.251906i	$-0.0810573\pi$
$224$	−0.539401	−	0.346652i	−0.0360402	−	0.0231617i
$225$	−3.15032	−	3.63566i	−0.210021	−	0.242377i
$226$	0.879676	−	0.258296i	0.0585152	−	0.0171816i
$227$	−12.8108	−	14.7845i	−0.850284	−	0.981280i	0.149689	−	0.988733i	$-0.452173\pi$
$227$	−12.8108	−	14.7845i	−0.850284	−	0.981280i	−0.999972	+	0.00745367i	$0.997627\pi$
$228$	0.159538	−	1.10961i	0.0105656	−	0.0734856i
$229$	−17.6410	−	5.17987i	−1.16575	−	0.342295i	−0.359086	−	0.933305i	$-0.616911\pi$
$229$	−17.6410	−	5.17987i	−1.16575	−	0.342295i	−0.806665	+	0.591009i	$0.798730\pi$
$230$	−0.567732			−0.0374352
$231$	−0.937694			−0.0616957
$232$	1.52264	+	0.447088i	0.0999663	+	0.0293528i
$233$	−8.52122	+	5.47626i	−0.558244	+	0.358762i	−0.789137	−	0.614218i	$-0.789472\pi$
$233$	−8.52122	+	5.47626i	−0.558244	+	0.358762i	0.230893	+	0.972979i	$0.425835\pi$
$234$	−0.610889	+	1.33766i	−0.0399351	+	0.0874456i
$235$	1.68683	−	3.69365i	0.110037	−	0.240947i
$236$	1.28190	−	0.823825i	0.0834444	−	0.0536264i
$237$	−3.24046	−	0.951486i	−0.210491	−	0.0618056i
$238$	−0.308725			−0.0200117
$239$	−11.7728			−0.761516			−0.380758	−	0.924675i	$-0.624337\pi$
$239$	−11.7728			−0.761516			−0.380758	+	0.924675i	$0.624337\pi$
$240$	−1.97672	−	0.580416i	−0.127596	−	0.0374657i
$241$	−2.33109	+	16.2131i	−0.150159	+	1.04438i	0.765792	+	0.643088i	$0.222347\pi$
$241$	−2.33109	+	16.2131i	−0.150159	+	1.04438i	−0.915951	+	0.401290i	$0.868562\pi$
$242$	−1.05289	−	1.21509i	−0.0676821	−	0.0781093i
$243$	7.11000	−	2.08768i	0.456107	−	0.133925i
$244$	−13.7198	−	15.8335i	−0.878321	−	1.01364i
$245$	10.2096	+	6.56133i	0.652269	+	0.419188i
$246$	−0.0581954	+	0.0373999i	−0.00371040	+	0.00238453i
$247$	1.60783	−	11.1827i	0.102304	−	0.711539i
$248$	1.21109	+	0.778321i	0.0769044	+	0.0494234i
$249$	0.388470	−	0.850631i	0.0246183	−	0.0539066i
$250$	−0.702657	+	0.810910i	−0.0444399	+	0.0512864i
$251$	9.08000	+	10.4789i	0.573125	+	0.661421i	0.966112	−	0.258123i	$-0.0831039\pi$
$251$	9.08000	+	10.4789i	0.573125	+	0.661421i	−0.392988	+	0.919544i	$0.628558\pi$
$252$	0.504228	+	3.50698i	0.0317634	+	0.220919i
$253$	−7.90135	+	17.3015i	−0.496754	+	1.08774i
$254$	−0.739588	+	0.853530i	−0.0464059	+	0.0535552i
$255$	−2.87399	+	0.843879i	−0.179976	+	0.0528458i
$256$	−14.7588	+	4.33358i	−0.922427	+	0.270849i
$257$	−0.366322	−	2.54783i	−0.0228506	−	0.158929i	0.975201	−	0.221320i	$-0.0710365\pi$
$257$	−0.366322	−	2.54783i	−0.0228506	−	0.158929i	−0.998052	+	0.0623909i	$0.980127\pi$
$258$	−0.138240	+	0.0888413i	−0.00860643	+	0.00553102i
$259$	−0.766604	−	1.67863i	−0.0476344	−	0.104305i
$260$	−19.9998	−	5.87247i	−1.24033	−	0.364195i
$261$	−5.46768	−	11.9726i	−0.338441	−	0.741083i
$262$	0.207835	−	1.44552i	0.0128401	−	0.0893047i
$263$	2.11259	+	14.6934i	0.130268	+	0.906033i	0.945204	+	0.326481i	$0.105863\pi$
$263$	2.11259	+	14.6934i	0.130268	+	0.906033i	−0.814936	+	0.579551i	$0.803228\pi$
$264$	0.354708	−	0.409355i	0.0218308	−	0.0251940i
$265$	−12.2222	−	7.85471i	−0.750802	−	0.482511i
$266$	0.0441096	+	0.0965866i	0.00270453	+	0.00592210i
$267$	−1.49632			−0.0915732
$268$	9.34790	−	13.3618i	0.571014	−	0.816203i
$269$	1.38543			0.0844712			0.0422356	−	0.999108i	$-0.486552\pi$
$269$	1.38543			0.0844712			0.0422356	+	0.999108i	$0.486552\pi$
$270$	−0.112956	−	0.247339i	−0.00687428	−	0.0150526i
$271$	−18.1863	−	11.6876i	−1.10474	−	0.709973i	−0.144599	−	0.989490i	$-0.546189\pi$
$271$	−18.1863	−	11.6876i	−1.10474	−	0.709973i	−0.960141	+	0.279517i	$0.909826\pi$
$272$	−14.8812	+	17.1738i	−0.902306	+	1.04132i
$273$	−0.141037	−	0.980933i	−0.00853594	−	0.0593688i
$274$	0.210467	−	1.46383i	0.0127148	−	0.0884332i
$275$	3.70195	+	8.10614i	0.223236	+	0.488819i
$276$	−1.91384	−	0.561954i	−0.115200	−	0.0338256i
$277$	−1.14858	−	2.51504i	−0.0690115	−	0.151114i	0.871983	−	0.489537i	$-0.162834\pi$
$277$	−1.14858	−	2.51504i	−0.0690115	−	0.151114i	−0.940994	+	0.338422i	$0.890107\pi$
$278$	−0.886752	+	0.569881i	−0.0531839	+	0.0341792i
$279$	−1.69928	−	11.8188i	−0.101733	−	0.707571i
$280$	0.376671	−	0.110601i	0.0225104	−	0.00660965i
$281$	18.2435	−	5.35677i	1.08831	−	0.319558i	0.312114	−	0.950045i	$-0.398963\pi$
$281$	18.2435	−	5.35677i	1.08831	−	0.319558i	0.776200	+	0.630487i	$0.217145\pi$
$282$	−0.0364437	+	0.0420583i	−0.00217019	+	0.00250453i
$283$	7.95612	−	17.4215i	0.472942	−	1.03560i	−0.511402	−	0.859342i	$-0.670874\pi$
$283$	7.95612	−	17.4215i	0.472942	−	1.03560i	0.984344	−	0.176257i	$-0.0563991\pi$
$284$	3.66468	+	25.4884i	0.217459	+	1.51246i
$285$	0.674638	+	0.778574i	0.0399621	+	0.0461187i
$286$	1.78391	−	2.05874i	0.105485	−	0.121736i
$287$	−0.697779	+	1.52792i	−0.0411886	+	0.0901905i
$288$	−2.58427	−	1.66081i	−0.152280	−	0.0978641i
$289$	−2.28262	+	15.8760i	−0.134272	+	0.933882i
$290$	−0.612231	+	0.393457i	−0.0359515	+	0.0231046i
$291$	2.21474	+	1.42333i	0.129830	+	0.0834369i
$292$	14.0190	+	16.1788i	0.820401	+	0.946793i
$293$	12.4636	−	3.65963i	0.728129	−	0.213798i	0.103401	−	0.994640i	$-0.467028\pi$
$293$	12.4636	−	3.65963i	0.728129	−	0.213798i	0.624729	+	0.780842i	$0.285209\pi$
$294$	−0.108922	−	0.125703i	−0.00635246	−	0.00733112i
$295$	−0.199290	+	1.38609i	−0.0116031	+	0.0807014i
$296$	1.02280	+	0.300322i	0.0594492	+	0.0174559i
$297$	−9.10967			−0.528596
$298$	0.648195			0.0375489
$299$	−19.2878	−	5.66341i	−1.11544	−	0.327523i
$300$	−0.786176	+	0.505244i	−0.0453899	+	0.0291703i
$301$	−1.65753	+	3.62949i	−0.0955387	+	0.209201i
$302$	0.169288	−	0.370688i	0.00974141	−	0.0213307i
$303$	1.23980	−	0.796771i	0.0712246	−	0.0457733i
$304$	7.49911	+	2.20194i	0.430103	+	0.126290i
$305$	19.2534			1.10245
$306$	−1.47910			−0.0845547
$307$	−6.51335	−	1.91249i	−0.371737	−	0.109152i	0.0905276	−	0.995894i	$-0.471145\pi$
$307$	−6.51335	−	1.91249i	−0.371737	−	0.109152i	−0.462264	+	0.886742i	$0.652963\pi$
$308$	0.934050	−	6.49646i	0.0532224	−	0.370170i
$309$	−1.86544	−	2.15283i	−0.106121	−	0.122470i
$310$	−0.633468	+	0.186003i	−0.0359785	+	0.0105643i
$311$	1.77969	+	2.05387i	0.100917	+	0.116464i	0.803961	−	0.594682i	$-0.202722\pi$
$311$	1.77969	+	2.05387i	0.100917	+	0.116464i	−0.703044	+	0.711146i	$0.748176\pi$
$312$	0.481582	+	0.309494i	0.0272642	+	0.0175217i
$313$	10.5780	−	6.79806i	0.597903	−	0.384249i	−0.206401	−	0.978468i	$-0.566175\pi$
$313$	10.5780	−	6.79806i	0.597903	−	0.384249i	0.804304	+	0.594219i	$0.202539\pi$
$314$	−0.0285793	+	0.198773i	−0.00161282	+	0.0112174i
$315$	−2.73913	−	1.76033i	−0.154333	−	0.0991835i
$316$	9.81988	−	21.5025i	0.552412	−	1.20961i
$317$	13.9644	−	16.1158i	0.784321	−	0.905155i	−0.213092	−	0.977032i	$-0.568354\pi$
$317$	13.9644	−	16.1158i	0.784321	−	0.905155i	0.997413	+	0.0718773i	$0.0228990\pi$
$318$	0.130393	+	0.150481i	0.00731207	+	0.00843858i
$319$	3.46988	+	24.1335i	0.194276	+	1.35122i
$320$	5.94304	−	13.0134i	0.332226	−	0.727473i
$321$	−1.59037	+	1.83538i	−0.0887657	+	0.102441i
$322$	0.181277	−	0.0532278i	0.0101022	−	0.00296627i
$323$	10.9031	−	3.20144i	0.606666	−	0.178133i
$324$	2.34685	+	16.3227i	0.130381	+	0.906816i
$325$	−7.92313	+	5.09189i	−0.439496	+	0.282447i
