LMFDB - Embedded newform 77.2.n.a.40.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(17,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 27]))

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

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

chi := DirichletCharacter("77.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.n (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			40.1
Character	$\chi$	$=$	77.40
Dual form			77.2.n.a.52.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.842093 - 1.89137i) q^{2} +(0.653128 + 3.07273i) q^{3} +(-1.52991 + 1.69913i) q^{4} +(1.18148 - 0.124179i) q^{5} +(5.26167 - 3.82283i) q^{6} +(2.63875 + 0.192354i) q^{7} +(0.563952 + 0.183239i) q^{8} +(-6.27443 + 2.79356i) q^{9} +O(q^{10})$	\(q+(-0.842093 - 1.89137i) q^{2} +(0.653128 + 3.07273i) q^{3} +(-1.52991 + 1.69913i) q^{4} +(1.18148 - 0.124179i) q^{5} +(5.26167 - 3.82283i) q^{6} +(2.63875 + 0.192354i) q^{7} +(0.563952 + 0.183239i) q^{8} +(-6.27443 + 2.79356i) q^{9} +(-1.22979 - 2.13006i) q^{10} +(-0.746987 - 3.23141i) q^{11} +(-6.22020 - 3.59123i) q^{12} +(-0.000347326 - 0.000252347i) q^{13} +(-1.85826 - 5.15284i) q^{14} +(1.15323 + 3.54927i) q^{15} +(0.349663 + 3.32682i) q^{16} +(-1.68310 - 0.749362i) q^{17} +(10.5673 + 9.51485i) q^{18} +(-1.29469 - 1.43790i) q^{19} +(-1.59656 + 2.19748i) q^{20} +(1.13239 + 8.23379i) q^{21} +(-5.48277 + 4.13398i) q^{22} +(2.83507 - 4.91048i) q^{23} +(-0.194711 + 1.85255i) q^{24} +(-3.51025 + 0.746128i) q^{25} +(-0.000184801 + 0.000869422i) q^{26} +(-7.14248 - 9.83078i) q^{27} +(-4.36388 + 4.18931i) q^{28} +(-4.88867 + 1.58843i) q^{29} +(5.74187 - 5.17000i) q^{30} +(0.431118 + 0.0453123i) q^{31} +(7.02487 - 4.05581i) q^{32} +(9.44136 - 4.40581i) q^{33} +3.81439i q^{34} +(3.14153 - 0.100414i) q^{35} +(4.85267 - 14.9350i) q^{36} +(-0.367944 - 0.0782088i) q^{37} +(-1.62935 + 3.65958i) q^{38} +(0.000548545 - 0.00123205i) q^{39} +(0.689054 + 0.146463i) q^{40} +(-0.760621 + 2.34095i) q^{41} +(14.6196 - 9.07539i) q^{42} -5.03264i q^{43} +(6.63342 + 3.67453i) q^{44} +(-7.06624 + 4.07969i) q^{45} +(-11.6749 - 1.22708i) q^{46} +(1.37886 - 1.24153i) q^{47} +(-9.99404 + 3.24726i) q^{48} +(6.92600 + 1.01515i) q^{49} +(4.36717 + 6.01089i) q^{50} +(1.20331 - 5.66112i) q^{51} +(0.000960148 - 0.000204086i) q^{52} +(-0.138336 + 1.31618i) q^{53} +(-12.5790 + 21.7875i) q^{54} +(-1.28383 - 3.72510i) q^{55} +(1.45288 + 0.592000i) q^{56} +(3.57267 - 4.91735i) q^{57} +(7.12103 + 7.90870i) q^{58} +(9.06645 + 8.16347i) q^{59} +(-7.79502 - 3.47057i) q^{60} +(0.795634 + 7.56996i) q^{61} +(-0.277339 - 0.853562i) q^{62} +(-17.0940 + 6.16458i) q^{63} +(-8.17409 - 5.93882i) q^{64} +(-0.000441696 - 0.000255013i) q^{65} +(-16.2835 - 14.1470i) q^{66} +(6.72641 + 11.6505i) q^{67} +(3.84825 - 1.71335i) q^{68} +(16.9402 + 5.50421i) q^{69} +(-2.83538 - 5.85724i) q^{70} +(-6.82813 + 4.96093i) q^{71} +(-4.05037 + 0.425711i) q^{72} +(9.12950 - 10.1393i) q^{73} +(0.161921 + 0.761777i) q^{74} +(-4.58529 - 10.2987i) q^{75} +4.42393 q^{76} +(-1.34954 - 8.67057i) q^{77} -0.00279219 q^{78} +(-0.667370 - 1.49894i) q^{79} +(0.826243 + 3.88717i) q^{80} +(11.7551 - 13.0554i) q^{81} +(5.06812 - 0.532681i) q^{82} +(-7.86628 + 5.71519i) q^{83} +(-15.7228 - 10.6728i) q^{84} +(-2.08161 - 0.676354i) q^{85} +(-9.51860 + 4.23795i) q^{86} +(-8.07373 - 13.9841i) q^{87} +(0.170856 - 1.95924i) q^{88} +(-6.24880 - 3.60774i) q^{89} +(13.6667 + 9.92940i) q^{90} +(-0.000867966 - 0.000732690i) q^{91} +(4.00617 + 12.3297i) q^{92} +(0.142343 + 1.35430i) q^{93} +(-3.50933 - 1.56245i) q^{94} +(-1.70821 - 1.53808i) q^{95} +(17.0505 + 18.9365i) q^{96} +(2.39869 - 3.30152i) q^{97} +(-3.91231 - 13.9545i) q^{98} +(13.7140 + 18.1885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.842093	−	1.89137i	−0.595450	−	1.33740i	−0.920143	−	0.391583i	$-0.871928\pi$
$2$	−0.842093	−	1.89137i	−0.595450	−	1.33740i	0.324693	−	0.945819i	$-0.394739\pi$
$3$	0.653128	+	3.07273i	0.377084	+	1.77404i	0.600815	+	0.799388i	$0.294843\pi$
$3$	0.653128	+	3.07273i	0.377084	+	1.77404i	−0.223731	+	0.974651i	$0.571824\pi$
$4$	−1.52991	+	1.69913i	−0.764954	+	0.849567i
$5$	1.18148	−	0.124179i	0.528376	−	0.0555345i	0.163415	−	0.986557i	$-0.447749\pi$
$5$	1.18148	−	0.124179i	0.528376	−	0.0555345i	0.364961	+	0.931023i	$0.381082\pi$
$6$	5.26167	−	3.82283i	2.14807	−	1.56066i
$7$	2.63875	+	0.192354i	0.997354	+	0.0727030i
$7$	2.63875	+	0.192354i	0.997354	+	0.0727030i
$8$	0.563952	+	0.183239i	0.199387	+	0.0647848i
$9$	−6.27443	+	2.79356i	−2.09148	+	0.931186i
$10$	−1.22979	−	2.13006i	−0.388893	−	0.673583i
$11$	−0.746987	−	3.23141i	−0.225225	−	0.974307i
$11$	−0.746987	−	3.23141i	−0.225225	−	0.974307i
$12$	−6.22020	−	3.59123i	−1.79562	−	1.03670i
$13$	−0.000347326	0	0.000252347i	−9.63308e−5	0	6.99885e-5i	0.587737	−	0.809052i	$-0.300019\pi$
$13$	−0.000347326	0	0.000252347i	−9.63308e−5	0	6.99885e-5i	−0.587833	+	0.808982i	$0.700019\pi$
$14$	−1.85826	−	5.15284i	−0.496641	−	1.37715i
$15$	1.15323	+	3.54927i	0.297762	+	0.916418i
$16$	0.349663	+	3.32682i	0.0874158	+	0.831706i
$17$	−1.68310	−	0.749362i	−0.408211	−	0.181747i	0.192350	−	0.981326i	$-0.438389\pi$
$17$	−1.68310	−	0.749362i	−0.408211	−	0.181747i	−0.600560	+	0.799579i	$0.705056\pi$
$18$	10.5673	+	9.51485i	2.49074	+	2.24267i
$19$	−1.29469	−	1.43790i	−0.297022	−	0.329876i	0.576099	−	0.817380i	$-0.304574\pi$
$19$	−1.29469	−	1.43790i	−0.297022	−	0.329876i	−0.873121	+	0.487504i	$0.837908\pi$
$20$	−1.59656	+	2.19748i	−0.357003	+	0.491372i
$21$	1.13239	+	8.23379i	0.247108	+	1.79676i
$22$	−5.48277	+	4.13398i	−1.16893	+	0.881367i
$23$	2.83507	−	4.91048i	0.591152	−	1.02391i	−0.402926	−	0.915233i	$-0.632007\pi$
$23$	2.83507	−	4.91048i	0.591152	−	1.02391i	0.994078	−	0.108673i	$-0.0346600\pi$
$24$	−0.194711	+	1.85255i	−0.0397451	+	0.378150i
$25$	−3.51025	+	0.746128i	−0.702051	+	0.149226i
$26$	−0.000184801	0	0.000869422i	−3.62425e−5	0	0.000170508i
$27$	−7.14248	−	9.83078i	−1.37457	−	1.89194i
$28$	−4.36388	+	4.18931i	−0.824695	+	0.791704i
$29$	−4.88867	+	1.58843i	−0.907804	+	0.294963i	−0.725454	−	0.688270i	$-0.758370\pi$
$29$	−4.88867	+	1.58843i	−0.907804	+	0.294963i	−0.182350	+	0.983234i	$0.558370\pi$
$30$	5.74187	−	5.17000i	1.04832	−	0.943909i
$31$	0.431118	+	0.0453123i	0.0774311	+	0.00813833i	0.143165	−	0.989699i	$-0.454272\pi$
$31$	0.431118	+	0.0453123i	0.0774311	+	0.00813833i	−0.0657337	+	0.997837i	$0.520939\pi$
$32$	7.02487	−	4.05581i	1.24183	−	0.716973i
$33$	9.44136	−	4.40581i	1.64353	−	0.766953i
$34$			3.81439i			0.654163i
$35$	3.14153	−	0.100414i	0.531015	−	0.0169731i
$36$	4.85267	−	14.9350i	0.808778	−	2.48916i
$37$	−0.367944	−	0.0782088i	−0.0604895	−	0.0128574i	0.177568	−	0.984109i	$-0.443177\pi$
$37$	−0.367944	−	0.0782088i	−0.0604895	−	0.0128574i	−0.238057	+	0.971251i	$0.576511\pi$
$38$	−1.62935	+	3.65958i	−0.264316	+	0.593663i
$39$	0.000548545	−	0.00123205i	8.78375e−5	−	0.000197286i
$40$	0.689054	+	0.146463i	0.108949	+	0.0231578i
$41$	−0.760621	+	2.34095i	−0.118789	+	0.365595i	−0.992718	−	0.120458i	$-0.961564\pi$
$41$	−0.760621	+	2.34095i	−0.118789	+	0.365595i	0.873929	+	0.486053i	$0.161564\pi$
$42$	14.6196	−	9.07539i	2.25585	−	1.40036i
$43$		−	5.03264i		−	0.767471i	−0.923443	−	0.383735i	$-0.874637\pi$
$43$		−	5.03264i		−	0.767471i	0.923443	−	0.383735i	$-0.125363\pi$
$44$	6.63342	+	3.67453i	1.00003	+	0.553956i
$45$	−7.06624	+	4.07969i	−1.05337	+	0.608165i
$46$	−11.6749	−	1.22708i	−1.72137	−	0.180924i
$47$	1.37886	−	1.24153i	0.201128	−	0.181096i	−0.562412	−	0.826857i	$-0.690126\pi$
$47$	1.37886	−	1.24153i	0.201128	−	0.181096i	0.763540	+	0.645761i	$0.223460\pi$
$48$	−9.99404	+	3.24726i	−1.44252	+	0.468702i
$49$	6.92600	+	1.01515i	0.989429	+	0.145021i
$50$	4.36717	+	6.01089i	0.617611	+	0.850068i
$51$	1.20331	−	5.66112i	0.168497	−	0.792715i
$52$	0.000960148	0	0.000204086i	0.000133149	0	2.83016e-5i
$53$	−0.138336	+	1.31618i	−0.0190019	+	0.180791i	−0.999906	−	0.0137002i	$-0.995639\pi$
$53$	−0.138336	+	1.31618i	−0.0190019	+	0.180791i	0.980904	+	0.194491i	$0.0623056\pi$
$54$	−12.5790	+	21.7875i	−1.71179	+	2.96491i
$55$	−1.28383	−	3.72510i	−0.173111	−	0.502292i
$56$	1.45288	+	0.592000i	0.194149	+	0.0791094i
$57$	3.57267	−	4.91735i	0.473211	−	0.651320i
$58$	7.12103	+	7.90870i	0.935037	+	1.03846i
$59$	9.06645	+	8.16347i	1.18035	+	1.06279i	0.996812	+	0.0797807i	$0.0254220\pi$
$59$	9.06645	+	8.16347i	1.18035	+	1.06279i	0.183539	+	0.983012i	$0.441245\pi$
$60$	−7.79502	−	3.47057i	−1.00633	−	0.448048i
$61$	0.795634	+	7.56996i	0.101871	+	0.969233i	0.919394	+	0.393338i	$0.128680\pi$
$61$	0.795634	+	7.56996i	0.101871	+	0.969233i	−0.817523	+	0.575895i	$0.804654\pi$
$62$	−0.277339	−	0.853562i	−0.0352221	−	0.108402i
$63$	−17.0940	+	6.16458i	−2.15364	+	0.776665i
$64$	−8.17409	−	5.93882i	−1.02176	−	0.742353i
$65$	−0.000441696	0	0.000255013i	−5.47856e−5	0	3.16305e-5i
$66$	−16.2835	−	14.1470i	−2.00436	−	1.74138i
$67$	6.72641	+	11.6505i	0.821762	+	1.42333i	0.904369	+	0.426751i	$0.140342\pi$
$67$	6.72641	+	11.6505i	0.821762	+	1.42333i	−0.0826073	+	0.996582i	$0.526325\pi$
$68$	3.84825	−	1.71335i	0.466668	−	0.207774i
$69$	16.9402	+	5.50421i	2.03936	+	0.662629i
$70$	−2.83538	−	5.85724i	−0.338893	−	0.700074i
$71$	−6.82813	+	4.96093i	−0.810350	+	0.588754i	−0.913932	−	0.405867i	$-0.866970\pi$
$71$	−6.82813	+	4.96093i	−0.810350	+	0.588754i	0.103582	+	0.994621i	$0.466970\pi$
$72$	−4.05037	+	0.425711i	−0.477340	+	0.0501705i
$73$	9.12950	−	10.1393i	1.06853	−	1.18672i	0.0868397	−	0.996222i	$-0.472323\pi$
$73$	9.12950	−	10.1393i	1.06853	−	1.18672i	0.981688	−	0.190498i	$-0.0610101\pi$
$74$	0.161921	+	0.761777i	0.0188229	+	0.0885548i
