LMFDB - Embedded newform 108.2.l.a.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(11,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("108.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.2
Character	$\chi$	$=$	108.59
Dual form			108.2.l.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36287 + 0.377622i) q^{2} +(-1.69735 - 0.344959i) q^{3} +(1.71480 - 1.02930i) q^{4} +(0.420820 + 1.15619i) q^{5} +(2.44353 - 0.170825i) q^{6} +(1.81474 - 0.319988i) q^{7} +(-1.94836 + 2.05034i) q^{8} +(2.76201 + 1.17103i) q^{9} +O(q^{10})$	\(q+(-1.36287 + 0.377622i) q^{2} +(-1.69735 - 0.344959i) q^{3} +(1.71480 - 1.02930i) q^{4} +(0.420820 + 1.15619i) q^{5} +(2.44353 - 0.170825i) q^{6} +(1.81474 - 0.319988i) q^{7} +(-1.94836 + 2.05034i) q^{8} +(2.76201 + 1.17103i) q^{9} +(-1.01013 - 1.41682i) q^{10} +(5.09161 + 1.85319i) q^{11} +(-3.26569 + 1.15554i) q^{12} +(2.61776 + 2.19656i) q^{13} +(-2.35241 + 1.12139i) q^{14} +(-0.315440 - 2.10763i) q^{15} +(1.88110 - 3.53008i) q^{16} +(-4.18778 - 2.41782i) q^{17} +(-4.20645 - 0.552967i) q^{18} +(-3.42957 + 1.98006i) q^{19} +(1.91169 + 1.54950i) q^{20} +(-3.19063 - 0.0828795i) q^{21} +(-7.63898 - 0.602949i) q^{22} +(0.674078 - 3.82288i) q^{23} +(4.01434 - 2.80804i) q^{24} +(2.67053 - 2.24084i) q^{25} +(-4.39712 - 2.00509i) q^{26} +(-4.28414 - 2.94044i) q^{27} +(2.78256 - 2.41662i) q^{28} +(1.76149 + 2.09927i) q^{29} +(1.22579 + 2.75330i) q^{30} +(0.190727 + 0.0336302i) q^{31} +(-1.23065 + 5.52137i) q^{32} +(-8.00298 - 4.90192i) q^{33} +(6.62041 + 1.71376i) q^{34} +(1.13365 + 1.96353i) q^{35} +(5.94164 - 0.834830i) q^{36} +(-3.47493 + 6.01875i) q^{37} +(3.92633 - 3.99364i) q^{38} +(-3.68553 - 4.63135i) q^{39} +(-3.19050 - 1.38986i) q^{40} +(2.51742 - 3.00014i) q^{41} +(4.37970 - 1.09190i) q^{42} +(-2.57902 + 7.08581i) q^{43} +(10.6386 - 2.06291i) q^{44} +(-0.191634 + 3.68621i) q^{45} +(0.524929 + 5.46462i) q^{46} +(0.343697 + 1.94920i) q^{47} +(-4.41062 + 5.34289i) q^{48} +(-3.38696 + 1.23275i) q^{49} +(-2.79338 + 4.06241i) q^{50} +(6.27409 + 5.54850i) q^{51} +(6.74984 + 1.07222i) q^{52} -11.2308i q^{53} +(6.94908 + 2.38963i) q^{54} +6.66675i q^{55} +(-2.87968 + 4.34428i) q^{56} +(6.50423 - 2.17780i) q^{57} +(-3.19341 - 2.19584i) q^{58} +(-3.62667 + 1.32000i) q^{59} +(-2.71030 - 3.28949i) q^{60} +(-2.54693 - 14.4444i) q^{61} +(-0.272634 + 0.0261891i) q^{62} +(5.38704 + 1.24131i) q^{63} +(-0.407785 - 7.98960i) q^{64} +(-1.43804 + 3.95099i) q^{65} +(12.7581 + 3.65855i) q^{66} +(1.34096 - 1.59809i) q^{67} +(-9.66988 + 0.164388i) q^{68} +(-2.46289 + 6.25625i) q^{69} +(-2.28648 - 2.24794i) q^{70} +(4.41692 - 7.65033i) q^{71} +(-7.78240 + 3.38146i) q^{72} +(2.62025 + 4.53841i) q^{73} +(2.46304 - 9.51495i) q^{74} +(-5.30582 + 2.88227i) q^{75} +(-3.84297 + 6.92547i) q^{76} +(9.83294 + 1.73381i) q^{77} +(6.77178 + 4.92017i) q^{78} +(-5.09766 - 6.07516i) q^{79} +(4.87306 + 0.689385i) q^{80} +(6.25736 + 6.46881i) q^{81} +(-2.29798 + 5.03942i) q^{82} +(1.39029 - 1.16659i) q^{83} +(-5.55662 + 3.14199i) q^{84} +(1.03316 - 5.85935i) q^{85} +(0.839103 - 10.6309i) q^{86} +(-2.26571 - 4.17084i) q^{87} +(-13.7200 + 6.82884i) q^{88} +(-14.2059 + 8.20179i) q^{89} +(-1.13082 - 5.09617i) q^{90} +(5.45341 + 3.14853i) q^{91} +(-2.77897 - 7.24932i) q^{92} +(-0.312129 - 0.122875i) q^{93} +(-1.20448 - 2.52671i) q^{94} +(-3.73257 - 3.13200i) q^{95} +(3.99349 - 8.94718i) q^{96} +(0.0876267 + 0.0318935i) q^{97} +(4.15046 - 2.95907i) q^{98} +(11.8929 + 11.0810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	−1.36287	+	0.377622i	−0.963691	+	0.267019i
$2$	−1.36287	+	0.377622i	−0.963691	+	0.267019i
$3$	−1.69735	−	0.344959i	−0.979967	−	0.199162i
$3$	−1.69735	−	0.344959i	−0.979967	−	0.199162i
$4$	1.71480	−	1.02930i	0.857401	−	0.514648i
$5$	0.420820	+	1.15619i	0.188196	+	0.517065i	0.997527	−	0.0702884i	$-0.0223919\pi$
$5$	0.420820	+	1.15619i	0.188196	+	0.517065i	−0.809330	+	0.587354i	$0.800170\pi$
$6$	2.44353	−	0.170825i	0.997565	−	0.0697390i
$7$	1.81474	−	0.319988i	0.685907	−	0.120944i	0.180175	−	0.983635i	$-0.442334\pi$
$7$	1.81474	−	0.319988i	0.685907	−	0.120944i	0.505732	+	0.862691i	$0.331222\pi$
$8$	−1.94836	+	2.05034i	−0.688849	+	0.724905i
$9$	2.76201	+	1.17103i	0.920669	+	0.390345i
$10$	−1.01013	−	1.41682i	−0.319430	−	0.448039i
$11$	5.09161	+	1.85319i	1.53518	+	0.558759i	0.964883	−	0.262681i	$-0.0846066\pi$
$11$	5.09161	+	1.85319i	1.53518	+	0.558759i	0.570295	+	0.821440i	$0.306829\pi$
$12$	−3.26569	+	1.15554i	−0.942723	+	0.333576i
$13$	2.61776	+	2.19656i	0.726035	+	0.609215i	0.929047	−	0.369961i	$-0.120629\pi$
$13$	2.61776	+	2.19656i	0.726035	+	0.609215i	−0.203013	+	0.979176i	$0.565073\pi$
$14$	−2.35241	+	1.12139i	−0.628708	+	0.299703i
$15$	−0.315440	−	2.10763i	−0.0814463	−	0.544188i
$16$	1.88110	−	3.53008i	0.470275	−	0.882520i
$17$	−4.18778	−	2.41782i	−1.01569	−	0.586407i	−0.102835	−	0.994698i	$-0.532791\pi$
$17$	−4.18778	−	2.41782i	−1.01569	−	0.586407i	−0.912852	+	0.408291i	$0.866125\pi$
$18$	−4.20645	−	0.552967i	−0.991470	−	0.130335i
$19$	−3.42957	+	1.98006i	−0.786798	+	0.454258i	−0.838834	−	0.544387i	$-0.816762\pi$
$19$	−3.42957	+	1.98006i	−0.786798	+	0.454258i	0.0520361	+	0.998645i	$0.483429\pi$
$20$	1.91169	+	1.54950i	0.427467	+	0.346478i
$21$	−3.19063	−	0.0828795i	−0.696253	−	0.0180858i
$22$	−7.63898	−	0.602949i	−1.62864	−	0.128549i
$23$	0.674078	−	3.82288i	0.140555	−	0.797126i	−0.830274	−	0.557355i	$-0.811816\pi$
$23$	0.674078	−	3.82288i	0.140555	−	0.797126i	0.970829	−	0.239772i	$-0.0770725\pi$
$24$	4.01434	−	2.80804i	0.819423	−	0.573189i
$25$	2.67053	−	2.24084i	0.534106	−	0.448168i
$26$	−4.39712	−	2.00509i	−0.862345	−	0.393230i
$27$	−4.28414	−	2.94044i	−0.824483	−	0.565887i
$28$	2.78256	−	2.41662i	0.525854	−	0.456698i
$29$	1.76149	+	2.09927i	0.327101	+	0.389824i	0.904384	−	0.426721i	$-0.140331\pi$
$29$	1.76149	+	2.09927i	0.327101	+	0.389824i	−0.577282	+	0.816545i	$0.695887\pi$
$30$	1.22579	+	2.75330i	0.223798	+	0.502682i
$31$	0.190727	+	0.0336302i	0.0342555	+	0.00604017i	0.190750	−	0.981639i	$-0.438908\pi$
$31$	0.190727	+	0.0336302i	0.0342555	+	0.00604017i	−0.156494	+	0.987679i	$0.550019\pi$
$32$	−1.23065	+	5.52137i	−0.217550	+	0.976049i
$33$	−8.00298	−	4.90192i	−1.39314	−	0.853315i
$34$	6.62041	+	1.71376i	1.13539	+	0.293907i
$35$	1.13365	+	1.96353i	0.191621	+	0.331898i
$36$	5.94164	−	0.834830i	0.990273	−	0.139138i
$37$	−3.47493	+	6.01875i	−0.571274	+	0.989476i	0.425161	+	0.905118i	$0.360217\pi$
$37$	−3.47493	+	6.01875i	−0.571274	+	0.989476i	−0.996435	+	0.0843584i	$0.973116\pi$
$38$	3.92633	−	3.99364i	0.636935	−	0.647855i
$39$	−3.68553	−	4.63135i	−0.590157	−	0.741609i
$40$	−3.19050	−	1.38986i	−0.504462	−	0.219756i
$41$	2.51742	−	3.00014i	0.393154	−	0.468543i	−0.532766	−	0.846263i	$-0.678847\pi$
$41$	2.51742	−	3.00014i	0.393154	−	0.468543i	0.925920	+	0.377720i	$0.123292\pi$
$42$	4.37970	−	1.09190i	0.675803	−	0.168484i
$43$	−2.57902	+	7.08581i	−0.393297	+	1.08058i	0.572189	+	0.820122i	$0.306094\pi$
$43$	−2.57902	+	7.08581i	−0.393297	+	1.08058i	−0.965486	+	0.260454i	$0.916128\pi$
$44$	10.6386	−	2.06291i	1.60383	−	0.310996i
$45$	−0.191634	+	3.68621i	−0.0285671	+	0.549507i
$46$	0.524929	+	5.46462i	0.0773965	+	0.805714i
$47$	0.343697	+	1.94920i	0.0501334	+	0.284321i	0.999560	−	0.0296691i	$-0.00944536\pi$
$47$	0.343697	+	1.94920i	0.0501334	+	0.284321i	−0.949426	+	0.313990i	$0.898334\pi$
$48$	−4.41062	+	5.34289i	−0.636618	+	0.771179i
$49$	−3.38696	+	1.23275i	−0.483852	+	0.176108i
$50$	−2.79338	+	4.06241i	−0.395044	+	0.574512i
$51$	6.27409	+	5.54850i	0.878549	+	0.776946i
$52$	6.74984	+	1.07222i	0.936035	+	0.148690i
$53$		−	11.2308i		−	1.54267i	−0.636432	−	0.771333i	$-0.719590\pi$
$53$		−	11.2308i		−	1.54267i	0.636432	−	0.771333i	$-0.280410\pi$
$54$	6.94908	+	2.38963i	0.945649	+	0.325188i
$55$			6.66675i			0.898944i
$56$	−2.87968	+	4.34428i	−0.384814	+	0.580529i
$57$	6.50423	−	2.17780i	0.861507	−	0.288457i
$58$	−3.19341	−	2.19584i	−0.419315	−	0.288328i
$59$	−3.62667	+	1.32000i	−0.472152	+	0.171849i	−0.567127	−	0.823630i	$-0.691945\pi$
$59$	−3.62667	+	1.32000i	−0.472152	+	0.171849i	0.0949749	+	0.995480i	$0.469723\pi$
$60$	−2.71030	−	3.28949i	−0.349898	−	0.424672i
$61$	−2.54693	−	14.4444i	−0.326101	−	1.84941i	−0.501820	−	0.864972i	$-0.667336\pi$
$61$	−2.54693	−	14.4444i	−0.326101	−	1.84941i	0.175719	−	0.984440i	$-0.443775\pi$
$62$	−0.272634	+	0.0261891i	−0.0346246	+	0.00332602i
$63$	5.38704	+	1.24131i	0.678703	+	0.156391i
$64$	−0.407785	−	7.98960i	−0.0509731	−	0.998700i
$65$	−1.43804	+	3.95099i	−0.178367	+	0.490060i
$66$	12.7581	+	3.65855i	1.57041	+	0.450337i
$67$	1.34096	−	1.59809i	0.163824	−	0.195238i	−0.677887	−	0.735166i	$-0.737104\pi$
$67$	1.34096	−	1.59809i	0.163824	−	0.195238i	0.841711	+	0.539928i	$0.181549\pi$
$68$	−9.66988	+	0.164388i	−1.17264	+	0.0199350i
$69$	−2.46289	+	6.25625i	−0.296497	+	0.753164i
$70$	−2.28648	−	2.24794i	−0.273287	−	0.268680i
$71$	4.41692	−	7.65033i	0.524192	−	0.907927i	−0.475411	−	0.879764i	$-0.657701\pi$
$71$	4.41692	−	7.65033i	0.524192	−	0.907927i	0.999603	−	0.0281636i	$-0.00896593\pi$
$72$	−7.78240	+	3.38146i	−0.917165	+	0.398508i
$73$	2.62025	+	4.53841i	0.306677	+	0.531180i	0.977633	−	0.210317i	$-0.0674495\pi$
$73$	2.62025	+	4.53841i	0.306677	+	0.531180i	−0.670956	+	0.741497i	$0.734116\pi$
$74$	2.46304	−	9.51495i	0.286323	−	1.10609i
$75$	−5.30582	+	2.88227i	−0.612664	+	0.332816i
$76$	−3.84297	+	6.92547i	−0.440819	+	0.794406i
$77$	9.83294	+	1.73381i	1.12057	+	0.197586i
