LMFDB - Embedded newform 572.2.bs.a.15.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(15,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 12, 5]))

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

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

chi := DirichletCharacter("572.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bs (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$80$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			15.5
Character	$\chi$	$=$	572.15
Dual form			572.2.bs.a.267.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40168 + 0.187875i) q^{2} +(0.525158 + 2.47067i) q^{3} +(1.92941 - 0.526680i) q^{4} +(-0.0408544 + 0.257944i) q^{5} +(-1.20028 - 3.36443i) q^{6} +(2.76404 - 1.79499i) q^{7} +(-2.60546 + 1.10072i) q^{8} +(-3.08781 + 1.37478i) q^{9} +O(q^{10})$	\(q+(-1.40168 + 0.187875i) q^{2} +(0.525158 + 2.47067i) q^{3} +(1.92941 - 0.526680i) q^{4} +(-0.0408544 + 0.257944i) q^{5} +(-1.20028 - 3.36443i) q^{6} +(2.76404 - 1.79499i) q^{7} +(-2.60546 + 1.10072i) q^{8} +(-3.08781 + 1.37478i) q^{9} +(0.00880344 - 0.369231i) q^{10} +(-2.46606 + 2.21778i) q^{11} +(2.31450 + 4.49034i) q^{12} +(-2.67665 + 2.41569i) q^{13} +(-3.53707 + 3.03529i) q^{14} +(-0.658752 + 0.0345237i) q^{15} +(3.44522 - 2.03236i) q^{16} +(-3.66074 + 0.384759i) q^{17} +(4.06983 - 2.50712i) q^{18} +(0.0203016 - 0.387378i) q^{19} +(0.0570296 + 0.519197i) q^{20} +(5.88640 + 5.88640i) q^{21} +(3.03995 - 3.57193i) q^{22} +(4.40503 + 7.62974i) q^{23} +(-4.08781 - 5.85918i) q^{24} +(4.69042 + 1.52401i) q^{25} +(3.29795 - 3.88890i) q^{26} +(-0.564212 - 0.776572i) q^{27} +(4.38758 - 4.91903i) q^{28} +(-3.77690 + 4.19467i) q^{29} +(0.916872 - 0.172154i) q^{30} +(0.421128 + 2.65890i) q^{31} +(-4.44726 + 3.49599i) q^{32} +(-6.77449 - 4.92813i) q^{33} +(5.05889 - 1.22707i) q^{34} +(0.350084 + 0.786303i) q^{35} +(-5.23356 + 4.27880i) q^{36} +(-6.52444 + 0.341931i) q^{37} +(0.0443223 + 0.546794i) q^{38} +(-7.37405 - 5.34451i) q^{39} +(-0.177481 - 0.717032i) q^{40} +(5.31054 - 8.17751i) q^{41} +(-9.35675 - 7.14493i) q^{42} +(-0.960567 + 1.66375i) q^{43} +(-3.58996 + 5.57783i) q^{44} +(-0.228466 - 0.852648i) q^{45} +(-7.60787 - 9.86685i) q^{46} +(0.892243 + 1.75113i) q^{47} +(6.83059 + 7.44470i) q^{48} +(1.57079 - 3.52805i) q^{49} +(-6.86078 - 1.25496i) q^{50} +(-2.87308 - 8.84243i) q^{51} +(-3.89204 + 6.07059i) q^{52} +(-3.05406 - 2.21891i) q^{53} +(0.936743 + 0.982503i) q^{54} +(-0.471316 - 0.726711i) q^{55} +(-5.22581 + 7.71922i) q^{56} +(0.967748 - 0.153276i) q^{57} +(4.50593 - 6.58917i) q^{58} +(-1.52074 + 0.987579i) q^{59} +(-1.25282 + 0.413562i) q^{60} +(0.0743889 + 0.707763i) q^{61} +(-1.08983 - 3.64780i) q^{62} +(-6.06711 + 9.34254i) q^{63} +(5.57681 - 5.73578i) q^{64} +(-0.513761 - 0.789117i) q^{65} +(10.4215 + 5.63490i) q^{66} +(1.19427 - 4.45707i) q^{67} +(-6.86040 + 2.67040i) q^{68} +(-16.5373 + 14.8902i) q^{69} +(-0.638432 - 1.03637i) q^{70} +(0.675652 - 0.834361i) q^{71} +(6.53190 - 6.98075i) q^{72} +(-1.97553 + 3.87719i) q^{73} +(9.08093 - 1.70506i) q^{74} +(-1.30212 + 12.3888i) q^{75} +(-0.164855 - 0.758103i) q^{76} +(-2.83538 + 10.5566i) q^{77} +(11.3401 + 6.10588i) q^{78} +(5.88565 - 8.10090i) q^{79} +(0.383484 + 0.971705i) q^{80} +(-5.16268 + 5.73374i) q^{81} +(-5.90732 + 12.4600i) q^{82} +(16.5342 + 2.61876i) q^{83} +(14.4575 + 8.25700i) q^{84} +(0.0503107 - 0.959986i) q^{85} +(1.03383 - 2.51251i) q^{86} +(-12.3471 - 7.12863i) q^{87} +(3.98403 - 8.49279i) q^{88} +(3.93129 - 14.6718i) q^{89} +(0.480428 + 1.15222i) q^{90} +(-3.06223 + 11.4816i) q^{91} +(12.5175 + 12.4008i) q^{92} +(-6.34811 + 2.43681i) q^{93} +(-1.57963 - 2.28689i) q^{94} +(0.0990927 + 0.0210628i) q^{95} +(-10.9730 - 9.15178i) q^{96} +(2.31981 - 6.04332i) q^{97} +(-1.53891 + 5.24030i) q^{98} +(4.56574 - 10.2384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−1.40168	+	0.187875i	−0.991136	+	0.132848i
$2$	−1.40168	+	0.187875i	−0.991136	+	0.132848i
$3$	0.525158	+	2.47067i	0.303200	+	1.42644i	0.820993	+	0.570939i	$0.193421\pi$
$3$	0.525158	+	2.47067i	0.303200	+	1.42644i	−0.517793	+	0.855506i	$0.673246\pi$