$75$	−4.58529	−	10.2987i	−0.529464	−	1.18920i
$76$	4.42393			0.507460
$77$	−1.34954	−	8.67057i	−0.153794	−	0.988103i
$78$	−0.00279219			−0.000316154
$79$	−0.667370	−	1.49894i	−0.0750850	−	0.168644i	0.872103	−	0.489322i	$-0.162756\pi$
$79$	−0.667370	−	1.49894i	−0.0750850	−	0.168644i	−0.947188	+	0.320678i	$0.896089\pi$
$80$	0.826243	+	3.88717i	0.0923768	+	0.434598i
$81$	11.7551	−	13.0554i	1.30613	−	1.45060i
$82$	5.06812	−	0.532681i	0.559680	−	0.0588248i
$83$	−7.86628	+	5.71519i	−0.863436	+	0.627323i	−0.928818	−	0.370537i	$-0.879174\pi$
$83$	−7.86628	+	5.71519i	−0.863436	+	0.627323i	0.0653813	+	0.997860i	$0.479174\pi$
$84$	−15.7228	−	10.6728i	−1.71549	−	1.16450i
$85$	−2.08161	−	0.676354i	−0.225782	−	0.0733609i
$86$	−9.51860	+	4.23795i	−1.02642	+	0.456990i
$87$	−8.07373	−	13.9841i	−0.865595	−	1.49925i
$88$	0.170856	−	1.95924i	0.0182133	−	0.208855i
$89$	−6.24880	−	3.60774i	−0.662371	−	0.382420i	0.130809	−	0.991408i	$-0.458243\pi$
$89$	−6.24880	−	3.60774i	−0.662371	−	0.382420i	−0.793180	+	0.608988i	$0.791576\pi$
$90$	13.6667	+	9.92940i	1.44059	+	1.04665i
$91$	−0.000867966	0	0.000732690i	−9.09875e−5	0	7.68068e-5i
$92$	4.00617	+	12.3297i	0.417672	+	1.28546i
$93$	0.142343	+	1.35430i	0.0147603	+	0.140435i
$94$	−3.50933	−	1.56245i	−0.361960	−	0.161155i
$95$	−1.70821	−	1.53808i	−0.175259	−	0.157804i
$96$	17.0505	+	18.9365i	1.74021	+	1.93270i
$97$	2.39869	−	3.30152i	0.243551	−	0.335219i	−0.669689	−	0.742642i	$-0.733573\pi$
$97$	2.39869	−	3.30152i	0.243551	−	0.335219i	0.913239	+	0.407423i	$0.133573\pi$
$98$	−3.91231	−	13.9545i	−0.395203	−	1.40962i
$99$	13.7140	+	18.1885i	1.37831	+	1.82801i
$100$	4.10259	−	7.10590i	0.410259	−	0.710590i
$101$	−1.52948	+	14.5520i	−0.152189	+	1.44798i	0.605749	+	0.795656i	$0.292874\pi$
$101$	−1.52948	+	14.5520i	−0.152189	+	1.44798i	−0.757938	+	0.652327i	$0.773793\pi$
$102$	−11.7206	+	2.49129i	−1.16051	+	0.246674i
$103$	2.53537	−	11.9280i	0.249817	−	1.17530i	−0.657039	−	0.753857i	$-0.728191\pi$
$103$	2.53537	−	11.9280i	0.249817	−	1.17530i	0.906856	−	0.421441i	$-0.138475\pi$
$104$	−0.000149635	0	0.000205955i	−1.46729e−5	0	2.01956e-5i
$105$	2.36036	+	9.58747i	0.230348	+	0.935641i
$106$	2.60588	−	0.846701i	0.253105	−	0.0822389i
$107$	−1.44332	+	1.29957i	−0.139531	+	0.125634i	−0.735941	−	0.677046i	$-0.763260\pi$
$107$	−1.44332	+	1.29957i	−0.139531	+	0.125634i	0.596410	+	0.802680i	$0.296593\pi$
$108$	27.6312	+	2.90415i	2.65881	+	0.279452i
$109$	−10.1746	+	5.87432i	−0.974552	+	0.562658i	−0.900621	−	0.434606i	$-0.856888\pi$
$109$	−10.1746	+	5.87432i	−0.974552	+	0.562658i	−0.0739308	+	0.997263i	$0.523554\pi$
$110$	−5.96445	+	5.56507i	−0.568688	+	0.530609i
$111$		−	1.18167i		−	0.112159i
$112$	0.282746	+	8.84591i	0.0267170	+	0.835860i
$113$	−1.58699	+	4.88424i	−0.149291	+	0.459471i	−0.997538	−	0.0701305i	$-0.977658\pi$
$113$	−1.58699	+	4.88424i	−0.149291	+	0.459471i	0.848247	+	0.529601i	$0.177658\pi$
$114$	−12.3091	−	2.61637i	−1.15285	−	0.245046i
$115$	2.73981	−	6.15371i	0.255488	−	0.573836i
$116$	4.78027	−	10.7367i	0.443837	−	0.996874i
$117$	0.00288422		0.000613059i	0.000266646		5.66774e-5i
$118$	7.80536	−	24.0224i	0.718542	−	2.21144i
$119$	−4.29712	−	2.30113i	−0.393917	−	0.210944i
$120$			2.21293i			0.202012i
$121$	−9.88402	+	4.82764i	−0.898547	+	0.438877i
$122$	13.6476	−	7.87945i	1.23560	−	0.713372i
$123$	−7.68988	−	0.808239i	−0.693373	−	0.0728764i
$124$	−0.736562	+	0.663203i	−0.0661452	+	0.0595574i
$125$	−9.70389	+	3.15299i	−0.867943	+	0.282012i
$126$	26.0543	+	27.1400i	2.32110	+	2.41782i
$127$	−0.721232	−	0.992691i	−0.0639990	−	0.0880870i	0.775818	−	0.630957i	$-0.217338\pi$
$127$	−0.721232	−	0.992691i	−0.0639990	−	0.0880870i	−0.839817	+	0.542870i	$0.817338\pi$
$128$	−0.976177	+	4.59255i	−0.0862826	+	0.405928i
$129$	15.4639	−	3.28696i	1.36152	−	0.289401i
$130$	−0.000110376		0.00105016i	−9.68061e−6		9.21048e-5i
$131$	6.38697	−	11.0626i	0.558032	−	0.966541i	−0.439628	−	0.898180i	$-0.644890\pi$
$131$	6.38697	−	11.0626i	0.558032	−	0.966541i	0.997661	−	0.0683607i	$-0.0217769\pi$
$132$	−6.95834	+	22.7826i	−0.605646	+	1.98297i
$133$	−3.13977	−	4.04329i	−0.272253	−	0.350598i
$134$	16.3711	−	22.5329i	1.41425	−	1.94655i
$135$	−9.65951	−	10.7280i	−0.831358	−	0.923316i
$136$	−0.811872	−	0.731013i	−0.0696175	−	0.0626839i
$137$	1.03639	+	0.461430i	0.0885447	+	0.0394227i	0.450531	−	0.892761i	$-0.351235\pi$
$137$	1.03639	+	0.461430i	0.0885447	+	0.0394227i	−0.361986	+	0.932183i	$0.617901\pi$
$138$	−3.85473	−	36.6753i	−0.328136	−	3.12201i
$139$	1.53841	+	4.73474i	0.130486	+	0.401595i	0.994861	−	0.101253i	$-0.0322853\pi$
$139$	1.53841	+	4.73474i	0.130486	+	0.401595i	−0.864374	+	0.502849i	$0.832285\pi$
$140$	−4.63563	+	5.49150i	−0.391782	+	0.464116i
$141$	4.71546	+	3.42598i	0.397114	+	0.288520i
$142$	15.1329	+	8.73697i	1.26992	+	0.733191i
$143$	−0.000555989		0.00131085i	−4.64941e−5		0.000109619i
$144$	−11.4876	−	19.8971i	−0.957301	−	1.65809i
$145$	−5.57864	+	2.48377i	−0.463281	+	0.206266i
$146$	−26.8652	−	8.72902i	−2.22338	−	0.722419i
$147$	1.40429	+	21.9447i	0.115824	+	1.80997i
$148$	0.695807	−	0.505533i	0.0571950	−	0.0415546i
$149$	−9.60650	+	1.00968i	−0.786995	+	0.0827165i	−0.489496	−	0.872006i	$-0.662819\pi$
$149$	−9.60650	+	1.00968i	−0.786995	+	0.0827165i	−0.297499	+	0.954722i	$0.596153\pi$
$150$	−15.6175	+	17.3450i	−1.27516	+	1.41621i
$151$	−1.79377	−	8.43904i	−0.145975	−	0.686759i	−0.988882	−	0.148700i	$-0.952491\pi$
$151$	−1.79377	−	8.43904i	−0.145975	−	0.686759i	0.842907	−	0.538059i	$-0.180842\pi$
$152$	−0.466663	−	1.04814i	−0.0378514	−	0.0850156i
$153$	12.6539			1.02300
$154$	−15.2628	+	9.85390i	−1.22991	+	0.794050i
$155$	0.514986			0.0413646
$156$	0.00125420	+	0.00281698i	0.000100416	+	0.000225539i
$157$	1.30900	+	6.15835i	0.104469	+	0.491490i	0.999009	+	0.0445016i	$0.0141700\pi$
$157$	1.30900	+	6.15835i	0.104469	+	0.491490i	−0.894540	+	0.446988i	$0.852497\pi$
$158$	−2.27306	+	2.52449i	−0.180835	+	0.200838i
$159$	−4.13461	+	0.434565i	−0.327896	+	0.0344633i
$160$	7.79613	−	5.66422i	0.616338	−	0.447796i
$161$	8.42558	−	12.4122i	0.664029	−	0.978217i
$162$	−34.5916	−	11.2395i	−2.71777	−	0.883057i
$163$	10.1059	−	4.49946i	0.791559	−	0.352425i	0.0291953	−	0.999574i	$-0.490706\pi$
$163$	10.1059	−	4.49946i	0.791559	−	0.352425i	0.762364	+	0.647149i	$0.224039\pi$
$164$	−2.81391	−	4.87383i	−0.219729	−	0.380582i
$165$	10.6077	−	6.37781i	0.825809	−	0.496512i
$166$	17.4337	+	10.0653i	1.35312	+	0.781222i
$167$	5.65523	+	4.10876i	0.437614	+	0.317946i	0.784686	−	0.619893i	$-0.212824\pi$
$167$	5.65523	+	4.10876i	0.437614	+	0.317946i	−0.347072	+	0.937839i	$0.612824\pi$
$168$	−0.870138	+	4.85096i	−0.0671326	+	0.374259i
$169$	−4.01722	−	12.3637i	−0.309017	−	0.951057i
$170$	0.473667	+	4.50664i	0.0363286	+	0.345644i
$171$	12.1403	+	5.40520i	0.928391	+	0.413346i
$172$	8.55113	+	7.69948i	0.652018	+	0.587080i
$173$	13.9445	+	15.4870i	1.06018	+	1.17745i	0.983595	+	0.180391i	$0.0577362\pi$
$173$	13.9445	+	15.4870i	1.06018	+	1.17745i	0.0765889	+	0.997063i	$0.475597\pi$
$174$	−19.6503	+	27.0464i	−1.48969	+	2.05038i
$175$	−9.40620	+	1.29363i	−0.711042	+	0.0977894i
$176$	10.4891	−	3.61500i	0.790648	−	0.272491i
$177$	−19.1625	+	33.1905i	−1.44035	+	2.49475i
$178$	−1.56152	+	14.8569i	−0.117041	+	1.11357i
$179$	14.0129	−	2.97853i	1.04737	−	0.222626i	0.348082	−	0.937464i	$-0.386833\pi$
$179$	14.0129	−	2.97853i	1.04737	−	0.222626i	0.699289	+	0.714839i	$0.253500\pi$
$180$	3.87874	−	18.2480i	0.289104	−	1.36013i
$181$	−7.72615	−	10.6341i	−0.574280	−	0.790429i	0.418774	−	0.908091i	$-0.362460\pi$
$181$	−7.72615	−	10.6341i	−0.574280	−	0.790429i	−0.993054	+	0.117662i	$0.962460\pi$
$182$	−0.000654881		0.00225864i	−4.85430e−5		0.000167422i
$183$	−22.7407	+	7.38892i	−1.68104	+	0.546204i
$184$	2.49863	−	2.24978i	0.184202	−	0.165856i
$185$	−0.444431	−	0.0467116i	−0.0326752	−	0.00343431i
$186$	2.44162	−	1.40967i	0.179028	−	0.103362i
$187$	−1.16425	+	5.99854i	−0.0851381	+	0.438656i
$188$			4.24230i			0.309402i
$189$	−16.9562	−	27.3149i	−1.23338	−	1.98686i
$190$	−1.47061	+	4.52607i	−0.106689	+	0.328356i
$191$	−0.275023	−	0.0584580i	−0.0199000	−	0.00422987i	0.197951	−	0.980212i	$-0.436571\pi$
$191$	−0.275023	−	0.0584580i	−0.0199000	−	0.00422987i	−0.217851	+	0.975982i	$0.569905\pi$
$192$	12.9096	−	28.9955i	0.931673	−	2.09257i
$193$	4.84324	−	10.8781i	0.348624	−	0.783023i	−0.651087	−	0.759003i	$-0.725687\pi$
$193$	4.84324	−	10.8781i	0.348624	−	0.783023i	0.999711	−	0.0240202i	$-0.00764659\pi$
$194$	−8.26433	−	1.75664i	−0.593344	−	0.126119i
$195$	0.000495102	−	0.00152377i	3.54550e−5	−	0.000109119i
$196$	−12.3210	+	10.2151i	−0.880072	+	0.729651i
$197$		−	8.08377i		−	0.575944i	−0.957639	−	0.287972i	$-0.907019\pi$
$197$		−	8.08377i		−	0.575944i	0.957639	−	0.287972i	$-0.0929811\pi$
$198$	22.8527	−	41.2548i	1.62407	−	2.93185i
$199$	1.36908	−	0.790438i	0.0970514	−	0.0560327i	−0.450689	−	0.892681i	$-0.648822\pi$
$199$	1.36908	−	0.790438i	0.0970514	−	0.0560327i	0.547740	+	0.836648i	$0.315488\pi$
$200$	−2.11633	−	0.222436i	−0.149647	−	0.0157286i
$201$	−31.4055	+	28.2777i	−2.21518	+	1.99455i
$202$	28.8113	−	9.36136i	2.02716	−	0.658663i
$203$	−13.2055	+	3.25110i	−0.926846	+	0.228183i
$204$	7.77805	+	10.7056i	0.544573	+	0.749540i
$205$	−0.607964	+	2.86025i	−0.0424621	+	0.199768i
$206$	−24.6952	+	5.24914i	−1.72060	+	0.365725i
$207$	−4.07073	+	38.7304i	−0.282935	+	2.69195i
$208$	0.000718067	−	0.00124373i	4.97890e−5	−	8.62370e-5i
$209$	−3.67932	+	5.25776i	−0.254504	+	0.363687i
$210$	16.1458	−	12.5379i	1.11417	−	0.865195i
$211$	1.71163	−	2.35586i	0.117834	−	0.162184i	−0.746026	−	0.665917i	$-0.768040\pi$
$211$	1.71163	−	2.35586i	0.117834	−	0.162184i	0.863859	+	0.503733i	$0.168040\pi$