$78$	6.77178	+	4.92017i	0.766753	+	0.557099i
$79$	−5.09766	−	6.07516i	−0.573532	−	0.683508i	0.398820	−	0.917029i	$-0.369420\pi$
$79$	−5.09766	−	6.07516i	−0.573532	−	0.683508i	−0.972352	+	0.233521i	$0.924975\pi$
$80$	4.87306	+	0.689385i	0.544825	+	0.0770756i
$81$	6.25736	+	6.46881i	0.695262	+	0.718756i
$82$	−2.29798	+	5.03942i	−0.253769	+	0.556510i
$83$	1.39029	−	1.16659i	0.152604	−	0.128050i	−0.563289	−	0.826260i	$-0.690464\pi$
$83$	1.39029	−	1.16659i	0.152604	−	0.128050i	0.715893	+	0.698210i	$0.246020\pi$
$84$	−5.55662	+	3.14199i	−0.606277	+	0.342819i
$85$	1.03316	−	5.85935i	0.112062	−	0.635536i
$86$	0.839103	−	10.6309i	0.0904828	−	1.14636i
$87$	−2.26571	−	4.17084i	−0.242910	−	0.447161i
$88$	−13.7200	+	6.82884i	−1.46255	+	0.727957i
$89$	−14.2059	+	8.20179i	−1.50582	+	0.869388i	−0.505848	+	0.862623i	$0.668820\pi$
$89$	−14.2059	+	8.20179i	−1.50582	+	0.869388i	−0.999977	+	0.00676565i	$0.997846\pi$
$90$	−1.13082	−	5.09617i	−0.119199	−	0.537183i
$91$	5.45341	+	3.14853i	0.571673	+	0.330056i
$92$	−2.77897	−	7.24932i	−0.289728	−	0.755794i
$93$	−0.312129	−	0.122875i	−0.0323663	−	0.0127416i
$94$	−1.20448	−	2.52671i	−0.124232	−	0.260611i
$95$	−3.73257	−	3.13200i	−0.382954	−	0.321336i
$96$	3.99349	−	8.94718i	0.407584	−	0.913168i
$97$	0.0876267	+	0.0318935i	0.00889714	+	0.00323830i	0.346465	−	0.938063i	$-0.387382\pi$
$97$	0.0876267	+	0.0318935i	0.00889714	+	0.00323830i	−0.337568	+	0.941301i	$0.609604\pi$
$98$	4.15046	−	2.95907i	0.419259	−	0.298911i
$99$	11.8929	+	11.0810i	1.19528	+	1.11368i
$100$	2.27294	−	6.59136i	0.227294	−	0.659136i
$101$	1.18836	−	0.209540i	0.118246	−	0.0208500i	−0.114212	−	0.993456i	$-0.536434\pi$
$101$	1.18836	−	0.209540i	0.118246	−	0.0208500i	0.232458	+	0.972606i	$0.425323\pi$
$102$	−10.6460	−	5.19262i	−1.05411	−	0.514146i
$103$	−5.38263	−	14.7887i	−0.530366	−	1.45717i	−0.858636	−	0.512586i	$-0.828688\pi$
$103$	−5.38263	−	14.7887i	−0.530366	−	1.45717i	0.328270	−	0.944584i	$-0.393534\pi$
$104$	−9.60402	+	1.08760i	−0.941752	+	0.106648i
$105$	−1.24686	−	3.72387i	−0.121681	−	0.363412i
$106$	4.24099	+	15.3060i	0.411921	+	1.48665i
$107$	−15.2848			−1.47764			−0.738820	−	0.673903i	$-0.764616\pi$
$107$	−15.2848			−1.47764			−0.738820	+	0.673903i	$0.764616\pi$
$108$	−10.3730	−	0.632621i	−0.998145	−	0.0608740i
$109$	−12.4401			−1.19154			−0.595772	−	0.803154i	$-0.703154\pi$
$109$	−12.4401			−1.19154			−0.595772	+	0.803154i	$0.703154\pi$
$110$	−2.51751	−	9.08588i	−0.240035	−	0.866304i
$111$	7.97439	−	9.01723i	0.756896	−	0.855877i
$112$	2.28412	−	7.00810i	0.215829	−	0.662204i
$113$	1.29655	+	3.56224i	0.121969	+	0.335107i	0.985619	−	0.168986i	$-0.0540492\pi$
$113$	1.29655	+	3.56224i	0.121969	+	0.335107i	−0.863649	+	0.504093i	$0.831827\pi$
$114$	−8.04201	+	5.42420i	−0.753203	+	0.508022i
$115$	4.70366	−	0.829382i	0.438618	−	0.0773403i
$116$	5.18138	+	1.78673i	0.481079	+	0.165894i
$117$	4.65801	+	9.13239i	0.430634	+	0.844289i
$118$	4.44420	−	3.16849i	0.409122	−	0.291683i
$119$	−8.37341	−	3.04767i	−0.767589	−	0.279380i
$120$	4.93595	+	3.45967i	0.450589	+	0.315823i
$121$	14.0637	+	11.8008i	1.27852	+	1.07280i
$122$	8.92564	+	18.7240i	0.808090	+	1.69519i
$123$	−5.30786	+	4.22389i	−0.478594	+	0.380855i
$124$	0.361674	−	0.138645i	0.0324793	−	0.0124507i
$125$	9.04242	+	5.22065i	0.808779	+	0.466949i
$126$	−7.81055	+	0.342522i	−0.695819	+	0.0305142i
$127$	10.8485	−	6.26340i	0.962651	−	0.555787i	0.0656631	−	0.997842i	$-0.479084\pi$
$127$	10.8485	−	6.26340i	0.962651	−	0.555787i	0.896988	+	0.442055i	$0.145750\pi$
$128$	3.57281	+	10.7348i	0.315794	+	0.948828i
$129$	6.82182	−	11.1374i	0.600628	−	0.980598i
$130$	0.467877	−	5.92770i	0.0410355	−	0.519894i
$131$	−0.603670	+	3.42359i	−0.0527429	+	0.299120i	−0.999756	−	0.0220740i	$-0.992973\pi$
$131$	−0.603670	+	3.42359i	−0.0527429	+	0.299120i	0.947013	+	0.321194i	$0.104084\pi$
$132$	−18.7691	−	0.168393i	−1.63364	−	0.0146568i
$133$	−5.59018	+	4.69072i	−0.484731	+	0.406737i
$134$	−1.22407	+	2.68436i	−0.105744	+	0.231893i
$135$	1.59686	−	6.19069i	0.137436	−	0.532809i
$136$	13.1167	−	3.87560i	1.12474	−	0.332330i
$137$	3.24936	+	3.87244i	0.277612	+	0.330845i	0.886776	−	0.462199i	$-0.152939\pi$
$137$	3.24936	+	3.87244i	0.277612	+	0.330845i	−0.609164	+	0.793044i	$0.708495\pi$
$138$	0.994082	−	9.45646i	0.0846219	−	0.804988i
$139$	6.37891	+	1.12477i	0.541052	+	0.0954022i	0.437494	−	0.899221i	$-0.355866\pi$
$139$	6.37891	+	1.12477i	0.541052	+	0.0954022i	0.103558	+	0.994623i	$0.466977\pi$
$140$	3.96504	+	2.20021i	0.335107	+	0.185952i
$141$	0.0890205	−	3.42705i	0.00749688	−	0.288609i
$142$	−3.13073	+	12.0943i	−0.262725	+	1.01493i
$143$	9.25794	+	16.0352i	0.774188	+	1.34093i
$144$	9.32945	−	7.54727i	0.777454	−	0.628940i
$145$	−1.68589	+	2.92004i	−0.140005	+	0.242496i
$146$	−5.28485	−	5.19577i	−0.437377	−	0.430005i
$147$	6.17411	−	0.924052i	0.509232	−	0.0762146i
$148$	0.236262	+	13.8977i	0.0194206	+	1.14238i
$149$	3.39500	−	4.04600i	0.278129	−	0.331461i	−0.608837	−	0.793295i	$-0.708364\pi$
$149$	3.39500	−	4.04600i	0.278129	−	0.331461i	0.886967	+	0.461834i	$0.152808\pi$
$150$	6.14271	−	5.93174i	0.501551	−	0.484325i
$151$	−3.02704	+	8.31673i	−0.246337	+	0.676806i	0.753476	+	0.657475i	$0.228376\pi$
$151$	−3.02704	+	8.31673i	−0.246337	+	0.676806i	−0.999813	+	0.0193304i	$0.993847\pi$
$152$	2.62224	−	10.8897i	0.212692	−	0.883269i
$153$	−8.73534	−	11.5821i	−0.706210	−	0.936355i
$154$	−14.0557	+	1.35018i	−1.13264	+	0.108801i
$155$	0.0413785	+	0.234669i	0.00332360	+	0.0188491i
$156$	−11.0870	−	4.14835i	−0.887669	−	0.332134i
$157$	9.32232	−	3.39305i	0.744002	−	0.270795i	0.0579223	−	0.998321i	$-0.481552\pi$
$157$	9.32232	−	3.39305i	0.744002	−	0.270795i	0.686079	+	0.727527i	$0.259330\pi$
$158$	9.24154	+	6.35463i	0.735217	+	0.505547i
$159$	−3.87416	+	19.0626i	−0.307241	+	1.51176i
$160$	−6.90165	+	0.900636i	−0.545623	+	0.0712015i
$161$		−	7.15323i		−	0.563754i
$162$	−10.9707	−	6.45319i	−0.861940	−	0.507011i
$163$		−	16.2908i		−	1.27600i	−0.770038	−	0.637998i	$-0.779763\pi$
$163$		−	16.2908i		−	1.27600i	0.770038	−	0.637998i	$-0.220237\pi$
$164$	1.22884	−	7.73581i	0.0959563	−	0.604066i
$165$	2.29976	−	11.3158i	0.179036	−	0.880935i
$166$	−1.45425	+	2.11491i	−0.112871	+	0.164149i
$167$	1.16436	−	0.423791i	0.0901007	−	0.0327940i	−0.296577	−	0.955009i	$-0.595845\pi$
$167$	1.16436	−	0.423791i	0.0901007	−	0.0327940i	0.386677	+	0.922215i	$0.373623\pi$
$168$	6.38644	−	6.38040i	0.492724	−	0.492259i
$169$	−0.229648	−	1.30240i	−0.0176653	−	0.100185i
$170$	0.804561	+	8.37566i	0.0617070	+	0.642383i
$171$	−11.7912	+	1.45281i	−0.901698	+	0.111099i
$172$	2.87088	+	14.8053i	0.218902	+	1.12890i
$173$	−4.93959	+	13.5714i	−0.375550	+	1.03181i	0.597631	+	0.801771i	$0.296109\pi$
$173$	−4.93959	+	13.5714i	−0.375550	+	1.03181i	−0.973180	+	0.230043i	$0.926113\pi$
$174$	4.66286	+	4.82871i	0.353491	+	0.366063i
$175$	4.12927	−	4.92108i	0.312144	−	0.371998i
$176$	16.1197	−	14.4878i	1.21507	−	1.09206i
$177$	6.61108	−	0.989451i	0.496919	−	0.0743717i
$178$	16.2636	−	16.5424i	1.21901	−	1.23991i
$179$	−4.99509	+	8.65175i	−0.373351	+	0.646662i	−0.990079	−	0.140514i	$-0.955124\pi$
$179$	−4.99509	+	8.65175i	−0.373351	+	0.646662i	0.616728	+	0.787176i	$0.288458\pi$
$180$	3.46559	+	6.51837i	0.258309	+	0.485851i
$181$	−5.92900	−	10.2693i	−0.440699	−	0.763314i	0.557042	−	0.830484i	$-0.311936\pi$
$181$	−5.92900	−	10.2693i	−0.440699	−	0.763314i	−0.997742	+	0.0671706i	$0.978603\pi$
$182$	−8.62122	−	2.23169i	−0.639048	−	0.165424i
$183$	−0.659677	+	25.3958i	−0.0487647	+	1.87731i
$184$	6.52486	+	8.83044i	0.481019	+	0.650989i
$185$	−8.42116	−	1.48488i	−0.619136	−	0.109170i
$186$	0.471790	+	0.0495955i	0.0345933	+	0.00363652i
$187$	−16.8419	−	20.0714i	−1.23160	−	1.46776i
$188$	2.59568	+	2.98873i	0.189310	+	0.217976i
$189$	−8.71550	−	3.96525i	−0.633959	−	0.288430i
$190$	6.26970	+	2.85899i	0.454852	+	0.207413i
$191$	−0.136281	+	0.114354i	−0.00986096	+	0.00827433i	−0.647705	−	0.761891i	$-0.724271\pi$
$191$	−0.136281	+	0.114354i	−0.00986096	+	0.00827433i	0.637844	+	0.770166i	$0.279827\pi$
$192$	−2.06393	+	13.7018i	−0.148951	+	0.988845i
$193$	−1.20989	+	6.86163i	−0.0870899	+	0.493911i	0.909796	+	0.415055i	$0.136238\pi$
$193$	−1.20989	+	6.86163i	−0.0870899	+	0.493911i	−0.996886	+	0.0788559i	$0.974873\pi$
$194$	−0.131467	−	0.0103768i	−0.00943879	−	0.000745009i
$195$	3.80379	−	6.21015i	0.272395	−	0.444718i
$196$	−4.53910	+	5.60011i	−0.324222	+	0.400008i
$197$	4.71520	−	2.72232i	0.335944	−	0.193957i	−0.322533	−	0.946558i	$-0.604534\pi$
$197$	4.71520	−	2.72232i	0.335944	−	0.193957i	0.658477	+	0.752601i	$0.271201\pi$
$198$	−20.3929	−	10.6109i	−1.44926	−	0.754081i
$199$	−5.18692	−	2.99467i	−0.367691	−	0.212287i	0.304758	−	0.952430i	$-0.401424\pi$
$199$	−5.18692	−	2.99467i	−0.367691	−	0.212287i	−0.672449	+	0.740143i	$0.734758\pi$
$200$	−0.608669	+	9.84145i	−0.0430394	+	0.695896i
$201$	−2.82736	+	2.24995i	−0.199426	+	0.158699i
$202$	−1.54045	+	0.734326i	−0.108386	+	0.0516670i
$203$	3.86839	+	3.24597i	0.271508	+	0.227822i
$204$	16.4699	+	3.05669i	1.15312	+	0.214011i
$205$	4.52812	+	1.64810i	0.316258	+	0.115108i
$206$	12.9203	+	18.1223i	0.900202	+	1.26264i
$207$	6.33853	−	9.76946i	0.440558	−	0.679024i
$208$	12.6783	−	5.10895i	0.879081	−	0.354242i
$209$	−21.1315	+	3.72605i	−1.46170	+	0.257736i
$210$	3.10551	+	4.60429i	0.214301	+	0.317726i
$211$	8.87740	+	24.3905i	0.611145	+	1.67911i	0.727676	+	0.685921i	$0.240600\pi$
$211$	8.87740	+	24.3905i	0.611145	+	1.67911i	−0.116531	+	0.993187i	$0.537177\pi$
$212$	−11.5598	−	19.2586i	−0.793930	−	1.32268i