$326$	−0.436426	−	0.955640i	−0.0241714	−	0.0529280i
$327$	1.52119	+	0.446662i	0.0841220	+	0.0247005i
$328$	−0.403069	−	0.882598i	−0.0222558	−	0.0487333i
$329$	−0.192308	+	1.33753i	−0.0106023	+	0.0737406i
$330$	0.0353513	+	0.245873i	0.00194602	+	0.0135349i
$331$	0.0106833	−	0.0123292i	0.000587207	−	0.000677673i	−0.755456	−	0.655200i	$-0.772585\pi$
$331$	0.0106833	−	0.0123292i	0.000587207	−	0.000677673i	0.756043	+	0.654522i	$0.227130\pi$
$332$	5.50632	+	3.53870i	0.302199	+	0.194211i
$333$	−3.67280	−	8.04231i	−0.201268	−	0.440716i
$334$	−1.64225			−0.0898597
$335$	3.65445	+	14.5336i	0.199664	+	0.794054i
$336$	0.685583			0.0374016
$337$	1.41867	+	3.10645i	0.0772797	+	0.169219i	0.944328	−	0.329005i	$-0.106713\pi$
$337$	1.41867	+	3.10645i	0.0772797	+	0.169219i	−0.867049	+	0.498224i	$0.833986\pi$
$338$	1.45789	+	0.936926i	0.0792985	+	0.0509621i
$339$	−1.93847	+	2.23711i	−0.105283	+	0.121503i
$340$	−2.98368	−	20.7520i	−0.161813	−	1.12543i
$341$	−3.14781	+	21.8935i	−0.170463	+	1.18560i
$342$	0.211329	+	0.462746i	0.0114274	+	0.0250225i
$343$	−7.96719	−	2.33938i	−0.430188	−	0.126315i
$344$	−0.957466	−	2.09656i	−0.0516231	−	0.113039i
$345$	1.54205	−	0.991017i	0.0830213	−	0.0533546i
$346$	0.115385	+	0.802519i	0.00620312	+	0.0431437i
$347$	31.1374	−	9.14275i	1.67154	−	0.490809i	0.697387	−	0.716694i	$-0.254346\pi$
$347$	31.1374	−	9.14275i	1.67154	−	0.490809i	0.974154	+	0.225886i	$0.0725276\pi$
$348$	−2.45330	+	0.720353i	−0.131511	+	0.0386150i
$349$	−13.0668	+	15.0799i	−0.699451	+	0.807210i	−0.988678	−	0.150051i	$-0.952056\pi$
$349$	−13.0668	+	15.0799i	−0.699451	+	0.807210i	0.289227	+	0.957260i	$0.406602\pi$
$350$	0.0367716	−	0.0805186i	0.00196553	−	0.00430390i
$351$	−1.37017	−	9.52974i	−0.0731342	−	0.508660i
$352$	3.72652	+	4.30063i	0.198624	+	0.229224i
$353$	17.0378	−	19.6627i	0.906832	−	1.04654i	−0.0918787	−	0.995770i	$-0.529287\pi$
$353$	17.0378	−	19.6627i	0.906832	−	1.04654i	0.998710	−	0.0507694i	$-0.0161673\pi$
$354$	0.00797262	−	0.0174576i	0.000423740	−	0.000927861i
$355$	−19.9078	−	12.7939i	−1.05659	−	0.679032i
$356$	1.49050	−	10.3667i	0.0789966	−	0.549433i
$357$	0.838548	−	0.538902i	0.0443807	−	0.0285217i
$358$	−1.29974	−	0.835291i	−0.0686933	−	0.0441465i
$359$	−1.65826	−	1.91374i	−0.0875198	−	0.101003i	0.710300	−	0.703899i	$-0.248559\pi$
$359$	−1.65826	−	1.91374i	−0.0875198	−	0.101003i	−0.797820	+	0.602895i	$0.794014\pi$
$360$	1.80463	−	0.529888i	0.0951125	−	0.0279275i
$361$	9.88296	+	11.4055i	0.520156	+	0.600292i
$362$	−0.243473	+	1.69339i	−0.0127967	+	0.0890028i
$363$	4.98084	+	1.46251i	0.261426	+	0.0767617i
$364$	6.93652			0.363572
$365$	−19.6733			−1.02975
$366$	−0.253183	−	0.0743411i	−0.0132341	−	0.00388587i
$367$	19.1827	−	12.3279i	1.00133	−	0.643513i	0.0661920	−	0.997807i	$-0.478915\pi$
$367$	19.1827	−	12.3279i	1.00133	−	0.643513i	0.935134	+	0.354294i	$0.115279\pi$
$368$	5.77698	−	12.6498i	0.301146	−	0.659417i
$369$	−3.34306	+	7.32028i	−0.174033	+	0.381079i
$370$	−0.411253	+	0.264296i	−0.0213800	+	0.0137401i
$371$	4.63896	+	1.36212i	0.240843	+	0.0707179i
$372$	−2.31954			−0.120263
$373$	19.9389			1.03240			0.516198	−	0.856469i	$-0.327347\pi$
$373$	19.9389			1.03240			0.516198	+	0.856469i	$0.327347\pi$
$374$	2.62896	+	0.771931i	0.135940	+	0.0399156i
$375$	0.493030	−	3.42910i	0.0254600	−	0.177078i
$376$	−0.511161	−	0.589911i	−0.0263611	−	0.0304223i
$377$	−24.7245	+	7.25977i	−1.27338	+	0.373897i
$378$	0.0592562	+	0.0683853i	0.00304781	+	0.00351736i
$379$	2.79789	+	1.79809i	0.143718	+	0.0923618i	0.610524	−	0.791998i	$-0.290959\pi$
$379$	2.79789	+	1.79809i	0.143718	+	0.0923618i	−0.466806	+	0.884360i	$0.654595\pi$
$380$	−6.06608	+	3.89843i	−0.311183	+	0.199985i
$381$	0.518943	−	3.60933i	0.0265862	−	0.184911i
$382$	1.09646	+	0.704650i	0.0560996	+	0.0360530i
$383$	−14.5032	+	31.7575i	−0.741077	+	1.62273i	0.0406989	+	0.999171i	$0.487042\pi$
$383$	−14.5032	+	31.7575i	−0.741077	+	1.62273i	−0.781776	+	0.623560i	$0.785686\pi$
$384$	−0.520716	+	0.600938i	−0.0265727	+	0.0306665i
$385$	3.94982	+	4.55834i	0.201302	+	0.232315i
$386$	−0.107447	−	0.747309i	−0.00546890	−	0.0380370i
$387$	−7.94124	+	17.3889i	−0.403676	+	0.883927i
$388$	−12.0671	+	13.9262i	−0.612616	+	0.706996i
$389$	−19.9764	+	5.86559i	−1.01284	+	0.297397i	−0.745716	−	0.666264i	$-0.767892\pi$
$389$	−19.9764	+	5.86559i	−1.01284	+	0.297397i	−0.267127	+	0.963661i	$0.586074\pi$
$390$	−0.251894	+	0.0739628i	−0.0127552	+	0.00374525i
$391$	−2.87746	−	20.0132i	−0.145519	−	1.01211i
$392$	1.96259	−	1.26128i	0.0991255	−	0.0637041i
$393$	1.95875	+	4.28907i	0.0988059	+	0.216355i
$394$	0.114509	+	0.0336229i	0.00576889	+	0.00169390i
$395$	9.02433	+	19.7605i	0.454064	+	0.994260i
$396$	4.47503	−	31.1245i	0.224879	−	1.56407i
$397$	1.61108	+	11.2053i	0.0808576	+	0.562377i	0.989470	+	0.144737i	$0.0462336\pi$
$397$	1.61108	+	11.2053i	0.0808576	+	0.562377i	−0.908613	+	0.417640i	$0.862857\pi$
$398$	−0.0885399	+	0.102181i	−0.00443811	+	0.00512185i
$399$	−0.288408	−	0.185348i	−0.0144384	−	0.00927902i
$400$	−2.70664	−	5.92671i	−0.135332	−	0.296335i
$401$	−28.6373			−1.43008			−0.715040	−	0.699084i	$-0.753592\pi$
$401$	−28.6373			−1.43008			−0.715040	+	0.699084i	$0.753592\pi$
$402$	0.00806088	−	0.205227i	0.000402040	−	0.0102358i
$403$	−23.3765			−1.16447
$404$	4.28515	+	9.38316i	0.213194	+	0.466830i
$405$	−12.7488	−	8.19318i	−0.633495	−	0.407123i
$406$	0.158597	−	0.183031i	0.00787105	−	0.00908367i
$407$	2.33082	+	16.2112i	0.115534	+	0.803559i
$408$	−0.0819431	+	0.569927i	−0.00405679	+	0.0282156i
$409$	−13.5827	−	29.7420i	−0.671622	−	1.47065i	−0.871282	−	0.490783i	$-0.836711\pi$
$409$	−13.5827	−	29.7420i	−0.671622	−	1.47065i	0.199660	−	0.979865i	$-0.436016\pi$
$410$	0.426945	+	0.125362i	0.0210853	+	0.00619120i
$411$	1.98356	+	4.34339i	0.0978417	+	0.214243i
$412$	16.7733	−	10.7795i	0.826359	−	0.531069i
$413$	−0.0663198	−	0.461264i	−0.00326338	−	0.0226973i
$414$	0.868499	−	0.255014i	0.0426844	−	0.0125333i
$415$	−5.77145	+	1.69465i	−0.283310	+	0.0831872i
$416$	−3.93844	+	4.54520i	−0.193098	+	0.222847i
$417$	1.41379	−	3.09578i	0.0692338	−	0.151601i
$418$	−0.134113	−	0.932775i	−0.00655967	−	0.0456235i
$419$	−13.7478	−	15.8658i	−0.671623	−	0.775095i	0.313006	−	0.949751i	$-0.398664\pi$
$419$	−13.7478	−	15.8658i	−0.671623	−	0.775095i	−0.984629	+	0.174656i	$0.944119\pi$
$420$	−0.414212	+	0.478026i	−0.0202115	+	0.0233253i
$421$	3.57395	−	7.82586i	0.174184	−	0.381409i	−0.802325	−	0.596888i	$-0.796404\pi$
$421$	3.57395	−	7.82586i	0.174184	−	0.381409i	0.976509	+	0.215478i	$0.0691311\pi$
$422$	−1.36075	−	0.874501i	−0.0662402	−	0.0425700i
$423$	−0.921349	+	6.40812i	−0.0447975	+	0.311574i
$424$	−2.34945	+	1.50990i	−0.114100	+	0.0733274i
$425$	−7.96921	−	5.12150i	−0.386564	−	0.248429i
$426$	0.212387	+	0.245108i	0.0102902	+	0.0118755i
$427$	−6.14763	+	1.80511i	−0.297505	+	0.0873553i
$428$	−11.1316	−	12.8465i	−0.538065	−	0.620960i
$429$	−1.25170	+	8.70580i	−0.0604329	+	0.420320i
$430$	1.01418	+	0.297791i	0.0489082	+	0.0143607i
$431$	12.6021			0.607023			0.303512	−	0.952828i	$-0.401841\pi$