$212$	−2.02473	−	2.24869i	−0.139059	−	0.154440i
$213$	−19.7032	−	17.7409i	−1.35004	−	1.21558i
$214$	3.67337	+	1.63549i	0.251106	+	0.111800i
$215$	−0.624948	−	5.94599i	−0.0426211	−	0.405513i
$216$	−2.22663	−	6.85287i	−0.151503	−	0.466279i
$217$	1.12890	+	0.202495i	0.0766345	+	0.0137463i
$218$	19.6785	+	14.2973i	1.33280	+	0.968333i
$219$	37.1181	+	21.4302i	2.50821	+	1.44812i
$220$	8.29358	+	3.51766i	0.559153	+	0.237161i
$221$	0.000395483	0	0.000684997i	2.66031e−5	0	4.60779e-5i
$222$	−2.23498	+	0.995076i	−0.150002	+	0.0667851i
$223$	21.1608	+	6.87555i	1.41703	+	0.460421i	0.914657	−	0.404231i	$-0.132461\pi$
$223$	21.1608	+	6.87555i	1.41703	+	0.460421i	0.502372	+	0.864652i	$0.332461\pi$
$224$	19.3170	−	9.35101i	1.29067	−	0.624791i
$225$	19.9405	−	14.4876i	1.32937	−	0.965841i
$226$	10.5743	−	1.11140i	0.703393	−	0.0739295i
$227$	−1.61628	+	1.79506i	−0.107276	+	0.119142i	−0.794391	−	0.607406i	$-0.792210\pi$
$227$	−1.61628	+	1.79506i	−0.107276	+	0.119142i	0.687115	+	0.726548i	$0.258877\pi$
$228$	2.88940	+	13.5935i	0.191355	+	0.900254i
$229$	−6.64643	−	14.9281i	−0.439209	−	0.986479i	−0.988552	−	0.150882i	$-0.951789\pi$
$229$	−6.64643	−	14.9281i	−0.439209	−	0.986479i	0.549343	−	0.835597i	$-0.314878\pi$
$230$	−13.9461			−0.919580
$231$	25.7609	−	9.80975i	1.69494	−	0.645434i
$232$	−3.04804			−0.200114
$233$	−6.54082	−	14.6909i	−0.428503	−	0.962435i	−0.990779	−	0.135485i	$-0.956741\pi$
$233$	−6.54082	−	14.6909i	−0.428503	−	0.962435i	0.562276	−	0.826950i	$-0.309926\pi$
$234$	−0.00126926	−	0.00597138i	−8.29739e−5	−	0.000390361i
$235$	1.47493	−	1.63808i	0.0962139	−	0.106856i
$236$	−27.7417	+	2.91577i	−1.80583	+	0.189800i
$237$	4.16995	−	3.02964i	0.270867	−	0.196796i
$238$	−0.733714	+	10.0652i	−0.0475596	+	0.652432i
$239$	−9.20478	−	2.99081i	−0.595408	−	0.193460i	−0.00421649	−	0.999991i	$-0.501342\pi$
$239$	−9.20478	−	2.99081i	−0.595408	−	0.193460i	−0.591191	+	0.806531i	$0.701342\pi$
$240$	−11.4046	+	5.07764i	−0.736161	+	0.327760i
$241$	5.21513	+	9.03287i	0.335936	+	0.581858i	0.983664	−	0.180013i	$-0.0576140\pi$
$241$	5.21513	+	9.03287i	0.335936	+	0.581858i	−0.647728	+	0.761872i	$0.724281\pi$
$242$	17.4541	+	14.6290i	1.12199	+	0.940390i
$243$	16.2227	+	9.36620i	1.04069	+	0.600842i
$244$	−14.0796	−	10.2294i	−0.901355	−	0.654873i
$245$	8.30902	+	0.339318i	0.530844	+	0.0216782i
$246$	4.94691	+	15.2250i	0.315404	+	0.970713i
$247$	8.68297e−5	0	0.000826130i	5.52484e−6	0	5.25654e-5i
$248$	0.234827	+	0.104552i	0.0149115	+	0.00663903i
$249$	−22.6989	−	20.4382i	−1.43848	−	1.29522i
$250$	14.1351	+	15.6986i	0.893979	+	0.992864i
$251$	13.9846	−	19.2482i	0.882701	−	1.21493i	−0.0929641	−	0.995669i	$-0.529634\pi$
$251$	13.9846	−	19.2482i	0.882701	−	1.21493i	0.975665	−	0.219265i	$-0.0703658\pi$
$252$	15.6778	−	38.4762i	0.987608	−	2.42378i
$253$	−17.9855	−	5.49320i	−1.13074	−	0.345354i
$254$	−1.27020	+	2.20006i	−0.0796996	+	0.138044i
$255$	0.718697	−	6.83795i	0.0450066	−	0.428209i
$256$	−10.2576	+	2.18032i	−0.641101	+	0.136270i
$257$	−1.50668	+	7.08838i	−0.0939843	+	0.442161i	0.905844	+	0.423612i	$0.139238\pi$
$257$	−1.50668	+	7.08838i	−0.0939843	+	0.442161i	−0.999828	+	0.0185492i	$0.994095\pi$
$258$	−19.2389	−	26.4801i	−1.19776	−	1.64858i
$259$	−0.955867	−	0.277149i	−0.0593947	−	0.0172212i
$260$	0.00110906		0.000360354i	6.87807e−5		2.23482e-5i
$261$	26.2363	−	23.6233i	1.62399	−	1.46224i
$262$	−26.3019	−	2.76444i	−1.62493	−	0.170787i
$263$	−13.2235	+	7.63460i	−0.815397	+	0.470770i	−0.848826	−	0.528672i	$-0.822690\pi$
$263$	−13.2235	+	7.63460i	−0.815397	+	0.470770i	0.0334298	+	0.999441i	$0.489357\pi$
$264$	6.13179	−	0.754639i	0.377385	−	0.0464448i
$265$			1.57222i			0.0965810i
$266$	−5.00338	+	9.34331i	−0.306777	+	0.572875i
$267$	7.00434	−	21.5572i	0.428659	−	1.31928i
$268$	−30.0865	−	6.39509i	−1.83783	−	0.390642i
$269$	−5.00730	+	11.2466i	−0.305301	+	0.685717i	−0.999417	−	0.0341464i	$-0.989129\pi$
$269$	−5.00730	+	11.2466i	−0.305301	+	0.685717i	0.694116	+	0.719863i	$0.255795\pi$
$270$	−12.1564	+	27.3037i	−0.739814	+	1.66165i
$271$	27.8212	+	5.91357i	1.69002	+	0.359224i	0.949731	−	0.313068i	$-0.101357\pi$
$271$	27.8212	+	5.91357i	1.69002	+	0.359224i	0.740286	+	0.672292i	$0.234690\pi$
$272$	1.90448	−	5.86139i	0.115476	−	0.355399i
$273$	0.00168446	−	0.00314556i	0.000101948	−	0.000190378i
$274$		−	2.34877i		−	0.141894i
$275$	5.03316	+	10.7857i	0.303511	+	0.650404i
$276$	−35.2693	+	20.3628i	−2.12296	+	1.22569i
$277$	3.11190	+	0.327074i	0.186976	+	0.0196520i	0.197554	−	0.980292i	$-0.436700\pi$
$277$	3.11190	+	0.327074i	0.186976	+	0.0196520i	−0.0105775	+	0.999944i	$0.503367\pi$
$278$	7.65967	−	6.89680i	0.459396	−	0.413642i
$279$	−2.83160	+	0.920043i	−0.169524	+	0.0550815i
$280$	1.79007	+	0.519022i	0.106977	+	0.0310175i
$281$	0.637471	+	0.877404i	0.0380283	+	0.0523415i	0.827608	−	0.561307i	$-0.189701\pi$
$281$	0.637471	+	0.877404i	0.0380283	+	0.0523415i	−0.789579	+	0.613648i	$0.789701\pi$
$282$	2.50895	−	11.8037i	0.149406	−	0.702900i
$283$	−9.87958	+	2.09997i	−0.587280	+	0.124830i	−0.491962	−	0.870617i	$-0.663720\pi$
$283$	−9.87958	+	2.09997i	−0.587280	+	0.124830i	−0.0953179	+	0.995447i	$0.530387\pi$
$284$	2.01713	−	19.1917i	0.119694	−	1.13882i
$285$	3.61042	−	6.25343i	0.213863	−	0.370421i
$286$	0.00294750		5.22780e-5i	0.000174290		3.09126e-6i
$287$	−2.45738	+	6.03087i	−0.145054	+	0.355991i
$288$	−32.7469	+	45.0723i	−1.92963	+	2.65591i
$289$	−9.10395	−	10.1110i	−0.535527	−	0.594763i
$290$	9.39547	+	8.45972i	0.551721	+	0.496772i
$291$	11.7113	+	5.21421i	0.686530	+	0.305663i
$292$	3.26081	+	31.0245i	0.190824	+	1.81557i
$293$	7.22252	+	22.2286i	0.421944	+	1.29861i	0.905890	+	0.423513i	$0.139203\pi$
$293$	7.22252	+	22.2286i	0.421944	+	1.29861i	−0.483946	+	0.875098i	$0.660797\pi$
$294$	40.3231	−	21.1355i	2.35169	−	1.23265i
$295$	11.7256	+	8.51914i	0.682691	+	0.496004i
$296$	−0.193172	−	0.111528i	−0.0112279	−	0.00648241i
$297$	−26.4320	+	30.4238i	−1.53374	+	1.76537i
$298$	9.99926	+	17.3192i	0.579241	+	1.00328i
$299$	−0.00222384		0.000990115i	−0.000128608		5.72599e-5i
$300$	24.5140	+	7.96508i	1.41532	+	0.459864i
$301$	0.968049	−	13.2799i	0.0557974	−	0.765440i
$302$	−14.4508	+	10.4991i	−0.831552	+	0.604158i
$303$	−45.7134	+	4.80467i	−2.62617	+	0.276021i
$304$	4.33093	−	4.80998i	0.248396	−	0.275871i
$305$	1.88006	+	8.84498i	0.107652	+	0.506462i
$306$	−10.6557	−	23.9331i	−0.609147	−	1.36817i
$307$	−31.5257			−1.79927			−0.899633	−	0.436646i	$-0.856166\pi$
$307$	−31.5257			−1.79927			−0.899633	+	0.436646i	$0.856166\pi$
$308$	16.7971	+	10.9721i	0.957105	+	0.625195i
$309$	38.3073			2.17923
$310$	−0.433666	−	0.974030i	−0.0246306	−	0.0553212i
$311$	−3.65313	−	17.1866i	−0.207150	−	0.974563i	−0.951708	−	0.307005i	$-0.900673\pi$
$311$	−3.65313	−	17.1866i	−0.207150	−	0.974563i	0.744558	−	0.667558i	$-0.232660\pi$
$312$	0.000535113	0	0.000594303i	3.02948e−5	0	3.36458e-5i
$313$	−20.6179	+	2.16703i	−1.16539	+	0.122488i	−0.667405	−	0.744695i	$-0.732595\pi$
$313$	−20.6179	+	2.16703i	−1.16539	+	0.122488i	−0.497990	+	0.867183i	$0.665928\pi$
$314$	10.5454	−	7.66170i	0.595113	−	0.432375i
$315$	−19.4308	+	9.40607i	−1.09480	+	0.529972i
$316$	3.56791	+	1.15928i	0.200711	+	0.0652148i
$317$	28.7091	−	12.7821i	1.61246	−	0.717916i	0.614963	−	0.788556i	$-0.289171\pi$
$317$	28.7091	−	12.7821i	1.61246	−	0.717916i	0.997502	+	0.0706403i	$0.0225042\pi$
$318$	4.30365	+	7.45415i	0.241337	+	0.418008i
$319$	8.78463	+	14.6108i	0.491845	+	0.818047i
$320$	−10.3950	−	6.00157i	−0.581100	−	0.335498i
$321$	−4.93588	−	3.58613i	−0.275494	−	0.200158i
$322$	−30.5712	−	5.48369i	−1.70367	−	0.305594i
$323$	1.10158	+	3.39031i	0.0612935	+	0.188642i
$324$	4.19861	+	39.9471i	0.233256	+	2.21928i
$325$	0.00140748		0.000626653i	7.80732e−5		3.47604e-5i
$326$	−17.0203	−	15.3251i	−0.942667	−	0.848781i
$327$	−24.6955	−	27.4271i	−1.36566	−	1.51672i
$328$	−0.857907	+	1.18081i	−0.0473700	+	0.0651992i
$329$	3.87728	−	3.01086i	0.213762	−	0.165994i
$330$	−20.9955	−	14.6924i	−1.15576	−	0.808790i
$331$	11.9178	−	20.6422i	0.655062	−	1.13460i	−0.326816	−	0.945088i	$-0.605976\pi$
$331$	11.9178	−	20.6422i	0.655062	−	1.13460i	0.981878	−	0.189513i	$-0.0606908\pi$
$332$	2.32381	−	22.1096i	0.127536	−	1.21342i
$333$	2.52712	−	0.537155i	0.138485	−	0.0294359i
$334$	3.00897	−	14.1561i	0.164644	−	0.774587i
$335$	9.39389	+	12.9296i	0.513243	+	0.706418i
$336$	−26.9964	+	6.64631i	−1.47277	+	0.362586i
$337$	−13.5619	+	4.40653i	−0.738765	+	0.240039i	−0.654140	−	0.756374i	$-0.726969\pi$
$337$	−13.5619	+	4.40653i	−0.738765	+	0.240039i	−0.0846249	+	0.996413i	$0.526969\pi$
$338$	−20.0016	+	18.0095i	−1.08794	+	0.979586i
$339$	−16.0444	−	1.68634i	−0.871414	−	0.0915893i
$340$	4.33388	−	2.50217i	0.235038	−	0.135699i
$341$	−0.175617	−	1.42697i	−0.00951018	−	0.0772746i
$342$		−	27.5135i		−	1.48776i
$343$	18.0807	+	4.01097i	0.976267	+	0.216572i
$344$	0.922177	−	2.83817i	0.0497204	−	0.153024i
$345$	20.6981	+	4.39952i	1.11435	+	0.236862i
$346$	17.5490	−	39.4158i	0.943443	−	2.11901i
$347$	6.56981	−	14.7560i	0.352686	−	0.792145i	−0.646878	−	0.762594i	$-0.723926\pi$
$347$	6.56981	−	14.7560i	0.352686	−	0.792145i	0.999563	−	0.0295511i	$-0.00940779\pi$
$348$	36.1129	+	7.67604i	1.93586	+	0.411479i
$349$	−4.01326	+	12.3515i	−0.214825	+	0.661163i	0.784341	+	0.620330i	$0.213001\pi$
$349$	−4.01326	+	12.3515i	−0.214825	+	0.661163i	−0.999166	+	0.0408333i	$0.986999\pi$
$350$	10.3676	+	16.7013i	0.554174	+	0.892721i
$351$			0.00521687i			0.000278456i
$352$	−18.3535	−	19.6706i	−0.978244	−	1.04845i
$353$	26.5104	−	15.3058i	1.41100	−	0.814644i	0.415521	−	0.909584i	$-0.363599\pi$
$353$	26.5104	−	15.3058i	1.41100	−	0.814644i	0.995483	+	0.0949399i	$0.0302659\pi$