$4$	1.92941	−	0.526680i	0.964703	−	0.263340i
$5$	−0.0408544	+	0.257944i	−0.0182706	+	0.115356i	−0.995138	−	0.0984894i	$-0.968599\pi$
$5$	−0.0408544	+	0.257944i	−0.0182706	+	0.115356i	0.976867	+	0.213846i	$0.0685989\pi$
$6$	−1.20028	−	3.36443i	−0.490013	−	1.37352i
$7$	2.76404	−	1.79499i	1.04471	−	0.678443i	0.0962558	−	0.995357i	$-0.469313\pi$
$7$	2.76404	−	1.79499i	1.04471	−	0.678443i	0.948454	+	0.316914i	$0.102647\pi$
$8$	−2.60546	+	1.10072i	−0.921168	+	0.389165i
$9$	−3.08781	+	1.37478i	−1.02927	+	0.458260i
$10$	0.00880344	−	0.369231i	0.00278389	−	0.116761i
$11$	−2.46606	+	2.21778i	−0.743544	+	0.668687i
$11$	−2.46606	+	2.21778i	−0.743544	+	0.668687i
$12$	2.31450	+	4.49034i	0.668138	+	1.29625i
$13$	−2.67665	+	2.41569i	−0.742368	+	0.669992i
$13$	−2.67665	+	2.41569i	−0.742368	+	0.669992i
$14$	−3.53707	+	3.03529i	−0.945321	+	0.811217i
$15$	−0.658752	+	0.0345237i	−0.170089	+	0.00891398i
$16$	3.44522	−	2.03236i	0.861304	−	0.508090i
$17$	−3.66074	+	0.384759i	−0.887859	+	0.0933178i	−0.537466	−	0.843285i	$-0.680619\pi$
$17$	−3.66074	+	0.384759i	−0.887859	+	0.0933178i	−0.350393	+	0.936603i	$0.613952\pi$
$18$	4.06983	−	2.50712i	0.959267	−	0.590934i
$19$	0.0203016	−	0.387378i	0.00465752	−	0.0888707i	−0.995312	−	0.0967195i	$-0.969165\pi$
$19$	0.0203016	−	0.387378i	0.00465752	−	0.0888707i	0.999969	+	0.00784877i	$0.00249837\pi$
$20$	0.0570296	+	0.519197i	0.0127522	+	0.116096i
$21$	5.88640	+	5.88640i	1.28452	+	1.28452i
$22$	3.03995	−	3.57193i	0.648120	−	0.761538i
$23$	4.40503	+	7.62974i	0.918512	+	1.59091i	0.801676	+	0.597759i	$0.203942\pi$
$23$	4.40503	+	7.62974i	0.918512	+	1.59091i	0.116837	+	0.993151i	$0.462725\pi$
$24$	−4.08781	−	5.85918i	−0.834420	−	1.19600i
$25$	4.69042	+	1.52401i	0.938083	+	0.304802i
$26$	3.29795	−	3.88890i	0.646782	−	0.762675i
$27$	−0.564212	−	0.776572i	−0.108583	−	0.149451i
$28$	4.38758	−	4.91903i	0.829174	−	0.929610i
$29$	−3.77690	+	4.19467i	−0.701353	+	0.778932i	−0.983591	−	0.180413i	$-0.942257\pi$
$29$	−3.77690	+	4.19467i	−0.701353	+	0.778932i	0.282238	+	0.959344i	$0.408923\pi$
$30$	0.916872	−	0.172154i	0.167397	−	0.0314309i
$31$	0.421128	+	2.65890i	0.0756368	+	0.477552i	0.996210	+	0.0869816i	$0.0277221\pi$
$31$	0.421128	+	2.65890i	0.0756368	+	0.477552i	−0.920573	+	0.390570i	$0.872278\pi$
$32$	−4.44726	+	3.49599i	−0.786171	+	0.618009i
$33$	−6.77449	−	4.92813i	−1.17929	−	0.857878i
$34$	5.05889	−	1.22707i	0.867593	−	0.210441i
$35$	0.350084	+	0.786303i	0.0591751	+	0.132909i
$36$	−5.23356	+	4.27880i	−0.872261	+	0.713133i
$37$	−6.52444	+	0.341931i	−1.07261	+	0.0562132i	−0.580454	−	0.814293i	$-0.697125\pi$
$37$	−6.52444	+	0.341931i	−1.07261	+	0.0562132i	−0.492157	+	0.870506i	$0.663792\pi$
$38$	0.0443223	+	0.546794i	0.00719003	+	0.0887017i
$39$	−7.37405	−	5.34451i	−1.18079	−	0.855806i
$40$	−0.177481	−	0.717032i	−0.0280622	−	0.113373i
$41$	5.31054	−	8.17751i	0.829367	−	1.27711i	−0.129021	−	0.991642i	$-0.541183\pi$
$41$	5.31054	−	8.17751i	0.829367	−	1.27711i	0.958387	−	0.285471i	$-0.0921499\pi$
$42$	−9.35675	−	7.14493i	−1.44378	−	1.10249i
$43$	−0.960567	+	1.66375i	−0.146485	+	0.253719i	−0.929926	−	0.367747i	$-0.880129\pi$
$43$	−0.960567	+	1.66375i	−0.146485	+	0.253719i	0.783441	+	0.621466i	$0.213463\pi$
$44$	−3.58996	+	5.57783i	−0.541207	+	0.840890i
$45$	−0.228466	−	0.852648i	−0.0340578	−	0.127105i
$46$	−7.60787	−	9.86685i	−1.12172	−	1.45479i
$47$	0.892243	+	1.75113i	0.130147	+	0.255428i	0.946879	−	0.321589i	$-0.104217\pi$
$47$	0.892243	+	1.75113i	0.130147	+	0.255428i	−0.816732	+	0.577017i	$0.804217\pi$
$48$	6.83059	+	7.44470i	0.985910	+	1.07455i
$49$	1.57079	−	3.52805i	0.224398	−	0.504007i
$50$	−6.86078	−	1.25496i	−0.970261	−	0.177478i
$51$	−2.87308	−	8.84243i	−0.402312	−	1.23819i
$52$	−3.89204	+	6.07059i	−0.539729	+	0.841839i
$53$	−3.05406	−	2.21891i	−0.419508	−	0.304790i	0.357932	−	0.933748i	$-0.383482\pi$
$53$	−3.05406	−	2.21891i	−0.419508	−	0.304790i	−0.777440	+	0.628958i	$0.783482\pi$
$54$	0.936743	+	0.982503i	0.127475	+	0.133702i
$55$	−0.471316	−	0.726711i	−0.0635522	−	0.0979897i
$56$	−5.22581	+	7.71922i	−0.698328	+	1.03152i
$57$	0.967748	−	0.153276i	0.128181	−	0.0203019i
$58$	4.50593	−	6.58917i	0.591657	−	0.865201i