$213$	−10.1361	+	11.4616i	−0.694515	+	0.785339i
$214$	20.8311	−	5.77189i	1.42399	−	0.394558i
$215$	−9.27787			−0.632745
$216$	14.3759	−	3.05491i	0.978159	−	0.207860i
$217$	0.356880			0.0242266
$218$	16.9541	−	4.69765i	1.14828	−	0.318165i
$219$	−2.88192	−	8.60715i	−0.194742	−	0.581617i
$220$	6.86206	+	11.4322i	0.462640	+	0.770756i
$221$	−5.65172	−	15.5280i	−0.380176	−	1.04452i
$222$	−7.46292	+	15.3006i	−0.500878	+	1.02691i
$223$	22.0110	−	3.88113i	1.47396	−	0.259900i	0.621801	−	0.783175i	$-0.286401\pi$
$223$	22.0110	−	3.88113i	1.47396	−	0.259900i	0.852164	+	0.523275i	$0.175290\pi$
$224$	−0.466535	+	10.4136i	−0.0311717	+	0.695790i
$225$	10.0001	−	3.06193i	0.666674	−	0.204129i
$226$	−3.11220	−	4.36525i	−0.207021	−	0.290372i
$227$	1.58931	+	0.578461i	0.105486	+	0.0383938i	0.394224	−	0.919014i	$-0.371013\pi$
$227$	1.58931	+	0.578461i	0.105486	+	0.0383938i	−0.288738	+	0.957408i	$0.593236\pi$
$228$	8.91187	−	10.4293i	0.590203	−	0.690696i
$229$	−20.3257	−	17.0553i	−1.34316	−	1.12704i	−0.980803	−	0.195003i	$-0.937528\pi$
$229$	−20.3257	−	17.0553i	−1.34316	−	1.12704i	−0.362355	−	0.932040i	$-0.618027\pi$
$230$	−6.09726	+	2.90654i	−0.402041	+	0.191652i
$231$	−16.0919	−	6.33485i	−1.05877	−	0.416803i
$232$	−7.73623	−	0.478467i	−0.507909	−	0.0314129i
$233$	4.08160	+	2.35651i	0.267395	+	0.154380i	0.627703	−	0.778453i	$-0.283995\pi$
$233$	4.08160	+	2.35651i	0.267395	+	0.154380i	−0.360308	+	0.932833i	$0.617329\pi$
$234$	−9.79684	−	10.6872i	−0.640439	−	0.698647i
$235$	−2.10902	+	1.21764i	−0.137577	+	0.0794304i
$236$	−4.86035	+	5.99646i	−0.316382	+	0.390336i
$237$	6.55684	+	12.0702i	0.425913	+	0.784041i
$238$	12.5627	+	0.991581i	0.814319	+	0.0642746i
$239$	0.585031	−	3.31788i	0.0378425	−	0.214616i	−0.960023	−	0.279922i	$-0.909691\pi$
$239$	0.585031	−	3.31788i	0.0378425	−	0.214616i	0.997865	+	0.0653065i	$0.0208025\pi$
$240$	−8.03349	−	2.85114i	−0.518559	−	0.184040i
$241$	−12.2315	+	10.2635i	−0.787901	+	0.661127i	−0.945225	−	0.326420i	$-0.894158\pi$
$241$	−12.2315	+	10.2635i	−0.787901	+	0.661127i	0.157324	+	0.987547i	$0.449713\pi$
$242$	−23.6231	−	10.7722i	−1.51855	−	0.692462i
$243$	−8.38947	−	13.1384i	−0.538184	−	0.842827i
$244$	−19.2350	−	22.1477i	−1.23140	−	1.41786i
$245$	−2.85060	−	3.39722i	−0.182118	−	0.217040i
$246$	5.63887	−	7.76095i	0.359521	−	0.494820i
$247$	−13.3271	−	2.34993i	−0.847984	−	0.149522i
$248$	−0.440557	+	0.325530i	−0.0279754	+	0.0206712i
$249$	−2.76223	+	1.50052i	−0.175049	+	0.0950917i
$250$	−14.2950	−	3.70042i	−0.904097	−	0.234035i
$251$	−8.45736	−	14.6486i	−0.533824	−	0.924610i	−0.999219	−	0.0395068i	$-0.987421\pi$
$251$	−8.45736	−	14.6486i	−0.533824	−	0.924610i	0.465396	−	0.885103i	$-0.345912\pi$
$252$	10.5154	−	3.41625i	0.662407	−	0.215203i
$253$	10.5167	−	18.2154i	0.661178	−	1.14519i
$254$	−12.4199	+	12.6328i	−0.779293	+	0.792653i
$255$	−3.77488	+	9.58899i	−0.236392	+	0.600486i
$256$	−8.92294	−	13.2809i	−0.557684	−	0.830054i
$257$	−1.87760	+	2.23763i	−0.117121	+	0.139580i	−0.821419	−	0.570325i	$-0.806817\pi$
$257$	−1.87760	+	2.23763i	−0.117121	+	0.139580i	0.704298	+	0.709904i	$0.251262\pi$
$258$	−5.09148	+	17.7549i	−0.316981	+	1.10537i
$259$	−4.38016	+	12.0344i	−0.272170	+	0.747781i
$260$	1.60078	+	8.25533i	0.0992760	+	0.511974i
$261$	2.40694	+	7.86096i	0.148986	+	0.486581i
$262$	−0.470100	−	4.89384i	−0.0290429	−	0.302343i
$263$	0.00324687	+	0.0184139i	0.000200211	+	0.00113545i	0.984908	−	0.173080i	$-0.0553721\pi$
$263$	0.00324687	+	0.0184139i	0.000200211	+	0.00113545i	−0.984707	+	0.174216i	$0.944261\pi$
$264$	25.6433	−	6.85811i	1.57823	−	0.422088i
$265$	12.9849	−	4.72613i	0.797659	−	0.290324i
$266$	5.84735	−	8.50380i	0.358524	−	0.521401i
$267$	26.9417	−	9.02087i	1.64881	−	0.552068i
$268$	0.654570	−	4.12066i	0.0399842	−	0.251709i
$269$			16.1328i			0.983634i	0.870699	+	0.491817i	$0.163667\pi$
$269$			16.1328i			0.983634i	−0.870699	+	0.491817i	$0.836333\pi$
$270$	0.161433	+	9.04008i	0.00982449	+	0.550162i
$271$			22.8808i			1.38991i	0.719053	+	0.694955i	$0.244576\pi$
$271$			22.8808i			1.38991i	−0.719053	+	0.694955i	$0.755424\pi$
$272$	−16.4127	+	10.2351i	−0.995168	+	0.620592i
$273$	−8.17025	−	7.22537i	−0.494486	−	0.437299i
$274$	−5.89076	−	4.05058i	−0.355874	−	0.244705i
$275$	17.7500	−	6.46047i	1.07037	−	0.389581i
$276$	2.21617	+	13.2633i	0.133398	+	0.798355i
$277$	1.19415	+	6.77238i	0.0717497	+	0.406913i	0.999437	+	0.0335545i	$0.0106827\pi$
$277$	1.19415	+	6.77238i	0.0717497	+	0.406913i	−0.927687	+	0.373358i	$0.878206\pi$
$278$	−9.11834	+	0.875903i	−0.546882	+	0.0525332i
$279$	0.487406	+	0.316234i	0.0291802	+	0.0189324i
$280$	−6.23466	−	1.50131i	−0.372592	−	0.0897204i
$281$	4.84953	−	13.3240i	0.289298	−	0.794841i	−0.706867	−	0.707347i	$-0.749892\pi$
$281$	4.84953	−	13.3240i	0.289298	−	0.794841i	0.996165	−	0.0874941i	$-0.0278859\pi$
$282$	1.17281	+	4.70422i	0.0698396	+	0.280132i
$283$	−7.76714	+	9.25651i	−0.461708	+	0.550243i	−0.945789	−	0.324781i	$-0.894710\pi$
$283$	−7.76714	+	9.25651i	−0.461708	+	0.550243i	0.484081	+	0.875023i	$0.339154\pi$
$284$	−0.300308	−	17.6651i	−0.0178200	−	1.04823i
$285$	5.25507	+	6.60369i	0.311284	+	0.391169i
$286$	−18.6726	−	18.3578i	−1.10413	−	1.08552i
$287$	3.60845	−	6.25001i	0.213000	−	0.368927i
$288$	−9.86476	+	13.8089i	−0.581287	+	0.813699i
$289$	3.19169	+	5.52817i	0.187747	+	0.325187i
$290$	1.19496	−	4.61625i	0.0701707	−	0.271076i
$291$	−0.137731	−	0.0843621i	−0.00807396	−	0.00494540i
$292$	9.16458	+	5.08546i	0.536316	+	0.297604i
$293$	5.78523	+	1.02009i	0.337977	+	0.0595944i	0.340061	−	0.940403i	$-0.389552\pi$
$293$	5.78523	+	1.02009i	0.337977	+	0.0595944i	−0.00208409	+	0.999998i	$0.500663\pi$
$294$	−8.06554	+	3.59084i	−0.470392	+	0.209422i
$295$	−3.05235	−	3.63765i	−0.177715	−	0.211792i
$296$	−5.57007	−	18.8515i	−0.323754	−	1.09572i
$297$	−16.3640	−	22.9109i	−0.949533	−	1.32942i
$298$	−3.09907	+	6.79618i	−0.179524	+	0.393692i
$299$	10.1618	−	8.52672i	0.587669	−	0.493113i
$300$	−6.13173	+	10.4038i	−0.354016	+	0.600663i
$301$	−2.41288	+	13.6841i	−0.139076	+	0.788741i
$302$	0.984869	−	12.4777i	0.0566728	−	0.718009i
$303$	−2.08935	−	0.0542727i	−0.120030	−	0.00311788i
$304$	0.538424	+	15.8314i	0.0308807	+	0.907991i
$305$	15.6287	−	9.02323i	0.894896	−	0.516668i
$306$	16.2787	+	12.4861i	0.930593	+	0.713785i
$307$	−3.55307	−	2.05137i	−0.202784	−	0.117078i	0.395169	−	0.918608i	$-0.370686\pi$
$307$	−3.55307	−	2.05137i	−0.202784	−	0.117078i	−0.597954	+	0.801531i	$0.704019\pi$
$308$	18.6462	−	7.14786i	1.06246	−	0.407287i
$309$	4.03474	+	26.9583i	0.229528	+	1.53361i
$310$	−0.145010	−	0.304197i	−0.00823599	−	0.0172772i
$311$	−2.76079	−	2.31658i	−0.156550	−	0.131361i	0.561148	−	0.827715i	$-0.310360\pi$
$311$	−2.76079	−	2.31658i	−0.156550	−	0.131361i	−0.717698	+	0.696354i	$0.754804\pi$
$312$	16.6766	+	1.46695i	0.944125	+	0.0830497i
$313$	20.0330	+	7.29141i	1.13233	+	0.412135i	0.839138	−	0.543919i	$-0.183060\pi$
$313$	20.0330	+	7.29141i	1.13233	+	0.412135i	0.293193	+	0.956053i	$0.405282\pi$
$314$	−11.4238	+	8.14458i	−0.644681	+	0.459625i
$315$	0.831774	+	6.75083i	0.0468652	+	0.380366i
$316$	−14.9946	−	5.17069i	−0.843513	−	0.290874i
$317$	34.5729	−	6.09614i	1.94181	−	0.342393i	0.941828	−	0.336095i	$-0.109106\pi$
$317$	34.5729	−	6.09614i	1.94181	−	0.342393i	0.999980	−	0.00629824i	$-0.00200481\pi$
$318$	−1.91850	−	27.4427i	−0.107584	−	1.53891i
$319$	5.07849	+	13.9530i	0.284341	+	0.781220i
$320$	9.06592	−	3.83366i	0.506800	−	0.214308i
$321$	25.9437	+	5.27264i	1.44804	+	0.294290i
$322$	2.70122	+	9.74889i	0.150533	+	0.543285i
$323$	19.1497			1.06552
$324$	17.3885	+	4.65205i	0.966025	+	0.258447i
$325$	11.9129			0.660810
$326$	6.15178	+	22.2022i	0.340715	+	1.22967i
$327$	21.1152	+	4.29132i	1.16767	+	0.237310i
$328$	1.24647	+	11.0069i	0.0688249	+	0.607755i
$329$	1.24744	+	3.42732i	0.0687737	+	0.188954i
$330$	1.13885	+	16.2904i	0.0626914	+	0.896755i
$331$	0.234592	−	0.0413648i	0.0128943	−	0.00227362i	−0.167197	−	0.985923i	$-0.553472\pi$
$331$	0.234592	−	0.0413648i	0.0128943	−	0.00227362i	0.180092	+	0.983650i	$0.442361\pi$
$332$	1.18330	−	3.43149i	0.0649422	−	0.188328i
$333$	−16.6459	+	12.5546i	−0.912191	+	0.687986i
$334$	−1.42683	+	1.01726i	−0.0780726	+	0.0556619i
$335$	2.41201	+	0.877898i	0.131782	+	0.0479647i
$336$	−6.29447	+	11.1073i	−0.343391	+	0.605952i
$337$	−5.13534	−	4.30906i	−0.279740	−	0.234729i	0.492112	−	0.870532i	$-0.336225\pi$
$337$	−5.13534	−	4.30906i	−0.279740	−	0.234729i	−0.771852	+	0.635802i	$0.780669\pi$
$338$	0.804795	+	1.68828i	0.0437751	+	0.0918301i
$339$	−0.971873	−	6.49363i	−0.0527849	−	0.352685i
$340$	−4.25934	−	11.1111i	−0.230995	−	0.602582i
$341$	0.908782	+	0.524685i	0.0492133	+	0.0284133i
$342$	15.5212	−	6.43261i	0.839292	−	0.347835i
$343$	−16.9230	+	9.77048i	−0.913755	+	0.527556i
$344$	−9.50345	−	19.0936i	−0.512391	−	1.02946i
$345$	−8.26987	−	0.214817i	−0.445235	−	0.0115654i
$346$	1.60713	−	20.3613i	0.0863997	−	1.09463i
$347$	−1.22136	+	6.92666i	−0.0655659	+	0.371843i	0.934316	+	0.356447i	$0.116012\pi$
$347$	−1.22136	+	6.92666i	−0.0655659	+	0.371843i	−0.999881	+	0.0153957i	$0.995099\pi$
$348$	−8.17828	−	4.82007i	−0.438402	−	0.258383i
$349$	−5.45858	+	4.58030i	−0.292191	+	0.245178i	−0.777085	−	0.629395i	$-0.783303\pi$
$349$	−5.45858	+	4.58030i	−0.292191	+	0.245178i	0.484894	+	0.874573i	$0.338858\pi$
$350$	−3.76933	+	8.26607i	−0.201479	+	0.441840i
$351$	−4.75599	−	17.1077i	−0.253856	−	0.913141i
$352$	−16.4981	+	25.8320i	−0.879354	+	1.37685i