$354$	78.9123	+	8.29401i	4.19414	+	0.440822i
$355$	−7.45128	+	6.70917i	−0.395473	+	0.356086i
$356$	15.6901	−	5.09803i	0.831575	−	0.270195i
$357$	4.26417	−	14.7068i	0.225684	−	0.778367i
$358$	−17.4336	−	23.9954i	−0.921397	−	1.26819i
$359$	3.89850	−	18.3410i	0.205755	−	0.968002i	−0.747132	−	0.664676i	$-0.768570\pi$
$359$	3.89850	−	18.3410i	0.205755	−	0.968002i	0.952887	−	0.303326i	$-0.0980970\pi$
$360$	−4.73258	+	1.00594i	−0.249429	+	0.0530177i
$361$	1.59471	−	15.1727i	0.0839321	−	0.798561i
$362$	−13.6070	+	23.5680i	−0.715166	+	1.23870i
$363$	−21.2896	−	27.2178i	−1.11741	−	1.42856i
$364$	0.00257285		0.000353843i	0.000134854		1.85464e-5i
$365$	9.52727	−	13.1132i	0.498680	−	0.686374i
$366$	33.1250	+	36.7891i	1.73147	+	1.92300i
$367$	16.4496	+	14.8113i	0.858661	+	0.773142i	0.975498	−	0.220009i	$-0.0706087\pi$
$367$	16.4496	+	14.8113i	0.858661	+	0.773142i	−0.116837	+	0.993151i	$0.537275\pi$
$368$	17.3276	+	7.71475i	0.903264	+	0.402159i
$369$	−1.76711	−	16.8130i	−0.0919923	−	0.875248i
$370$	0.285903	+	0.879920i	0.0148634	+	0.0457449i
$371$	−0.618207	+	3.44646i	−0.0320957	+	0.178931i
$372$	−2.51891	−	1.83010i	−0.130599	−	0.0948861i
$373$	−17.2376	−	9.95215i	−0.892531	−	0.515303i	−0.0177612	−	0.999842i	$-0.505654\pi$
$373$	−17.2376	−	9.95215i	−0.892531	−	0.515303i	−0.874769	+	0.484540i	$0.838987\pi$
$374$	12.3259	−	2.84930i	0.637355	−	0.147334i
$375$	−16.0261	−	27.7581i	−0.827587	−	1.43342i
$376$	1.00511	−	0.447503i	0.0518345	−	0.0230782i
$377$	0.00209880		0.000681941i	0.000108094		3.51217e-5i
$378$	−37.3839	+	55.0722i	−1.92282	+	2.83261i
$379$	−11.5817	+	8.41461i	−0.594913	+	0.432229i	−0.844070	−	0.536234i	$-0.819847\pi$
$379$	−11.5817	+	8.41461i	−0.594913	+	0.432229i	0.249157	+	0.968463i	$0.419847\pi$
$380$	5.22681	−	0.549360i	0.268130	−	0.0281816i
$381$	2.57921	−	2.86450i	0.132137	−	0.146753i
$382$	0.121029	+	0.569399i	0.00619240	+	0.0291330i
$383$	6.54185	+	14.6932i	0.334273	+	0.750789i	0.999989	+	0.00458463i	$0.00145934\pi$
$383$	6.54185	+	14.6932i	0.334273	+	0.750789i	−0.665717	+	0.746205i	$0.731874\pi$
$384$	−14.7492			−0.752668
$385$	−2.67116	−	10.0766i	−0.136135	−	0.513549i
$386$	−24.6530			−1.25481
$387$	14.0590	+	31.5770i	0.714658	+	1.60515i
$388$	1.93994	+	9.12672i	0.0984858	+	0.463339i
$389$	−22.7282	+	25.2422i	−1.15237	+	1.27983i	−0.198332	+	0.980135i	$0.563553\pi$
$389$	−22.7282	+	25.2422i	−1.15237	+	1.27983i	−0.954034	+	0.299698i	$0.903114\pi$
$390$	−0.00329893		0.000346732i	−0.000167048		1.75574e-5i
$391$	−8.45141	+	6.14031i	−0.427406	+	0.310529i
$392$	3.71992	+	1.84161i	0.187884	+	0.0930153i
$393$	38.1637	+	12.4001i	1.92511	+	0.625505i
$394$	−15.2894	+	6.80728i	−0.770269	+	0.342946i
$395$	−0.974623	−	1.68810i	−0.0490386	−	0.0849374i
$396$	−51.8859	−	4.52473i	−2.60737	−	0.227376i
$397$	−19.3209	−	11.1549i	−0.969687	−	0.559849i	−0.0705464	−	0.997508i	$-0.522474\pi$
$397$	−19.3209	−	11.1549i	−0.969687	−	0.559849i	−0.899141	+	0.437659i	$0.855808\pi$
$398$	−2.64790	−	1.92381i	−0.132727	−	0.0964321i
$399$	10.3732	−	12.2885i	0.519312	−	0.615192i
$400$	−3.70964	−	11.4171i	−0.185482	−	0.570855i
$401$	0.740905	+	7.04924i	0.0369990	+	0.352022i	0.997322	+	0.0731328i	$0.0232997\pi$
$401$	0.740905	+	7.04924i	0.0369990	+	0.352022i	−0.960323	+	0.278890i	$0.910034\pi$
$402$	79.9300	+	35.5871i	3.98655	+	1.77492i
$403$	−0.000138304	0	0.000124529i	−6.88941e−6	0	6.20325e-6i
$404$	−22.3859	−	24.8621i	−1.11374	−	1.23693i
$405$	12.2673	−	16.8845i	0.609567	−	0.838997i
$406$	17.2693	+	22.2388i	0.857063	+	1.10370i
$407$	0.0221243	+	1.24740i	0.00109666	+	0.0618312i
$408$	1.71595	−	2.97211i	0.0849520	−	0.147141i
$409$	−1.70746	+	16.2454i	−0.0844284	+	0.803283i	0.867598	+	0.497266i	$0.165663\pi$
$409$	−1.70746	+	16.2454i	−0.0844284	+	0.803283i	−0.952026	+	0.306016i	$0.901004\pi$
$410$	5.92176	−	1.25871i	0.292455	−	0.0621632i
$411$	−0.740954	+	3.48591i	−0.0365486	+	0.171947i
$412$	16.3883	+	22.5566i	0.807396	+	1.11128i
$413$	22.3538	+	23.2853i	1.09996	+	1.14580i
$414$	76.6815	−	24.9153i	3.76869	−	1.22452i
$415$	−8.58418	+	7.72923i	−0.421381	+	0.379413i
$416$	−0.00346339		0.000364017i	−0.000169807		1.78474e-5i
$417$	−13.5438	+	7.81950i	−0.663241	+	0.382923i
$418$	13.0427	+	2.53144i	0.637940	+	0.123817i
$419$			33.3519i			1.62935i	0.579921	+	0.814673i	$0.303083\pi$
$419$			33.3519i			1.62935i	−0.579921	+	0.814673i	$0.696917\pi$
$420$	−19.9015	−	10.6574i	−0.971095	−	0.520026i
$421$	1.80630	−	5.55923i	0.0880338	−	0.270940i	−0.897342	−	0.441336i	$-0.854505\pi$
$421$	1.80630	−	5.55923i	0.0880338	−	0.270940i	0.985376	+	0.170396i	$0.0545047\pi$
$422$	−5.89716	−	1.25348i	−0.287069	−	0.0610184i
$423$	−5.18328	+	11.6418i	−0.252020	+	0.566046i
$424$	−0.319191	+	0.716914i	−0.0155013	+	0.0348164i
$425$	6.46721	+	1.37465i	0.313706	+	0.0666802i
$426$	−16.9626	+	52.2056i	−0.821841	+	2.52937i
$427$	0.643369	+	20.1283i	0.0311348	+	0.974075i
$428$		−	4.44060i		−	0.214645i
$429$	−0.00439102		0.000852246i	−0.000212000		4.11468e-5i
$430$	−10.7198	+	6.18908i	−0.516955	+	0.298464i
$431$	−19.5487	−	2.05465i	−0.941629	−	0.0989692i	−0.378742	−	0.925502i	$-0.623643\pi$
$431$	−19.5487	−	2.05465i	−0.941629	−	0.0989692i	−0.562888	+	0.826533i	$0.690310\pi$
$432$	30.2078	−	27.1992i	1.45337	−	1.30862i
$433$	0.490372	−	0.159332i	0.0235658	−	0.00765699i	−0.297210	−	0.954812i	$-0.596056\pi$
$433$	0.490372	−	0.159332i	0.0235658	−	0.00765699i	0.320776	+	0.947155i	$0.396056\pi$
$434$	−0.567642	−	2.30568i	−0.0272477	−	0.110676i
$435$	−11.2755	−	15.5194i	−0.540620	−	0.744099i
$436$	5.58497	−	26.2752i	0.267471	−	1.25835i
$437$	−10.7313	+	2.28101i	−0.513347	+	0.109115i
$438$	9.27549	−	88.2504i	0.443200	−	4.21677i
$439$	−11.7590	+	20.3672i	−0.561227	+	0.972073i	0.436163	+	0.899868i	$0.356337\pi$
$439$	−11.7590	+	20.3672i	−0.561227	+	0.972073i	−0.997390	+	0.0722055i	$0.976996\pi$
$440$	−0.0414326	−	2.33602i	−0.00197522	−	0.111366i
$441$	−46.2926	+	12.9787i	−2.20441	+	0.618033i
$442$	0.000962550	−	0.00132484i	4.57839e−5	−	6.30161e-5i
$443$	−11.9474	−	13.2690i	−0.567640	−	0.630428i	0.389162	−	0.921169i	$-0.372765\pi$
$443$	−11.9474	−	13.2690i	−0.567640	−	0.630428i	−0.956802	+	0.290741i	$0.906098\pi$
$444$	2.00782	+	1.80785i	0.0952867	+	0.0857965i
$445$	−7.83086	−	3.48652i	−0.371218	−	0.165277i
$446$	−4.81511	−	45.8127i	−0.228002	−	2.16930i
$447$	−9.37676	−	28.8587i	−0.443505	−	1.36497i
$448$	−20.4270	−	17.2434i	−0.965086	−	0.814673i
$449$	−5.77400	−	4.19506i	−0.272492	−	0.197977i	0.443144	−	0.896450i	$-0.353863\pi$
$449$	−5.77400	−	4.19506i	−0.272492	−	0.197977i	−0.715636	+	0.698473i	$0.753863\pi$
$450$	−44.1932	−	25.5150i	−2.08329	−	1.20279i
$451$	8.13274	+	0.709218i	0.382956	+	0.0333958i
$452$	−5.87104	−	10.1689i	−0.276150	−	0.478307i
$453$	24.7593	−	11.0235i	1.16329	−	0.517931i
$454$	4.75618	+	1.54538i	0.223218	+	0.0725280i
$455$	−0.00111647		0.000757878i	−5.23410e−5		3.55299e-5i
$456$	2.91586	−	2.11850i	0.136548	−	0.0992078i
$457$	24.1649	−	2.53983i	1.13038	−	0.118808i	0.479184	−	0.877714i	$-0.340933\pi$
$457$	24.1649	−	2.53983i	1.13038	−	0.118808i	0.651200	+	0.758906i	$0.274266\pi$
$458$	−22.6377	+	25.1418i	−1.05779	+	1.17480i
$459$	4.65466	+	21.8985i	0.217261	+	1.02213i
$460$	6.26432	+	14.0699i	0.292076	+	0.656012i
$461$	20.4135			0.950750			0.475375	−	0.879783i	$-0.342312\pi$
$461$	20.4135			0.950750			0.475375	+	0.879783i	$0.342312\pi$
$462$	−40.2469	−	40.4627i	−1.87246	−	1.88249i
$463$	−35.5035			−1.64999			−0.824994	−	0.565142i	$-0.808822\pi$
$463$	−35.5035			−1.64999			−0.824994	+	0.565142i	$0.808822\pi$
$464$	−6.99380	−	15.7083i	−0.324679	−	0.729241i
$465$	0.336352	+	1.58241i	0.0155979	+	0.0733825i
$466$	−22.2780	+	24.7423i	−1.03201	+	1.14616i
$467$	22.2227	−	2.33570i	1.02834	−	0.108083i	0.424698	−	0.905335i	$-0.360380\pi$
$467$	22.2227	−	2.33570i	1.02834	−	0.108083i	0.603647	+	0.797252i	$0.293714\pi$
$468$	−0.00545425	+	0.00396275i	−0.000252123	+	0.000183178i
$469$	15.5083	+	32.0366i	0.716107	+	1.47931i
$470$	−4.34024	−	1.41023i	−0.200200	−	0.0650491i
$471$	−18.0680	+	8.04438i	−0.832528	+	0.370665i
$472$	3.61718	+	6.26513i	0.166494	+	0.288376i
$473$	−16.2625	+	3.75932i	−0.747752	+	0.172854i
$474$	−9.24167	−	5.33568i	−0.424484	−	0.245076i
$475$	5.61754	+	4.08138i	0.257750	+	0.187267i
$476$	10.4841	−	3.78088i	0.480539	−	0.173296i
$477$	−2.80884	−	8.64473i	−0.128608	−	0.395815i
$478$	2.09454	+	19.9282i	0.0958020	+	0.911495i
$479$	−35.2270	−	15.6841i	−1.60956	−	0.716624i	−0.612306	−	0.790621i	$-0.709758\pi$
$479$	−35.2270	−	15.6841i	−1.60956	−	0.716624i	−0.997259	+	0.0739964i	$0.976425\pi$
$480$	22.4965	+	20.2559i	1.02682	+	0.924551i
$481$	0.000108061	0	0.000120013i	4.92714e−6	0	5.47214e-6i
$482$	12.6929	−	17.4703i	0.578146	−	0.795749i
$483$	43.6422	+	17.7827i	1.98579	+	0.809143i
$484$	6.91882	−	24.1801i	0.314492	−	1.09910i
$485$	2.42404	−	4.19856i	0.110070	−	0.190647i
$486$	4.05392	−	38.5704i	0.183889	−	1.74959i
$487$	38.7458	−	8.23568i	1.75574	−	0.373194i	0.786172	−	0.618008i	$-0.212060\pi$
$487$	38.7458	−	8.23568i	1.75574	−	0.373194i	0.969570	+	0.244814i	$0.0787269\pi$
$488$	−0.938412	+	4.41488i	−0.0424799	+	0.199852i
$489$	20.4261	+	28.1141i	0.923699	+	1.27136i
$490$	−6.35519	−	16.0012i	−0.287098	−	0.722860i
$491$	5.67873	−	1.84513i	0.256277	−	0.0832696i	−0.178061	−	0.984020i	$-0.556982\pi$
$491$	5.67873	−	1.84513i	0.256277	−	0.0832696i	0.434338	+	0.900750i	$0.356982\pi$
$492$	13.1381	−	11.8296i	0.592312	−	0.533320i
$493$	9.41841	+	0.989915i	0.424184	+	0.0445835i
$494$	0.00148940		0.000859906i	6.70113e−5		3.86890e-5i
$495$	18.4616	+	19.7864i	0.829785	+	0.889334i
$496$			1.45010i			0.0651113i
$497$	−18.9720	+	11.7772i	−0.851010	+	0.528281i