$59$	−1.52074	+	0.987579i	−0.197983	+	0.128572i	−0.639823	−	0.768522i	$-0.720993\pi$
$59$	−1.52074	+	0.987579i	−0.197983	+	0.128572i	0.441840	+	0.897094i	$0.354326\pi$
$60$	−1.25282	+	0.413562i	−0.161738	+	0.0533906i
$61$	0.0743889	+	0.707763i	0.00952452	+	0.0906198i	0.998251	−	0.0591100i	$-0.0188263\pi$
$61$	0.0743889	+	0.707763i	0.00952452	+	0.0906198i	−0.988727	+	0.149730i	$0.952160\pi$
$62$	−1.08983	−	3.64780i	−0.138408	−	0.463271i
$63$	−6.06711	+	9.34254i	−0.764385	+	1.17705i
$64$	5.57681	−	5.73578i	0.697102	−	0.716972i
$65$	−0.513761	−	0.789117i	−0.0637242	−	0.0978780i
$66$	10.4215	+	5.63490i	1.28280	+	0.693609i
$67$	1.19427	−	4.45707i	0.145903	−	0.544518i	−0.853810	−	0.520584i	$-0.825714\pi$
$67$	1.19427	−	4.45707i	0.145903	−	0.544518i	0.999714	−	0.0239338i	$-0.00761909\pi$
$68$	−6.86040	+	2.67040i	−0.831946	+	0.323833i
$69$	−16.5373	+	14.8902i	−1.99085	+	1.79257i
$70$	−0.638432	−	1.03637i	−0.0763073	−	0.123870i
$71$	0.675652	−	0.834361i	0.0801851	−	0.0990204i	−0.735475	−	0.677552i	$-0.763041\pi$
$71$	0.675652	−	0.834361i	0.0801851	−	0.0990204i	0.815660	+	0.578532i	$0.196374\pi$
$72$	6.53190	−	6.98075i	0.769791	−	0.822690i
$73$	−1.97553	+	3.87719i	−0.231218	+	0.453790i	−0.977242	−	0.212129i	$-0.931960\pi$
$73$	−1.97553	+	3.87719i	−0.231218	+	0.453790i	0.746024	+	0.665919i	$0.231960\pi$
$74$	9.08093	−	1.70506i	1.05564	−	0.198209i
$75$	−1.30212	+	12.3888i	−0.150356	+	1.43054i
$76$	−0.164855	−	0.758103i	−0.0189101	−	0.0869604i
$77$	−2.83538	+	10.5566i	−0.323122	+	1.20304i
$78$	11.3401	+	6.10588i	1.28402	+	0.691355i
$79$	5.88565	−	8.10090i	0.662187	−	0.911422i	−0.337364	−	0.941374i	$-0.609535\pi$
$79$	5.88565	−	8.10090i	0.662187	−	0.911422i	0.999551	+	0.0299520i	$0.00953545\pi$
$80$	0.383484	+	0.971705i	0.0428748	+	0.108640i
$81$	−5.16268	+	5.73374i	−0.573631	+	0.637082i
$82$	−5.90732	+	12.4600i	−0.652354	+	1.37597i
$83$	16.5342	+	2.61876i	1.81486	+	0.287446i	0.969201	−	0.246270i	$-0.0792050\pi$
$83$	16.5342	+	2.61876i	1.81486	+	0.287446i	0.845664	+	0.533716i	$0.179205\pi$
$84$	14.4575	+	8.25700i	1.57744	+	0.900913i
$85$	0.0503107	−	0.959986i	0.00545696	−	0.104125i
$86$	1.03383	−	2.51251i	0.111481	−	0.270931i
$87$	−12.3471	−	7.12863i	−1.32375	−	0.764269i
$88$	3.98403	−	8.49279i	0.424699	−	0.905334i
$89$	3.93129	−	14.6718i	0.416716	−	1.55521i	−0.364657	−	0.931142i	$-0.618814\pi$
$89$	3.93129	−	14.6718i	0.416716	−	1.55521i	0.781373	−	0.624064i	$-0.214519\pi$
$90$	0.480428	+	1.15222i	0.0506415	+	0.121454i
$91$	−3.06223	+	11.4816i	−0.321009	+	1.20360i
$92$	12.5175	+	12.4008i	1.30504	+	1.29287i
$93$	−6.34811	+	2.43681i	−0.658268	+	0.252685i
$94$	−1.57963	−	2.28689i	−0.162926	−	0.235874i
$95$	0.0990927	+	0.0210628i	0.0101667	+	0.00216100i
$96$	−10.9730	−	9.15178i	−1.11992	−	0.934049i
$97$	2.31981	−	6.04332i	0.235541	−	0.613606i	−0.763957	−	0.645267i	$-0.776746\pi$
$97$	2.31981	−	6.04332i	0.235541	−	0.613606i	0.999499	+	0.0316606i	$0.0100796\pi$
$98$	−1.53891	+	5.24030i	−0.155453	+	0.529350i
$99$	4.56574	−	10.2384i	0.458874	−	1.02900i
$100$	9.85238	+	0.470081i	0.985238	+	0.0470081i
$101$	−10.1325	−	1.06497i	−1.00823	−	0.105969i	−0.414008	−	0.910273i	$-0.635871\pi$
$101$	−10.1325	−	1.06497i	−1.00823	−	0.105969i	−0.594217	+	0.804304i	$0.702538\pi$
$102$	5.68841	+	11.8545i	0.563236	+	1.17377i
$103$	1.65967	+	5.10795i	0.163533	+	0.503302i	0.998925	−	0.0463522i	$-0.0147597\pi$
$103$	1.65967	+	5.10795i	0.163533	+	0.503302i	−0.835393	+	0.549654i	$0.814760\pi$
$104$	4.31488	−	9.24023i	0.423109	−	0.906079i
$105$	−1.75885	+	1.27788i	−0.171646	+	0.124708i
$106$	4.69769	+	2.53641i	0.456280	+	0.246358i
$107$	−3.68226	−	17.3237i	−0.355977	−	1.67474i	−0.683541	−	0.729912i	$-0.739561\pi$
$107$	−3.68226	−	17.3237i	−0.355977	−	1.67474i	0.327564	−	0.944829i	$-0.393772\pi$
$108$	−1.49760	−	1.20116i	−0.144107	−	0.115582i
$109$	8.29074	−	8.29074i	0.794109	−	0.794109i	−0.188051	−	0.982159i	$-0.560217\pi$
$109$	8.29074	−	8.29074i	0.794109	−	0.794109i	0.982159	+	0.188051i	$0.0602169\pi$
$110$	0.797164	+	0.930067i	0.0760066	+	0.0886784i
$111$	−4.27116	−	15.9402i	−0.405401	−	1.51298i
$112$	5.87466	−	11.8017i	0.555103	−	1.11515i