$353$	−10.1110	−	12.0498i	−0.538152	−	0.641344i	0.426620	−	0.904431i	$-0.359704\pi$
$353$	−10.1110	−	12.0498i	−0.538152	−	0.641344i	−0.964772	+	0.263086i	$0.915260\pi$
$354$	−8.63637	+	3.84498i	−0.459018	+	0.204358i
$355$	10.7040	+	1.88740i	0.568109	+	0.100173i
$356$	−15.9183	+	28.6866i	−0.843667	+	1.52038i
$357$	13.1613	+	8.06145i	0.696570	+	0.426657i
$358$	3.54054	−	13.6774i	0.187123	−	0.722874i
$359$	6.28667	+	10.8888i	0.331798	+	0.574691i	0.982864	−	0.184330i	$-0.0590115\pi$
$359$	6.28667	+	10.8888i	0.331798	+	0.574691i	−0.651067	+	0.759021i	$0.725678\pi$
$360$	−7.18461	−	7.57498i	−0.378662	−	0.399236i
$361$	−1.65869	+	2.87293i	−0.0872993	+	0.151207i
$362$	11.9584	+	11.7568i	0.628517	+	0.617923i
$363$	−19.8002	−	24.8815i	−1.03924	−	1.30594i
$364$	12.5923	−	0.214070i	0.660016	−	0.0112203i
$365$	−4.14462	+	4.93937i	−0.216939	+	0.258538i
$366$	−8.69095	−	34.8601i	−0.454283	−	1.82217i
$367$	−7.46561	+	20.5116i	−0.389702	+	1.07070i	0.577434	+	0.816437i	$0.304054\pi$
$367$	−7.46561	+	20.5116i	−0.389702	+	1.07070i	−0.967136	+	0.254260i	$0.918168\pi$
$368$	−12.2271	−	9.57077i	−0.637381	−	0.498911i
$369$	10.4664	−	5.33842i	0.544858	−	0.277907i
$370$	12.0376	−	1.15633i	0.625806	−	0.0601146i
$371$	−3.59371	−	20.3809i	−0.186576	−	1.05813i
$372$	−0.661715	+	0.110566i	−0.0343083	+	0.00573260i
$373$	−14.2207	+	5.17591i	−0.736320	+	0.267999i	−0.682838	−	0.730570i	$-0.739254\pi$
$373$	−14.2207	+	5.17591i	−0.736320	+	0.267999i	−0.0534826	+	0.998569i	$0.517032\pi$
$374$	30.5326	+	20.9947i	1.57880	+	1.08561i
$375$	−13.5473	−	11.9805i	−0.699578	−	0.618672i
$376$	−4.66618	−	3.09306i	−0.240640	−	0.159512i
$377$			9.36459i			0.482301i
$378$	13.3754	+	2.11294i	0.687957	+	0.108678i
$379$		−	25.8363i		−	1.32712i	−0.748122	−	0.663561i	$-0.769044\pi$
$379$		−	25.8363i		−	1.32712i	0.748122	−	0.663561i	$-0.230956\pi$
$380$	−9.62438	−	1.52884i	−0.493720	−	0.0784278i
$381$	−20.5744	+	6.88889i	−1.05406	+	0.352929i
$382$	0.142550	−	0.207311i	0.00729352	−	0.0106070i
$383$	4.37364	−	1.59187i	0.223482	−	0.0813410i	−0.227852	−	0.973696i	$-0.573170\pi$
$383$	4.37364	−	1.59187i	0.223482	−	0.0813410i	0.451335	+	0.892355i	$0.350948\pi$
$384$	−2.36126	−	19.4531i	−0.120497	−	0.992714i
$385$	2.13328	+	12.0984i	0.108722	+	0.616592i
$386$	−0.942187	−	9.80836i	−0.0479560	−	0.499233i
$387$	−15.4210	+	16.5509i	−0.783893	+	0.841331i
$388$	0.183090	−	0.0355027i	0.00929501	−	0.00180238i
$389$	9.75902	−	26.8127i	0.494802	−	1.35946i	−0.401438	−	0.915886i	$-0.631489\pi$
$389$	9.75902	−	26.8127i	0.494802	−	1.35946i	0.896239	−	0.443571i	$-0.146288\pi$
$390$	−2.83896	+	9.89999i	−0.143757	+	0.501306i
$391$	−12.0659	+	14.3796i	−0.610200	+	0.727208i
$392$	4.07146	−	9.34627i	0.205640	−	0.472058i
$393$	2.20564	−	5.60279i	0.111260	−	0.282623i
$394$	−5.39817	+	5.49072i	−0.271956	+	0.276619i
$395$	4.87886	−	8.45043i	0.245482	−	0.425187i
$396$	31.7996	+	6.76038i	1.59799	+	0.339722i
$397$	−0.983521	−	1.70351i	−0.0493615	−	0.0854966i	0.840289	−	0.542139i	$-0.182385\pi$
$397$	−0.983521	−	1.70351i	−0.0493615	−	0.0854966i	−0.889650	+	0.456642i	$0.849052\pi$
$398$	8.19993	+	2.12264i	0.411025	+	0.106398i
$399$	11.1066	−	6.03342i	0.556026	−	0.302049i
$400$	−2.88682	−	13.6424i	−0.144341	−	0.682121i
$401$	−18.7451	−	3.30527i	−0.936087	−	0.165057i	−0.315260	−	0.949005i	$-0.602092\pi$
$401$	−18.7451	−	3.30527i	−0.936087	−	0.165057i	−0.620827	+	0.783948i	$0.713203\pi$
$402$	3.00367	−	4.13405i	0.149810	−	0.206188i
$403$	0.425405	+	0.506978i	0.0211909	+	0.0252544i
$404$	1.82213	−	1.58250i	0.0906542	−	0.0787321i
$405$	−4.84597	+	9.95692i	−0.240798	+	0.494763i
$406$	−6.49784	−	2.96302i	−0.322483	−	0.147052i
$407$	−28.8469	+	24.2054i	−1.42989	+	1.19982i
$408$	−23.6005	+	2.05354i	−1.16840	+	0.101666i
$409$	2.54702	−	14.4449i	0.125942	−	0.714252i	−0.854802	−	0.518954i	$-0.826322\pi$
$409$	2.54702	−	14.4449i	0.125942	−	0.714252i	0.980744	−	0.195298i	$-0.0625674\pi$
$410$	−6.79358	−	0.536221i	−0.335511	−	0.0264821i
$411$	−4.17948	−	7.69379i	−0.206158	−	0.379507i
$412$	−24.4521	−	19.8193i	−1.20467	−	0.976427i
$413$	−6.15908	+	3.55594i	−0.303068	+	0.174977i
$414$	−4.94940	+	15.7080i	−0.243250	+	0.772008i
$415$	1.93387	+	1.11652i	0.0949297	+	0.0548077i
$416$	−15.3495	+	11.7504i	−0.752573	+	0.576111i
$417$	−10.4393	−	4.10960i	−0.511213	−	0.201248i
$418$	27.3923	−	13.0578i	1.33980	−	0.638679i
$419$	8.87113	+	7.44376i	0.433383	+	0.363651i	0.833226	−	0.552932i	$-0.186491\pi$
$419$	8.87113	+	7.44376i	0.433383	+	0.363651i	−0.399843	+	0.916583i	$0.630936\pi$
$420$	−5.97108	−	5.10231i	−0.291359	−	0.248967i
$421$	1.16623	+	0.424473i	0.0568386	+	0.0206876i	0.370283	−	0.928919i	$-0.379261\pi$
$421$	1.16623	+	0.424473i	0.0568386	+	0.0206876i	−0.313444	+	0.949607i	$0.601483\pi$
$422$	−21.3091	−	29.8886i	−1.03731	−	1.45495i
$423$	−1.33329	+	5.78619i	−0.0648268	+	0.281334i
$424$	23.0269	+	21.8816i	1.11829	+	1.06266i
$425$	−16.6015	+	2.92730i	−0.805293	+	0.141995i
$426$	9.48599	−	19.4483i	0.459598	−	0.942273i
$427$	−9.24404	−	25.3978i	−0.447350	−	1.22908i
$428$	−26.2105	+	15.7326i	−1.26693	+	0.760464i
$429$	−10.1825	−	30.4110i	−0.491615	−	1.46826i
$430$	12.6445	−	3.50353i	0.609771	−	0.168955i
$431$	33.8486			1.63043			0.815214	−	0.579159i	$-0.196619\pi$
$431$	33.8486			1.63043			0.815214	+	0.579159i	$0.196619\pi$
$432$	−18.4389	+	9.59210i	−0.887140	+	0.461500i
$433$	21.7047			1.04306			0.521531	−	0.853232i	$-0.325361\pi$
$433$	21.7047			1.04306			0.521531	+	0.853232i	$0.325361\pi$
$434$	−0.486380	+	0.134766i	−0.0233470	+	0.00646897i
$435$	3.86884	−	4.37478i	0.185497	−	0.209754i
$436$	−21.3323	+	12.8045i	−1.02163	+	0.613225i
$437$	5.25776	+	14.4456i	0.251513	+	0.691026i
$438$	7.17792	+	10.6421i	0.342974	+	0.508500i
$439$	36.8270	−	6.49360i	1.75766	−	0.309923i	0.800467	−	0.599377i	$-0.204585\pi$
$439$	36.8270	−	6.49360i	1.75766	−	0.309923i	0.957192	+	0.289454i	$0.0934737\pi$
$440$	−13.6691	−	12.9892i	−0.651649	−	0.619237i
$441$	−10.7984	−	0.561375i	−0.514210	−	0.0267321i
$442$	13.5662	+	19.0283i	0.645280	+	0.905084i
$443$	5.77721	+	2.10273i	0.274484	+	0.0999039i	0.475595	−	0.879665i	$-0.342233\pi$
$443$	5.77721	+	2.10273i	0.274484	+	0.0999039i	−0.201111	+	0.979568i	$0.564455\pi$
$444$	4.39312	−	23.6708i	0.208488	−	1.12337i
$445$	−15.4610	−	12.9733i	−0.732922	−	0.614994i
$446$	−28.5324	+	13.6013i	−1.35105	+	0.644040i
$447$	−7.15821	+	5.69635i	−0.338572	+	0.269428i
$448$	−3.29660	−	14.3686i	−0.155750	−	0.678850i
$449$	4.30776	+	2.48709i	0.203296	+	0.117373i	0.598192	−	0.801353i	$-0.295886\pi$
$449$	4.30776	+	2.48709i	0.203296	+	0.117373i	−0.394896	+	0.918726i	$0.629219\pi$
$450$	−12.4726	+	7.94927i	−0.587962	+	0.374732i
$451$	18.3775	−	10.6103i	0.865364	−	0.499618i
$452$	5.88992	+	4.77400i	0.277039	+	0.224550i
$453$	8.00689	−	13.0722i	0.376196	−	0.614186i
$454$	−2.38445	−	0.188206i	−0.111908	−	0.00883296i
$455$	−1.34540	+	7.63017i	−0.0630735	+	0.357708i
$456$	−8.20735	+	17.5790i	−0.384344	+	0.823214i
$457$	8.14455	−	6.83409i	0.380986	−	0.319685i	−0.432103	−	0.901824i	$-0.642228\pi$
$457$	8.14455	−	6.83409i	0.380986	−	0.319685i	0.813089	+	0.582139i	$0.197784\pi$
$458$	34.1416	+	15.5686i	1.59533	+	0.727473i
$459$	10.8316	+	22.6722i	0.505576	+	1.05825i
$460$	7.21217	−	6.26368i	0.336269	−	0.292046i
$461$	−9.23017	−	11.0001i	−0.429892	−	0.512325i	0.506999	−	0.861946i	$-0.330755\pi$
$461$	−9.23017	−	11.0001i	−0.429892	−	0.512325i	−0.936891	+	0.349621i	$0.886310\pi$
$462$	24.3232	+	2.55691i	1.13162	+	0.118958i
$463$	−17.9752	−	3.16951i	−0.835377	−	0.147300i	−0.260433	−	0.965492i	$-0.583865\pi$
$463$	−17.9752	−	3.16951i	−0.835377	−	0.147300i	−0.574944	+	0.818192i	$0.694976\pi$
$464$	10.7241	−	2.26929i	0.497855	−	0.105349i
$465$	0.0107174	−	0.412590i	0.000497007	−	0.0191334i
$466$	−6.45255	−	1.67031i	−0.298908	−	0.0773755i
$467$	−11.4763	−	19.8775i	−0.531060	−	0.919823i	−0.999343	−	0.0362446i	$-0.988460\pi$
$467$	−11.4763	−	19.8775i	−0.531060	−	0.919823i	0.468283	−	0.883579i	$-0.344873\pi$
$468$	17.3875	+	10.8658i	0.803738	+	0.502270i
$469$	1.92212	−	3.32921i	0.0887553	−	0.153729i
$470$	2.41450	−	2.45590i	0.111373	−	0.113282i
$471$	−16.9937	+	2.54337i	−0.783029	+	0.117192i
$472$	4.35961	−	10.0077i	0.200667	−	0.460644i
$473$	−26.2628	+	31.2987i	−1.20756	+	1.43912i
$474$	−13.4941	−	13.9740i	−0.619803	−	0.641847i
$475$	−4.72176	+	12.9729i	−0.216649	+	0.595239i
$476$	−17.4957	+	3.39256i	−0.801914	+	0.155498i
$477$	13.1516	−	31.0195i	0.602171	−	1.42028i
$478$	0.455585	+	4.74274i	0.0208380	+	0.216928i
$479$	3.05382	+	17.3191i	0.139533	+	0.791329i	0.971596	+	0.236648i	$0.0760487\pi$
$479$	3.05382	+	17.3191i	0.139533	+	0.791329i	−0.832063	+	0.554681i	$0.812840\pi$
$480$	12.0252	+	0.852091i	0.548873	+	0.0388925i
$481$	−22.3170	+	8.12274i	−1.01757	+	0.370365i
$482$	12.7942	−	18.6066i	0.582759	−	0.847507i
$483$	−2.46757	+	12.1416i	−0.112278	+	0.552460i
$484$	36.2630	+	5.76040i	1.64832	+	0.261836i
$485$			0.114735i			0.00520984i
$486$	16.3951	+	14.7378i	0.743695	+	0.668519i
$487$			15.6716i			0.710147i	0.934838	+	0.355073i	$0.115544\pi$
$487$			15.6716i			0.710147i	−0.934838	+	0.355073i	$0.884456\pi$
$488$	34.5782	+	22.9208i	1.56528	+	1.03757i
$489$	−5.61967	+	27.6513i	−0.254130	+	1.25043i
$490$	5.16785	+	3.55350i	0.233460	+	0.160531i
$491$	−37.6017	+	13.6859i	−1.69694	+	0.617636i	−0.995471	−	0.0950638i	$-0.969694\pi$
$491$	−37.6017	+	13.6859i	−1.69694	+	0.617636i	−0.701469	+	0.712700i	$0.747472\pi$
$492$	−4.75431	+	12.7065i	−0.214341	+	0.572853i
$493$	−2.30111	−	13.0502i	−0.103637	−	0.587754i