$431$	12.6021			0.607023			0.303512	+	0.952828i	$0.401841\pi$
$432$	6.66042			0.320450
$433$	16.9210	+	4.96844i	0.813169	+	0.238768i	0.661772	−	0.749705i	$-0.269805\pi$
$433$	16.9210	+	4.96844i	0.813169	+	0.238768i	0.151397	+	0.988473i	$0.451623\pi$
$434$	0.184828	−	0.118782i	0.00887202	−	0.00570170i
$435$	0.976112	−	2.13739i	0.0468010	−	0.102480i
$436$	−4.60981	+	10.0941i	−0.220770	+	0.483419i
$437$	−5.85012	+	3.75964i	−0.279849	+	0.179848i
$438$	0.258704	+	0.0759623i	0.0123614	+	0.00362962i
$439$	−14.6293			−0.698218			−0.349109	−	0.937082i	$-0.613516\pi$
$439$	−14.6293			−0.698218			−0.349109	+	0.937082i	$0.613516\pi$
$440$	−3.48409			−0.166098
$441$	−18.5656	−	5.45135i	−0.884075	−	0.259588i
$442$	−0.412110	+	2.86629i	−0.0196021	+	0.136335i
$443$	16.1101	+	18.5920i	0.765413	+	0.883334i	0.995967	−	0.0897255i	$-0.0285990\pi$
$443$	16.1101	+	18.5920i	0.765413	+	0.883334i	−0.230553	+	0.973060i	$0.574054\pi$
$444$	−1.64795	+	0.483882i	−0.0782083	+	0.0229640i
$445$	6.30291	+	7.27394i	0.298786	+	0.344818i
$446$	2.10489	+	1.35273i	0.0996692	+	0.0640535i
$447$	−1.76060	+	1.13147i	−0.0832736	+	0.0535167i
$448$	−0.677539	+	4.71239i	−0.0320107	+	0.222639i
$449$	6.96526	+	4.47630i	0.328711	+	0.211250i	0.694578	−	0.719417i	$-0.255591\pi$
$449$	6.96526	+	4.47630i	0.328711	+	0.211250i	−0.365867	+	0.930667i	$0.619228\pi$
$450$	0.176173	−	0.385765i	0.00830487	−	0.0181851i
$451$	9.76234	−	11.2663i	0.459691	−	0.530511i
$452$	−13.5681	−	15.6584i	−0.638188	−	0.736508i
$453$	0.187250	+	1.30235i	0.00879778	+	0.0611899i
$454$	0.716410	−	1.56872i	0.0336228	−	0.0736236i
$455$	−4.17445	+	4.81757i	−0.195701	+	0.225851i
$456$	0.190013	−	0.0557928i	0.00889816	−	0.00261274i
$457$	17.1852	−	5.04602i	0.803888	−	0.236043i	0.146123	−	0.989266i	$-0.453320\pi$
$457$	17.1852	−	5.04602i	0.803888	−	0.236043i	0.657764	+	0.753224i	$0.271502\pi$
$458$	−0.230666	−	1.60432i	−0.0107783	−	0.0749647i
$459$	8.14647	−	5.23542i	0.380245	−	0.244368i
$460$	5.32983	+	11.6707i	0.248505	+	0.544149i
$461$	29.9290	+	8.78795i	1.39393	+	0.409295i	0.890596	−	0.454795i	$-0.150288\pi$
$461$	29.9290	+	8.78795i	1.39393	+	0.409295i	0.503336	+	0.864091i	$0.332106\pi$
$462$	−0.0343396	−	0.0751931i	−0.00159762	−	0.00349830i
$463$	−1.52541	+	10.6095i	−0.0708919	+	0.493064i	0.923182	+	0.384362i	$0.125579\pi$
$463$	−1.52541	+	10.6095i	−0.0708919	+	0.493064i	−0.994074	+	0.108702i	$0.965331\pi$
$464$	−2.53696	−	17.6449i	−0.117775	−	0.819146i
$465$	1.39592	−	1.61098i	0.0647342	−	0.0747072i
$466$	−0.751196	−	0.482765i	−0.0347985	−	0.0223636i
$467$	−6.39935	−	14.0126i	−0.296126	−	0.648427i	0.701829	−	0.712346i	$-0.252367\pi$
$467$	−6.39935	−	14.0126i	−0.296126	−	0.648427i	−0.997955	+	0.0639193i	$0.979640\pi$
$468$	33.2329			1.53619
$469$	−2.52946	−	4.29796i	−0.116800	−	0.198461i
$470$	0.357966			0.0165117
$471$	−0.269347	−	0.589787i	−0.0124108	−	0.0271760i
$472$	0.226454	+	0.145533i	0.0104234	+	0.00669872i
$473$	23.1899	−	26.7625i	1.06627	−	1.23054i
$474$	−0.0423708	−	0.294695i	−0.00194616	−	0.0135358i
$475$	−0.463679	+	3.22496i	−0.0212750	+	0.147971i
$476$	2.89829	+	6.34638i	0.132843	+	0.290886i
$477$	22.2253	+	6.52593i	1.01763	+	0.298802i
$478$	−0.431133	−	0.944050i	−0.0197196	−	0.0431799i
$479$	4.08518	−	2.62539i	0.186657	−	0.119957i	−0.443975	−	0.896039i	$-0.646432\pi$
$479$	4.08518	−	2.62539i	0.186657	−	0.119957i	0.630632	+	0.776082i	$0.282796\pi$
$480$	−0.0780472	−	0.542830i	−0.00356235	−	0.0247767i
$481$	−16.6082	+	4.87659i	−0.757266	+	0.222354i
$482$	−1.38549	+	0.406816i	−0.0631073	+	0.0185300i
$483$	−0.399465	+	0.461008i	−0.0181763	+	0.0209766i
$484$	−15.0939	+	33.0511i	−0.686087	+	1.50232i
$485$	−2.40998	−	16.7618i	−0.109432	−	0.761114i
$486$	0.427788	+	0.493693i	0.0194048	+	0.0223944i
$487$	−20.0466	+	23.1350i	−0.908397	+	1.04835i	0.0902277	+	0.995921i	$0.471241\pi$
$487$	−20.0466	+	23.1350i	−0.908397	+	1.04835i	−0.998625	+	0.0524251i	$0.983305\pi$
$488$	1.53748	−	3.36661i	0.0695984	−	0.152399i
$489$	2.85354	+	1.83386i	0.129042	+	0.0829300i
$490$	−0.152260	+	1.05899i	−0.00687838	+	0.0478402i
$491$	−34.8002	+	22.3647i	−1.57051	+	1.00931i	−0.591301	+	0.806451i	$0.701385\pi$
$491$	−34.8002	+	22.3647i	−1.57051	+	1.00931i	−0.979209	+	0.202855i	$0.934978\pi$
$492$	1.31515	+	0.845198i	0.0592917	+	0.0381045i
$493$	−16.9728	−	19.5876i	−0.764416	−	0.882183i
$494$	0.955616	−	0.280594i	0.0429952	−	0.0126245i
$495$	18.9236	+	21.8390i	0.850553	+	0.981590i
$496$	2.30148	−	16.0072i	0.103340	−	0.718742i
$497$	7.55605	+	2.21866i	0.338935	+	0.0995204i
$498$	0.0824379			0.00369413
$499$	19.2162			0.860234			0.430117	−	0.902773i	$-0.358472\pi$
$499$	19.2162			0.860234			0.430117	+	0.902773i	$0.358472\pi$
$500$	23.2661	+	6.83155i	1.04049	+	0.305516i
$501$	4.46061	−	2.86666i	0.199285	−	0.128073i
$502$	−0.507774	+	1.11187i	−0.0226631	+	0.0496252i
$503$	13.2513	−	29.0164i	0.590848	−	1.29378i	−0.344080	−	0.938940i	$-0.611809\pi$
$503$	13.2513	−	29.0164i	0.590848	−	1.29378i	0.934928	−	0.354836i	$-0.115463\pi$
$504$	−0.526540	+	0.338387i	−0.0234540	+	0.0150730i
$505$	−9.09566	−	2.67073i	−0.404751	−	0.118846i
$506$	−1.67676			−0.0745410
$507$	−5.59532			−0.248497
$508$	24.4889	+	7.19060i	1.08652	+	0.319031i
$509$	5.05555	−	35.1621i	0.224083	−	1.55853i	−0.498277	−	0.867018i	$-0.666034\pi$
$509$	5.05555	−	35.1621i	0.224083	−	1.55853i	0.722361	−	0.691516i	$-0.243057\pi$
$510$	−0.172919	−	0.199560i	−0.00765700	−	0.00883665i
$511$	6.28170	−	1.84447i	0.277886	−	0.0815947i
$512$	−4.54690	−	5.24740i	−0.200946	−	0.231904i
$513$	−2.80187	−	1.80065i	−0.123706	−	0.0795008i
$514$	0.190894	−	0.122680i	0.00841996	−	0.00541118i
$515$	−2.60765	+	18.1366i	−0.114907	+	0.799195i
$516$	3.12407	+	2.00772i	0.137529	+	0.0883848i
$517$	4.98195	−	10.9089i	0.219106	−	0.479775i
$518$	0.106534	−	0.122947i	0.00468085	−	0.00540198i
$519$	−1.71426	−	1.97836i	−0.0752475	−	0.0868403i
$520$	−0.524037	−	3.64475i	−0.0229805	−	0.159833i
$521$	0.968264	−	2.12020i	0.0424204	−	0.0928878i	−0.887235	−	0.461317i	$-0.847377\pi$
$521$	0.968264	−	2.12020i	0.0424204	−	0.0928878i	0.929656	+	0.368429i	$0.120104\pi$
$522$	0.759839	−	0.876901i	0.0332572	−	0.0383809i
$523$	15.9480	−	4.68275i	0.697357	−	0.204762i	0.0862069	−	0.996277i	$-0.472525\pi$
$523$	15.9480	−	4.68275i	0.697357	−	0.204762i	0.611150	+	0.791515i	$0.290707\pi$
$524$	−31.6663	+	9.29807i	−1.38335	+	0.406188i
$525$	0.0406733	+	0.282889i	0.00177513	+	0.0123463i
$526$	−1.10089	+	0.707498i	−0.0480010	+	0.0308484i
$527$	−9.76743	−	21.3877i	−0.425476	−	0.931662i
$528$	−5.83809	−	1.71422i	−0.254070	−	0.0746018i
$529$	−4.41446	−	9.66631i	−0.191933	−	0.420274i
$530$	0.182273	−	1.26774i	0.00791745	−	0.0550670i
$531$	−0.317738	−	2.20992i	−0.0137887	−	0.0959022i
$532$	1.57140	−	1.81350i	0.0681290	−	0.0786250i
$533$	13.2542	+	8.51796i	0.574103	+	0.368954i
$534$	−0.0547971	−	0.119989i	−0.00237130	−	0.00519243i
$535$	15.6213			0.675367
$536$	2.83313	+	0.521568i	0.122373	+	0.0225283i
$537$	4.98836			0.215264
$538$	0.0507363	+	0.111097i	0.00218740	+	0.00478973i
$539$	30.1534	+	19.3784i	1.29880	+	0.834688i