$113$	11.8087	+	13.1149i	1.11087	+	1.23375i	0.969840	+	0.243741i	$0.0783746\pi$
$113$	11.8087	+	13.1149i	1.11087	+	1.23375i	0.141029	+	0.990005i	$0.454959\pi$
$114$	−1.32767	+	0.396659i	−0.124348	+	0.0371506i
$115$	−2.14801	+	0.824545i	−0.200303	+	0.0768892i
$116$	−5.07792	+	10.0825i	−0.471473	+	0.936132i
$117$	4.94393	−	11.1390i	0.457066	−	1.02980i
$118$	1.94605	−	1.66998i	0.179148	−	0.153734i
$119$	−9.42780	+	7.63448i	−0.864245	+	0.699852i
$120$	1.67835	−	0.815054i	0.153212	−	0.0744039i
$121$	1.16286	−	10.9384i	0.105715	−	0.994397i
$122$	−0.237240	−	0.978081i	−0.0214787	−	0.0885513i
$123$	22.9928	+	8.82612i	2.07319	+	0.795825i
$124$	2.21291	+	4.90829i	0.198726	+	0.440777i
$125$	−1.17755	+	2.31108i	−0.105324	+	0.206709i
$126$	6.74892	−	14.2351i	0.601241	−	1.26816i
$127$	17.7381	+	7.89753i	1.57400	+	0.700792i	0.993539	−	0.113492i	$-0.0362038\pi$
$127$	17.7381	+	7.89753i	1.57400	+	0.700792i	0.580466	+	0.814284i	$0.302870\pi$
$128$	−6.73929	+	9.08746i	−0.595675	+	0.803226i
$129$	−4.61503	−	1.49952i	−0.406331	−	0.132025i
$130$	0.868383	+	1.00957i	0.0761622	+	0.0885448i
$131$			19.9542i			1.74341i	0.490034	+	0.871703i	$0.336984\pi$
$131$			19.9542i			1.74341i	−0.490034	+	0.871703i	$0.663016\pi$
$132$	−15.6663	−	5.94038i	−1.36358	−	0.517043i
$133$	−0.639226	−	1.10717i	−0.0554279	−	0.0960040i
$134$	−0.836609	+	6.47175i	−0.0722720	+	0.559074i
$135$	0.223363	−	0.113809i	0.0192240	−	0.00979512i
$136$	9.11438	−	5.03193i	0.781552	−	0.431485i
$137$	6.87360	−	8.48819i	0.587251	−	0.725195i	−0.393746	−	0.919219i	$-0.628821\pi$
$137$	6.87360	−	8.48819i	0.587251	−	0.725195i	0.980997	+	0.194025i	$0.0621542\pi$
$138$	20.3824	−	23.9782i	1.73507	−	2.04116i
$139$	0.945499	−	4.44822i	0.0801962	−	0.377293i	−0.919686	−	0.392655i	$-0.871557\pi$
$139$	0.945499	−	4.44822i	0.0801962	−	0.377293i	0.999882	+	0.0153616i	$0.00488995\pi$
$140$	1.08959	+	1.33271i	0.0920868	+	0.112635i
$141$	−3.85789	+	3.12406i	−0.324893	+	0.263093i
$142$	−0.790292	+	1.29644i	−0.0663198	+	0.108795i
$143$	1.24328	−	11.8935i	0.103968	−	0.994581i
$144$	−7.84411	+	11.0120i	−0.653676	+	0.917663i
$145$	−0.927690	−	1.14560i	−0.0770404	−	0.0951370i
$146$	2.04063	−	5.80572i	0.168883	−	0.480485i
$147$	9.54157	+	2.02812i	0.786975	+	0.167277i
$148$	−12.4082	+	4.09602i	−1.01995	+	0.336691i
$149$	−6.31421	−	5.11315i	−0.517280	−	0.418885i	0.334806	−	0.942287i	$-0.391329\pi$
$149$	−6.31421	−	5.11315i	−0.517280	−	0.418885i	−0.852086	+	0.523402i	$0.824663\pi$
$150$	−0.502399	−	17.6098i	−0.0410207	−	1.43783i
$151$	1.00612	+	1.97462i	0.0818766	+	0.160692i	0.928315	−	0.371795i	$-0.121258\pi$
$151$	1.00612	+	1.97462i	0.0818766	+	0.160692i	−0.846438	+	0.532487i	$0.821258\pi$
$152$	0.373502	+	1.03164i	0.0302950	+	0.0836774i
$153$	10.7747	−	6.22077i	0.871082	−	0.502920i
$154$	1.99097	−	15.3297i	0.160437	−	1.23530i
$155$	−0.703052			−0.0564705
$156$	−17.0424	−	6.42795i	−1.36448	−	0.514648i
$157$	−1.11195	+	3.42223i	−0.0887432	+	0.273124i	−0.985573	−	0.169253i	$-0.945865\pi$
$157$	−1.11195	+	3.42223i	−0.0887432	+	0.273124i	0.896829	+	0.442377i	$0.145865\pi$
$158$	−6.72783	+	12.4606i	−0.535237	+	0.991314i
$159$	3.87833	−	8.71087i	0.307571	−	0.690817i
$160$	−0.720080	−	1.28997i	−0.0569273	−	0.101981i
$161$	25.8710	+	13.1819i	2.03892	+	1.03888i
$162$	6.15919	−	9.00679i	0.483912	−	0.707641i
$163$	−4.57263	+	11.9121i	−0.358156	+	0.933028i	0.629586	+	0.776931i	$0.283225\pi$
$163$	−4.57263	+	11.9121i	−0.358156	+	0.933028i	−0.987742	+	0.156097i	$0.950109\pi$
$164$	5.93925	−	18.5747i	0.463777	−	1.45044i
$165$	1.54795	−	1.54611i	0.120508	−	0.120364i
$166$	−23.6676	−	0.564299i	−1.83697	−	0.0437981i
$167$	−11.2266	−	13.8637i	−0.868738	−	1.07280i	−0.996712	−	0.0810245i	$-0.974181\pi$
$167$	−11.2266	−	13.8637i	−0.868738	−	1.07280i	0.127974	−	0.991778i	$-0.459153\pi$
$168$	−21.8161	−	8.85746i	−1.68315	−	0.683368i
$169$	1.32888	−	12.9319i	0.102222	−	0.994762i
$170$	0.109838	+	1.35504i	0.00842417	+	0.103927i
$171$	0.469873	+	1.22406i	0.0359321	+	0.0936062i
$172$	−0.977058	+	3.71596i	−0.0745000	+	0.283339i
$173$	16.0985	−	14.4951i	1.22394	−	1.10204i	0.232352	−	0.972632i	$-0.425358\pi$
$173$	16.0985	−	14.4951i	1.22394	−	1.10204i	0.991591	−	0.129411i	$-0.0413088\pi$