$494$	19.0504	−	1.82998i	0.857120	−	0.0823345i
$495$	−7.80699	+	18.4136i	−0.350898	+	0.827630i
$496$	0.477493	−	0.610018i	0.0214401	−	0.0273906i
$497$	5.56755	−	15.2967i	0.249739	−	0.686152i
$498$	3.19792	−	3.08809i	0.143302	−	0.138381i
$499$	13.3375	−	15.8950i	0.597067	−	0.711556i	−0.379881	−	0.925035i	$-0.624035\pi$
$499$	13.3375	−	15.8950i	0.597067	−	0.711556i	0.976948	+	0.213479i	$0.0684795\pi$
$500$	20.8796	−	0.354954i	0.933763	−	0.0158740i
$501$	−2.12251	+	0.317667i	−0.0948270	+	0.0141923i
$502$	17.0579	+	16.7703i	0.761330	+	0.748497i
$503$	2.51174	−	4.35046i	0.111993	−	0.193977i	−0.804581	−	0.593843i	$-0.797610\pi$
$503$	2.51174	−	4.35046i	0.111993	−	0.193977i	0.916574	+	0.399866i	$0.130943\pi$
$504$	−13.0410	+	8.62673i	−0.580893	+	0.384265i
$505$	0.742355	+	1.28580i	0.0330344	+	0.0572172i
$506$	−7.45427	+	28.7965i	−0.331383	+	1.28016i
$507$	−0.0594809	+	2.28985i	−0.00264164	+	0.101696i
$508$	12.1562	−	21.9068i	0.539344	−	0.971959i
$509$	−21.4633	−	3.78456i	−0.951344	−	0.167748i	−0.323623	−	0.946186i	$-0.604901\pi$
$509$	−21.4633	−	3.78456i	−0.951344	−	0.167748i	−0.627721	+	0.778438i	$0.716012\pi$
$510$	1.52364	−	14.4940i	0.0674677	−	0.641804i
$511$	6.20730	+	7.39758i	0.274595	+	0.327250i
$512$	17.1759	+	14.7305i	0.759075	+	0.651003i
$513$	20.5150	+	1.60157i	0.905760	+	0.0707110i
$514$	1.71393	−	3.75862i	0.0755983	−	0.165785i
$515$	14.8334	−	12.4467i	0.653639	−	0.548468i
$516$	0.234347	−	26.1202i	0.0103165	−	1.14988i
$517$	−1.86228	+	10.5615i	−0.0819030	+	0.464495i
$518$	1.42511	−	18.0553i	0.0626160	−	0.793304i
$519$	13.0658	−	21.3315i	0.573525	−	0.936348i
$520$	−5.29904	−	10.6464i	−0.232378	−	0.466876i
$521$	−8.39768	+	4.84840i	−0.367909	+	0.212412i	−0.672545	−	0.740057i	$-0.734799\pi$
$521$	−8.39768	+	4.84840i	−0.367909	+	0.212412i	0.304635	+	0.952469i	$0.401465\pi$
$522$	−6.24881	−	9.80451i	−0.273503	−	0.429132i
$523$	−3.03420	−	1.75180i	−0.132676	−	0.0766007i	0.432193	−	0.901781i	$-0.357740\pi$
$523$	−3.03420	−	1.75180i	−0.132676	−	0.0766007i	−0.564869	+	0.825181i	$0.691073\pi$
$524$	2.48871	+	6.49213i	0.108720	+	0.283610i
$525$	−8.70640	+	6.92837i	−0.379978	+	0.302379i
$526$	−0.0113786	−	0.0238696i	−0.000496129	−	0.00104076i
$527$	−0.717410	−	0.601978i	−0.0312509	−	0.0262226i
$528$	−32.3586	+	19.0302i	−1.40823	+	0.828181i
$529$	7.45287	+	2.71262i	0.324038	+	0.117940i
$530$	−15.9120	+	11.3445i	−0.691175	+	0.492773i
$531$	−11.5626	−	0.601105i	−0.501776	−	0.0260858i
$532$	−4.75792	+	13.7976i	−0.206282	+	0.598203i
$533$	13.1800	−	2.32398i	0.570887	−	0.100663i
$534$	−33.3115	+	22.4680i	−1.44153	+	0.972286i
$535$	−6.43216	−	17.6722i	−0.278086	−	0.764036i
$536$	0.663962	+	5.86308i	0.0286788	+	0.253247i
$537$	11.4629	−	12.9620i	0.494662	−	0.559350i
$538$	−6.09210	−	21.9868i	−0.262649	−	0.947919i
$539$	−19.5296			−0.841200
$540$	−3.63375	−	12.2595i	−0.156372	−	0.527563i
$541$	25.3365			1.08930			0.544652	−	0.838662i	$-0.316662\pi$
$541$	25.3365			1.08930			0.544652	+	0.838662i	$0.316662\pi$
$542$	−8.64030	−	31.1835i	−0.371133	−	1.33944i
$543$	6.52110	+	19.4759i	0.279847	+	0.835792i
$544$	18.5033	−	20.1468i	0.793325	−	0.863788i
$545$	−5.23503	−	14.3831i	−0.224244	−	0.616106i
$546$	13.8634	+	6.76194i	0.593299	+	0.289384i
$547$	−6.82129	+	1.20278i	−0.291657	+	0.0514270i	−0.317562	−	0.948237i	$-0.602864\pi$
$547$	−6.82129	+	1.20278i	−0.291657	+	0.0514270i	0.0259052	+	0.999664i	$0.491753\pi$
$548$	9.55790	+	3.29591i	0.408293	+	0.140794i
$549$	9.88021	−	42.8780i	0.421677	−	1.82999i
$550$	−21.7512	+	15.5075i	−0.927476	+	0.661244i
$551$	−10.1979	−	3.71172i	−0.434443	−	0.158124i
$552$	−8.02885	−	17.2392i	−0.341730	−	0.733748i
$553$	−11.1949	−	9.39364i	−0.476056	−	0.399458i
$554$	−4.18487	−	8.77890i	−0.177798	−	0.372980i
$555$	13.7814	+	5.42531i	0.584990	+	0.230292i
$556$	12.0963	−	4.63703i	0.512998	−	0.196654i
$557$	−1.26444	−	0.730025i	−0.0535761	−	0.0309322i	0.472973	−	0.881077i	$-0.343181\pi$
$557$	−1.26444	−	0.730025i	−0.0535761	−	0.0309322i	−0.526549	+	0.850145i	$0.676514\pi$
$558$	−0.783685	−	0.246929i	−0.0331760	−	0.0104534i
$559$	−22.3156	+	12.8839i	−0.943851	+	0.544932i
$560$	9.06393	−	0.308264i	0.383021	−	0.0130265i
$561$	21.6628	+	39.8779i	0.914604	+	1.68365i
$562$	−1.57783	+	19.9901i	−0.0665566	+	0.843229i
$563$	−5.77946	+	32.7770i	−0.243575	+	1.38138i	0.580203	+	0.814472i	$0.302973\pi$
$563$	−5.77946	+	32.7770i	−0.243575	+	1.38138i	−0.823778	+	0.566912i	$0.808138\pi$
$564$	−3.37479	−	5.96834i	−0.142104	−	0.251312i
$565$	−3.57302	+	2.99812i	−0.150318	+	0.126132i
$566$	7.09010	−	15.5484i	0.298019	−	0.653549i
$567$	13.4254	+	9.73692i	0.563814	+	0.408912i
$568$	7.08002	+	23.9618i	0.297071	+	1.00541i
$569$	27.7062	+	33.0189i	1.16150	+	1.38423i	0.909087	+	0.416607i	$0.136781\pi$
$569$	27.7062	+	33.0189i	1.16150	+	1.38423i	0.252417	+	0.967619i	$0.418775\pi$
$570$	−9.65566	−	7.01550i	−0.404431	−	0.293847i
$571$	8.94615	+	1.57745i	0.374385	+	0.0660141i	0.357675	−	0.933846i	$-0.383570\pi$
$571$	8.94615	+	1.57745i	0.374385	+	0.0660141i	0.0167100	+	0.999860i	$0.494681\pi$
$572$	32.3805	+	17.9681i	1.35390	+	0.751283i
$573$	0.270764	−	0.147087i	0.0113113	−	0.00614463i
$574$	−2.55768	+	9.88055i	−0.106756	+	0.412406i
$575$	−6.76632	−	11.7196i	−0.282175	−	0.488742i
$576$	8.22979	−	22.5449i	0.342908	−	0.939369i
$577$	−1.27460	+	2.20767i	−0.0530622	+	0.0919064i	−0.891336	−	0.453342i	$-0.850231\pi$
$577$	−1.27460	+	2.20767i	−0.0530622	+	0.0919064i	0.838274	+	0.545249i	$0.183565\pi$
$578$	−6.43740	−	6.32890i	−0.267761	−	0.263247i
$579$	4.42059	−	11.2292i	0.183714	−	0.466671i
$580$	0.114624	+	6.74257i	0.00475950	+	0.279970i
$581$	2.14972	−	2.56193i	0.0891853	−	0.106287i
$582$	0.219566	+	0.0629638i	0.00910132	+	0.00260993i
$583$	20.8128	−	57.1827i	0.861978	−	2.36827i
$584$	−14.4105	−	3.47005i	−0.596309	−	0.143592i
$585$	−8.59862	+	9.22866i	−0.355509	+	0.381558i
$586$	−8.26970	+	0.794383i	−0.341618	+	0.0328157i
$587$	0.223906	+	1.26984i	0.00924160	+	0.0524117i	0.989080	−	0.147381i	$-0.0470843\pi$
$587$	0.223906	+	1.26984i	0.00924160	+	0.0524117i	−0.979838	+	0.199793i	$0.935973\pi$
$588$	9.63627	−	7.93956i	0.397393	−	0.327422i
$589$	−0.720701	+	0.262314i	−0.0296959	+	0.0108084i
$590$	5.53360	+	3.80499i	0.227815	+	0.156649i
$591$	−8.94244	+	2.99419i	−0.367843	+	0.123164i
$592$	14.7100	+	23.5886i	0.604577	+	0.969487i
$593$			10.8961i			0.447448i	0.974652	+	0.223724i	$0.0718215\pi$
$593$			10.8961i			0.447448i	−0.974652	+	0.223724i	$0.928179\pi$
$594$	30.9535	+	25.0451i	1.27004	+	1.02761i
$595$		−	10.9638i		−	0.449472i
$596$	1.65722	−	10.4326i	0.0678823	−	0.427334i
$597$	7.77100	+	6.87229i	0.318046	+	0.281264i
$598$	−10.6292	+	15.4581i	−0.434661	+	0.632128i
$599$	−9.33315	+	3.39699i	−0.381342	+	0.138797i	−0.525576	−	0.850746i	$-0.676150\pi$
$599$	−9.33315	+	3.39699i	−0.381342	+	0.138797i	0.144234	+	0.989544i	$0.453928\pi$
$600$	4.42803	−	16.4944i	0.180773	−	0.673383i
$601$	−1.10305	−	6.25571i	−0.0449943	−	0.255176i	0.954011	−	0.299772i	$-0.0969108\pi$
$601$	−1.10305	−	6.25571i	−0.0449943	−	0.255176i	−0.999005	+	0.0445969i	$0.985800\pi$
$602$	−1.87900	−	19.5608i	−0.0765824	−	0.797239i
$603$	5.57516	−	2.84363i	0.227038	−	0.115802i
$604$	3.36960	+	17.3773i	0.137107	+	0.707071i
$605$	−7.72576	+	21.2263i	−0.314097	+	0.862974i
$606$	2.86800	−	0.715018i	0.116504	−	0.0290456i
$607$	20.0100	−	23.8470i	0.812182	−	0.967921i	−0.187715	−	0.982223i	$-0.560108\pi$
$607$	20.0100	−	23.8470i	0.812182	−	0.967921i	0.999898	+	0.0143022i	$0.00455270\pi$
$608$	−6.71207	−	21.3727i	−0.272211	−	0.866777i
$609$	−5.44630	−	6.84398i	−0.220695	−	0.277332i
$610$	−17.8924	+	18.1992i	−0.724443	+	0.736863i
$611$	−3.38182	+	5.85749i	−0.136814	+	0.236969i
$612$	−26.9008	−	10.8697i	−1.08740	−	0.439382i
$613$	5.32449	+	9.22228i	0.215054	+	0.372484i	0.953289	−	0.302059i	$-0.0976739\pi$
$613$	5.32449	+	9.22228i	0.215054	+	0.372484i	−0.738235	+	0.674543i	$0.764341\pi$
$614$	5.61700	+	1.45402i	0.226683	+	0.0586793i
$615$	−7.11728	−	4.35942i	−0.286997	−	0.175789i
$616$	−22.7130	+	16.7828i	−0.915134	+	0.676198i
$617$	12.1176	+	2.13666i	0.487835	+	0.0860185i	0.412155	−	0.911114i	$-0.364776\pi$
$617$	12.1176	+	2.13666i	0.487835	+	0.0860185i	0.0756800	+	0.997132i	$0.475887\pi$
$618$	−15.6789	−	35.2170i	−0.630697	−	1.41663i
$619$	−2.32369	−	2.76926i	−0.0933968	−	0.111306i	0.717322	−	0.696742i	$-0.245368\pi$
$619$	−2.32369	−	2.76926i	−0.0933968	−	0.111306i	−0.810719	+	0.585436i	$0.800923\pi$
$620$	0.312500	+	0.359820i	0.0125503	+	0.0144507i
$621$	−14.1288	+	14.3957i	−0.566969	+	0.577679i
$622$	4.63738	+	2.11465i	0.185942	+	0.0847897i
$623$	−23.1556	+	19.4298i	−0.927709	+	0.778440i
$624$	−23.2819	+	4.29819i	−0.932021	+	0.172065i
$625$	0.795955	−	4.51408i	0.0318382	−	0.180563i
$626$	−30.0556	−	2.37231i	−1.20126	−	0.0948165i
$627$	37.1529	+	0.965079i	1.48374	+	0.0385416i
$628$	12.4935	−	15.4138i	0.498544	−	0.615079i
$629$	29.1045	−	16.8035i	1.16047	−	0.669999i
$630$	−3.68286	−	8.88637i	−0.146729	−	0.354042i
$631$	0.363542	+	0.209891i	0.0144724	+	0.00835562i	0.507219	−	0.861817i	$-0.330674\pi$
$631$	0.363542	+	0.209891i	0.0144724	+	0.00835562i	−0.492746	+	0.870173i	$0.664007\pi$
$632$	22.3882	+	1.38466i	0.890555	+	0.0550786i
$633$	−6.65436	−	44.4615i	−0.264487	−	1.76719i
$634$	−44.8162	+	21.3637i	−1.77988	+	0.848461i
$635$	11.8070	+	9.90723i	0.468546	+	0.393156i
$636$	12.9776	+	36.6762i	0.514596	+	1.45431i
$637$	−11.5740	−	4.21261i	−0.458581	−	0.166910i
$638$	−12.1903	−	17.0984i	−0.482618	−	0.676930i