$540$	−4.02405	+	4.64400i	−0.173168	+	0.199846i
$541$	0.587839	+	4.08851i	0.0252732	+	0.175779i	0.998548	−	0.0538633i	$-0.0171535\pi$
$541$	0.587839	+	4.08851i	0.0252732	+	0.175779i	−0.973275	+	0.229642i	$0.926244\pi$
$542$	0.271219	−	1.88637i	0.0116498	−	0.0810264i
$543$	−2.29463	−	5.02453i	−0.0984718	−	0.215623i
$544$	−5.80411	−	1.70424i	−0.248849	−	0.0730688i
$545$	−4.23635	−	9.27632i	−0.181465	−	0.397354i
$546$	0.0734955	−	0.0472327i	0.00314532	−	0.00202137i
$547$	5.22380	+	36.3323i	0.223354	+	1.55346i	0.725222	+	0.688515i	$0.241737\pi$
$547$	5.22380	+	36.3323i	0.223354	+	1.55346i	−0.501869	+	0.864944i	$0.667354\pi$
$548$	−32.0674	+	9.41583i	−1.36985	+	0.402224i
$549$	−29.4533	+	8.64827i	−1.25704	+	0.369099i
$550$	−0.514457	+	0.593715i	−0.0219365	+	0.0253161i
$551$	−3.70310	+	8.10865i	−0.157757	+	0.345440i
$552$	−0.0501466	−	0.348777i	−0.00213438	−	0.0148449i
$553$	−4.73413	−	5.46347i	−0.201316	−	0.232330i
$554$	0.159617	−	0.184208i	0.00678149	−	0.00782625i
$555$	0.655682	−	1.43574i	0.0278322	−	0.0609439i
$556$	20.0396	+	12.8787i	0.849870	+	0.546178i
$557$	2.08976	−	14.5346i	0.0885460	−	0.615851i	−0.896433	−	0.443178i	$-0.853851\pi$
$557$	2.08976	−	14.5346i	0.0885460	−	0.615851i	0.984979	−	0.172672i	$-0.0552401\pi$
$558$	0.885510	−	0.569083i	0.0374866	−	0.0240912i
$559$	31.4846	+	20.2339i	1.33166	+	0.855803i
$560$	−2.88787	−	3.33278i	−0.122035	−	0.140835i
$561$	−8.48813	+	2.49234i	−0.358369	+	0.105227i
$562$	1.09766	+	1.26676i	0.0463018	+	0.0534351i
$563$	−1.57990	+	10.9884i	−0.0665847	+	0.463107i	0.929064	+	0.369919i	$0.120615\pi$
$563$	−1.57990	+	10.9884i	−0.0665847	+	0.463107i	−0.995649	+	0.0931876i	$0.970294\pi$
$564$	1.20671	+	0.354322i	0.0508117	+	0.0149197i
$565$	19.0405			0.801039
$566$	1.68838			0.0709680
$567$	4.83887	+	1.42082i	0.203213	+	0.0596688i
$568$	−3.82685	+	2.45937i	−0.160571	+	0.103193i
$569$	5.08937	−	11.1442i	0.213357	−	0.467187i	−0.772448	−	0.635078i	$-0.780968\pi$
$569$	5.08937	−	11.1442i	0.213357	−	0.467187i	0.985806	+	0.167890i	$0.0536954\pi$
$570$	−0.0377273	+	0.0826112i	−0.00158022	+	0.00346020i
$571$	−1.45466	+	0.934851i	−0.0608754	+	0.0391223i	−0.570725	−	0.821142i	$-0.693338\pi$
$571$	−1.45466	+	0.934851i	−0.0608754	+	0.0391223i	0.509849	+	0.860264i	$0.329701\pi$
$572$	−59.0680	−	17.3439i	−2.46976	−	0.725186i
$573$	−4.20817			−0.175799
$574$	−0.148077			−0.00618061
$575$	5.56236	+	1.63326i	0.231967	+	0.0681115i
$576$	−3.24609	+	22.5770i	−0.135254	+	0.940710i
$577$	−11.1528	−	12.8710i	−0.464297	−	0.535827i	0.474520	−	0.880245i	$-0.342622\pi$
$577$	−11.1528	−	12.8710i	−0.464297	−	0.535827i	−0.938817	+	0.344418i	$0.888076\pi$
$578$	−1.35668	+	0.398357i	−0.0564304	+	0.0165695i
$579$	1.59632	+	1.84225i	0.0663409	+	0.0765615i
$580$	13.8358	+	8.89171i	0.574499	+	0.369208i
$581$	1.68395	−	1.08221i	0.0698619	−	0.0448975i
$582$	−0.0330292	+	0.229723i	−0.00136910	+	0.00952232i
$583$	−36.0973	−	23.1983i	−1.49500	−	0.960777i
$584$	−1.57101	+	3.44003i	−0.0650088	+	0.142349i
$585$	−19.9998	+	23.0810i	−0.826890	+	0.954282i
$586$	0.749896	+	0.865426i	0.0309779	+	0.0357504i
$587$	−6.82036	−	47.4367i	−0.281507	−	1.95792i	−0.286981	−	0.957936i	$-0.592652\pi$
$587$	−6.82036	−	47.4367i	−0.281507	−	1.95792i	0.00547471	−	0.999985i	$-0.498257\pi$
$588$	−1.56148	+	3.41916i	−0.0643943	+	0.141004i
$589$	−5.29573	+	6.11160i	−0.218207	+	0.251824i
$590$	−0.118448	+	0.0347795i	−0.00487643	+	0.00143185i
$591$	−0.369717	+	0.108559i	−0.0152081	+	0.00446550i
$592$	−1.70415	−	11.8526i	−0.0700401	−	0.487139i
$593$	−9.45013	+	6.07323i	−0.388070	+	0.249398i	−0.720099	−	0.693872i	$-0.755903\pi$
$593$	−9.45013	+	6.07323i	−0.388070	+	0.249398i	0.332028	+	0.943269i	$0.392267\pi$
$594$	−0.333608	−	0.730499i	−0.0136881	−	0.0299727i
$595$	−6.15192	−	1.80637i	−0.252204	−	0.0740538i
$596$	−6.08520	−	13.3247i	−0.249260	−	0.545803i
$597$	0.0621254	−	0.432092i	0.00254262	−	0.0176843i
$598$	−0.252198	−	1.75408i	−0.0103132	−	0.0717296i
$599$	−10.9098	+	12.5906i	−0.445762	+	0.514436i	−0.933512	−	0.358547i	$-0.883272\pi$
$599$	−10.9098	+	12.5906i	−0.445762	+	0.514436i	0.487750	+	0.872983i	$0.337818\pi$
$600$	−0.138882	−	0.0892543i	−0.00566985	−	0.00364379i
$601$	2.76753	+	6.06004i	0.112890	+	0.247194i	0.957641	−	0.287965i	$-0.0929788\pi$
$601$	2.76753	+	6.06004i	0.112890	+	0.247194i	−0.844751	+	0.535160i	$0.820251\pi$
$602$	−0.351748			−0.0143362
$603$	−12.1187	−	20.5915i	−0.493510	−	0.838551i
$604$	−9.20939			−0.374725
$605$	−13.8711	−	30.3735i	−0.563941	−	1.23486i
$606$	0.109296	+	0.0702400i	0.00443983	+	0.00285331i
$607$	1.23245	−	1.42233i	0.0500238	−	0.0577305i	−0.730186	−	0.683248i	$-0.760567\pi$
$607$	1.23245	−	1.42233i	0.0500238	−	0.0577305i	0.780210	+	0.625518i	$0.215112\pi$
$608$	0.296089	+	2.05935i	0.0120080	+	0.0835176i
$609$	−0.111282	+	0.773984i	−0.00450938	+	0.0313634i
$610$	0.705086	+	1.54392i	0.0285481	+	0.0625116i
$611$	12.1613	+	3.57088i	0.491994	+	0.144462i
$612$	13.8857	+	30.4055i	0.561297	+	1.22907i
$613$	−12.6595	+	8.13578i	−0.511313	+	0.328601i	−0.770727	−	0.637165i	$-0.780107\pi$
$613$	−12.6595	+	8.13578i	−0.511313	+	0.328601i	0.259414	+	0.965766i	$0.416471\pi$
$614$	−0.0851656	−	0.592340i	−0.00343701	−	0.0239049i
$615$	−1.37848	+	0.404758i	−0.0555856	+	0.0163214i
$616$	1.11247	−	0.326652i	0.0448228	−	0.0131612i
$617$	17.5223	−	20.2218i	0.705422	−	0.814100i	−0.284053	−	0.958809i	$-0.591679\pi$
$617$	17.5223	−	20.2218i	0.705422	−	0.814100i	0.989474	+	0.144709i	$0.0462245\pi$
$618$	0.104319	−	0.228428i	0.00419634	−	0.00918871i
$619$	−1.17040	−	8.14034i	−0.0470425	−	0.327188i	−0.999730	−	0.0232363i	$-0.992603\pi$
$619$	−1.17040	−	8.14034i	−0.0470425	−	0.327188i	0.952687	−	0.303952i	$-0.0983061\pi$
$620$	9.77055	+	11.2758i	0.392395	+	0.452848i
$621$	−3.88079	+	4.47868i	−0.155731	+	0.179723i
$622$	−0.0995242	+	0.217928i	−0.00399056	+	0.00873810i
$623$	−2.69449	−	1.73164i	−0.107952	−	0.0693768i
$624$	0.915169	−	6.36514i	0.0366361	−	0.254809i
$625$	−11.8142	+	7.59254i	−0.472569	+	0.303701i
$626$	0.932512	+	0.599289i	0.0372707	+	0.0239524i
$627$	1.99250	+	2.29946i	0.0795727	+	0.0918318i
$628$	4.35442	−	1.27857i	0.173760	−	0.0510206i
$629$	−11.4011	−	13.1576i	−0.454592	−	0.524627i
$630$	0.0408496	−	0.284115i	0.00162749	−	0.0113194i
$631$	6.08050	+	1.78540i	0.242061	+	0.0710755i	0.400513	−	0.916291i	$-0.368832\pi$
$631$	6.08050	+	1.78540i	0.242061	+	0.0710755i	−0.158452	+	0.987367i	$0.550650\pi$
$632$	4.17592			0.166109
$633$	5.22252			0.207576
$634$	1.80371	+	0.529618i	0.0716347	+	0.0210338i
$635$	−19.7317	+	12.6808i	−0.783028	+	0.503222i
$636$	1.86928	−	4.09316i	0.0741219	−	0.162304i
$637$	−15.7367	+	34.4585i	−0.623510	+	1.36530i
$638$	−1.80818	+	1.16205i	−0.0715867	+	0.0460060i
$639$	36.2010	+	10.6296i	1.43209	+	0.420500i
$640$	5.11470			0.202176
$641$	31.3903			1.23984			0.619920	−	0.784665i	$-0.287165\pi$
$641$	31.3903			1.23984			0.619920	+	0.784665i	$0.287165\pi$
$642$	−0.205420	−	0.0603166i	−0.00810727	−	0.00238051i
$643$	−1.53429	+	10.6712i	−0.0605064	+	0.420832i	0.936945	+	0.349478i	$0.113641\pi$