$498$	−19.5416	+	60.1429i	−0.875681	+	2.69507i
$499$	−11.0809	−	2.35532i	−0.496050	−	0.105439i	−0.0469085	−	0.998899i	$-0.514937\pi$
$499$	−11.0809	−	2.35532i	−0.496050	−	0.105439i	−0.449142	+	0.893460i	$0.648270\pi$
$500$	9.48871	−	21.3120i	0.424348	−	0.953101i
$501$	−8.93151	+	20.0605i	−0.399031	+	0.896237i
$502$	−48.1818	−	10.2414i	−2.15046	−	0.457094i
$503$	8.56066	−	26.3470i	0.381701	−	1.17475i	−0.557145	−	0.830416i	$-0.688103\pi$
$503$	8.56066	−	26.3470i	0.381701	−	1.17475i	0.938845	−	0.344339i	$-0.111897\pi$
$504$	−10.7698	+	0.344240i	−0.479725	+	0.0153337i
$505$			17.3829i			0.773530i
$506$	4.75581	+	38.6431i	0.211421	+	1.71790i
$507$	35.3666	−	20.4189i	1.57069	−	0.906836i
$508$	2.79013	+	0.293255i	0.123792	+	0.0130111i
$509$	9.95332	−	8.96201i	0.441173	−	0.397234i	−0.418387	−	0.908269i	$-0.637404\pi$
$509$	9.95332	−	8.96201i	0.441173	−	0.397234i	0.859560	+	0.511035i	$0.170738\pi$
$510$	−13.5383	+	4.39887i	−0.599487	+	0.194785i
$511$	26.0408	−	24.9991i	1.15198	−	1.10589i
$512$	18.2812	+	25.1619i	0.807921	+	1.11201i
$513$	−4.88837	+	22.9980i	−0.215827	+	1.01538i
$514$	14.6755	−	3.11938i	0.647310	−	0.137590i
$515$	1.51429	−	14.4075i	0.0667278	−	0.634872i
$516$	−18.0734	+	31.3040i	−0.795637	+	1.37808i
$517$	−5.04189	−	3.52826i	−0.221742	−	0.155173i
$518$	0.280737	+	2.04129i	0.0123349	+	0.0896889i
$519$	−38.4797	+	52.9627i	−1.68907	+	2.32481i
$520$	−0.000202367	0	0.000224751i	−8.87437e−6	0	9.85599e-6i
$521$	−12.4550	−	11.2145i	−0.545663	−	0.491317i	0.349573	−	0.936909i	$-0.386327\pi$
$521$	−12.4550	−	11.2145i	−0.545663	−	0.491317i	−0.895236	+	0.445592i	$0.852993\pi$
$522$	−66.7738	−	29.7296i	−2.92261	−	1.30123i
$523$	4.48420	+	42.6644i	0.196081	+	1.86558i	0.442967	+	0.896538i	$0.353926\pi$
$523$	4.48420	+	42.6644i	0.196081	+	1.86558i	−0.246887	+	0.969044i	$0.579408\pi$
$524$	9.02530	+	27.7770i	0.394272	+	1.21344i
$525$	−10.1184	−	28.0578i	−0.441605	−	1.22454i
$526$	25.5753	+	18.5815i	1.11514	+	0.810194i
$527$	−0.691657	−	0.399328i	−0.0301291	−	0.0173950i
$528$	17.9586	+	29.8692i	0.781550	+	1.29989i
$529$	−4.57519	−	7.92447i	−0.198921	−	0.344542i
$530$	2.97366	−	1.32396i	0.129168	−	0.0575091i
$531$	−79.6919	−	25.8935i	−3.45834	−	1.12368i
$532$	11.6737	+	0.850962i	0.506117	+	0.0368939i
$533$	0.000854915	0	0.000621132i	3.70305e−5	0	2.69042e-5i
$534$	−46.6709	+	4.90531i	−2.01965	+	0.212274i
$535$	−1.54387	+	1.71465i	−0.0667475	+	0.0741306i
$536$	1.65855	+	7.80285i	0.0716383	+	0.337032i
$537$	18.3044	+	41.1123i	0.789893	+	1.77413i
$538$	25.4881			1.09887
$539$	−1.89327	−	23.1390i	−0.0815490	−	0.996669i
$540$	33.0064			1.42037
$541$	15.3700	+	34.5217i	0.660810	+	1.48420i	0.863181	+	0.504894i	$0.168468\pi$
$541$	15.3700	+	34.5217i	0.660810	+	1.48420i	−0.202372	+	0.979309i	$0.564865\pi$
$542$	−12.2433	−	57.6000i	−0.525893	−	2.47413i
$543$	27.6296	−	30.6858i	1.18570	−	1.31685i
$544$	−14.8628	+	1.56214i	−0.637238	+	0.0669764i
$545$	−11.2917	+	8.20389i	−0.483682	+	0.351416i
$546$	−0.00736790		0.000537090i	−0.000315317		2.29853e-5i
$547$	33.2931	+	10.8176i	1.42351	+	0.462527i	0.916716	−	0.399540i	$-0.130830\pi$
$547$	33.2931	+	10.8176i	1.42351	+	0.462527i	0.506795	+	0.862067i	$0.330830\pi$
$548$	−2.36961	+	1.05502i	−0.101225	+	0.0450682i
$549$	−26.1393	−	45.2745i	−1.11560	−	1.93227i
$550$	16.1614	−	18.6022i	0.689126	−	0.793199i
$551$	8.61331	+	4.97290i	0.366939	+	0.211852i
$552$	8.54488	+	6.20822i	0.363694	+	0.264239i
$553$	−1.47270	−	4.08369i	−0.0626254	−	0.173656i
$554$	−2.00189	−	6.16120i	−0.0850523	−	0.261764i
$555$	−0.146739	−	1.39612i	−0.00622870	−	0.0592622i
$556$	−10.3986	−	4.62974i	−0.440998	−	0.196345i
$557$	12.7004	+	11.4355i	0.538135	+	0.484539i	0.892799	−	0.450455i	$-0.148738\pi$
$557$	12.7004	+	11.4355i	0.538135	+	0.484539i	−0.354664	+	0.934994i	$0.615405\pi$
$558$	4.12462	+	4.58085i	0.174609	+	0.193923i
$559$	−0.00126997	+	0.00174797i	−5.37141e−5	+	7.39311e-5i
$560$	1.43254	+	10.4162i	0.0605357	+	0.440164i
$561$	−19.1923	+	0.340401i	−0.810298	+	0.0143717i
$562$	1.12269	−	1.94455i	0.0473577	−	0.0820259i
$563$	1.29998	−	12.3685i	0.0547877	−	0.521270i	−0.932368	−	0.361510i	$-0.882261\pi$
$563$	1.29998	−	12.3685i	0.0547877	−	0.521270i	0.987156	−	0.159760i	$-0.0510720\pi$
$564$	−13.0354	+	2.77077i	−0.548891	+	0.116670i
$565$	−1.26848	+	5.96772i	−0.0533653	+	0.251064i
$566$	12.2913	+	16.9176i	0.516644	+	0.711099i
$567$	33.5301	−	32.1888i	1.40813	−	1.35180i
$568$	−4.75977	+	1.54654i	−0.199716	+	0.0648915i
$569$	18.9733	−	17.0836i	0.795400	−	0.716182i	−0.167549	−	0.985864i	$-0.553585\pi$
$569$	18.9733	−	17.0836i	0.795400	−	0.716182i	0.962949	+	0.269682i	$0.0869186\pi$
$570$	−14.8679	−	1.56268i	−0.622746	−	0.0654533i
$571$	18.4338	−	10.6428i	0.771431	−	0.445386i	−0.0619540	−	0.998079i	$-0.519733\pi$
$571$	18.4338	−	10.6428i	0.771431	−	0.445386i	0.833385	+	0.552693i	$0.186400\pi$
$572$	−0.00137670	−	0.00295018i	−5.75628e−5	−	0.000123353i
$573$		−	0.883252i		−	0.0368984i
$574$	13.4760	−	0.430738i	0.562476	−	0.0179787i
$575$	−6.28796	+	19.3523i	−0.262226	+	0.807049i
$576$	67.8782	+	14.4280i	2.82826	+	0.601165i
$577$	6.98450	−	15.6874i	0.290768	−	0.653077i	−0.707809	−	0.706404i	$-0.750316\pi$
$577$	6.98450	−	15.6874i	0.290768	−	0.653077i	0.998577	+	0.0533276i	$0.0169827\pi$
$578$	−11.4572	+	25.7333i	−0.476558	+	1.07037i
$579$	36.5887	+	7.77717i	1.52057	+	0.323208i
$580$	4.31454	−	13.2788i	0.179152	−	0.551372i
$581$	−21.8565	+	13.5678i	−0.906760	+	0.562889i
$582$		−	26.5413i		−	1.10017i
$583$	4.35645	−	0.536149i	0.180426	−	0.0222050i
$584$	7.00652	−	4.04522i	0.289932	−	0.167392i
$585$	0.00348379		0.000366161i	0.000144037		1.51389e-5i
$586$	35.9606	−	32.3791i	1.48552	−	1.33757i
$587$	8.45024	−	2.74565i	0.348779	−	0.113325i	−0.129388	−	0.991594i	$-0.541301\pi$
$587$	8.45024	−	2.74565i	0.348779	−	0.113325i	0.478167	+	0.878269i	$0.341301\pi$
$588$	−39.4355	−	31.1873i	−1.62629	−	1.28614i
$589$	−0.493009	−	0.678569i	−0.0203141	−	0.0279599i
$590$	6.23883	−	29.3514i	0.256849	−	1.20838i
$591$	24.8392	−	5.27973i	1.02175	−	0.217179i
$592$	0.131531	−	1.25143i	0.00540587	−	0.0514334i
$593$	4.15338	−	7.19387i	0.170559	−	0.295417i	−0.768056	−	0.640382i	$-0.778776\pi$
$593$	4.15338	−	7.19387i	0.170559	−	0.295417i	0.938615	+	0.344965i	$0.112109\pi$
$594$	79.8008	+	24.3730i	3.27427	+	1.00004i
$595$	−5.36274	−	2.18514i	−0.219851	−	0.0895818i
$596$	12.9815	−	17.8675i	0.531742	−	0.731879i
$597$	3.32298	+	3.69055i	0.136001	+	0.151044i
$598$	0.00374535	+	0.00337233i	0.000153159	+	0.000137905i
$599$	−14.7864	−	6.58332i	−0.604155	−	0.268987i	0.0817794	−	0.996650i	$-0.473940\pi$
$599$	−14.7864	−	6.58332i	−0.604155	−	0.268987i	−0.685935	+	0.727663i	$0.740606\pi$
$600$	−0.698753	−	6.64819i	−0.0285265	−	0.271411i
$601$	−2.71097	−	8.34352i	−0.110583	−	0.340339i	0.880417	−	0.474200i	$-0.157263\pi$
$601$	−2.71097	−	8.34352i	−0.110583	−	0.340339i	−0.991000	+	0.133861i	$0.957263\pi$
$602$	−25.9324	+	9.35196i	−1.05693	+	0.381157i
$603$	−74.7507	−	54.3096i	−3.04408	−	2.21166i
$604$	17.0834	+	9.86308i	0.695112	+	0.401323i
$605$	−11.0783	+	6.93117i	−0.450398	+	0.281792i
$606$	47.5824	+	82.4151i	1.93290	+	3.34788i
$607$	−15.7742	+	7.02312i	−0.640254	+	0.285060i	−0.701073	−	0.713089i	$-0.747295\pi$
$607$	−15.7742	+	7.02312i	−0.640254	+	0.285060i	0.0608189	+	0.998149i	$0.480629\pi$
$608$	−14.9269	−	4.85003i	−0.605364	−	0.196695i
$609$	−18.6147	−	38.4536i	−0.754304	−	1.55822i
$610$	15.1460	−	11.0042i	0.613242	−	0.445547i
$611$	−0.000792211	0	8.32648e-5i	−3.20494e−5	0	3.36853e-6i
$612$	−19.3592	+	21.5006i	−0.782550	+	0.869110i
$613$	−2.88153	−	13.5565i	−0.116384	−	0.547544i	−0.997246	−	0.0741699i	$-0.976369\pi$
$613$	−2.88153	−	13.5565i	−0.116384	−	0.547544i	0.880862	−	0.473374i	$-0.156964\pi$
$614$	26.5476	+	59.6268i	1.07137	+	2.40634i
$615$	−9.18583			−0.370409
$616$	0.827713	−	5.13707i	0.0333495	−	0.206978i
$617$	1.77082			0.0712903			0.0356452	−	0.999365i	$-0.488651\pi$
$617$	1.77082			0.0712903			0.0356452	+	0.999365i	$0.488651\pi$
$618$	−32.2583	−	72.4534i	−1.29762	−	2.91450i
$619$	2.30441	+	10.8414i	0.0926221	+	0.435753i	0.999885	+	0.0151880i	$0.00483468\pi$
$619$	2.30441	+	10.8414i	0.0926221	+	0.435753i	−0.907263	+	0.420565i	$0.861832\pi$
$620$	−0.787880	+	0.875030i	−0.0316420	+	0.0351420i
$621$	−68.5233	+	7.20208i	−2.74974	+	0.289010i
$622$	−29.4300	+	21.3821i	−1.18004	+	0.857346i
$623$	−15.7950	−	10.7219i	−0.632815	−	0.429564i
$624$	0.00429062	+	0.00139411i	0.000171762	+	5.58090e-5i
$625$	5.31863	−	2.36801i	0.212745	−	0.0947203i
$626$	21.4609	+	37.1713i	0.857749	+	1.48567i
$627$	−18.5587	−	7.87155i	−0.741164	−	0.314360i
$628$	−12.4665	−	7.19754i	−0.497468	−	0.287213i
$629$	0.560677	+	0.407356i	0.0223557	+	0.0162423i
$630$	34.1529	+	28.8300i	1.36068	+	1.14862i
$631$	13.8840	+	42.7304i	0.552712	+	1.70107i	0.701911	+	0.712265i	$0.252330\pi$
$631$	13.8840	+	42.7304i	0.552712	+	1.70107i	−0.149199	+	0.988807i	$0.547670\pi$
$632$	−0.101701	−	0.967617i	−0.00404543	−	0.0384897i
$633$	8.35682	+	3.72070i	0.332154	+	0.147884i
$634$	−48.3515	−	43.5359i	−1.92028	−	1.72903i
$635$	−0.975395	−	1.08329i	−0.0387074	−	0.0429889i
$636$	5.58719	−	7.69010i	0.221546	−	0.304932i
$637$	−0.00214941	−	0.00210034i	−8.51627e−5	−	8.32186e-5i
$638$	20.2369	−	28.9187i	0.801188	−	1.14490i
$639$	28.9840	−	50.2018i	1.14659	−	1.98595i
$640$	−0.583039	+	5.54724i	−0.0230466	+	0.219274i
$641$	17.5178	−	3.72353i	0.691912	−	0.147070i	0.151483	−	0.988460i	$-0.451595\pi$
$641$	17.5178	−	3.72353i	0.691912	−	0.147070i	0.540429	+	0.841389i	$0.318262\pi$
$642$	−2.62623	+	12.3554i	−0.103649	+	0.487631i
$643$	−28.9300	−	39.8187i	−1.14089	−	1.57030i	−0.765508	−	0.643427i	$-0.777512\pi$