$639$	21.1584	−	15.9579i	0.837012	−	0.631285i
$640$	−10.9079	+	8.64826i	−0.431175	+	0.341852i
$641$	27.4445	−	4.83920i	1.08399	−	0.191137i	0.397012	−	0.917813i	$-0.370047\pi$
$641$	27.4445	−	4.83920i	1.08399	−	0.191137i	0.686980	+	0.726676i	$0.258936\pi$
$642$	−37.3489	+	2.61103i	−1.47404	+	0.103049i
$643$	9.89822	+	27.1951i	0.390348	+	1.07247i	0.966843	+	0.255371i	$0.0821977\pi$
$643$	9.89822	+	27.1951i	0.390348	+	1.07247i	−0.576495	+	0.817100i	$0.695580\pi$
$644$	−7.36280	−	12.2664i	−0.290135	−	0.483363i
$645$	15.7478	+	3.20048i	0.620069	+	0.126019i
$646$	−26.0985	+	7.23137i	−1.02683	+	0.284514i
$647$	20.3805			0.801241			0.400620	−	0.916244i	$-0.368795\pi$
$647$	20.3805			0.801241			0.400620	+	0.916244i	$0.368795\pi$
$648$	−25.4548	+	0.226145i	−0.999961	+	0.00888383i
$649$	−20.9118			−0.820860
$650$	−16.2357	+	4.49858i	−0.636817	+	0.176449i
$651$	−0.605751	−	0.123109i	−0.0237413	−	0.00482503i
$652$	−16.7681	−	27.9355i	−0.656689	−	1.09404i
$653$	14.1421	+	38.8551i	0.553424	+	1.52052i	0.829005	+	0.559241i	$0.188907\pi$
$653$	14.1421	+	38.8551i	0.553424	+	1.52052i	−0.275581	+	0.961278i	$0.588870\pi$
$654$	−30.3976	+	2.12507i	−1.18864	+	0.0830970i
$655$	−4.21236	+	0.742753i	−0.164591	+	0.0290218i
$656$	−5.85523	−	14.5302i	−0.228608	−	0.567310i
$657$	1.92252	+	15.6035i	0.0750046	+	0.608751i
$658$	−2.99433	−	4.19991i	−0.116731	−	0.163730i
$659$	−14.0070	−	5.09812i	−0.545634	−	0.198595i	0.0544714	−	0.998515i	$-0.482653\pi$
$659$	−14.0070	−	5.09812i	−0.545634	−	0.198595i	−0.600106	+	0.799921i	$0.704875\pi$
$660$	−7.70370	−	21.7715i	−0.299866	−	0.847455i
$661$	17.3934	+	14.5948i	0.676525	+	0.567672i	0.914989	−	0.403479i	$-0.132199\pi$
$661$	17.3934	+	14.5948i	0.676525	+	0.567672i	−0.238463	+	0.971151i	$0.576644\pi$
$662$	−0.304096	+	0.144962i	−0.0118190	+	0.00563409i
$663$	4.23644	+	28.3060i	0.164530	+	1.09932i
$664$	−0.316876	+	5.12350i	−0.0122972	+	0.198830i
$665$	−7.77584	−	4.48939i	−0.301534	−	0.174091i
$666$	17.9453	−	23.3960i	0.695365	−	0.906579i
$667$	9.21264	−	5.31892i	0.356715	−	0.205949i
$668$	1.56044	−	1.92519i	0.0603751	−	0.0744877i
$669$	−38.6992	−	1.00525i	−1.49620	−	0.0388651i
$670$	−3.61875	−	0.285630i	−0.139805	−	0.0110349i
$671$	13.8002	−	78.2651i	0.532752	−	3.02139i
$672$	4.38415	−	17.5147i	0.169122	−	0.675643i
$673$	−25.8262	+	21.6708i	−0.995527	+	0.835346i	−0.986358	−	0.164612i	$-0.947363\pi$
$673$	−25.8262	+	21.6708i	−0.995527	+	0.835346i	−0.00916851	+	0.999958i	$0.502918\pi$
$674$	8.62597	+	3.93345i	0.332260	+	0.151511i
$675$	−18.0300	+	1.74755i	−0.693973	+	0.0672631i
$676$	−1.73436	−	1.99698i	−0.0667060	−	0.0768071i
$677$	−21.5588	−	25.6927i	−0.828571	−	0.987452i	−0.999997	−	0.00225532i	$-0.999282\pi$
$677$	−21.5588	−	25.6927i	−0.828571	−	0.987452i	0.171427	−	0.985197i	$-0.445162\pi$
$678$	3.77667	+	8.48294i	0.145042	+	0.325785i
$679$	0.169225	+	0.0298390i	0.00649427	+	0.00114511i
$680$	10.0007	+	13.5345i	0.383509	+	0.519023i
$681$	−2.49807	−	1.53010i	−0.0957263	−	0.0586335i
$682$	−1.43668	−	0.371899i	−0.0550133	−	0.0142408i
$683$	−13.6418	−	23.6283i	−0.521989	−	0.904112i	−0.999673	−	0.0255798i	$-0.991857\pi$
$683$	−13.6418	−	23.6283i	−0.521989	−	0.904112i	0.477684	−	0.878532i	$-0.341477\pi$
$684$	−18.7243	+	14.6279i	−0.715940	+	0.559313i
$685$	−3.10989	+	5.38649i	−0.118823	+	0.205807i
$686$	19.3742	−	19.7063i	0.739710	−	0.752392i
$687$	28.6164	+	35.9603i	1.09179	+	1.37197i
$688$	20.1621	+	22.4333i	0.768672	+	0.855260i
$689$	24.6690	−	29.3994i	0.939816	−	1.12003i
$690$	11.3518	−	2.83012i	0.432157	−	0.107741i
$691$	−7.43220	+	20.4198i	−0.282734	+	0.776806i	0.714299	+	0.699840i	$0.246745\pi$
$691$	−7.43220	+	20.4198i	−0.282734	+	0.776806i	−0.997034	+	0.0769659i	$0.975477\pi$
$692$	5.49857	+	28.3566i	0.209024	+	1.07796i
$693$	25.1283	+	16.3035i	0.954545	+	0.619319i
$694$	−0.951115	−	9.90131i	−0.0361038	−	0.375849i
$695$	1.38392	+	7.84859i	0.0524950	+	0.297714i
$696$	12.9661	+	3.48081i	0.491477	+	0.131940i
$697$	−17.7962	+	6.47728i	−0.674079	+	0.245345i
$698$	5.70969	−	8.30361i	0.216115	−	0.314296i
$699$	−6.11501	−	5.40782i	−0.231291	−	0.204543i
$700$	2.01564	−	12.6889i	0.0761842	−	0.479596i
$701$			16.5491i			0.625051i	0.949909	+	0.312526i	$0.101175\pi$
$701$			16.5491i			0.625051i	−0.949909	+	0.312526i	$0.898825\pi$
$702$	12.9420	+	21.5195i	0.488465	+	0.812202i
$703$		−	27.5223i		−	1.03802i
$704$	12.7300	−	41.4356i	0.479780	−	1.56166i
$705$	3.99979	−	1.33924i	0.150641	−	0.0504389i
$706$	18.3301	+	12.6041i	0.689863	+	0.474361i
$707$	2.08952	−	0.760521i	0.0785843	−	0.0286023i
$708$	10.3183	−	8.50147i	0.387784	−	0.319505i
$709$	4.05285	+	22.9848i	0.152208	+	0.863214i	0.961294	+	0.275524i	$0.0888514\pi$
$709$	4.05285	+	22.9848i	0.152208	+	0.863214i	−0.809086	+	0.587690i	$0.800038\pi$
$710$	−15.3008	+	1.46979i	−0.574230	+	0.0551602i
$711$	−6.96556	−	22.7492i	−0.261229	−	0.853160i
$712$	10.8618	−	45.1070i	0.407063	−	1.69046i
$713$	0.257129	−	0.706456i	0.00962955	−	0.0264570i
$714$	−20.9813	−	6.01668i	−0.785204	−	0.225168i
$715$	−14.6439	+	17.4519i	−0.547651	+	0.652665i
$716$	0.339618	+	19.9775i	0.0126921	+	0.746593i
$717$	−2.13753	+	5.42979i	−0.0798277	+	0.202779i
$718$	−12.6797	−	12.4660i	−0.473204	−	0.465228i
$719$	−25.8381	+	44.7529i	−0.963599	+	1.66900i	−0.250265	+	0.968177i	$0.580518\pi$
$719$	−25.8381	+	44.7529i	−0.963599	+	1.66900i	−0.713334	+	0.700825i	$0.752816\pi$
$720$	12.6521	+	7.61061i	0.471517	+	0.283631i
$721$	−14.5003	−	25.1152i	−0.540018	−	0.935338i
$722$	1.17568	−	4.54177i	0.0437545	−	0.169027i
$723$	24.3016	−	13.2013i	0.903788	−	0.490963i
$724$	−20.7373	−	11.5072i	−0.770694	−	0.427661i
$725$	9.40824	+	1.65893i	0.349413	+	0.0616110i
$726$	36.3808	+	26.4332i	1.35022	+	0.981028i
$727$	7.38738	+	8.80393i	0.273983	+	0.326520i	0.885437	−	0.464760i	$-0.153859\pi$
$727$	7.38738	+	8.80393i	0.273983	+	0.326520i	−0.611454	+	0.791280i	$0.709415\pi$
$728$	−17.0808	+	5.04688i	−0.633056	+	0.187050i
$729$	9.70767	+	25.1945i	0.359543	+	0.933128i
$730$	3.78335	−	8.29679i	0.140028	−	0.307078i
$731$	27.9326	−	23.4382i	1.03312	−	0.866894i
$732$	25.0086	+	44.2277i	0.924343	+	1.63470i
$733$	4.49588	−	25.4974i	0.166059	−	0.941768i	−0.781906	−	0.623396i	$-0.785753\pi$
$733$	4.49588	−	25.4974i	0.166059	−	0.941768i	0.947966	−	0.318373i	$-0.103136\pi$
$734$	2.42899	−	30.7737i	0.0896556	−	1.13588i
$735$	3.66657	+	6.74961i	0.135244	+	0.248963i
$736$	20.2780	+	8.42645i	0.747457	+	0.310603i
$737$	9.78921	−	5.65181i	0.360590	−	0.208187i
$738$	−12.2484	+	11.2279i	−0.450868	+	0.413304i
$739$	−27.0700	−	15.6289i	−0.995786	−	0.574917i	−0.0887874	−	0.996051i	$-0.528299\pi$
$739$	−27.0700	−	15.6289i	−0.995786	−	0.574917i	−0.906999	+	0.421133i	$0.861633\pi$
$740$	−15.9690	+	6.12159i	−0.587032	+	0.225034i
$741$	21.8102	+	8.58596i	0.801216	+	0.315413i
$742$	12.5940	+	26.4194i	0.462341	+	0.969887i
$743$	−36.0136	−	30.2190i	−1.32121	−	1.10863i	−0.986047	−	0.166470i	$-0.946763\pi$
$743$	−36.0136	−	30.2190i	−1.32121	−	1.10863i	−0.335166	−	0.942159i	$-0.608792\pi$
$744$	0.860076	−	0.400565i	0.0315319	−	0.0146854i
$745$	6.10664	+	2.22264i	0.223730	+	0.0814311i
$746$	17.4264	−	12.4241i	0.638025	−	0.454880i
$747$	5.20610	−	1.59406i	0.190481	−	0.0583234i
$748$	−49.5399	−	17.0832i	−1.81136	−	0.624622i
$749$	−27.7380	+	4.89095i	−1.01352	+	0.178711i
$750$	22.9872	+	11.2121i	0.839374	+	0.409408i
$751$	−3.24256	−	8.90885i	−0.118323	−	0.325089i	0.866366	−	0.499409i	$-0.166449\pi$
$751$	−3.24256	−	8.90885i	−0.118323	−	0.325089i	−0.984689	+	0.174320i	$0.944227\pi$
$752$	7.52738	+	2.45337i	0.274495	+	0.0894650i
$753$	9.30195	+	27.7812i	0.338982	+	1.01240i
$754$	−3.53628	−	12.7627i	−0.128784	−	0.464789i
$755$	−10.8896			−0.396313
$756$	−19.0268	+	2.17120i	−0.691997	+	0.0789657i
$757$	−46.0979			−1.67546			−0.837728	−	0.546087i	$-0.816117\pi$
$757$	−46.0979			−1.67546			−0.837728	+	0.546087i	$0.816117\pi$
$758$	9.75636	+	35.2114i	0.354367	+	1.27894i
$759$	−24.1341	+	27.2902i	−0.876012	+	0.990571i
$760$	13.6941	−	1.55078i	0.496736	−	0.0562526i
$761$	−1.59797	−	4.39038i	−0.0579263	−	0.159151i	0.907354	−	0.420367i	$-0.138099\pi$
$761$	−1.59797	−	4.39038i	−0.0579263	−	0.159151i	−0.965280	+	0.261216i	$0.915876\pi$
$762$	25.4387	−	17.1580i	0.921547	−	0.621568i
$763$	−22.5755	+	3.98067i	−0.817288	+	0.144110i
$764$	−0.115992	+	0.336367i	−0.00419644	+	0.0121693i
$765$	9.71510	−	14.9737i	0.351250	−	0.541376i
$766$	−5.35955	+	3.82109i	−0.193649	+	0.138062i
$767$	−12.3932	−	4.51075i	−0.447492	−	0.162874i
$768$	10.5640	+	25.6203i	0.381196	+	0.924494i
$769$	18.4826	+	15.5088i	0.666501	+	0.559261i	0.912028	−	0.410129i	$-0.134516\pi$
$769$	18.4826	+	15.5088i	0.666501	+	0.559261i	−0.245526	+	0.969390i	$0.578961\pi$
$770$	−7.47599	−	15.6829i	−0.269416	−	0.565173i
$771$	3.95884	−	3.15036i	0.142574	−	0.113457i
$772$	4.98793	+	13.0117i	0.179519	+	0.468301i
$773$	−37.2078	−	21.4820i	−1.33827	−	0.772652i	−0.351722	−	0.936105i	$-0.614404\pi$
$773$	−37.2078	−	21.4820i	−1.33827	−	0.772652i	−0.986551	+	0.163452i	$0.947737\pi$
$774$	14.7667	−	28.3800i	0.530780	−	1.02010i
$775$	0.584701	−	0.337577i	0.0210031	−	0.0121261i
$776$	−0.236121	+	0.117524i	−0.00847625	+	0.00421888i
$777$	11.5860	−	18.9156i	0.415647	−	0.678594i
$778$	−3.17516	+	40.2273i	−0.113835	+	1.44222i
$779$	−2.69319	+	15.2738i	−0.0964935	+	0.547242i
$780$	0.130670	−	14.5644i	0.00467873	−	0.521490i
$781$	36.6668	−	30.7671i	1.31204	−	1.10093i
$782$	11.0142	−	24.1538i	0.393866	−	0.863739i
$783$	−1.37372	−	14.1731i	−0.0490929	−	0.506506i