$643$	−1.53429	+	10.6712i	−0.0605064	+	0.420832i	−0.997451	+	0.0713537i	$0.977268\pi$
$644$	−2.79601	−	3.22676i	−0.110178	−	0.127152i
$645$	−3.27450	+	0.961479i	−0.128933	+	0.0378582i
$646$	0.656008	+	0.757074i	0.0258103	+	0.0297867i
$647$	−17.5914	−	11.3053i	−0.691590	−	0.444458i	0.147060	−	0.989128i	$-0.453019\pi$
$647$	−17.5914	−	11.3053i	−0.691590	−	0.444458i	−0.838651	+	0.544669i	$0.816655\pi$
$648$	−2.45070	+	1.57497i	−0.0962725	+	0.0618706i
$649$	−0.588589	+	4.09373i	−0.0231041	+	0.160693i
$650$	−0.698471	−	0.448880i	−0.0273963	−	0.0176065i
$651$	−0.294680	+	0.645260i	−0.0115494	+	0.0252897i
$652$	−15.5477	+	17.9430i	−0.608893	+	0.702701i
$653$	−7.64947	−	8.82796i	−0.299347	−	0.345465i	0.586072	−	0.810259i	$-0.300674\pi$
$653$	−7.64947	−	8.82796i	−0.299347	−	0.345465i	−0.885419	+	0.464794i	$0.846128\pi$
$654$	0.0198904	+	0.138341i	0.000777776	+	0.00540955i
$655$	12.5993	−	27.5887i	0.492296	−	1.07798i
$656$	−7.13762	+	8.23725i	−0.278677	+	0.321611i
$657$	30.0956	−	8.83687i	1.17414	−	0.344759i
$658$	−0.114299	+	0.0335611i	−0.00445582	+	0.00130835i
$659$	1.85448	+	12.8982i	0.0722403	+	0.502442i	0.993530	+	0.113566i	$0.0362274\pi$
$659$	1.85448	+	12.8982i	0.0722403	+	0.502442i	−0.921290	+	0.388876i	$0.872863\pi$
$660$	4.72247	−	3.03495i	0.183822	−	0.118135i
$661$	−2.67480	−	5.85700i	−0.104038	−	0.227811i	0.850453	−	0.526051i	$-0.176328\pi$
$661$	−2.67480	−	5.85700i	−0.104038	−	0.227811i	−0.954491	+	0.298240i	$0.903601\pi$
$662$	0.00137991		0.000405177i	5.36316e−5		1.57477e-5i
$663$	−3.88395	−	8.50467i	−0.150840	−	0.330294i
$664$	−0.164556	+	1.14451i	−0.00638599	+	0.0444156i
$665$	0.313832	+	2.18275i	0.0121699	+	0.0846435i
$666$	0.510406	−	0.589039i	0.0197778	−	0.0228248i
$667$	13.3432	+	8.57516i	0.516651	+	0.332031i
$668$	15.4173	+	33.7592i	0.596513	+	1.30618i
$669$	−8.07849			−0.312333
$670$	−1.03161	+	0.825287i	−0.0398545	+	0.0318836i
$671$	56.8637			2.19520
$672$	0.0758136	+	0.166009i	0.00292457	+	0.00640392i
$673$	24.8760	+	15.9868i	0.958898	+	0.616247i	0.923693	−	0.383134i	$-0.125155\pi$
$673$	24.8760	+	15.9868i	0.958898	+	0.616247i	0.0352054	+	0.999380i	$0.488791\pi$
$674$	−0.197151	+	0.227524i	−0.00759397	+	0.00876390i
$675$	0.395140	+	2.74826i	0.0152089	+	0.105781i
$676$	5.57358	−	38.7651i	0.214369	−	1.49097i
$677$	−0.770116	−	1.68632i	−0.0295980	−	0.0648105i	0.894256	−	0.447557i	$-0.147706\pi$
$677$	−0.770116	−	1.68632i	−0.0295980	−	0.0648105i	−0.923854	+	0.382746i	$0.874978\pi$
$678$	−0.250382	−	0.0735188i	−0.00961586	−	0.00282347i
$679$	2.34101	+	5.12610i	0.0898398	+	0.196722i
$680$	3.11571	−	2.00234i	0.119482	−	0.0767864i
$681$	0.792425	+	5.51144i	0.0303658	+	0.211199i
$682$	−1.87090	+	0.549347i	−0.0716406	+	0.0210356i
$683$	−20.1696	+	5.92233i	−0.771768	+	0.226612i	−0.643828	−	0.765170i	$-0.722655\pi$
$683$	−20.1696	+	5.92233i	−0.771768	+	0.226612i	−0.127940	+	0.991782i	$0.540837\pi$
$684$	7.52859	−	8.68846i	0.287863	−	0.332212i
$685$	12.7589	−	27.9381i	0.487492	−	1.06746i
$686$	−0.104175	−	0.724556i	−0.00397743	−	0.0276637i
$687$	3.42697	+	3.95494i	0.130747	+	0.150890i
$688$	−16.9550	+	19.5671i	−0.646403	+	0.745989i
$689$	18.8387	−	41.2511i	0.717699	−	1.57154i
$690$	0.135941	+	0.0873640i	0.00517519	+	0.00332589i
$691$	0.260219	−	1.80986i	0.00989918	−	0.0688503i	−0.984273	−	0.176654i	$-0.943473\pi$
$691$	0.260219	−	1.80986i	0.00989918	−	0.0688503i	0.994172	+	0.107804i	$0.0343818\pi$
$692$	15.4139	−	9.90592i	0.585949	−	0.376567i
$693$	−8.08984	−	5.19902i	−0.307307	−	0.197495i
$694$	1.87344	+	2.16207i	0.0711149	+	0.0820710i
$695$	−21.0046	+	6.16750i	−0.796749	+	0.233947i
$696$	−0.295791	−	0.341361i	−0.0112119	−	0.0129393i
$697$	−2.25525	+	15.6856i	−0.0854238	+	0.594136i
$698$	−1.68777	−	0.495575i	−0.0638832	−	0.0187578i
$699$	2.88307			0.109048
$700$	−2.00041			−0.0756083
$701$	−37.4058	−	10.9833i	−1.41280	−	0.414835i	−0.515739	−	0.856746i	$-0.672483\pi$
$701$	−37.4058	−	10.9833i	−1.41280	−	0.414835i	−0.897059	+	0.441911i	$0.854301\pi$
$702$	0.714007	−	0.458864i	0.0269485	−	0.0173187i
$703$	−2.48748	+	5.44681i	−0.0938169	+	0.205430i
$704$	17.5524	−	38.4343i	0.661529	−	1.44855i
$705$	−0.972293	+	0.624854i	−0.0366187	+	0.0235334i
$706$	2.20069	+	0.646180i	0.0828240	+	0.0243193i
$707$	3.15464			0.118643
$708$	−0.433717			−0.0163001
$709$	−11.9961	−	3.52237i	−0.450523	−	0.132286i	0.0485967	−	0.998818i	$-0.484525\pi$
$709$	−11.9961	−	3.52237i	−0.450523	−	0.132286i	−0.499120	+	0.866533i	$0.666343\pi$
$710$	0.296891	−	2.06492i	0.0111421	−	0.0774951i
$711$	−22.6812	−	26.1755i	−0.850611	−	0.981658i
$712$	1.77522	−	0.521252i	0.0665292	−	0.0195347i
$713$	9.42272	+	10.8744i	0.352884	+	0.407249i
$714$	0.0739230	+	0.0475074i	0.00276650	+	0.00177792i
$715$	47.5934	−	30.5864i	1.77989	−	1.14387i
$716$	−4.96897	+	34.5600i	−0.185699	+	1.29157i
$717$	2.81893	+	1.81162i	0.105275	+	0.0676562i
$718$	0.0927339	−	0.203059i	0.00346080	−	0.00757809i
$719$	2.50283	−	2.88841i	0.0933396	−	0.107720i	−0.707158	−	0.707055i	$-0.750023\pi$
$719$	2.50283	−	2.88841i	0.0933396	−	0.107720i	0.800498	+	0.599336i	$0.204569\pi$
$720$	−13.8358	−	15.9673i	−0.515629	−	0.595067i
$721$	−0.867776	−	6.03551i	−0.0323177	−	0.224774i
$722$	−0.552678	+	1.21020i	−0.0205685	+	0.0450388i
$723$	3.05308	−	3.52345i	0.113545	−	0.131038i
$724$	37.0963	−	10.8925i	1.37867	−	0.404815i
$725$	7.13024	−	2.09363i	0.264811	−	0.0777554i
$726$	0.0651272	+	0.452970i	0.00241710	+	0.0168113i
$727$	−40.4373	+	25.9874i	−1.49973	+	0.963821i	−0.504807	+	0.863232i	$0.668436\pi$
$727$	−40.4373	+	25.9874i	−1.49973	+	0.963821i	−0.994928	+	0.100589i	$0.967927\pi$
$728$	0.509039	+	1.11464i	0.0188663	+	0.0413113i
$729$	21.8027	+	6.40185i	0.807508	+	0.237106i
$730$	−0.720462	−	1.57759i	−0.0266655	−	0.0583893i
$731$	−5.35722	+	37.2603i	−0.198144	+	1.37812i
$732$	0.848652	+	5.90251i	0.0313671	+	0.218163i
$733$	4.59960	−	5.30822i	0.169890	−	0.196064i	−0.664420	−	0.747360i	$-0.731321\pi$
$733$	4.59960	−	5.30822i	0.169890	−	0.196064i	0.834310	+	0.551296i	$0.185867\pi$
$734$	1.69106	+	1.08678i	0.0624183	+	0.0401138i
$735$	−1.43498	−	3.14216i	−0.0529299	−	0.115900i
$736$	3.70189			0.136453
$737$	10.7932	+	42.9239i	0.397571	+	1.58112i
$738$	−0.709437			−0.0261147
$739$	9.72934	+	21.3043i	0.357899	+	0.783691i	0.999856	+	0.0169498i	$0.00539555\pi$
$739$	9.72934	+	21.3043i	0.357899	+	0.783691i	−0.641957	+	0.766741i	$0.721877\pi$
$740$	9.29388	+	5.97281i	0.341650	+	0.219565i
$741$	−2.10581	+	2.43024i	−0.0773589	+	0.0892769i
$742$	0.0606570	+	0.421879i	0.00222679	+	0.0154877i
$743$	−5.34442	+	37.1713i	−0.196068	+	1.36368i	0.619489	+	0.785005i	$0.287340\pi$
$743$	−5.34442	+	37.1713i	−0.196068	+	1.36368i	−0.815557	+	0.578677i	$0.803569\pi$
$744$	−0.170221	−	0.372731i	−0.00624059	−	0.0136650i
$745$	12.9165	+	3.79262i	0.473223	+	0.138951i
$746$	0.730187	+	1.59889i	0.0267341	+	0.0585394i
$747$	8.06779	−	5.18485i	0.295185	−	0.189704i
$748$	−8.81210	−	61.2895i	−0.322202	−	2.24097i
$749$	−4.98788	+	1.46457i	−0.182253	+	0.0535144i
$750$	0.293033	−	0.0860422i	0.0107001	−	0.00314182i