$643$	−28.9300	−	39.8187i	−1.14089	−	1.57030i	−0.375380	−	0.926871i	$-0.622488\pi$
$644$	8.19961	+	33.3057i	0.323110	+	1.31243i
$645$	17.8622	−	5.80378i	0.703324	−	0.228524i
$646$	5.48471	−	4.93845i	0.215793	−	0.194301i
$647$	−42.0212	−	4.41660i	−1.65202	−	0.173634i	−0.767796	−	0.640694i	$-0.778647\pi$
$647$	−42.0212	−	4.41660i	−1.65202	−	0.173634i	−0.884226	+	0.467060i	$0.845313\pi$
$648$	9.02159	−	5.20862i	0.354402	−	0.204614i
$649$	19.6070	−	35.3954i	0.769642	−	1.38939i
$650$		−	0.00318978i		−	0.000125113i
$651$	0.115102	+	3.60104i	0.00451119	+	0.141136i
$652$	−7.81598	+	24.0551i	−0.306097	+	0.942071i
$653$	−11.0975	−	2.35885i	−0.434279	−	0.0923089i	−0.0144157	−	0.999896i	$-0.504589\pi$
$653$	−11.0975	−	2.35885i	−0.434279	−	0.0923089i	−0.419864	+	0.907587i	$0.637922\pi$
$654$	−31.0790	+	69.8046i	−1.21529	+	2.72958i
$655$	6.17237	−	13.8634i	0.241174	−	0.541687i
$656$	−8.05389	−	1.71191i	−0.314451	−	0.0668387i
$657$	−28.9576	+	89.1224i	−1.12974	+	3.47699i
$658$	−8.95970	−	4.79796i	−0.349286	−	0.187044i
$659$		−	13.2959i		−	0.517935i	−0.965886	−	0.258968i	$-0.916618\pi$
$659$		−	13.2959i		−	0.517935i	0.965886	−	0.258968i	$-0.0833823\pi$
$660$	−5.39204	+	27.7814i	−0.209885	+	1.08139i
$661$	−8.51808	+	4.91791i	−0.331315	+	0.191285i	−0.656425	−	0.754392i	$-0.727932\pi$
$661$	−8.51808	+	4.91791i	−0.331315	+	0.191285i	0.325110	+	0.945676i	$0.394599\pi$
$662$	−49.0781	−	5.15831i	−1.90747	−	0.200484i
$663$	−0.00184651	+	0.00166260i	−7.17124e−5	+	6.45701e-5i
$664$	−5.48345	+	1.78168i	−0.212799	+	0.0691426i
$665$	−4.21168	−	4.38719i	−0.163322	−	0.170128i
$666$	−3.14403	−	4.32738i	−0.121829	−	0.167683i
$667$	−6.05978	+	28.5090i	−0.234636	+	1.10387i
$668$	−15.6333	+	3.32296i	−0.604871	+	0.128569i
$669$	−7.30599	+	69.5118i	−0.282466	+	2.68748i
$670$	16.5441	−	28.6553i	0.639155	−	1.10705i
$671$	23.8673	−	8.22568i	0.921387	−	0.317549i
$672$	41.3496	+	53.2485i	1.59510	+	2.05411i
$673$	22.9971	−	31.6528i	0.886473	−	1.22013i	−0.0881121	−	0.996111i	$-0.528083\pi$
$673$	22.9971	−	31.6528i	0.886473	−	1.22013i	0.974586	−	0.224016i	$-0.0719166\pi$
$674$	19.7548	+	21.9399i	0.760926	+	0.845094i
$675$	32.4070	+	29.1794i	1.24734	+	1.12311i
$676$	27.1536	+	12.0896i	1.04437	+	0.464983i
$677$	−1.80242	−	17.1488i	−0.0692725	−	0.659084i	−0.972973	−	0.230919i	$-0.925827\pi$
$677$	−1.80242	−	17.1488i	−0.0692725	−	0.659084i	0.903701	−	0.428165i	$-0.140840\pi$
$678$	10.3214	+	31.7661i	0.396392	+	1.21997i
$679$	6.96461	−	8.25049i	0.267277	−	0.316625i
$680$	−1.04999	−	0.762863i	−0.0402653	−	0.0292545i
$681$	−6.57135	−	3.79397i	−0.251815	−	0.145385i
$682$	−2.55104	+	1.53380i	−0.0976843	+	0.0587321i
$683$	−3.17953	−	5.50711i	−0.121661	−	0.210724i	0.798762	−	0.601648i	$-0.205489\pi$
$683$	−3.17953	−	5.50711i	−0.121661	−	0.210724i	−0.920423	+	0.390924i	$0.872156\pi$
$684$	−27.7577	+	12.3585i	−1.06134	+	0.472539i
$685$	1.28178	+	0.416475i	0.0489742	+	0.0159127i
$686$	−7.63942	−	37.5750i	−0.291674	−	1.43462i
$687$	41.5291	−	30.1727i	1.58443	−	1.15116i
$688$	16.7427	−	1.75973i	0.638310	−	0.0670891i
$689$	0.000380182	0	0.000422235i	1.44838e−5	0	1.60859e-5i
$690$	−9.10860	−	42.8526i	−0.346759	−	1.63137i
$691$	−8.07679	−	18.1408i	−0.307256	−	0.690107i	0.692246	−	0.721661i	$-0.256621\pi$
$691$	−8.07679	−	18.1408i	−0.307256	−	0.690107i	−0.999502	+	0.0315538i	$0.989954\pi$
$692$	−47.6483			−1.81132
$693$	32.6893	+	50.6329i	1.24176	+	1.92338i
$694$	−33.4415			−1.26942
$695$	2.40556	+	5.40298i	0.0912481	+	0.204947i
$696$	−1.99076	−	9.36579i	−0.0754596	−	0.355009i
$697$	3.03442	−	3.37006i	0.114937	−	0.127650i
$698$	26.7409	−	2.81058i	1.01216	−	0.106382i
$699$	40.8692	−	29.6932i	1.54581	−	1.12310i
$700$	12.1926	−	17.9615i	0.460836	−	0.678882i
$701$	−40.7737	−	13.2482i	−1.54000	−	0.500376i	−0.588624	−	0.808407i	$-0.700330\pi$
$701$	−40.7737	−	13.2482i	−1.54000	−	0.500376i	−0.951376	+	0.308031i	$0.900330\pi$
$702$	0.00986704	−	0.00439309i	0.000372407	−	0.000165807i
$703$	0.363916	+	0.630321i	0.0137254	+	0.0237730i
$704$	−13.0848	+	30.8500i	−0.493153	+	1.16270i
$705$	5.99668	+	3.46218i	0.225848	+	0.130393i
$706$	−51.2731	−	37.2521i	−1.92969	−	1.40200i
$707$	−6.83506	+	38.1050i	−0.257059	+	1.43309i
$708$	−27.0782	−	83.3381i	−1.01766	−	3.13204i
$709$	3.71239	+	35.3210i	0.139422	+	1.32651i	0.810769	+	0.585366i	$0.199049\pi$
$709$	3.71239	+	35.3210i	0.139422	+	1.32651i	−0.671347	+	0.741143i	$0.734284\pi$
$710$	18.9642	+	8.44341i	0.711714	+	0.316875i
$711$	8.37473	+	7.54064i	0.314077	+	0.282796i
$712$	−2.86294	−	3.17962i	−0.107293	−	0.119161i
$713$	1.44475	−	1.98853i	0.0541064	−	0.0744711i
$714$	−31.4069	+	4.31938i	−1.17537	+	0.161649i
$715$	−0.000494111		0.00161779i	−1.84787e−5		6.05020e-5i
$716$	−16.3775	+	28.3666i	−0.612055	+	1.06011i
$717$	3.17805	−	30.2371i	0.118687	−	1.12923i
$718$	−37.9726	+	8.07132i	−1.41712	+	0.301219i
$719$	−2.16074	+	10.1655i	−0.0805819	+	0.379108i	−0.999896	−	0.0144163i	$-0.995411\pi$
$719$	−2.16074	+	10.1655i	−0.0805819	+	0.379108i	0.919314	+	0.393524i	$0.128744\pi$
$720$	−16.0432	−	22.0816i	−0.597896	−	0.822933i
$721$	8.98459	−	30.9872i	0.334604	−	1.15402i
$722$	−30.0400	+	9.76060i	−1.11797	+	0.363252i
$723$	−24.3494	+	21.9243i	−0.905564	+	0.815373i
$724$	29.8891	+	3.14147i	1.11082	+	0.116752i
$725$	15.9753	−	9.22336i	0.593309	−	0.342547i
$726$	−33.5512	+	63.1864i	−1.24520	+	2.34507i
$727$			6.55794i			0.243220i	0.992578	+	0.121610i	$0.0388058\pi$
$727$			6.55794i			0.243220i	−0.992578	+	0.121610i	$0.961194\pi$
$728$	−0.000355234	0	0.000572247i	−1.31658e−5	0	2.12089e-5i
$729$	−1.89800	+	5.84145i	−0.0702964	+	0.216350i
$730$	−32.8247	−	6.97711i	−1.21490	−	0.258234i
$731$	−3.77127	+	8.47042i	−0.139486	+	0.313290i
$732$	22.2365	−	49.9439i	0.821884	−	1.84598i
$733$	−48.4357	−	10.2953i	−1.78901	−	0.380267i	−0.810385	−	0.585898i	$-0.800742\pi$
$733$	−48.4357	−	10.2953i	−1.78901	−	0.380267i	−0.978630	+	0.205631i	$0.934075\pi$
$734$	14.1615	−	43.5848i	0.522712	−	1.60874i
$735$	4.38422	+	25.7529i	0.161714	+	0.949912i
$736$		−	45.9940i		−	1.69536i
$737$	32.6230	−	30.4385i	1.20168	−	1.12122i
$738$	−30.3115	+	17.5004i	−1.11578	+	0.644197i
$739$	1.83535	+	0.192903i	0.0675143	+	0.00709604i	0.138225	−	0.990401i	$-0.455860\pi$
$739$	1.83535	+	0.192903i	0.0675143	+	0.00709604i	−0.0707111	+	0.997497i	$0.522527\pi$
$740$	0.759308	−	0.683684i	0.0279127	−	0.0251327i
$741$	−0.00248176		0.000806372i	−9.11697e−5		2.96228e-5i
$742$	7.03913	−	1.73298i	0.258415	−	0.0636198i
$743$	26.0131	+	35.8039i	0.954327	+	1.31352i	0.949578	+	0.313529i	$0.101511\pi$
$743$	26.0131	+	35.8039i	0.954327	+	1.31352i	0.00474837	+	0.999989i	$0.498489\pi$
$744$	−0.167886	+	0.789844i	−0.00615502	+	0.0289571i
$745$	−11.2245	+	2.38585i	−0.411235	+	0.0874108i
$746$	−4.30753	+	40.9834i	−0.157710	+	1.50051i
$747$	33.3907	−	57.8344i	1.22170	−	2.11605i
$748$	−8.41113	−	11.1554i	−0.307541	−	0.407882i
$749$	−4.05852	+	3.15160i	−0.148295	+	0.115157i
$750$	−39.0054	+	53.6863i	−1.42428	+	1.96035i
$751$	−0.611105	−	0.678701i	−0.0222995	−	0.0247662i	0.731892	−	0.681421i	$-0.238638\pi$
$751$	−0.611105	−	0.678701i	−0.0222995	−	0.0247662i	−0.754191	+	0.656655i	$0.771971\pi$
$752$	4.61250	+	4.15311i	0.168200	+	0.151448i
$753$	68.2781	+	30.3994i	2.48819	+	1.10781i
$754$	−0.000477579	−	0.00454387i	−1.73924e−5	−	0.000165478i
$755$	−3.16726	−	9.74784i	−0.115269	−	0.354760i
$756$	72.3531	+	12.9783i	2.63146	+	0.472016i
$757$	13.3894	+	9.72799i	0.486647	+	0.353570i	0.803893	−	0.594773i	$-0.202758\pi$
$757$	13.3894	+	9.72799i	0.486647	+	0.353570i	−0.317246	+	0.948343i	$0.602758\pi$
$758$	25.6680	+	14.8195i	0.932305	+	0.538267i
$759$	5.13224	−	58.8523i	0.186288	−	2.13620i
$760$	−0.681512	−	1.18041i	−0.0247210	−	0.0428181i
$761$	29.7219	−	13.2330i	1.07742	−	0.479697i	0.210216	−	0.977655i	$-0.432583\pi$
$761$	29.7219	−	13.2330i	1.07742	−	0.479697i	0.867201	+	0.497958i	$0.165917\pi$
$762$	−7.58977	−	2.46607i	−0.274949	−	0.0893362i
$763$	−27.9782	+	13.5437i	−1.01288	+	0.490316i
$764$	0.520088	−	0.377866i	0.0188161	−	0.0136707i
$765$	14.9503	−	1.57134i	0.540530	−	0.0568120i
$766$	22.2815	−	24.7462i	0.805065	−	0.894115i
$767$	−0.00108899	−	0.00512327i	−3.93210e−5	−	0.000184991i
$768$	−13.3991	−	30.0948i	−0.483498	−	1.08595i
$769$	3.13977			0.113223			0.0566116	−	0.998396i	$-0.481970\pi$
$769$	3.13977			0.113223			0.0566116	+	0.998396i	$0.481970\pi$
$770$	−16.8091	+	13.5376i	−0.605760	+	0.487859i
$771$	−22.7647			−0.819851
$772$	11.0736	+	24.8718i	0.398549	+	0.895156i
$773$	1.61630	+	7.60409i	0.0581343	+	0.273500i	0.997608	−	0.0691197i	$-0.0220190\pi$
$773$	1.61630	+	7.60409i	0.0581343	+	0.273500i	−0.939474	+	0.342620i	$0.888686\pi$
$774$	47.8848	−	53.1815i	1.72119	−	1.91157i
$775$	−1.54714	+	0.162611i	−0.0555750	+	0.00584117i
$776$	1.95772	−	1.42236i	0.0702779	−	0.0510599i
$777$	0.227299	−	3.11813i	0.00815430	−	0.111862i
$778$	66.8818	+	21.7312i	2.39783	+	0.779101i
$779$	4.35081	−	1.93711i	0.155884	−	0.0694041i
$780$	0.00183162	+	0.00317247i	6.55827e−5	+	0.000113593i
$781$	21.1313	+	18.3587i	0.756138	+	0.656927i
$782$	18.7305	+	10.8141i	0.669801	+	0.386710i
$783$	50.5328	+	36.7142i	1.80589	+	1.31206i
$784$	−0.955451	+	23.3965i	−0.0341233	+	0.835591i
$785$	2.31130	+	7.11344i	0.0824937	+	0.253889i
$786$	−8.68412	−	82.6239i	−0.309752	−	2.94710i
$787$	−47.4107	−	21.1086i	−1.69001	−	0.752440i	−0.999578	−	0.0290413i	$-0.990755\pi$
$787$	−47.4107	−	21.1086i	−1.69001	−	0.752440i	−0.690430	−	0.723399i	$-0.742579\pi$
$788$	13.7354	+	12.3674i	0.489303	+	0.440571i
$789$	−32.0957	−	35.6459i	−1.14264	−	1.26903i
$790$	−2.37210	+	3.26491i	−0.0843954	+	0.116160i
$791$	−5.12716	+	12.5830i	−0.182301	+	0.447401i