$784$	−2.01949	+	14.2752i	−0.0721247	+	0.509828i
$785$	7.84603	+	9.35054i	0.280037	+	0.333735i
$786$	−0.890251	+	8.46874i	−0.0317542	+	0.302070i
$787$	19.5797	+	3.45243i	0.697940	+	0.123066i	0.511350	−	0.859372i	$-0.329145\pi$
$787$	19.5797	+	3.45243i	0.697940	+	0.123066i	0.186590	+	0.982438i	$0.440257\pi$
$788$	5.28356	−	9.52158i	0.188219	−	0.339192i
$789$	0.000840968	−	0.0323749i	2.99392e−5	−	0.00115258i
$790$	−3.45816	+	13.3592i	−0.123036	+	0.475298i
$791$	3.49277	+	6.04966i	0.124189	+	0.215101i
$792$	−45.8914	+	2.79475i	−1.63068	+	0.0993071i
$793$	25.0606	−	43.4063i	0.889930	−	1.54140i
$794$	1.98369	+	1.95025i	0.0703985	+	0.0692119i
$795$	−23.6703	+	3.54264i	−0.839501	+	0.125644i
$796$	−11.9770	+	0.203609i	−0.424512	+	0.00721673i
$797$	0.657198	−	0.783218i	0.0232792	−	0.0277430i	−0.754279	−	0.656554i	$-0.772014\pi$
$797$	0.657198	−	0.783218i	0.0232792	−	0.0277430i	0.777558	+	0.628811i	$0.216458\pi$
$798$	−12.8585	+	12.4168i	−0.455185	+	0.439552i
$799$	3.27349	−	8.99384i	0.115808	−	0.318179i
$800$	9.08602	+	17.5027i	0.321239	+	0.618812i
$801$	−48.8414	+	6.01779i	−1.72573	+	0.212628i
$802$	26.7952	−	2.57394i	0.946172	−	0.0908888i
$803$	4.93074	+	27.9636i	0.174002	+	0.986815i
$804$	−2.53249	+	6.76841i	−0.0893142	+	0.238703i
$805$	8.27052	−	3.01022i	0.291498	−	0.106096i
$806$	−0.771215	−	0.530300i	−0.0271649	−	0.0186790i
$807$	5.56515	−	27.3830i	0.195903	−	0.963928i
$808$	−1.88573	+	2.84480i	−0.0663396	+	0.100080i
$809$			7.34131i			0.258107i	0.991638	+	0.129053i	$0.0411938\pi$
$809$			7.34131i			0.258107i	−0.991638	+	0.129053i	$0.958806\pi$
$810$	2.84445	−	15.3999i	0.0999438	−	0.541097i
$811$			51.3514i			1.80319i	0.432581	+	0.901595i	$0.357603\pi$
$811$			51.3514i			1.80319i	−0.432581	+	0.901595i	$0.642397\pi$
$812$	9.97459	+	1.58447i	0.350039	+	0.0556040i
$813$	7.89294	−	38.8368i	0.276818	−	1.36207i
$814$	30.1739	−	43.8819i	1.05759	−	1.53806i
$815$	18.8353	−	6.85550i	0.659773	−	0.240138i
$816$	31.3889	−	11.7108i	1.09883	−	0.409959i
$817$	−5.18541	−	29.4079i	−0.181415	−	1.02885i
$818$	1.98346	+	20.6482i	0.0693499	+	0.721947i
$819$	11.3753	+	15.0824i	0.397486	+	0.527022i
$820$	9.46122	−	1.83461i	0.330400	−	0.0640673i
$821$	−11.7882	+	32.3878i	−0.411411	+	1.13034i	0.545030	+	0.838416i	$0.316518\pi$
$821$	−11.7882	+	32.3878i	−0.411411	+	1.13034i	−0.956441	+	0.291926i	$0.905704\pi$
$822$	8.60141	+	8.90733i	0.300009	+	0.310679i
$823$	−30.1050	+	35.8777i	−1.04939	+	1.25062i	−0.0821894	+	0.996617i	$0.526191\pi$
$823$	−30.1050	+	35.8777i	−1.04939	+	1.25062i	−0.967204	+	0.254001i	$0.918253\pi$
$824$	40.8091	+	17.7774i	1.42165	+	0.619305i
$825$	−32.3566	+	4.84267i	−1.12651	+	0.168600i
$826$	7.05119	−	7.17208i	0.245342	−	0.249548i
$827$	−19.3141	+	33.4530i	−0.671616	+	1.16327i	0.305830	+	0.952086i	$0.401066\pi$
$827$	−19.3141	+	33.4530i	−0.671616	+	1.16327i	−0.977446	+	0.211187i	$0.932267\pi$
$828$	0.813666	−	23.2769i	0.0282768	−	0.808929i
$829$	13.2958	+	23.0290i	0.461782	+	0.799830i	0.999050	−	0.0435815i	$-0.0138768\pi$
$829$	13.2958	+	23.0290i	0.461782	+	0.799830i	−0.537268	+	0.843412i	$0.680543\pi$
$830$	−3.05722	−	0.791393i	−0.106118	−	0.0274696i
$831$	0.309296	−	11.9070i	0.0107294	−	0.413051i
$832$	16.4821	−	21.8105i	0.571415	−	0.756145i
$833$	17.1644	+	3.02655i	0.594712	+	0.104864i
$834$	15.7792	+	1.65874i	0.546388	+	0.0574374i
$835$	0.979970	+	1.16788i	0.0339132	+	0.0404162i
$836$	−32.4011	+	28.1400i	−1.12062	+	0.973243i
$837$	−0.718211	−	0.704896i	−0.0248250	−	0.0243648i
$838$	−14.9011	−	6.79491i	−0.514749	−	0.234726i
$839$	38.1735	−	32.0314i	1.31790	−	1.10585i	0.331150	−	0.943578i	$-0.392563\pi$
$839$	38.1735	−	32.0314i	1.31790	−	1.10585i	0.986747	−	0.162268i	$-0.0518811\pi$
$840$	10.0645	+	4.69895i	0.347259	+	0.162129i
$841$	3.73174	−	21.1637i	0.128681	−	0.729784i
$842$	−1.74971	−	0.138105i	−0.0602988	−	0.00475942i
$843$	−12.8276	+	20.9426i	−0.441805	+	0.721300i
$844$	40.3280	+	32.6873i	1.38815	+	1.12514i
$845$	1.40919	−	0.813594i	0.0484775	−	0.0279885i
$846$	−0.367901	−	8.38928i	−0.0126487	−	0.288430i
$847$	29.2980	+	16.9152i	1.00669	+	0.581214i
$848$	−39.6455	−	21.1262i	−1.36143	−	0.725476i
$849$	16.3767	−	13.0322i	0.562046	−	0.447264i
$850$	21.5202	−	10.2586i	0.738138	−	0.351868i
$851$	20.6666	+	17.3413i	0.708442	+	0.594453i
$852$	−5.58402	+	30.0875i	−0.191305	+	1.03078i
$853$	−34.7953	−	12.6644i	−1.19137	−	0.433622i	−0.331164	−	0.943573i	$-0.607441\pi$
$853$	−34.7953	−	12.6644i	−1.19137	−	0.433622i	−0.860203	+	0.509951i	$0.829664\pi$
$854$	22.1891	+	31.1230i	0.759297	+	1.06501i
$855$	−6.64171	−	13.0216i	−0.227142	−	0.445328i
$856$	29.7803	−	31.3391i	1.01787	−	1.07115i
$857$	−30.2150	+	5.32771i	−1.03212	+	0.181991i	−0.663959	−	0.747769i	$-0.731125\pi$
$857$	−30.2150	+	5.32771i	−1.03212	+	0.181991i	−0.368165	+	0.929761i	$0.620014\pi$
$858$	25.3612	+	37.6010i	0.865818	+	1.28368i
$859$	6.72321	+	18.4719i	0.229393	+	0.630252i	0.999975	−	0.00708895i	$-0.00225650\pi$
$859$	6.72321	+	18.4719i	0.229393	+	0.630252i	−0.770582	+	0.637341i	$0.780034\pi$
$860$	−15.9097	+	9.54967i	−0.542517	+	0.325641i
$861$	−8.28080	+	9.36370i	−0.282209	+	0.319114i
$862$	−46.1311	+	12.7820i	−1.57123	+	0.435356i
$863$	5.14051			0.174985			0.0874925	−	0.996165i	$-0.472115\pi$
$863$	5.14051			0.174985			0.0874925	+	0.996165i	$0.472115\pi$
$864$	21.5075	−	20.0357i	0.731700	−	0.681627i
$865$	−17.7698			−0.604193
$866$	−29.5806	+	8.19618i	−1.00519	+	0.278518i
$867$	−3.51043	−	10.4843i	−0.119220	−	0.356064i
$868$	0.611979	−	0.367335i	0.0207719	−	0.0124682i
$869$	−14.6969	−	40.3793i	−0.498557	−	1.36977i
$870$	−3.62069	+	7.42319i	−0.122753	+	0.251670i
$871$	7.02060	−	1.23792i	0.237884	−	0.0419454i
$872$	24.2377	−	25.5064i	0.820794	−	0.863755i
$873$	0.204677	+	0.190704i	0.00692727	+	0.00645435i
$874$	−12.6206	−	17.7019i	−0.426898	−	0.598776i
$875$	18.0802	+	6.58065i	0.611222	+	0.222467i
$876$	−13.8012	−	11.7932i	−0.466301	−	0.398456i
$877$	39.7096	+	33.3203i	1.34090	+	1.12515i	0.981394	+	0.192004i	$0.0614986\pi$
$877$	39.7096	+	33.3203i	1.34090	+	1.12515i	0.359504	+	0.933143i	$0.382946\pi$
$878$	−47.7382	+	22.7566i	−1.61109	+	0.767999i
$879$	−9.46768	−	3.72712i	−0.319337	−	0.125713i
$880$	23.5342	+	12.5408i	0.793336	+	0.422751i
$881$	−28.7442	−	16.5955i	−0.968418	−	0.559116i	−0.0696643	−	0.997570i	$-0.522193\pi$
$881$	−28.7442	−	16.5955i	−0.968418	−	0.559116i	−0.898754	+	0.438454i	$0.855526\pi$
$882$	14.9288	−	3.31264i	0.502677	−	0.111542i
$883$	31.2856	−	18.0627i	1.05284	−	0.607859i	0.129399	−	0.991593i	$-0.458695\pi$
$883$	31.2856	−	18.0627i	1.05284	−	0.607859i	0.923444	+	0.383733i	$0.125362\pi$
$884$	−25.6745	−	20.8101i	−0.863525	−	0.699920i
$885$	3.92607	+	7.22731i	0.131973	+	0.242943i
$886$	−8.66760	−	0.684138i	−0.291194	−	0.0229841i
$887$	−4.04900	+	22.9630i	−0.135952	+	0.771023i	0.838240	+	0.545302i	$0.183585\pi$
$887$	−4.04900	+	22.9630i	−0.135952	+	0.771023i	−0.974192	+	0.225721i	$0.927526\pi$
$888$	2.95138	+	33.9190i	0.0990420	+	1.13825i
$889$	17.6830	−	14.8378i	0.593070	−	0.497645i
$890$	25.9703	+	11.8425i	0.870525	+	0.396960i
$891$	19.8721	+	44.5327i	0.665739	+	1.49190i
$892$	33.7497	−	29.3112i	1.13002	−	0.981412i
$893$	−5.03828	−	6.00439i	−0.168600	−	0.200929i
$894$	7.60461	−	10.4665i	0.254336	−	0.350051i
$895$	−12.1051	−	2.13446i	−0.404630	−	0.0713472i
$896$	9.91870	+	18.3375i	0.331361	+	0.612614i
$897$	−20.1894	+	10.9675i	−0.674106	+	0.366193i
$898$	−6.81008	−	1.76286i	−0.227255	−	0.0588273i
$899$	0.265365	+	0.459625i	0.00885041	+	0.0153294i
$900$	13.9966	−	15.5437i	0.466553	−	0.518123i
$901$	−27.1540	+	47.0321i	−0.904630	+	1.56687i
$902$	−21.0394	+	21.4001i	−0.700536	+	0.712547i
$903$	8.81599	−	22.3945i	0.293378	−	0.745241i
$904$	−9.82994	−	4.28216i	−0.326939	−	0.142422i
$905$	9.37829	−	11.1766i	0.311745	−	0.371523i
$906$	−5.97595	+	20.8392i	−0.198538	+	0.692337i
$907$	4.67374	−	12.8410i	0.155189	−	0.426379i	−0.837595	−	0.546291i	$-0.816039\pi$
$907$	4.67374	−	12.8410i	0.155189	−	0.426379i	0.992784	+	0.119913i	$0.0382614\pi$
$908$	3.32076	−	0.643923i	0.110203	−	0.0213693i
$909$	3.52764	+	0.812860i	0.117004	+	0.0269609i
$910$	−1.04772	−	10.9069i	−0.0347314	−	0.361562i
$911$	−4.68110	−	26.5479i	−0.155092	−	0.879570i	−0.958702	−	0.284413i	$-0.908201\pi$
$911$	−4.68110	−	26.5479i	−0.155092	−	0.879570i	0.803610	−	0.595156i	$-0.202910\pi$
$912$	4.54728	−	27.0571i	0.150575	−	0.895951i
$913$	9.24072	−	3.36335i	0.305823	−	0.111311i
$914$	−8.51922	+	12.3895i	−0.281791	+	0.409808i
$915$	−29.6400	+	9.92433i	−0.979869	+	0.328088i
$916$	−52.4094	−	8.32528i	−1.73166	−	0.275075i
$917$			6.40608i			0.211547i
$918$	−23.3235	−	26.8089i	−0.769791	−	0.884824i
$919$			10.8263i			0.357127i	0.983928	+	0.178563i	$0.0571449\pi$
$919$			10.8263i			0.357127i	−0.983928	+	0.178563i	$0.942855\pi$
$920$	−7.46391	+	11.2600i	−0.246078	+	0.371232i
$921$	5.32317	+	4.70755i	0.175404	+	0.155119i
$922$	16.7334	+	11.5061i	0.551084	+	0.378934i
$923$	28.3668	−	10.3247i	0.933705	−	0.339841i
$924$	−34.1148	+	5.70027i	−1.12230	+	0.187525i
$925$	4.20716	+	23.8600i	0.138331	+	0.784512i
$926$	25.6946	−	2.46821i	0.844377	−	0.0811105i
$927$	2.45116	−	47.1496i	0.0805066	−	1.54860i
$928$	−13.7586	+	7.14240i	−0.451648	+	0.234461i
$929$	5.88119	−	16.1584i	0.192956	−	0.530141i	−0.805054	−	0.593201i	$-0.797864\pi$
$929$	5.88119	−	16.1584i	0.192956	−	0.530141i	0.998010	+	0.0630604i	$0.0200861\pi$
$930$	0.141197	+	0.566351i	0.00463002	+	0.0185714i
$931$	9.17490	−	10.9342i	0.300695	−	0.358355i