$751$	−13.8434	+	15.9762i	−0.505153	+	0.582978i	−0.949851	−	0.312703i	$-0.898766\pi$
$751$	−13.8434	+	15.9762i	−0.505153	+	0.582978i	0.444698	+	0.895681i	$0.353311\pi$
$752$	−3.64249	+	7.97594i	−0.132828	+	0.290853i
$753$	−0.561652	−	3.90637i	−0.0204677	−	0.142356i
$754$	−1.48760	−	1.71678i	−0.0541752	−	0.0625215i
$755$	5.54228	−	6.39614i	0.201704	−	0.232779i
$756$	0.849483	−	1.86011i	0.0308954	−	0.0676515i
$757$	−36.7982	−	23.6488i	−1.33745	−	0.859529i	−0.340709	−	0.940169i	$-0.610667\pi$
$757$	−36.7982	−	23.6488i	−1.33745	−	0.859529i	−0.996743	+	0.0806401i	$0.974304\pi$
$758$	−0.0417258	+	0.290210i	−0.00151555	+	0.0105409i
$759$	4.55435	−	2.92690i	0.165312	−	0.106240i
$760$	−1.07161	−	0.688680i	−0.0388713	−	0.0249810i
$761$	25.9898	+	29.9938i	0.942129	+	1.08727i	0.996056	+	0.0887296i	$0.0282807\pi$
$761$	25.9898	+	29.9938i	0.942129	+	1.08727i	−0.0539270	+	0.998545i	$0.517174\pi$
$762$	0.308434	−	0.0905645i	0.0111734	−	0.00328080i
$763$	2.22237	+	2.56475i	0.0804552	+	0.0928503i
$764$	4.19182	−	29.1547i	0.151655	−	1.05478i
$765$	−29.4739	−	8.65430i	−1.06563	−	0.312897i
$766$	−3.07774			−0.111203
$767$	−4.37103			−0.157829
$768$	4.20080	+	1.23347i	0.151583	+	0.0445089i
$769$	4.07970	−	2.62187i	0.147118	−	0.0945469i	−0.465011	−	0.885305i	$-0.653950\pi$
$769$	4.07970	−	2.62187i	0.147118	−	0.0945469i	0.612129	+	0.790758i	$0.290313\pi$
$770$	−0.220883	+	0.483667i	−0.00796007	+	0.0174301i
$771$	−0.304352	+	0.666437i	−0.0109610	+	0.0240011i
$772$	−14.3535	+	9.22443i	−0.516594	+	0.331995i
$773$	18.6381	+	5.47263i	0.670365	+	0.196837i	0.599166	−	0.800625i	$-0.295499\pi$
$773$	18.6381	+	5.47263i	0.670365	+	0.196837i	0.0711995	+	0.997462i	$0.477317\pi$
$774$	−1.68522			−0.0605742
$775$	6.74150			0.242162
$776$	−3.12338	−	0.917106i	−0.112123	−	0.0329222i
$777$	−0.0747514	+	0.519907i	−0.00268169	+	0.0186516i
$778$	−1.20192	−	1.38709i	−0.0430909	−	0.0497296i
$779$	5.22957	−	1.53554i	0.187369	−	0.0550164i
$780$	3.88520	+	4.48375i	0.139112	+	0.160544i
$781$	−58.7962	−	37.7860i	−2.10389	−	1.35209i
$782$	1.49947	−	0.963651i	0.0536209	−	0.0344601i
$783$	−1.08110	+	7.51923i	−0.0386354	+	0.268715i
$784$	−22.0463	−	14.1683i	−0.787368	−	0.506011i
$785$	−1.73253	+	3.79370i	−0.0618365	+	0.135403i
$786$	−0.272206	+	0.314142i	−0.00970926	+	0.0112051i
$787$	5.58375	+	6.44399i	0.199039	+	0.229703i	0.846491	−	0.532403i	$-0.178711\pi$
$787$	5.58375	+	6.44399i	0.199039	+	0.229703i	−0.647452	+	0.762106i	$0.724165\pi$
$788$	−0.383828	−	2.66958i	−0.0136733	−	0.0950999i
$789$	1.75520	−	3.84336i	0.0624869	−	0.136827i
$790$	−1.25410	+	1.44731i	−0.0446190	+	0.0514931i
$791$	−6.07963	+	1.78514i	−0.216167	+	0.0634723i
$792$	5.32986	−	1.56499i	0.189388	−	0.0556094i
$793$	8.55277	+	59.4858i	0.303718	+	2.11240i
$794$	−0.839546	+	0.539543i	−0.0297944	+	0.0191477i
$795$	1.71784	+	3.76155i	0.0609256	+	0.133409i
$796$	2.93170	+	0.860825i	0.103911	+	0.0305111i
$797$	8.92659	+	19.5465i	0.316196	+	0.692373i	0.999279	−	0.0379681i	$-0.0120885\pi$
$797$	8.92659	+	19.5465i	0.316196	+	0.692373i	−0.683083	+	0.730341i	$0.739361\pi$
$798$	0.00430112	−	0.0299149i	0.000152258	−	0.00105898i
$799$	1.81429	+	12.6187i	0.0641850	+	0.446417i
$800$	1.13580	−	1.31078i	0.0401565	−	0.0463431i
$801$	−12.9093	−	8.29630i	−0.456128	−	0.293135i
$802$	−1.04874	−	2.29641i	−0.0370322	−	0.0810891i
$803$	−58.1038			−2.05044
$804$	−4.29446	+	1.76095i	−0.151454	+	0.0621039i
$805$	3.92372			0.138293
$806$	−0.856078	−	1.87455i	−0.0301541	−	0.0660282i
$807$	−0.331736	−	0.213194i	−0.0116776	−	0.00750477i
$808$	−1.19333	+	1.37717i	−0.0419812	+	0.0484488i
$809$	−2.98856	−	20.7859i	−0.105072	−	0.730793i	−0.972445	−	0.233133i	$-0.925102\pi$
$809$	−2.98856	−	20.7859i	−0.105072	−	0.730793i	0.867373	−	0.497659i	$-0.165807\pi$
$810$	0.190128	−	1.32237i	0.00668041	−	0.0464633i
$811$	−13.0404	−	28.5545i	−0.457910	−	1.00268i	−0.987959	−	0.154716i	$-0.950554\pi$
$811$	−13.0404	−	28.5545i	−0.457910	−	1.00268i	0.530049	−	0.847967i	$-0.322174\pi$
$812$	−5.25141	−	1.54195i	−0.184288	−	0.0541119i
$813$	2.55611	+	5.59711i	0.0896468	+	0.196299i
$814$	−1.21461	+	0.780581i	−0.0425720	+	0.0273594i
$815$	−3.10510	−	21.5964i	−0.108767	−	0.756490i
$816$	6.20599	−	1.82224i	0.217253	−	0.0637913i
$817$	12.4225	−	3.64758i	0.434609	−	0.127613i
$818$	1.88758	−	2.17838i	0.0659976	−	0.0761653i
$819$	4.22198	−	9.24486i	0.147528	−	0.323041i
$820$	−1.43109	−	9.95346i	−0.0499759	−	0.347590i
$821$	10.6982	+	12.3464i	0.373370	+	0.430892i	0.911075	−	0.412241i	$-0.135254\pi$
$821$	10.6982	+	12.3464i	0.373370	+	0.430892i	−0.537704	+	0.843133i	$0.680708\pi$
$822$	−0.275653	+	0.318121i	−0.00961451	+	0.0110957i
$823$	14.5611	−	31.8845i	0.507570	−	1.11142i	−0.466365	−	0.884593i	$-0.654437\pi$
$823$	14.5611	−	31.8845i	0.507570	−	1.11142i	0.973934	−	0.226830i	$-0.0728362\pi$
$824$	2.96309	+	1.90426i	0.103224	+	0.0663382i
$825$	0.360976	−	2.51065i	0.0125676	−	0.0874095i
$826$	0.0345598	−	0.0222102i	0.00120249	−	0.000772793i
$827$	−45.1650	−	29.0258i	−1.57054	−	1.00933i	−0.979198	−	0.202908i	$-0.934961\pi$
$827$	−45.1650	−	29.0258i	−1.57054	−	1.00933i	−0.591345	−	0.806419i	$-0.701403\pi$
$828$	−13.3957	−	15.4594i	−0.465532	−	0.537252i
$829$	−15.7651	+	4.62906i	−0.547546	+	0.160774i	−0.543793	−	0.839219i	$-0.683013\pi$
$829$	−15.7651	+	4.62906i	−0.547546	+	0.160774i	−0.00375207	+	0.999993i	$0.501194\pi$
$830$	−0.347251	−	0.400749i	−0.0120533	−	0.0139102i
$831$	−0.111998	+	0.778962i	−0.00388516	+	0.0270219i
$832$	42.8466	+	12.5809i	1.48544	+	0.436164i
$833$	−38.1022			−1.32016
$834$	0.300024			0.0103890
$835$	−32.7248	−	9.60886i	−1.13249	−	0.332528i
$836$	−17.9157	+	11.5137i	−0.619629	+	0.398211i
$837$	−2.86281	+	6.26868i	−0.0989532	+	0.216677i
$838$	0.768807	−	1.68345i	0.0265580	−	0.0581539i
$839$	−19.1274	+	12.2924i	−0.660350	+	0.424381i	−0.827435	−	0.561561i	$-0.810201\pi$
$839$	−19.1274	+	12.2924i	−0.660350	+	0.424381i	0.167085	+	0.985943i	$0.446565\pi$
$840$	−0.107212	−	0.0314802i	−0.00369916	−	0.00108617i
$841$	−8.66809			−0.298900
$842$	0.758434			0.0261374
$843$	−5.19263	−	1.52469i	−0.178844	−	0.0525133i
$844$	−5.20223	+	36.1823i	−0.179068	+	1.24545i
$845$	23.5691	+	27.2001i	0.810800	+	0.935713i
$846$	−0.547605	+	0.160791i	−0.0188270	+	0.00552812i
$847$	7.27672	+	8.39778i	0.250031	+	0.288551i
$848$	26.3921	+	16.9612i	0.906309	+	0.582450i
$849$	−4.58592	+	2.94719i	−0.157388	+	0.101147i
$850$	0.118848	−	0.826603i	0.00407644	−	0.0283522i
$851$	8.96301	+	5.76018i	0.307248	+	0.197456i
$852$	3.04473	−	6.66703i	0.104311	−	0.228409i
$853$	−28.5348	+	32.9309i	−0.977012	+	1.12753i	0.0148083	+	0.999890i	$0.495286\pi$
$853$	−28.5348	+	32.9309i	−0.977012	+	1.12753i	−0.991820	+	0.127642i	$0.959259\pi$
$854$	−0.369885	−	0.426870i	−0.0126572	−	0.0146072i
$855$	1.50357	+	10.4576i	0.0514210	+	0.357641i
$856$	1.24743	−	2.73150i	0.0426364	−	0.0933607i
$857$	10.2674	−	11.8492i	0.350727	−	0.404761i	−0.552784	−	0.833324i	$-0.686435\pi$
$857$	10.2674	−	11.8492i	0.350727	−	0.404761i	0.903512	+	0.428563i	$0.140980\pi$
$858$	−0.743952	+	0.218444i	−0.0253981	+	0.00745756i