$174$	18.6460	+	7.67233i	1.41355	+	0.581638i
$175$	15.7001	−	4.20683i	1.18682	−	0.318006i
$176$	−3.98875	+	12.6527i	−0.300664	+	0.953730i
$177$	−3.23861	−	3.23861i	−0.243429	−	0.243429i
$178$	−2.75395	+	21.3037i	−0.206417	+	1.59678i
$179$	−1.05369	+	0.223970i	−0.0787568	+	0.0167403i	−0.247122	−	0.968984i	$-0.579485\pi$
$179$	−1.05369	+	0.223970i	−0.0787568	+	0.0167403i	0.168365	+	0.985725i	$0.446151\pi$
$180$	−0.889877	−	1.52478i	−0.0663276	−	0.113650i
$181$	−2.31770	−	3.19004i	−0.172273	−	0.237114i	0.714146	−	0.699996i	$-0.246815\pi$
$181$	−2.31770	−	3.19004i	−0.172273	−	0.237114i	−0.886419	+	0.462883i	$0.846815\pi$
$182$	2.13515	−	16.6689i	0.158268	−	1.23558i
$183$	−1.70959	+	0.555478i	−0.126376	+	0.0410621i
$184$	−19.8754	−	15.0302i	−1.46523	−	1.10804i
$185$	0.178353	−	1.69691i	0.0131127	−	0.124759i
$186$	8.44019	−	4.60827i	0.618865	−	0.337895i
$187$	8.17427	−	9.06757i	0.597762	−	0.663086i
$188$	2.64378	+	2.90871i	0.192818	+	0.212139i
$189$	−2.95345	−	1.13372i	−0.214832	−	0.0824661i
$190$	−0.142853	−	0.0109062i	−0.0103637	−	0.000791222i
$191$	−1.07727	+	5.06816i	−0.0779485	+	0.366719i	−0.999782	−	0.0208665i	$-0.993357\pi$
$191$	−1.07727	+	5.06816i	−0.0779485	+	0.366719i	0.921834	+	0.387586i	$0.126691\pi$
$192$	17.0999	+	10.7663i	1.23408	+	0.776991i
$193$	3.50667	+	9.13518i	0.252415	+	0.657564i	0.999978	−	0.00662678i	$-0.00210939\pi$
$193$	3.50667	+	9.13518i	0.252415	+	0.657564i	−0.747563	+	0.664191i	$0.768776\pi$
$194$	−2.11624	+	8.90663i	−0.151937	+	0.639459i
$195$	1.67985	−	1.68375i	0.120296	−	0.120576i
$196$	1.17253	−	7.63434i	0.0837524	−	0.545310i
$197$	20.7857	+	5.56950i	1.48092	+	0.396811i	0.906659	−	0.421864i	$-0.138624\pi$
$197$	20.7857	+	5.56950i	1.48092	+	0.396811i	0.574258	+	0.818674i	$0.305291\pi$
$198$	−4.47616	+	15.2087i	−0.318107	+	1.08084i
$199$	−1.17775	+	2.03992i	−0.0834883	+	0.144606i	−0.904746	−	0.425951i	$-0.859939\pi$
$199$	−1.17775	+	2.03992i	−0.0834883	+	0.144606i	0.821258	+	0.570557i	$0.193273\pi$
$200$	−13.8982	+	1.19211i	−0.982751	+	0.0842951i
$201$	11.6392	+	0.609982i	0.820963	+	0.0430248i
$202$	14.4026	−	0.410900i	1.01337	−	0.0289108i
$203$	−2.91012	+	18.3738i	−0.204250	+	1.28959i
$204$	−10.2005	−	15.5474i	−0.714176	−	1.08854i
$205$	1.89238	+	1.70391i	0.132170	+	0.119006i
$206$	−3.28599	−	6.84790i	−0.228946	−	0.477116i
$207$	−24.0911	−	17.5032i	−1.67445	−	1.21656i
$208$	−4.31207	+	13.7625i	−0.298988	+	0.954257i
$209$	0.809057	+	1.00032i	0.0559636	+	0.0691937i
$210$	2.22526	−	2.12162i	0.153557	−	0.146406i
$211$	−13.2732	−	1.39507i	−0.913765	−	0.0960406i	−0.364037	−	0.931384i	$-0.618602\pi$
$211$	−13.2732	−	1.39507i	−0.913765	−	0.0960406i	−0.549728	+	0.835344i	$0.685269\pi$
$212$	−7.06118	−	2.67266i	−0.484964	−	0.183559i
$213$	2.41626	+	1.23115i	0.165559	+	0.0843567i
$214$	8.41602	+	23.5904i	0.575307	+	1.61261i
$215$	−0.389912	−	0.315744i	−0.0265917	−	0.0215336i
$216$	2.32482	+	1.40228i	0.158184	+	0.0954132i
$217$	5.93671	+	6.59338i	0.403010	+	0.447588i
$218$	−10.0633	+	13.1786i	−0.681575	+	0.892566i
$219$	−10.6167	−	2.84475i	−0.717412	−	0.192230i
$220$	−1.29210	−	1.15389i	−0.0871137	−	0.0777951i
$221$	8.86904	−	9.87307i	0.596596	−	0.664135i
$222$	8.98156	+	21.5406i	0.602803	+	1.44571i
$223$	17.0969	+	11.1028i	1.14489	+	0.743501i	0.970482	−	0.241173i	$-0.0775320\pi$
$223$	17.0969	+	11.1028i	1.14489	+	0.743501i	0.174409	+	0.984673i	$0.444199\pi$
$224$	−6.01714	+	17.6458i	−0.402037	+	1.17901i
$225$	−16.5783	+	1.74245i	−1.10522	+	0.116163i
$226$	−19.0160	−	16.1643i	−1.26492	−	1.07523i
$227$	4.97455	+	7.66013i	0.330172	+	0.508421i	0.964302	−	0.264806i	$-0.0853080\pi$
$227$	4.97455	+	7.66013i	0.330172	+	0.508421i	−0.634129	+	0.773227i	$0.718641\pi$
$228$	1.78645	−	0.805426i	0.118311	−	0.0533406i
$229$	−1.53218	−	9.67381i	−0.101249	−	0.639263i	−0.985164	−	0.171615i	$-0.945101\pi$
$229$	−1.53218	−	9.67381i	−0.101249	−	0.639263i	0.883915	−	0.467648i	$-0.154899\pi$
$230$	2.85591	−	1.55930i	0.188313	−	0.102817i
$231$	−27.5710	−	1.46142i	−1.81404	−	0.0961544i
$232$	5.22338	−	15.0864i	0.342932	−	0.990469i
$233$	1.83047	−	2.51942i	0.119918	−	0.165053i	−0.744838	−	0.667245i	$-0.767473\pi$