$932$	9.42470	−	0.160220i	0.308716	−	0.00524819i
$933$	3.88691	+	4.88441i	0.127252	+	0.159908i
$934$	23.1469	+	22.7567i	0.757389	+	0.744622i
$935$	16.1190	−	27.9189i	0.527147	−	0.913046i
$936$	−27.8000	−	8.24267i	−0.908671	−	0.269420i
$937$	9.74943	+	16.8865i	0.318500	+	0.551658i	0.980175	−	0.198132i	$-0.0634876\pi$
$937$	9.74943	+	16.8865i	0.318500	+	0.551658i	−0.661675	+	0.749791i	$0.730154\pi$
$938$	−1.36241	+	5.26310i	−0.0444842	+	0.171846i
$939$	−31.4878	−	19.2866i	−1.02756	−	0.629396i
$940$	−2.36324	+	4.25883i	−0.0770804	+	0.138908i
$941$	−2.10956	−	0.371973i	−0.0687698	−	0.0121260i	0.139157	−	0.990270i	$-0.455561\pi$
$941$	−2.10956	−	0.371973i	−0.0687698	−	0.0121260i	−0.207927	+	0.978144i	$0.566672\pi$
$942$	22.1997	−	9.88348i	0.723305	−	0.322021i
$943$	−9.77225	−	11.6461i	−0.318228	−	0.379250i
$944$	−2.16242	+	15.2855i	−0.0703807	+	0.497500i
$945$	0.916946	−	11.7455i	0.0298283	−	0.382080i
$946$	23.9735	−	52.5733i	0.779446	−	1.70931i
$947$	−32.2731	+	27.0803i	−1.04873	+	0.879992i	−0.992960	−	0.118452i	$-0.962207\pi$
$947$	−32.2731	+	27.0803i	−1.04873	+	0.879992i	−0.0557737	+	0.998443i	$0.517763\pi$
$948$	23.6675	+	13.9490i	0.768684	+	0.453043i
$949$	−3.10970	+	17.6360i	−0.100945	+	0.572488i
$950$	1.53626	−	19.4634i	0.0498428	−	0.631476i
$951$	−60.7853	−	1.57895i	−1.97110	−	0.0512010i
$952$	22.5632	−	11.2304i	0.731277	−	0.363978i
$953$	19.8498	−	11.4603i	0.642999	−	0.371236i	−0.142770	−	0.989756i	$-0.545601\pi$
$953$	19.8498	−	11.4603i	0.642999	−	0.371236i	0.785769	+	0.618520i	$0.212268\pi$
$954$	−6.21024	+	47.2417i	−0.201064	+	1.52951i
$955$	−0.189565	−	0.109445i	−0.00613417	−	0.00354156i
$956$	−2.41186	−	6.29167i	−0.0780053	−	0.203487i
$957$	−3.80676	−	25.4351i	−0.123055	−	0.822199i
$958$	−10.7020	−	22.4504i	−0.345766	−	0.725339i
$959$	7.13588	+	5.98771i	0.230430	+	0.193353i
$960$	−16.7105	+	3.37970i	−0.539329	+	0.109079i
$961$	−29.0952	−	10.5898i	−0.938556	−	0.341606i
$962$	27.3478	−	19.4976i	0.881728	−	0.628628i
$963$	−42.2168	−	17.8990i	−1.36042	−	0.576789i
$964$	−10.4105	+	30.1897i	−0.335299	+	0.972343i
$965$	−8.44252	+	1.48864i	−0.271774	+	0.0479212i
$966$	−1.22195	−	17.4791i	−0.0393156	−	0.562381i
$967$	−14.1549	−	38.8902i	−0.455190	−	1.25062i	−0.929027	−	0.370012i	$-0.879354\pi$
$967$	−14.1549	−	38.8902i	−0.455190	−	1.25062i	0.473837	−	0.880613i	$-0.342869\pi$
$968$	−51.5968	+	5.84305i	−1.65838	+	0.187803i
$969$	−32.5039	−	6.60588i	−1.04417	−	0.212211i
$970$	−0.0433264	−	0.156368i	−0.00139113	−	0.00502068i
$971$	14.7098			0.472061			0.236030	−	0.971746i	$-0.424153\pi$
$971$	14.7098			0.472061			0.236030	+	0.971746i	$0.424153\pi$
$972$	−27.9096	−	13.8945i	−0.895200	−	0.445666i
$973$	11.9360			0.382650
$974$	−5.91793	−	21.3582i	−0.189623	−	0.684362i
$975$	−20.2204	−	4.10947i	−0.647572	−	0.131608i
$976$	−55.7808	−	18.1804i	−1.78550	−	0.581941i
$977$	−11.1196	−	30.5509i	−0.355748	−	0.977409i	−0.980488	−	0.196577i	$-0.937017\pi$
$977$	−11.1196	−	30.5509i	−0.355748	−	0.977409i	0.624741	−	0.780832i	$-0.285205\pi$
$978$	−2.78288	−	39.8070i	−0.0889866	−	1.27289i
$979$	−87.5305	+	15.4340i	−2.79749	+	0.493273i
$980$	−8.38496	−	2.89144i	−0.267848	−	0.0923637i
$981$	−34.3596	−	14.5677i	−1.09702	−	0.465112i
$982$	46.0779	−	32.8513i	1.47041	−	1.04833i
$983$	49.0400	+	17.8491i	1.56413	+	0.569298i	0.971679	−	0.236306i	$-0.0759367\pi$
$983$	49.0400	+	17.8491i	1.56413	+	0.569298i	0.592455	+	0.805604i	$0.298159\pi$
$984$	1.68123	−	19.1126i	0.0535957	−	0.609287i
$985$	5.13178	+	4.30607i	0.163512	+	0.137203i
$986$	8.06417	+	16.9168i	0.256815	+	0.538740i
$987$	−0.935063	−	6.24768i	−0.0297634	−	0.198866i
$988$	−25.2721	+	9.68788i	−0.804014	+	0.308212i
$989$	25.3498	+	14.6357i	0.806075	+	0.465388i
$990$	3.68649	−	28.0433i	0.117164	−	0.891276i
$991$	−17.1645	+	9.90990i	−0.545247	+	0.314798i	−0.747203	−	0.664596i	$-0.768604\pi$
$991$	−17.1645	+	9.90990i	−0.545247	+	0.314798i	0.201956	+	0.979395i	$0.435270\pi$
$992$	−0.420402	+	1.01168i	−0.0133478	+	0.0321210i
$993$	−0.412453	−	0.0107138i	−0.0130888	−	0.000339993i
$994$	−1.81144	+	22.9498i	−0.0574554	+	0.727923i
$995$	1.27966	−	7.25731i	0.0405679	−	0.230072i
$996$	−3.19221	+	5.41626i	−0.101149	+	0.171621i
$997$	1.62058	−	1.35983i	0.0513244	−	0.0430663i	−0.616765	−	0.787148i	$-0.711557\pi$
$997$	1.62058	−	1.35983i	0.0513244	−	0.0430663i	0.668089	+	0.744081i	$0.267113\pi$
$998$	−12.1749	+	26.6992i	−0.385389	+	0.845149i
$999$	32.5848	−	15.5673i	1.03094	−	0.492529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.l.a.59.2	yes	96
3.2	odd	2		324.2.l.a.287.15		96
4.3	odd	2	inner	108.2.l.a.59.12	yes	96
9.2	odd	6		972.2.l.b.539.4		96
9.4	even	3		972.2.l.d.215.9		96
9.5	odd	6		972.2.l.a.215.8		96
9.7	even	3		972.2.l.c.539.13		96
12.11	even	2		324.2.l.a.287.5		96
27.2	odd	18		972.2.l.c.431.1		96
27.7	even	9		972.2.l.a.755.6		96
27.11	odd	18	inner	108.2.l.a.11.12	yes	96
27.16	even	9		324.2.l.a.35.5		96
27.20	odd	18		972.2.l.d.755.11		96
27.25	even	9		972.2.l.b.431.16		96
36.7	odd	6		972.2.l.c.539.1		96
36.11	even	6		972.2.l.b.539.16		96
36.23	even	6		972.2.l.a.215.6		96
36.31	odd	6		972.2.l.d.215.11		96
108.7	odd	18		972.2.l.a.755.8		96
108.11	even	18	inner	108.2.l.a.11.2	✓	96
108.43	odd	18		324.2.l.a.35.15		96
108.47	even	18		972.2.l.d.755.9		96
108.79	odd	18		972.2.l.b.431.4		96
108.83	even	18		972.2.l.c.431.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.2	✓	96	108.11	even	18	inner
108.2.l.a.11.12	yes	96	27.11	odd	18	inner
108.2.l.a.59.2	yes	96	1.1	even	1	trivial
108.2.l.a.59.12	yes	96	4.3	odd	2	inner
324.2.l.a.35.5		96	27.16	even	9
324.2.l.a.35.15		96	108.43	odd	18
324.2.l.a.287.5		96	12.11	even	2
324.2.l.a.287.15		96	3.2	odd	2
972.2.l.a.215.6		96	36.23	even	6
972.2.l.a.215.8		96	9.5	odd	6
972.2.l.a.755.6		96	27.7	even	9
972.2.l.a.755.8		96	108.7	odd	18
972.2.l.b.431.4		96	108.79	odd	18
972.2.l.b.431.16		96	27.25	even	9
972.2.l.b.539.4		96	9.2	odd	6
972.2.l.b.539.16		96	36.11	even	6
972.2.l.c.431.1		96	27.2	odd	18
972.2.l.c.431.13		96	108.83	even	18
972.2.l.c.539.1		96	36.7	odd	6
972.2.l.c.539.13		96	9.7	even	3
972.2.l.d.215.9		96	9.4	even	3
972.2.l.d.215.11		96	36.31	odd	6
972.2.l.d.755.9		96	108.47	even	18
972.2.l.d.755.11		96	27.20	odd	18

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36287 + 0.377622i) q^{2} +(-1.69735 - 0.344959i) q^{3} +(1.71480 - 1.02930i) q^{4} +(0.420820 + 1.15619i) q^{5} +(2.44353 - 0.170825i) q^{6} +(1.81474 - 0.319988i) q^{7} +(-1.94836 + 2.05034i) q^{8} +(2.76201 + 1.17103i) q^{9} +O(q^{10})\)	\(q+(-1.36287 + 0.377622i) q^{2} +(-1.69735 - 0.344959i) q^{3} +(1.71480 - 1.02930i) q^{4} +(0.420820 + 1.15619i) q^{5} +(2.44353 - 0.170825i) q^{6} +(1.81474 - 0.319988i) q^{7} +(-1.94836 + 2.05034i) q^{8} +(2.76201 + 1.17103i) q^{9} +(-1.01013 - 1.41682i) q^{10} +(5.09161 + 1.85319i) q^{11} +(-3.26569 + 1.15554i) q^{12} +(2.61776 + 2.19656i) q^{13} +(-2.35241 + 1.12139i) q^{14} +(-0.315440 - 2.10763i) q^{15} +(1.88110 - 3.53008i) q^{16} +(-4.18778 - 2.41782i) q^{17} +(-4.20645 - 0.552967i) q^{18} +(-3.42957 + 1.98006i) q^{19} +(1.91169 + 1.54950i) q^{20} +(-3.19063 - 0.0828795i) q^{21} +(-7.63898 - 0.602949i) q^{22} +(0.674078 - 3.82288i) q^{23} +(4.01434 - 2.80804i) q^{24} +(2.67053 - 2.24084i) q^{25} +(-4.39712 - 2.00509i) q^{26} +(-4.28414 - 2.94044i) q^{27} +(2.78256 - 2.41662i) q^{28} +(1.76149 + 2.09927i) q^{29} +(1.22579 + 2.75330i) q^{30} +(0.190727 + 0.0336302i) q^{31} +(-1.23065 + 5.52137i) q^{32} +(-8.00298 - 4.90192i) q^{33} +(6.62041 + 1.71376i) q^{34} +(1.13365 + 1.96353i) q^{35} +(5.94164 - 0.834830i) q^{36} +(-3.47493 + 6.01875i) q^{37} +(3.92633 - 3.99364i) q^{38} +(-3.68553 - 4.63135i) q^{39} +(-3.19050 - 1.38986i) q^{40} +(2.51742 - 3.00014i) q^{41} +(4.37970 - 1.09190i) q^{42} +(-2.57902 + 7.08581i) q^{43} +(10.6386 - 2.06291i) q^{44} +(-0.191634 + 3.68621i) q^{45} +(0.524929 + 5.46462i) q^{46} +(0.343697 + 1.94920i) q^{47} +(-4.41062 + 5.34289i) q^{48} +(-3.38696 + 1.23275i) q^{49} +(-2.79338 + 4.06241i) q^{50} +(6.27409 + 5.54850i) q^{51} +(6.74984 + 1.07222i) q^{52} -11.2308i q^{53} +(6.94908 + 2.38963i) q^{54} +6.66675i q^{55} +(-2.87968 + 4.34428i) q^{56} +(6.50423 - 2.17780i) q^{57} +(-3.19341 - 2.19584i) q^{58} +(-3.62667 + 1.32000i) q^{59} +(-2.71030 - 3.28949i) q^{60} +(-2.54693 - 14.4444i) q^{61} +(-0.272634 + 0.0261891i) q^{62} +(5.38704 + 1.24131i) q^{63} +(-0.407785 - 7.98960i) q^{64} +(-1.43804 + 3.95099i) q^{65} +(12.7581 + 3.65855i) q^{66} +(1.34096 - 1.59809i) q^{67} +(-9.66988 + 0.164388i) q^{68} +(-2.46289 + 6.25625i) q^{69} +(-2.28648 - 2.24794i) q^{70} +(4.41692 - 7.65033i) q^{71} +(-7.78240 + 3.38146i) q^{72} +(2.62025 + 4.53841i) q^{73} +(2.46304 - 9.51495i) q^{74} +(-5.30582 + 2.88227i) q^{75} +(-3.84297 + 6.92547i) q^{76} +(9.83294 + 1.73381i) q^{77} +(6.77178 + 4.92017i) q^{78} +(-5.09766 - 6.07516i) q^{79} +(4.87306 + 0.689385i) q^{80} +(6.25736 + 6.46881i) q^{81} +(-2.29798 + 5.03942i) q^{82} +(1.39029 - 1.16659i) q^{83} +(-5.55662 + 3.14199i) q^{84} +(1.03316 - 5.85935i) q^{85} +(0.839103 - 10.6309i) q^{86} +(-2.26571 - 4.17084i) q^{87} +(-13.7200 + 6.82884i) q^{88} +(-14.2059 + 8.20179i) q^{89} +(-1.13082 - 5.09617i) q^{90} +(5.45341 + 3.14853i) q^{91} +(-2.77897 - 7.24932i) q^{92} +(-0.312129 - 0.122875i) q^{93} +(-1.20448 - 2.52671i) q^{94} +(-3.73257 - 3.13200i) q^{95} +(3.99349 - 8.94718i) q^{96} +(0.0876267 + 0.0318935i) q^{97} +(4.15046 - 2.95907i) q^{98} +(11.8929 + 11.0810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more