$792$	4.40122	+	12.7704i	0.156390	+	0.453776i
$793$	0.00163391	−	0.00283002i	5.80219e−5	−	0.000100497i
$794$	−4.82812	+	45.9365i	−0.171343	+	1.63022i
$795$	−4.83101	+	1.02686i	−0.171338	+	0.0364191i
$796$	−0.751503	+	3.53554i	−0.0266363	+	0.125314i
$797$	15.0416	+	20.7030i	0.532800	+	0.733337i	0.987554	−	0.157281i	$-0.0502727\pi$
$797$	15.0416	+	20.7030i	0.532800	+	0.733337i	−0.454754	+	0.890617i	$0.650273\pi$
$798$	−31.9773	−	9.27165i	−1.13198	−	0.328213i
$799$	−3.25111	+	1.05635i	−0.115016	+	0.0373710i
$800$	−21.6329	+	19.4784i	−0.764840	+	0.688665i
$801$	49.2861	+	5.18018i	1.74144	+	0.183032i
$802$	12.7088	−	7.33745i	0.448764	−	0.259094i
$803$	−39.5840	−	21.9272i	−1.39689	−	0.773794i
$804$		−	96.6244i		−	3.40768i
$805$	8.41335	−	15.7111i	0.296532	−	0.553743i
$806$	−0.000119067	0	0.000366450i	−4.19395e−6	0	1.29076e-5i
$807$	−37.8281	−	8.04061i	−1.33161	−	0.283043i
$808$	−3.52906	+	7.92639i	−0.124152	+	0.278849i
$809$	−5.33679	+	11.9866i	−0.187631	+	0.421427i	−0.982728	−	0.185056i	$-0.940753\pi$
$809$	−5.33679	+	11.9866i	−0.187631	+	0.421427i	0.795097	+	0.606483i	$0.207420\pi$
$810$	−42.2651	−	8.98372i	−1.48504	−	0.315656i
$811$	−12.0585	+	37.1123i	−0.423431	+	1.30319i	0.481057	+	0.876689i	$0.340253\pi$
$811$	−12.0585	+	37.1123i	−0.423431	+	1.30319i	−0.904488	+	0.426498i	$0.859747\pi$
$812$	14.6792	−	27.4119i	0.515138	−	0.961967i
$813$			89.3492i			3.13361i
$814$	2.34066	−	1.09227i	0.0820402	−	0.0382840i
$815$	11.3813	−	6.57098i	0.398669	−	0.230171i
$816$	19.2543	+	2.02371i	0.674035	+	0.0708440i
$817$	−7.23642	+	6.51571i	−0.253170	+	0.227956i
$818$	32.1639	−	10.4507i	1.12458	−	0.365400i
$819$	0.00749280	+	0.00217250i	0.000261820	+	7.59133e-5i
$820$	−3.92982	−	5.40893i	−0.137235	−	0.188888i
$821$	−5.04690	+	23.7438i	−0.176138	+	0.828664i	0.797991	+	0.602670i	$0.205896\pi$
$821$	−5.04690	+	23.7438i	−0.176138	+	0.828664i	−0.974129	+	0.225994i	$0.927437\pi$
$822$	7.21711	−	1.53405i	0.251726	−	0.0535060i
$823$	−1.05927	+	10.0783i	−0.0369237	+	0.351306i	0.960425	+	0.278538i	$0.0898499\pi$
$823$	−1.05927	+	10.0783i	−0.0369237	+	0.351306i	−0.997349	+	0.0727678i	$0.976817\pi$
$824$	3.61550	−	6.26222i	0.125952	−	0.218155i
$825$	−29.8543	+	22.5100i	−1.03939	+	0.783697i
$826$	25.2172	−	61.8878i	0.877419	−	2.15335i
$827$	3.75863	−	5.17332i	0.130701	−	0.179894i	−0.738651	−	0.674088i	$-0.764537\pi$
$827$	3.75863	−	5.17332i	0.130701	−	0.179894i	0.869352	+	0.494194i	$0.164537\pi$
$828$	−59.5803	−	66.1706i	−2.07056	−	2.29959i
$829$	27.1232	+	24.4218i	0.942026	+	0.848204i	0.988578	−	0.150712i	$-0.0481565\pi$
$829$	27.1232	+	24.4218i	0.942026	+	0.848204i	−0.0465516	+	0.998916i	$0.514823\pi$
$830$	21.8475	+	9.72714i	0.758339	+	0.337634i
$831$	1.02746	+	9.77565i	0.0356423	+	0.339113i
$832$	0.00134043	+	0.00412541i	4.64710e−5	+	0.000143023i
$833$	−10.8964	−	6.89867i	−0.377538	−	0.239025i
$834$	26.1947	+	19.0316i	0.907048	+	0.659009i
$835$	7.19178	+	4.15218i	0.248882	+	0.143692i
$836$	−3.30462	−	14.2955i	−0.114293	−	0.494422i
$837$	−2.63380	−	4.56187i	−0.0910373	−	0.157681i
$838$	63.0808	−	28.0854i	2.17909	−	0.970193i
$839$	−41.7978	−	13.5809i	−1.44302	−	0.468866i	−0.520184	−	0.854054i	$-0.674137\pi$
$839$	−41.7978	−	13.5809i	−1.44302	−	0.468866i	−0.922838	+	0.385188i	$0.874137\pi$
$840$	−0.425667	+	5.83938i	−0.0146869	+	0.201478i
$841$	−2.08545	+	1.51517i	−0.0719121	+	0.0522472i
$842$	−12.0356	+	1.26500i	−0.414776	+	0.0435947i
$843$	−2.27967	+	2.53183i	−0.0785160	+	0.0872009i
$844$	1.38428	+	6.51254i	0.0476490	+	0.224171i
$845$	−6.28160	−	14.1087i	−0.216094	−	0.485354i
$846$	26.3839			0.907096
$847$	−27.0101	+	10.8377i	−0.928077	+	0.372388i
$848$	−4.42707			−0.152026
$849$	−12.9053	−	28.9857i	−0.442907	−	0.994786i
$850$	−2.84602	−	13.3895i	−0.0976178	−	0.459256i
$851$	−1.42719	+	1.58505i	−0.0489233	+	0.0543349i
$852$	60.2882	−	6.33654i	2.06544	−	0.217086i
$853$	28.6425	−	20.8100i	0.980699	−	0.712520i	0.0228344	−	0.999739i	$-0.492731\pi$
$853$	28.6425	−	20.8100i	0.980699	−	0.712520i	0.957865	+	0.287220i	$0.0927310\pi$
$854$	37.5283	−	18.1667i	1.28419	−	0.621652i
$855$	15.0148	+	4.87859i	0.513494	+	0.166844i
$856$	−1.05209	+	0.468421i	−0.0359598	+	0.0160103i
$857$	3.84956	+	6.66764i	0.131499	+	0.227762i	0.924254	−	0.381777i	$-0.124688\pi$
$857$	3.84956	+	6.66764i	0.131499	+	0.227762i	−0.792756	+	0.609539i	$0.791354\pi$
$858$	0.00208573	+	0.00902273i	7.12058e−5	+	0.000308031i
$859$	32.8820	+	18.9844i	1.12192	+	0.647740i	0.941890	−	0.335921i	$-0.109047\pi$
$859$	32.8820	+	18.9844i	1.12192	+	0.647740i	0.180029	+	0.983661i	$0.442381\pi$
$860$	11.0591	+	8.03494i	0.377114	+	0.273989i
$861$	−20.1362	−	3.61192i	−0.686240	−	0.123094i
$862$	12.5757	+	38.7041i	0.428331	+	1.31827i
$863$	−1.24761	−	11.8702i	−0.0424691	−	0.404067i	−0.995019	−	0.0996845i	$-0.968217\pi$
$863$	−1.24761	−	11.8702i	−0.0424691	−	0.404067i	0.952550	−	0.304382i	$-0.0984500\pi$
$864$	−90.0469	−	40.0914i	−3.06346	−	1.36394i
$865$	18.3984	+	16.5660i	0.625565	+	0.563261i
$866$	−0.714295	−	0.793305i	−0.0242727	−	0.0269576i
$867$	25.1222	−	34.5777i	0.853194	−	1.17432i
$868$	−2.07117	+	1.60835i	−0.0703002	+	0.0545909i
$869$	−4.34517	+	3.27623i	−0.147400	+	0.111139i
$870$	−19.8580	+	34.3950i	−0.673248	+	1.16610i
$871$	0.000603709	−	0.00574390i	2.04559e−5	−	0.000194625i
$872$	−6.81440	+	1.44845i	−0.230765	+	0.0490505i
$873$	−5.82746	+	27.4160i	−0.197230	+	0.927893i
$874$	13.3510	+	18.3760i	0.451604	+	0.621579i
$875$	−26.2126	+	6.45336i	−0.886149	+	0.218163i
$876$	−93.2000	+	30.2825i	−3.14894	+	1.02315i
$877$	−17.2679	+	15.5481i	−0.583096	+	0.525022i	−0.907035	−	0.421056i	$-0.861660\pi$
$877$	−17.2679	+	15.5481i	−0.583096	+	0.525022i	0.323938	+	0.946078i	$0.394993\pi$
$878$	48.4241	+	5.08958i	1.63424	+	0.171765i
$879$	−63.5853	+	36.7110i	−2.14468	+	1.23823i
$880$	11.9438	−	5.57359i	0.402627	−	0.187886i
$881$		−	36.6233i		−	1.23387i	−0.787014	−	0.616935i	$-0.788374\pi$
$881$		−	36.6233i		−	1.23387i	0.787014	−	0.616935i	$-0.211626\pi$
$882$	63.5302	+	76.6272i	2.13917	+	2.58017i
$883$	4.94860	−	15.2302i	0.166534	−	0.512537i	−0.832613	−	0.553856i	$-0.813156\pi$
$883$	4.94860	−	15.2302i	0.166534	−	0.512537i	0.999146	+	0.0413185i	$0.0131558\pi$
$884$	−0.00176895		0.000376003i	−5.94964e−5		1.26463e-5i
$885$	−18.5187	+	41.5936i	−0.622499	+	1.39815i
$886$	−15.0357	+	33.7708i	−0.505135	+	1.13455i
$887$	17.3005	+	3.67733i	0.580893	+	0.123473i	0.488981	−	0.872294i	$-0.337369\pi$
$887$	17.3005	+	3.67733i	0.580893	+	0.123473i	0.0919122	+	0.995767i	$0.470702\pi$
$888$	0.216528	−	0.666405i	0.00726621	−	0.0223631i
$889$	−1.71220	−	2.75819i	−0.0574254	−	0.0925069i
$890$			17.7470i			0.594882i
$891$	−50.9683	−	28.2335i	−1.70750	−	0.945857i
$892$	−44.0565	+	25.4360i	−1.47512	+	0.851661i
$893$	−3.57039	−	0.375264i	−0.119479	−	0.0125577i
$894$	−46.6864	+	42.0366i	−1.56143	+	1.40592i
$895$	16.1861	−	5.25919i	0.541042	−	0.175795i
$896$	−3.45928	+	11.9308i	−0.115566	+	0.398581i
$897$	−0.00449480	−	0.00618656i	−0.000150077	−	0.000206563i
$898$	−3.07217	+	14.4534i	−0.102520	+	0.482317i
$899$	−2.17957	+	0.463282i	−0.0726927	+	0.0154513i
$900$	−5.89070	+	56.0463i	−0.196357	+	1.86821i
$901$	1.21913	−	2.11159i	0.0406151	−	0.0703474i
$902$	−5.50713	−	15.9793i	−0.183367	−	0.532052i
$903$	41.4377	−	5.69892i	1.37896	−	0.189648i
$904$	−1.78997	+	2.46368i	−0.0595334	+	0.0819407i
$905$	−10.4489	−	11.6046i	−0.347332	−	0.385751i
$906$	−41.6992	−	37.5462i	−1.38536	−	1.24739i
$907$	−25.1387	−	11.1925i	−0.834715	−	0.371639i	−0.0555487	−	0.998456i	$-0.517691\pi$
$907$	−25.1387	−	11.1925i	−0.834715	−	0.371639i	−0.779167	+	0.626817i	$0.784357\pi$
$908$	−0.577289	−	5.49254i	−0.0191580	−	0.182276i
$909$	−31.0553	−	95.5785i	−1.03004	−	3.17014i
$910$	−0.000493256		0.00274987i	−1.63513e−5		9.11573e-5i
$911$	−19.5497	−	14.2037i	−0.647709	−	0.470588i	0.214781	−	0.976662i	$-0.431096\pi$
$911$	−19.5497	−	14.2037i	−0.647709	−	0.470588i	−0.862490	+	0.506074i	$0.831096\pi$
$912$	17.6084	+	10.1662i	0.583072	+	0.336637i
$913$	24.3441	+	21.1500i	0.805673	+	0.699963i
$914$	−25.1528	−	43.5660i	−0.831981	−	1.44103i
$915$	−25.9503	+	11.5538i	−0.857890	+	0.381957i
$916$	35.5333	+	11.5455i	1.17405	+	0.381473i
$917$	18.9816	−	27.9628i	0.626826	−	0.923412i
$918$	37.4985	−	27.2442i	1.23763	−	0.899194i
$919$	38.2015	−	4.01514i	1.26015	−	0.132447i	0.549201	−	0.835690i	$-0.314932\pi$
$919$	38.2015	−	4.01514i	1.26015	−	0.132447i	0.710950	+	0.703243i	$0.248265\pi$
$920$	2.67272	−	2.96835i	0.0881169	−	0.0978637i
$921$	−20.5903	−	96.8698i	−0.678474	−	3.19197i
$922$	−17.1900	−	38.6095i	−0.566124	−	1.27154i
$923$	0.00362346			0.000119268
$924$	−22.7436	+	58.7792i	−0.748211	+	1.93369i
$925$	1.34993			0.0443854
$926$	29.8973	+	67.1504i	0.982485	+	2.20670i
$927$	17.4135	+	81.9239i	0.571933	+	2.69073i
$928$	−27.9000	+	30.9860i	−0.915861	+	1.01717i
$929$	−3.26028	+	0.342669i	−0.106966	+	0.0112426i	−0.157860	−	0.987461i	$-0.550460\pi$
$929$	−3.26028	+	0.342669i	−0.106966	+	0.0112426i	0.0508941	+	0.998704i	$0.483793\pi$
$930$	2.70969	−	1.96870i	0.0888541	−	0.0645563i
$931$	−7.50734	−	11.2732i	−0.246043	−	0.369464i
$932$	34.9687	+	11.3620i	1.14544	+	0.372175i
$933$	50.4238	−	22.4501i	1.65080	−	0.734983i
$934$	−23.1313	−	40.0645i	−0.756878	−	1.31095i
$935$	−0.630647	+	7.23175i	−0.0206244	+	0.236503i
$936$	0.00151422		0.000874237i	4.94939e−5		2.85753e-5i
$937$	−34.0171	−	24.7148i	−1.11129	−	0.807398i	−0.128423	−	0.991720i	$-0.540991\pi$
$937$	−34.0171	−	24.7148i	−1.11129	−	0.807398i	−0.982866	+	0.184321i	$0.940991\pi$
$938$	47.5336	−	56.3097i	1.55203	−	1.83858i
$939$	−20.1248	−	61.9379i	−0.656749	−	2.02127i
$940$	0.526805	+	5.01221i	0.0171825	+	0.163480i