$233$	1.83047	−	2.51942i	0.119918	−	0.165053i	0.864756	+	0.502193i	$0.167473\pi$
$234$	−4.83706	+	16.5421i	−0.316209	+	1.08139i
$235$	−0.488145	+	0.158608i	−0.0318431	+	0.0103464i
$236$	−2.41398	+	2.70638i	−0.157137	+	0.176171i
$237$	23.1056	+	10.2873i	1.50087	+	0.668230i
$238$	11.7804	−	12.4723i	0.763611	−	0.808461i
$239$	−14.6073	+	7.44280i	−0.944868	+	0.481435i	−0.857353	−	0.514729i	$-0.827893\pi$
$239$	−14.6073	+	7.44280i	−0.944868	+	0.481435i	−0.0875153	+	0.996163i	$0.527893\pi$
$240$	−2.19938	+	1.45776i	−0.141969	+	0.0940982i
$241$	−19.2428	+	5.15608i	−1.23954	+	0.332132i	−0.818285	−	0.574812i	$-0.805075\pi$
$241$	−19.2428	+	5.15608i	−1.23954	+	0.332132i	−0.421250	+	0.906945i	$0.638408\pi$
$242$	0.425087	+	15.5505i	0.0273256	+	0.999627i
$243$	−19.3713	−	11.1840i	−1.24267	−	0.717456i
$244$	0.516291	+	1.32638i	0.0330522	+	0.0849130i
$245$	0.845866	+	0.549312i	0.0540404	+	0.0350942i
$246$	−33.8868	−	8.05161i	−2.16054	−	0.513352i
$247$	0.881446	+	1.08592i	0.0560851	+	0.0690953i
$248$	−4.02394	−	6.46409i	−0.255520	−	0.410470i
$249$	2.21297	+	42.2259i	0.140241	+	2.67596i
$250$	1.21636	−	3.46062i	0.0769292	−	0.218869i
$251$	5.76763	−	2.56791i	0.364049	−	0.162085i	−0.216556	−	0.976270i	$-0.569482\pi$
$251$	5.76763	−	2.56791i	0.364049	−	0.162085i	0.580606	+	0.814185i	$0.302816\pi$
$252$	−6.78540	+	21.2210i	−0.427440	+	1.33680i
$253$	−27.7842	−	9.04595i	−1.74678	−	0.568714i
$254$	−26.3469	−	7.73724i	−1.65315	−	0.485478i
$255$	2.39823	−	0.379843i	0.150183	−	0.0237867i
$256$	7.73902	−	14.0038i	0.483689	−	0.875240i
$257$	3.05818	+	2.75360i	0.190764	+	0.171765i	0.758978	−	0.651116i	$-0.225699\pi$
$257$	3.05818	+	2.75360i	0.190764	+	0.171765i	−0.568214	+	0.822881i	$0.692365\pi$
$258$	6.75052	+	1.23479i	0.420269	+	0.0768747i
$259$	−17.4201	+	12.6564i	−1.08243	+	0.786432i
$260$	−1.40687	−	1.25194i	−0.0872501	−	0.0776420i
$261$	5.89559	−	18.1448i	0.364928	−	1.12313i
$262$	−3.74889	−	27.9694i	−0.231607	−	1.72795i
$263$	−15.3114	+	8.84004i	−0.944141	+	0.545100i	−0.891256	−	0.453500i	$-0.850175\pi$
$263$	−15.3114	+	8.84004i	−0.944141	+	0.545100i	−0.0528852	+	0.998601i	$0.516842\pi$
$264$	23.0752	+	5.38320i	1.42018	+	0.331313i
$265$	0.697126	−	0.697126i	0.0428241	−	0.0428241i
$266$	1.10400	+	1.43180i	0.0676905	+	0.0877896i
$267$	38.3137	+	2.00794i	2.34476	+	0.122884i
$268$	−0.0432230	−	9.22850i	−0.00264027	−	0.563720i
$269$	2.80157	+	26.6552i	0.170815	+	1.62520i	0.658782	+	0.752334i	$0.271072\pi$
$269$	2.80157	+	26.6552i	0.170815	+	1.62520i	−0.487967	+	0.872862i	$0.662261\pi$
$270$	−0.291701	+	0.201488i	−0.0177524	+	0.0122622i
$271$	0.985590	+	18.8062i	0.0598703	+	1.14239i	0.849078	+	0.528268i	$0.177158\pi$
$271$	0.985590	+	18.8062i	0.0598703	+	1.14239i	−0.789208	+	0.614126i	$0.789508\pi$
$272$	−11.8301	+	8.76552i	−0.717303	+	0.531488i
$273$	−29.9755	−	1.53610i	−1.81420	−	0.0929687i
$274$	−8.03986	+	13.1891i	−0.485706	+	0.796782i
$275$	−14.9468	+	6.64404i	−0.901323	+	0.400651i
$276$	−24.0647	+	37.4391i	−1.44853	+	2.25357i
$277$	1.59622	+	3.58517i	0.0959077	+	0.215412i	0.955128	−	0.296194i	$-0.0957174\pi$
$277$	1.59622	+	3.58517i	0.0959077	+	0.215412i	−0.859220	+	0.511606i	$0.829051\pi$
$278$	−0.489577	+	6.41262i	−0.0293628	+	0.384603i
$279$	−4.95576	−	7.63120i	−0.296693	−	0.456868i
$280$	−1.77763	−	1.66333i	−0.106234	−	0.0994031i
$281$	14.6553	+	2.32117i	0.874259	+	0.138469i	0.577409	−	0.816455i	$-0.304064\pi$
$281$	14.6553	+	2.32117i	0.874259	+	0.138469i	0.296850	+	0.954924i	$0.404064\pi$
$282$	4.82059	−	5.10373i	0.287062	−	0.303923i
$283$	26.5478	−	5.64291i	1.57810	−	0.335436i	0.666178	−	0.745793i	$-0.267929\pi$
$283$	26.5478	−	5.64291i	1.57810	−	0.335436i	0.911925	+	0.410356i	$0.134596\pi$
$284$	0.864166	−	1.96567i	0.0512788	−	0.116641i
$285$			0.255887i			0.0151574i
$286$	0.491804	+	16.9044i	0.0290810	+	0.999577i
$287$		−	32.1354i		−	1.89689i
$288$	8.92605	−	16.9089i	0.525973	−	0.996368i
$289$	−3.37555	+	0.717495i	−0.198562	+	0.0422056i
$290$	1.51555	+	1.43148i	0.0889963	+	0.0840591i
$291$	16.1493	+	2.55781i	0.946691	+	0.149941i
$292$	−1.76955	+	8.52114i	−0.103555	+	0.498662i