$859$	53.1792	−	15.6148i	1.81445	−	0.532771i	0.815510	−	0.578744i	$-0.196457\pi$
$859$	53.1792	−	15.6148i	1.81445	−	0.532771i	0.998943	+	0.0459724i	$0.0146386\pi$
$860$	−3.39947	−	23.6439i	−0.115921	−	0.806249i
$861$	0.402201	−	0.258479i	0.0137070	−	0.00880894i
$862$	0.461506	+	1.01056i	0.0157190	+	0.0344197i
$863$	6.85007	+	2.01136i	0.233179	+	0.0684676i	0.396235	−	0.918149i	$-0.370317\pi$
$863$	6.85007	+	2.01136i	0.233179	+	0.0684676i	−0.163055	+	0.986617i	$0.552135\pi$
$864$	0.736527	+	1.61277i	0.0250572	+	0.0548675i
$865$	−2.39632	+	16.6668i	−0.0814774	+	0.566687i
$866$	0.221251	+	1.53883i	0.00751841	+	0.0522917i
$867$	2.98960	−	3.45018i	0.101532	−	0.117174i
$868$	−4.17691	−	2.68434i	−0.141774	−	0.0911123i
$869$	26.6528	+	58.3614i	0.904133	+	1.97977i
$870$	0.207142			0.00702278
$871$	−43.2799	+	17.7470i	−1.46648	+	0.601333i
$872$	−1.96033			−0.0663851
$873$	11.2158	+	24.5592i	0.379597	+	0.831202i
$874$	−0.515723	−	0.331435i	−0.0174446	−	0.0112110i
$875$	4.85621	−	5.60437i	0.164170	−	0.189462i
$876$	−0.867160	−	6.03123i	−0.0292986	−	0.203776i
$877$	7.02816	−	48.8819i	0.237324	−	1.65062i	−0.427787	−	0.903880i	$-0.640707\pi$
$877$	7.02816	−	48.8819i	0.237324	−	1.65062i	0.665111	−	0.746745i	$-0.268384\pi$
$878$	−0.535744	−	1.17312i	−0.0180805	−	0.0395907i
$879$	−3.54750	−	1.04164i	−0.119654	−	0.0351337i
$880$	16.2585	+	35.6011i	0.548073	+	1.20011i
$881$	30.4594	−	19.5751i	1.02620	−	0.659501i	0.0846666	−	0.996409i	$-0.473017\pi$
$881$	30.4594	−	19.5751i	1.02620	−	0.659501i	0.941538	+	0.336908i	$0.109381\pi$
$882$	−0.242755	−	1.68840i	−0.00817399	−	0.0568513i
$883$	−8.13126	+	2.38755i	−0.273639	+	0.0803475i	−0.415673	−	0.909514i	$-0.636454\pi$
$883$	−8.13126	+	2.38755i	−0.273639	+	0.0803475i	0.142034	+	0.989862i	$0.454636\pi$
$884$	62.7903	−	18.4369i	2.11187	−	0.620100i
$885$	0.261014	−	0.301226i	0.00877390	−	0.0101256i
$886$	−0.900913	+	1.97272i	−0.0302668	+	0.0662749i
$887$	2.31772	+	16.1201i	0.0778214	+	0.541260i	0.991017	+	0.133738i	$0.0426980\pi$
$887$	2.31772	+	16.1201i	0.0778214	+	0.541260i	−0.913195	+	0.407522i	$0.866393\pi$
$888$	−0.198691	−	0.229302i	−0.00666765	−	0.00769487i
$889$	5.11145	−	5.89893i	0.171432	−	0.197844i
$890$	−0.352473	+	0.771808i	−0.0118149	+	0.0258710i
$891$	−37.6528	−	24.1980i	−1.26142	−	0.810664i
$892$	8.04710	−	55.9688i	0.269437	−	1.87397i
$893$	3.68861	−	2.37052i	0.123435	−	0.0793266i
$894$	−0.155207	−	0.0997457i	−0.00519091	−	0.00333600i
$895$	−21.0123	−	24.2495i	−0.702365	−	0.810572i
$896$	−1.63313	+	0.479529i	−0.0545589	+	0.0160199i
$897$	3.74688	+	4.32413i	0.125105	+	0.144379i
$898$	−0.103875	+	0.722468i	−0.00346636	+	0.0241091i
$899$	17.6976	+	5.19648i	0.590247	+	0.173312i
$900$	−9.58395			−0.319465
$901$	45.6130			1.51959
$902$	1.26095	+	0.370249i	0.0419851	+	0.0123279i
$903$	0.955405	−	0.614001i	0.0317939	−	0.0204327i
$904$	1.52047	−	3.32937i	0.0505702	−	0.110733i
$905$	−14.7598	+	32.3194i	−0.490631	+	1.07433i
$906$	−0.0975777	+	0.0627094i	−0.00324180	+	0.00208338i
$907$	22.8509	+	6.70964i	0.758753	+	0.222790i	0.638151	−	0.769911i	$-0.279699\pi$
$907$	22.8509	+	6.70964i	0.758753	+	0.222790i	0.120602	+	0.992701i	$0.461518\pi$
$908$	−38.9733			−1.29337
$909$	15.1139			0.501296
$910$	−0.539192	−	0.158321i	−0.0178741	−	0.00524830i
$911$	3.93263	−	27.3520i	0.130294	−	0.906214i	−0.814876	−	0.579635i	$-0.803195\pi$
$911$	3.93263	−	27.3520i	0.130294	−	0.906214i	0.945170	−	0.326579i	$-0.105896\pi$
$912$	−1.45679	−	1.68123i	−0.0482392	−	0.0556709i
$913$	−17.0456	+	5.00504i	−0.564127	+	0.165643i
$914$	1.03398	+	1.19328i	0.0342010	+	0.0394701i
$915$	−4.61015	−	2.96277i	−0.152407	−	0.0979460i
$916$	−30.8140	+	19.8029i	−1.01812	+	0.654307i
$917$	−1.43639	+	9.99032i	−0.0474338	+	0.329910i
$918$	0.718160	+	0.461533i	0.0237028	+	0.0152329i
$919$	9.95976	−	21.8088i	0.328542	−	0.719407i	−0.671219	−	0.741259i	$-0.734229\pi$
$919$	9.95976	−	21.8088i	0.328542	−	0.719407i	0.999761	+	0.0218519i	$0.00695622\pi$
$920$	−1.48425	+	1.71292i	−0.0489344	+	0.0564733i
$921$	1.26530	+	1.46023i	0.0416929	+	0.0481162i
$922$	0.391338	+	2.72182i	0.0128880	+	0.0896382i
$923$	30.6850	−	67.1908i	1.01001	−	2.21161i
$924$	−1.22335	+	1.41182i	−0.0402451	+	0.0464453i
$925$	4.78959	−	1.40635i	0.157481	−	0.0462405i
$926$	−0.906631	+	0.266211i	−0.0297937	+	0.00874823i
$927$	−4.15751	−	28.9161i	−0.136551	−	0.949731i
$928$	3.99204	−	2.56553i	0.131045	−	0.0842176i
$929$	−5.99449	−	13.1261i	−0.196673	−	0.430653i	0.785442	−	0.618935i	$-0.212436\pi$
$929$	−5.99449	−	13.1261i	−0.196673	−	0.430653i	−0.982115	+	0.188282i	$0.939708\pi$
$930$	0.180304	+	0.0529419i	0.00591239	+	0.00173603i
$931$	5.44391	+	11.9205i	0.178417	+	0.390678i
$932$	−2.87187	+	19.9743i	−0.0940711	+	0.654279i
$933$	−0.110084	−	0.765653i	−0.00360400	−	0.0250663i
$934$	0.889312	−	1.02632i	0.0290992	−	0.0335822i
$935$	47.8702	+	30.7643i	1.56552	+	1.00610i
$936$	2.43881	+	5.34024i	0.0797149	+	0.174551i
$937$	46.5263			1.51995			0.759974	−	0.649954i	$-0.225212\pi$
$937$	46.5263			1.51995			0.759974	+	0.649954i	$0.225212\pi$
$938$	0.252018	−	0.360233i	0.00822869	−	0.0117620i
$939$	−3.57895			−0.116795
$940$	−3.36056	−	7.35859i	−0.109609	−	0.240011i
$941$	18.2882	+	11.7531i	0.596178	+	0.383140i	0.803651	−	0.595100i	$-0.202888\pi$
$941$	18.2882	+	11.7531i	0.596178	+	0.383140i	−0.207474	+	0.978241i	$0.566524\pi$
$942$	0.0374309	−	0.0431975i	0.00121956	−	0.00140745i
$943$	−1.38014	−	9.59912i	−0.0449437	−	0.312590i
$944$	0.430340	−	2.99308i	0.0140064	−	0.0974164i
$945$	0.780663	+	1.70941i	0.0253950	+	0.0556072i
$946$	2.99532	+	0.879504i	0.0973861	+	0.0285951i
$947$	11.0735	+	24.2476i	0.359840	+	0.787941i	0.999809	+	0.0195397i	$0.00622007\pi$
$947$	11.0735	+	24.2476i	0.359840	+	0.787941i	−0.639969	+	0.768401i	$0.721053\pi$
$948$	−5.66019	+	3.63758i	−0.183835	+	0.118143i
$949$	−8.73929	−	60.7831i	−0.283689	−	1.97310i
$950$	−0.275588	+	0.0809200i	−0.00894126	+	0.00262539i
$951$	−5.82367	+	1.70998i	−0.188845	+	0.0554500i
$952$	−0.807118	+	0.931463i	−0.0261588	+	0.0301889i
$953$	−19.2026	+	42.0478i	−0.622032	+	1.36206i	0.291999	+	0.956419i	$0.405680\pi$
$953$	−19.2026	+	42.0478i	−0.622032	+	1.36206i	−0.914032	+	0.405643i	$0.867048\pi$
$954$	0.290608	+	2.02122i	0.00940877	+	0.0654394i
$955$	17.7260	+	20.4569i	0.573599	+	0.661969i
$956$	−15.3591	+	17.7254i	−0.496749	+	0.573279i
$957$	2.88288	−	6.31262i	0.0931902	−	0.204058i
$958$	0.360133	+	0.231443i	0.0116354	+	0.00747760i
$959$	−1.45458	+	10.1168i	−0.0469709	+	0.326690i
$960$	−3.42557	+	2.20148i	−0.110560	+	0.0710526i
$961$	−12.0024	−	7.71348i	−0.387175	−	0.248822i
$962$	−0.999263	−	1.15321i	−0.0322175	−	0.0371810i
$963$	−23.8969	+	7.01677i	−0.770068	+	0.226112i
$964$	21.3697	+	24.6619i	0.688271	+	0.794307i
$965$	2.23146	−	15.5202i	0.0718334	−	0.499612i
$966$	−0.0515969	−	0.0151502i	−0.00166010	−	0.000487450i
$967$	−15.5543			−0.500191			−0.250096	−	0.968221i	$-0.580462\pi$
$967$	−15.5543			−0.500191			−0.250096	+	0.968221i	$0.580462\pi$
$968$	−6.41871			−0.206305
$969$	−3.10335	−	0.911226i	−0.0996940	−	0.0292728i