$941$	29.2204	+	13.0098i	0.952558	+	0.424106i	0.823364	−	0.567513i	$-0.192095\pi$
$941$	29.2204	+	13.0098i	0.952558	+	0.424106i	0.129193	+	0.991619i	$0.458761\pi$
$942$	30.4298	+	27.3991i	0.991457	+	0.892712i
$943$	9.33877	+	10.3718i	0.304112	+	0.337751i
$944$	−23.9882	+	33.0169i	−0.780750	+	1.07461i
$945$	−23.4254	−	30.1665i	−0.762030	−	0.981315i
$946$	20.8048	+	27.5928i	0.676424	+	0.897119i
$947$	−14.5194	+	25.1484i	−0.471818	+	0.817212i	−0.999480	−	0.0322419i	$-0.989735\pi$
$947$	−14.5194	+	25.1484i	−0.471818	+	0.817212i	0.527662	+	0.849454i	$0.323069\pi$
$948$	−1.23186	+	11.7204i	−0.0400090	+	0.380660i
$949$	−0.00572954	+	0.00121785i	−0.000185989	+	3.95331e-5i
$950$	2.98892	−	14.0618i	0.0969734	−	0.456224i
$951$	58.0267	+	79.8669i	1.88164	+	2.58986i
$952$	−2.00171	−	2.08513i	−0.0648759	−	0.0675794i
$953$	9.63423	−	3.13035i	0.312083	−	0.101402i	−0.148788	−	0.988869i	$-0.547537\pi$
$953$	9.63423	−	3.13035i	0.312083	−	0.101402i	0.460871	+	0.887467i	$0.347537\pi$
$954$	−13.9851	+	12.5922i	−0.452784	+	0.407689i
$955$	−0.332195	−	0.0349151i	−0.0107496	−	0.00112983i
$956$	19.1643	−	11.0645i	0.619816	−	0.357851i
$957$	−39.1574	+	36.5355i	−1.26578	+	1.18102i
$958$			79.8349i			2.57935i
$959$	2.64602	+	1.41695i	0.0854443	+	0.0457558i
$960$	11.6519	−	35.8609i	0.376064	−	1.15740i
$961$	−30.1388	−	6.40619i	−0.972218	−	0.206651i
$962$	0.000135993	0	0.000305445i	4.38459e−6	0	9.84795e-6i
$963$	5.42557	−	12.1860i	0.174837	−	0.392689i
$964$	−23.3267	−	4.95825i	−0.751303	−	0.159694i
$965$	4.37138	−	13.4537i	0.140720	−	0.433091i
$966$	−3.11703	−	97.5184i	−0.100289	−	3.13760i
$967$			6.35801i			0.204460i	0.994761	+	0.102230i	$0.0325978\pi$
$967$			6.35801i			0.204460i	−0.994761	+	0.102230i	$0.967402\pi$
$968$	−6.45872	+	0.911419i	−0.207591	+	0.0292941i
$969$	−9.69802	+	5.59915i	−0.311545	+	0.179871i
$970$	−9.98231	−	1.04918i	−0.320513	−	0.0336872i
$971$	−37.6879	+	33.9343i	−1.20946	+	1.08900i	−0.215818	+	0.976434i	$0.569242\pi$
$971$	−37.6879	+	33.9343i	−1.20946	+	1.08900i	−0.993644	+	0.112570i	$0.964092\pi$
$972$	−40.7337	+	13.2352i	−1.30653	+	0.424519i
$973$	3.14873	+	12.7897i	0.100944	+	0.410019i
$974$	−48.2044	−	66.3476i	−1.54457	−	2.12591i
$975$	−0.00100626	+	0.00473410i	−3.22262e−5	+	0.000151613i
$976$	−24.9057	+	5.29387i	−0.797212	+	0.169453i
$977$	0.500031	−	4.75747i	0.0159974	−	0.152205i	−0.983607	−	0.180325i	$-0.942285\pi$
$977$	0.500031	−	4.75747i	0.0159974	−	0.152205i	0.999605	+	0.0281194i	$0.00895187\pi$
$978$	35.9735	−	62.3080i	1.15031	−	1.99239i
$979$	−6.99033	+	22.8874i	−0.223412	+	0.731483i
$980$	−13.2886	+	13.5990i	−0.424488	+	0.434404i
$981$	47.4297	−	65.2814i	1.51431	−	2.08427i
$982$	−8.27185	−	9.18682i	−0.263965	−	0.293163i
$983$	−16.2786	−	14.6573i	−0.519206	−	0.467495i	0.367372	−	0.930074i	$-0.380257\pi$
$983$	−16.2786	−	14.6573i	−0.519206	−	0.467495i	−0.886578	+	0.462579i	$0.846924\pi$
$984$	−4.18862	−	1.86489i	−0.133528	−	0.0594507i
$985$	−1.00383	−	9.55084i	−0.0319848	−	0.304315i
$986$	−6.05888	−	18.6473i	−0.192954	−	0.593852i
$987$	11.7839	+	9.94735i	0.375086	+	0.316628i
$988$	−0.00153655	−	0.00111637i	−4.88841e−5	−	3.55163e-5i
$989$	−24.7127	−	14.2679i	−0.785817	−	0.453692i
$990$	21.8772	−	51.5797i	0.695302	−	1.63931i
$991$	−15.6744	−	27.1488i	−0.497912	−	0.862410i	0.502085	−	0.864818i	$-0.332567\pi$
$991$	−15.6744	−	27.1488i	−0.497912	−	0.862410i	−0.999997	+	0.00240886i	$0.999233\pi$
$992$	3.21233	−	1.43022i	0.101991	−	0.0454095i
$993$	71.2118	+	23.1381i	2.25984	+	0.734266i
$994$	38.2513	+	25.9656i	1.21326	+	0.823578i
$995$	1.51939	−	1.10390i	0.0481679	−	0.0349960i
$996$	69.4544	−	7.29995i	2.20075	−	0.231308i
$997$	−18.3711	+	20.4032i	−0.581818	+	0.646175i	−0.960147	−	0.279497i	$-0.909832\pi$
$997$	−18.3711	+	20.4032i	−0.581818	+	0.646175i	0.378328	+	0.925671i	$0.376499\pi$
$998$	4.87638	+	22.9416i	0.154359	+	0.726202i
$999$	1.85918	+	4.17578i	0.0588217	+	0.132116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.40.1	yes	48
3.2	odd	2		693.2.cg.a.271.6		48
7.2	even	3		539.2.m.a.293.1		48
7.3	odd	6	inner	77.2.n.a.73.6	yes	48
7.4	even	3		539.2.s.d.227.6		48
7.5	odd	6		539.2.m.a.293.2		48
7.6	odd	2		539.2.s.d.117.1		48
11.2	odd	10		847.2.r.d.215.6		48
11.3	even	5		847.2.r.c.481.1		48
11.4	even	5		847.2.r.d.838.6		48
11.5	even	5		847.2.i.b.362.21		48
11.6	odd	10		847.2.i.b.362.4		48
11.7	odd	10		847.2.r.a.838.1		48
11.8	odd	10	inner	77.2.n.a.19.6	✓	48
11.9	even	5		847.2.r.a.215.1		48
11.10	odd	2		847.2.r.c.40.6		48
21.17	even	6		693.2.cg.a.73.1		48
33.8	even	10		693.2.cg.a.19.1		48
77.3	odd	30		847.2.r.c.360.6		48
77.10	even	6		847.2.r.c.766.1		48
77.17	even	30		847.2.i.b.241.21		48
77.19	even	30		539.2.m.a.195.1		48
77.24	even	30		847.2.r.d.94.6		48
77.30	odd	30		539.2.m.a.195.2		48
77.31	odd	30		847.2.r.a.94.1		48
77.38	odd	30		847.2.i.b.241.4		48
77.41	even	10		539.2.s.d.19.6		48
77.52	even	30	inner	77.2.n.a.52.1	yes	48
77.59	odd	30		847.2.r.d.717.6		48
77.73	even	30		847.2.r.a.717.1		48
77.74	odd	30		539.2.s.d.129.1		48
231.206	odd	30		693.2.cg.a.514.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.19.6	✓	48	11.8	odd	10	inner
77.2.n.a.40.1	yes	48	1.1	even	1	trivial
77.2.n.a.52.1	yes	48	77.52	even	30	inner
77.2.n.a.73.6	yes	48	7.3	odd	6	inner
539.2.m.a.195.1		48	77.19	even	30
539.2.m.a.195.2		48	77.30	odd	30
539.2.m.a.293.1		48	7.2	even	3
539.2.m.a.293.2		48	7.5	odd	6
539.2.s.d.19.6		48	77.41	even	10
539.2.s.d.117.1		48	7.6	odd	2
539.2.s.d.129.1		48	77.74	odd	30
539.2.s.d.227.6		48	7.4	even	3
693.2.cg.a.19.1		48	33.8	even	10
693.2.cg.a.73.1		48	21.17	even	6
693.2.cg.a.271.6		48	3.2	odd	2
693.2.cg.a.514.6		48	231.206	odd	30
847.2.i.b.241.4		48	77.38	odd	30
847.2.i.b.241.21		48	77.17	even	30
847.2.i.b.362.4		48	11.6	odd	10
847.2.i.b.362.21		48	11.5	even	5
847.2.r.a.94.1		48	77.31	odd	30
847.2.r.a.215.1		48	11.9	even	5
847.2.r.a.717.1		48	77.73	even	30
847.2.r.a.838.1		48	11.7	odd	10
847.2.r.c.40.6		48	11.10	odd	2
847.2.r.c.360.6		48	77.3	odd	30
847.2.r.c.481.1		48	11.3	even	5
847.2.r.c.766.1		48	77.10	even	6
847.2.r.d.94.6		48	77.24	even	30
847.2.r.d.215.6		48	11.2	odd	10
847.2.r.d.717.6		48	77.59	odd	30
847.2.r.d.838.6		48	11.4	even	5

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.n (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.842093 - 1.89137i) q^{2} +(0.653128 + 3.07273i) q^{3} +(-1.52991 + 1.69913i) q^{4} +(1.18148 - 0.124179i) q^{5} +(5.26167 - 3.82283i) q^{6} +(2.63875 + 0.192354i) q^{7} +(0.563952 + 0.183239i) q^{8} +(-6.27443 + 2.79356i) q^{9} +O(q^{10})\)	\(q+(-0.842093 - 1.89137i) q^{2} +(0.653128 + 3.07273i) q^{3} +(-1.52991 + 1.69913i) q^{4} +(1.18148 - 0.124179i) q^{5} +(5.26167 - 3.82283i) q^{6} +(2.63875 + 0.192354i) q^{7} +(0.563952 + 0.183239i) q^{8} +(-6.27443 + 2.79356i) q^{9} +(-1.22979 - 2.13006i) q^{10} +(-0.746987 - 3.23141i) q^{11} +(-6.22020 - 3.59123i) q^{12} +(-0.000347326 - 0.000252347i) q^{13} +(-1.85826 - 5.15284i) q^{14} +(1.15323 + 3.54927i) q^{15} +(0.349663 + 3.32682i) q^{16} +(-1.68310 - 0.749362i) q^{17} +(10.5673 + 9.51485i) q^{18} +(-1.29469 - 1.43790i) q^{19} +(-1.59656 + 2.19748i) q^{20} +(1.13239 + 8.23379i) q^{21} +(-5.48277 + 4.13398i) q^{22} +(2.83507 - 4.91048i) q^{23} +(-0.194711 + 1.85255i) q^{24} +(-3.51025 + 0.746128i) q^{25} +(-0.000184801 + 0.000869422i) q^{26} +(-7.14248 - 9.83078i) q^{27} +(-4.36388 + 4.18931i) q^{28} +(-4.88867 + 1.58843i) q^{29} +(5.74187 - 5.17000i) q^{30} +(0.431118 + 0.0453123i) q^{31} +(7.02487 - 4.05581i) q^{32} +(9.44136 - 4.40581i) q^{33} +3.81439i q^{34} +(3.14153 - 0.100414i) q^{35} +(4.85267 - 14.9350i) q^{36} +(-0.367944 - 0.0782088i) q^{37} +(-1.62935 + 3.65958i) q^{38} +(0.000548545 - 0.00123205i) q^{39} +(0.689054 + 0.146463i) q^{40} +(-0.760621 + 2.34095i) q^{41} +(14.6196 - 9.07539i) q^{42} -5.03264i q^{43} +(6.63342 + 3.67453i) q^{44} +(-7.06624 + 4.07969i) q^{45} +(-11.6749 - 1.22708i) q^{46} +(1.37886 - 1.24153i) q^{47} +(-9.99404 + 3.24726i) q^{48} +(6.92600 + 1.01515i) q^{49} +(4.36717 + 6.01089i) q^{50} +(1.20331 - 5.66112i) q^{51} +(0.000960148 - 0.000204086i) q^{52} +(-0.138336 + 1.31618i) q^{53} +(-12.5790 + 21.7875i) q^{54} +(-1.28383 - 3.72510i) q^{55} +(1.45288 + 0.592000i) q^{56} +(3.57267 - 4.91735i) q^{57} +(7.12103 + 7.90870i) q^{58} +(9.06645 + 8.16347i) q^{59} +(-7.79502 - 3.47057i) q^{60} +(0.795634 + 7.56996i) q^{61} +(-0.277339 - 0.853562i) q^{62} +(-17.0940 + 6.16458i) q^{63} +(-8.17409 - 5.93882i) q^{64} +(-0.000441696 - 0.000255013i) q^{65} +(-16.2835 - 14.1470i) q^{66} +(6.72641 + 11.6505i) q^{67} +(3.84825 - 1.71335i) q^{68} +(16.9402 + 5.50421i) q^{69} +(-2.83538 - 5.85724i) q^{70} +(-6.82813 + 4.96093i) q^{71} +(-4.05037 + 0.425711i) q^{72} +(9.12950 - 10.1393i) q^{73} +(0.161921 + 0.761777i) q^{74} +(-4.58529 - 10.2987i) q^{75} +4.42393 q^{76} +(-1.34954 - 8.67057i) q^{77} -0.00279219 q^{78} +(-0.667370 - 1.49894i) q^{79} +(0.826243 + 3.88717i) q^{80} +(11.7551 - 13.0554i) q^{81} +(5.06812 - 0.532681i) q^{82} +(-7.86628 + 5.71519i) q^{83} +(-15.7228 - 10.6728i) q^{84} +(-2.08161 - 0.676354i) q^{85} +(-9.51860 + 4.23795i) q^{86} +(-8.07373 - 13.9841i) q^{87} +(0.170856 - 1.95924i) q^{88} +(-6.24880 - 3.60774i) q^{89} +(13.6667 + 9.92940i) q^{90} +(-0.000867966 - 0.000732690i) q^{91} +(4.00617 + 12.3297i) q^{92} +(0.142343 + 1.35430i) q^{93} +(-3.50933 - 1.56245i) q^{94} +(-1.70821 - 1.53808i) q^{95} +(17.0505 + 18.9365i) q^{96} +(2.39869 - 3.30152i) q^{97} +(-3.91231 - 13.9545i) q^{98} +(13.7140 + 18.1885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Introduction

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