$293$	−5.63633	−	8.67919i	−0.329278	−	0.507044i	0.634795	−	0.772681i	$-0.281085\pi$
$293$	−5.63633	−	8.67919i	−0.329278	−	0.507044i	−0.964073	+	0.265637i	$0.914418\pi$
$294$	−13.7552	−	1.05016i	−0.802222	−	0.0612463i
$295$	−0.192612	−	0.432613i	−0.0112143	−	0.0251877i
$296$	16.6228	−	8.07249i	0.966179	−	0.469204i
$297$	3.11365	+	0.663767i	0.180672	+	0.0385157i
$298$	9.81112	+	5.98071i	0.568343	+	0.346453i
$299$	−30.2218	−	9.78092i	−1.74777	−	0.565645i
$300$	4.01264	+	24.5889i	0.231670	+	1.41964i
$301$	0.331368	+	6.32288i	0.0190998	+	0.364445i
$302$	−1.78123	−	2.57875i	−0.102498	−	0.148390i
$303$	−2.68998	−	25.5935i	−0.154536	−	1.47031i
$304$	−0.717349	−	1.37586i	−0.0411428	−	0.0789111i
$305$	−0.185603	−	0.00972702i	−0.0106276	−	0.000556968i
$306$	−13.9339	+	10.7438i	−0.796550	+	0.614183i
$307$	2.53501	−	2.53501i	0.144680	−	0.144680i	−0.631056	−	0.775737i	$-0.717378\pi$
$307$	2.53501	−	2.53501i	0.144680	−	0.144680i	0.775737	+	0.631056i	$0.217378\pi$
$308$	0.0893531	+	21.8613i	0.00509137	+	1.24566i
$309$	−11.7485	+	6.78300i	−0.668349	+	0.385871i
$310$	0.985453	−	0.132086i	0.0559700	−	0.00750197i
$311$	8.30923	−	25.5732i	0.471173	−	1.45012i	−0.379877	−	0.925037i	$-0.624034\pi$
$311$	8.30923	−	25.5732i	0.471173	−	1.45012i	0.851050	−	0.525085i	$-0.175966\pi$
$312$	25.0956	+	5.80809i	1.42076	+	0.328818i
$313$	14.5784	−	10.5918i	0.824018	−	0.598684i	−0.0938423	−	0.995587i	$-0.529915\pi$
$313$	14.5784	−	10.5918i	0.824018	−	0.598684i	0.917861	+	0.396903i	$0.129915\pi$
$314$	0.915645	−	5.00577i	0.0516728	−	0.282492i
$315$	−2.16199	−	1.94666i	−0.121814	−	0.109682i
$316$	7.08922	−	18.7298i	0.398800	−	1.05363i
$317$	−16.8201	+	2.66404i	−0.944710	+	0.149627i	−0.609740	−	0.792602i	$-0.708726\pi$
$317$	−16.8201	+	2.66404i	−0.944710	+	0.149627i	−0.334970	+	0.942229i	$0.608726\pi$
$318$	−3.79962	+	12.9385i	−0.213072	+	0.725554i
$319$	0.0111643	−	18.7207i	0.000625082	−	1.04816i
$320$	1.25167	+	1.67284i	0.0699707	+	0.0935146i
$321$	40.8673	−	18.1953i	2.28099	−	1.01556i
$322$	−38.7394	−	13.6163i	−2.15886	−	0.758808i
$323$	0.0747284	+	1.42590i	0.00415800	+	0.0793393i
$324$	−6.94106	+	13.7818i	−0.385614	+	0.765655i
$325$	−16.2361	+	7.25136i	−0.900618	+	0.402233i
$326$	4.17137	−	17.5560i	0.231031	−	0.972338i
$327$	24.8377	+	16.1298i	1.37353	+	0.891978i
$328$	−4.83520	+	27.1516i	−0.266979	+	1.49920i
$329$	5.60945	+	3.23862i	0.309259	+	0.178551i
$330$	−1.87926	+	2.45797i	−0.103450	+	0.135307i
$331$	23.9568	−	6.41920i	1.31678	−	0.352831i	0.469012	−	0.883192i	$-0.344610\pi$
$331$	23.9568	−	6.41920i	1.31678	−	0.352831i	0.847772	+	0.530361i	$0.177944\pi$
$332$	33.2804	−	3.65559i	1.82650	−	0.200627i
$333$	19.6761	−	10.0255i	1.07825	−	0.549393i
$334$	18.3407	+	17.3232i	1.00356	+	0.947883i
$335$	1.10089	+	0.490146i	0.0601478	+	0.0267795i
$336$	32.2432	+	8.31663i	1.75901	+	0.453709i
$337$	4.76474	−	1.54816i	0.259552	−	0.0843336i	−0.176351	−	0.984327i	$-0.556429\pi$
$337$	4.76474	−	1.54816i	0.259552	−	0.0843336i	0.435903	+	0.899994i	$0.356429\pi$
$338$	0.566917	+	18.3760i	0.0308362	+	0.999524i
$339$	−26.2012	+	36.0629i	−1.42305	+	1.95867i
$340$	−0.408536	−	1.87870i	−0.0221560	−	0.101887i
$341$	−6.93538	−	5.62301i	−0.375572	−	0.304503i
$342$	−0.888581	−	1.62746i	−0.0480489	−	0.0880030i
$343$	1.61789	+	10.2150i	0.0873578	+	0.551556i
$344$	0.671386	−	5.39215i	0.0361987	−	0.290725i
$345$	−3.16523	−	4.87402i	−0.170410	−	0.262409i
$346$	−19.8416	+	23.3420i	−1.06669	+	1.25487i
$347$	4.25799	−	0.447532i	0.228581	−	0.0240248i	0.0104544	−	0.999945i	$-0.496672\pi$
$347$	4.25799	−	0.447532i	0.228581	−	0.0240248i	0.218126	+	0.975921i	$0.430006\pi$
$348$	−27.5772	−	7.25102i	−1.47829	−	0.388695i
$349$	8.53184	+	5.54064i	0.456699	+	0.296584i	0.752412	−	0.658693i	$-0.228890\pi$
$349$	8.53184	+	5.54064i	0.456699	+	0.296584i	−0.295713	+	0.955277i	$0.595557\pi$
$350$	−21.2161	+	8.84627i	−1.13405	+	0.472853i
$351$	3.38615	+	0.715646i	0.180740	+	0.0381984i
$352$	3.21383	−	18.4844i	0.171298	−	0.985219i
$353$	13.9289	+	3.73225i	0.741363	+	0.198648i	0.609684	−	0.792645i	$-0.291296\pi$
$353$	13.9289	+	3.73225i	0.741363	+	0.198648i	0.131679	+	0.991292i	$0.457963\pi$
$354$	5.14795	+	3.93104i	0.273611	+	0.208933i