$970$	1.25586	−	0.807094i	0.0403233	−	0.0259142i
$971$	10.9719	−	24.0251i	0.352104	−	0.771001i	−0.647853	−	0.761765i	$-0.724333\pi$
$971$	10.9719	−	24.0251i	0.352104	−	0.771001i	0.999957	−	0.00923549i	$-0.00293979\pi$
$972$	6.13266	−	13.4287i	0.196705	−	0.430724i
$973$	6.12854	−	3.93857i	0.196472	−	0.126265i
$974$	−2.58931	−	0.760291i	−0.0829669	−	0.0243613i
$975$	2.68071			0.0858515
$976$	−41.5752			−1.33079
$977$	23.9357	+	7.02816i	0.765771	+	0.224851i	0.641215	−	0.767362i	$-0.278431\pi$
$977$	23.9357	+	7.02816i	0.765771	+	0.224851i	0.124557	+	0.992212i	$0.460249\pi$
$978$	−0.0425558	+	0.295982i	−0.00136078	+	0.00946447i
$979$	18.6152	+	21.4831i	0.594944	+	0.686602i
$980$	23.1987	−	6.81175i	0.741055	−	0.217593i
$981$	10.6474	+	12.2877i	0.339945	+	0.392317i
$982$	−3.06784	−	1.97158i	−0.0978988	−	0.0629157i
$983$	−15.8752	+	10.2024i	−0.506340	+	0.325405i	−0.768748	−	0.639552i	$-0.779120\pi$
$983$	−15.8752	+	10.2024i	−0.506340	+	0.325405i	0.262407	+	0.964957i	$0.415484\pi$
$984$	−0.0393032	+	0.273359i	−0.00125294	+	0.00871438i
$985$	2.08508	+	1.34000i	0.0664360	+	0.0426959i
$986$	0.949157	−	2.07836i	0.0302273	−	0.0661886i
$987$	0.251870	−	0.290674i	0.00801712	−	0.00925225i
$988$	−14.7394	−	17.0101i	−0.468921	−	0.541164i
$989$	−3.27845	−	22.8021i	−0.104249	−	0.725066i
$990$	−1.05825	+	2.31725i	−0.0336334	+	0.0736469i
$991$	12.0999	−	13.9641i	0.384367	−	0.443584i	−0.530288	−	0.847817i	$-0.677916\pi$
$991$	12.0999	−	13.9641i	0.384367	−	0.443584i	0.914656	+	0.404234i	$0.132462\pi$
$992$	4.13051	−	1.21283i	0.131144	−	0.0385073i
$993$	−0.00445532	+	0.00130820i	−0.000141385	+	4.15144e-5i
$994$	0.0987995	+	0.687166i	0.00313373	+	0.0217956i
$995$	−2.36218	+	1.51808i	−0.0748863	+	0.0481265i
$996$	−0.773922	−	1.69465i	−0.0245226	−	0.0536971i
$997$	−2.80076	−	0.822378i	−0.0887011	−	0.0260450i	0.237081	−	0.971490i	$-0.423809\pi$
$997$	−2.80076	−	0.822378i	−0.0887011	−	0.0260450i	−0.325782	+	0.945445i	$0.605628\pi$
$998$	0.703721	+	1.54094i	0.0222759	+	0.0487774i
$999$	−0.726207	+	5.05088i	−0.0229762	+	0.159803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.2.e.a.14.1	✓	10
3.2	odd	2		603.2.u.b.550.1		10
67.15	even	11		4489.2.a.f.1.4		5
67.24	even	11	inner	67.2.e.a.24.1	yes	10
67.52	odd	22		4489.2.a.k.1.2		5
201.158	odd	22		603.2.u.b.91.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.a.14.1	✓	10	1.1	even	1	trivial
67.2.e.a.24.1	yes	10	67.24	even	11	inner
603.2.u.b.91.1		10	201.158	odd	22
603.2.u.b.550.1		10	3.2	odd	2
4489.2.a.f.1.4		5	67.15	even	11
4489.2.a.k.1.2		5	67.52	odd	22

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0366213 + 0.0801894i) q^{2} +(-0.239446 - 0.153882i) q^{3} +(1.30463 - 1.50563i) q^{4} +(0.260554 + 1.81219i) q^{5} +(0.00357093 - 0.0248364i) q^{6} +(-0.253098 - 0.554206i) q^{7} +(0.337683 + 0.0991526i) q^{8} +(-1.21259 - 2.65520i) q^{9} +(-0.135777 + 0.0872586i) q^{10} +(0.769529 + 5.35219i) q^{11} +(-0.544078 + 0.159756i) q^{12} +(-5.48325 + 1.61003i) q^{13} +(0.0351727 - 0.0405915i) q^{14} +(0.216476 - 0.474017i) q^{15} +(-0.562632 - 3.91319i) q^{16} +(-3.76413 - 4.34403i) q^{17} +(0.168513 - 0.194474i) q^{18} +(-0.821251 + 1.79829i) q^{19} +(3.06841 + 1.97195i) q^{20} +(-0.0246795 + 0.171650i) q^{21} +(-0.401008 + 0.257712i) q^{22} +(2.95918 + 1.90175i) q^{23} +(-0.0655988 - 0.0757051i) q^{24} +(1.58130 - 0.464313i) q^{25} +(-0.329911 - 0.380738i) q^{26} +(-0.239761 + 1.66757i) q^{27} +(-1.16463 - 0.341965i) q^{28} +4.50909 q^{29} +0.0459388 q^{30} +(3.92487 + 1.15244i) q^{31} +(0.885331 - 0.568968i) q^{32} +(0.639348 - 1.39998i) q^{33} +(0.210498 - 0.460927i) q^{34} +(0.938384 - 0.603063i) q^{35} +(-5.57973 - 1.63836i) q^{36} +3.02889 q^{37} -0.174279 q^{38} +(1.56070 + 0.458262i) q^{39} +(-0.0916991 + 0.637781i) q^{40} +(-1.80542 - 2.08357i) q^{41} +(-0.0146683 + 0.00430700i) q^{42} +(-4.28868 - 4.94940i) q^{43} +(9.06235 + 5.82402i) q^{44} +(4.49580 - 2.88927i) q^{45} +(-0.0441312 + 0.306939i) q^{46} +(-1.86582 - 1.19909i) q^{47} +(-0.467452 + 1.02358i) q^{48} +(4.34094 - 5.00971i) q^{49} +(0.0951423 + 0.109800i) q^{50} +(0.232834 + 1.61939i) q^{51} +(-4.72953 + 10.3562i) q^{52} +(-5.19664 + 5.99724i) q^{53} +(-0.142502 + 0.0418423i) q^{54} +(-9.49871 + 2.78907i) q^{55} +(-0.0305157 - 0.212241i) q^{56} +(0.473370 - 0.304216i) q^{57} +(0.165129 + 0.361582i) q^{58} +(0.733886 + 0.215488i) q^{59} +(-0.431270 - 0.944350i) q^{60} +(1.49662 - 10.4092i) q^{61} +(0.0513198 + 0.356937i) q^{62} +(-1.16463 + 1.34405i) q^{63} +(-6.57363 - 4.22462i) q^{64} +(-4.34637 - 9.51722i) q^{65} +0.135677 q^{66} +(8.14151 - 0.846014i) q^{67} -11.4513 q^{68} +(-0.415917 - 0.910731i) q^{69} +(0.0827241 + 0.0531636i) q^{70} +(-8.46440 + 9.76844i) q^{71} +(-0.146201 - 1.01685i) q^{72} +(-1.52925 + 10.6362i) q^{73} +(0.110922 + 0.242885i) q^{74} +(-0.450086 - 0.132157i) q^{75} +(1.63612 + 3.58260i) q^{76} +(2.77145 - 1.78111i) q^{77} +(0.0204070 + 0.141934i) q^{78} +(11.3848 - 3.34289i) q^{79} +(6.94487 - 2.03920i) q^{80} +(-5.42057 + 6.25567i) q^{81} +(0.100963 - 0.221079i) q^{82} +(0.467569 + 3.25201i) q^{83} +(0.226242 + 0.261098i) q^{84} +(6.89147 - 7.95318i) q^{85} +(0.239833 - 0.525160i) q^{86} +(-1.07968 - 0.693870i) q^{87} +(-0.270827 + 1.88364i) q^{88} +(4.42253 - 2.84219i) q^{89} +(0.396331 + 0.254707i) q^{90} +(2.28009 + 2.63136i) q^{91} +(6.72396 - 1.97433i) q^{92} +(-0.762451 - 0.879916i) q^{93} +(0.0278255 - 0.193531i) q^{94} +(-3.47283 - 1.01971i) q^{95} -0.299543 q^{96} -9.24945 q^{97} +(0.560697 + 0.164635i) q^{98} +(13.2780 - 8.53328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 6 q^{2} - 2 q^{3} + 10 q^{4} + 3 q^{5} - 12 q^{6} + 6 q^{8} - q^{9} - 15 q^{10} + 15 q^{11} - 2 q^{12} - 18 q^{13} + 6 q^{15} - 6 q^{16} - 26 q^{17} - 6 q^{18} - q^{19} + 25 q^{20} + 11 q^{21}+ \cdots + 15 q^{99}+O(q^{100}) \) 10 * q - 6 * q^2 - 2 * q^3 + 10 * q^4 + 3 * q^5 - 12 * q^6 + 6 * q^8 - q^9 - 15 * q^10 + 15 * q^11 - 2 * q^12 - 18 * q^13 + 6 * q^15 - 6 * q^16 - 26 * q^17 - 6 * q^18 - q^19 + 25 * q^20 + 11 * q^21 - 9 * q^22 - 6 * q^23 + q^24 - 4 * q^25 + 24 * q^26 - 29 * q^27 + 11 * q^28 + 28 * q^29 - 8 * q^30 - 10 * q^31 - 4 * q^32 + 8 * q^33 + 64 * q^34 - q^36 - 22 * q^37 - 6 * q^38 + 8 * q^39 - 18 * q^40 + 9 * q^41 + 11 * q^42 + 21 * q^43 + 48 * q^44 + 3 * q^45 - 25 * q^46 - 22 * q^47 - 12 * q^48 + 7 * q^49 - 35 * q^50 + 3 * q^51 - 62 * q^52 + 20 * q^53 + 13 * q^54 - 23 * q^55 - 11 * q^56 + 9 * q^57 - 8 * q^58 - 17 * q^59 + 17 * q^60 + 13 * q^61 + 50 * q^62 + 11 * q^63 + 10 * q^64 + 10 * q^65 - 62 * q^66 + 23 * q^67 - 114 * q^68 - 12 * q^69 + 11 * q^70 + q^71 - 16 * q^72 - 18 * q^73 + 22 * q^74 + 14 * q^75 + 21 * q^76 - 22 * q^77 + 37 * q^78 + 5 * q^79 + 18 * q^80 + 11 * q^81 - 12 * q^82 - 12 * q^83 - 11 * q^84 + 23 * q^85 - 61 * q^86 - 10 * q^87 - 2 * q^88 + 51 * q^89 + 18 * q^90 - 11 * q^91 + 38 * q^92 + 13 * q^93 + 11 * q^94 + 3 * q^95 - 8 * q^96 - 10 * q^97 - 2 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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