$355$	0.187615	+	0.208368i	0.00995759	+	0.0110590i
$356$	−0.142282	−	30.3784i	−0.00754091	−	1.61005i
$357$	−23.8134	−	19.2837i	−1.26034	−	1.02060i
$358$	1.43486	−	0.511896i	0.0758348	−	0.0270545i
$359$	−23.4793	−	11.9633i	−1.23919	−	0.631398i	−0.293340	−	0.956008i	$-0.594767\pi$
$359$	−23.4793	−	11.9633i	−1.23919	−	0.631398i	−0.945848	+	0.324610i	$0.894767\pi$
$360$	1.53379	+	1.97006i	0.0808378	+	0.103831i
$361$	18.7463	+	1.97031i	0.986646	+	0.103701i
$362$	3.84799	+	4.03597i	0.202246	+	0.212126i
$363$	27.6358	−	2.87132i	1.45050	−	0.150705i
$364$	0.138871	+	23.7655i	0.00727880	+	1.24565i
$365$	−0.919390	−	0.667976i	−0.0481231	−	0.0349634i
$366$	2.29193	−	1.09979i	0.119801	−	0.0574870i
$367$	−1.06548	−	0.959360i	−0.0556174	−	0.0500782i	0.640853	−	0.767663i	$-0.278581\pi$
$367$	−1.06548	−	0.959360i	−0.0556174	−	0.0500782i	−0.696471	+	0.717585i	$0.745247\pi$
$368$	30.6827	+	17.3335i	1.59944	+	0.903570i
$369$	−5.15563	+	32.5514i	−0.268392	+	1.69456i
$370$	0.0688141	+	2.41203i	0.00357747	+	0.125396i
$371$	−12.4245	−	0.651139i	−0.645046	−	0.0338054i
$372$	−10.9647	+	8.04502i	−0.568491	+	0.417115i
$373$	2.05795	−	3.56447i	0.106557	−	0.184561i	−0.807817	−	0.589434i	$-0.799351\pi$
$373$	2.05795	−	3.56447i	0.106557	−	0.184561i	0.914373	+	0.404873i	$0.132684\pi$
$374$	−9.75413	+	14.2456i	−0.504374	+	0.736620i
$375$	−6.32833	−	1.69567i	−0.326793	−	0.0875640i
$376$	−4.25221	−	3.58037i	−0.219291	−	0.184643i
$377$	−0.0236012	−	20.3515i	−0.00121552	−	1.04816i
$378$	4.35278	+	1.03424i	0.223883	+	0.0531953i
$379$	−7.77434	−	20.2529i	−0.399341	−	1.04032i	−0.974917	−	0.222571i	$-0.928555\pi$
$379$	−7.77434	−	20.2529i	−0.399341	−	1.04032i	0.575575	−	0.817749i	$-0.304778\pi$
$380$	0.202283	−	0.0115515i	0.0103769	−	0.000592578i
$381$	−10.1969	+	47.9726i	−0.522403	+	2.45771i
$382$	0.557807	−	7.30632i	0.0285399	−	0.373824i
$383$	−6.31524	−	2.42419i	−0.322694	−	0.123871i	0.191628	−	0.981468i	$-0.438623\pi$
$383$	−6.31524	−	2.42419i	−0.322694	−	0.123871i	−0.514322	+	0.857597i	$0.671956\pi$
$384$	−25.9914	−	11.8783i	−1.32637	−	0.606159i
$385$	−2.60718	−	1.16265i	−0.132874	−	0.0592543i
$386$	−6.63149	−	12.1458i	−0.337534	−	0.618203i
$387$	0.678753	−	6.45791i	0.0345030	−	0.328274i
$388$	1.29296	−	12.8818i	0.0656403	−	0.653975i
$389$	3.94124	−	1.28059i	0.199829	−	0.0649283i	−0.207393	−	0.978258i	$-0.566498\pi$
$389$	3.94124	−	1.28059i	0.199829	−	0.0649283i	0.407221	+	0.913330i	$0.366498\pi$
$390$	−2.03827	+	2.67567i	−0.103212	+	0.135488i
$391$	−19.0613	−	26.2356i	−0.963970	−	1.32679i
$392$	−0.209215	+	10.9212i	−0.0105670	+	0.551603i
$393$	−49.3003	+	10.4791i	−2.48687	+	0.528601i
$394$	−30.1812	−	3.90155i	−1.52051	−	0.196557i
$395$	1.84913	+	1.84913i	0.0930396	+	0.0930396i
$396$	3.41681	−	22.1587i	0.171701	−	1.11352i
$397$	1.40368	−	0.376115i	0.0704487	−	0.0188767i	−0.223423	−	0.974722i	$-0.571723\pi$
$397$	1.40368	−	0.376115i	0.0704487	−	0.0188767i	0.293871	+	0.955845i	$0.405056\pi$
$398$	1.26757	−	3.08058i	0.0635377	−	0.154415i
$399$	2.39977	−	2.16076i	0.120139	−	0.108173i
$400$	19.2568	−	4.28208i	0.962842	−	0.214104i
$401$	−0.484817	−	1.26299i	−0.0242106	−	0.0630707i	0.920942	−	0.389699i	$-0.127421\pi$
$401$	−0.484817	−	1.26299i	−0.0242106	−	0.0630707i	−0.945153	+	0.326628i	$0.894088\pi$
$402$	−16.4290	+	1.33171i	−0.819402	+	0.0664194i
$403$	−7.55028	−	6.09961i	−0.376106	−	0.303843i
$404$	−20.1107	+	3.28185i	−1.00054	+	0.163278i
$405$	−1.26807	−	1.56593i	−0.0630108	−	0.0778118i
$406$	0.627082	−	26.3009i	0.0311216	−	1.30529i
$407$	15.3313	−	15.3130i	0.759944	−	0.759039i
$408$	17.2188	+	19.8761i	0.852456	+	0.984014i
$409$	−1.64833	+	4.29405i	−0.0815048	+	0.212327i	−0.968277	−	0.249880i	$-0.919609\pi$
$409$	−1.64833	+	4.29405i	−0.0815048	+	0.212327i	0.886772	+	0.462207i	$0.152942\pi$
$410$	−2.97264	−	2.03280i	−0.146808	−	0.100393i
$411$	24.5813	+	12.5248i	1.21250	+	0.617802i
$412$	5.89244	+	8.98120i	0.290300	+	0.442472i
$413$	−2.43069	+	5.45942i	−0.119607	+	0.268641i
$414$	37.0564	+	20.0078i	1.82122	+	0.983328i
$415$	−1.35099	+	4.15792i	−0.0663174	+	0.204104i
$416$	3.45851	−	20.1007i	0.169568	−	0.985519i
$417$	11.4867			0.562504
$418$	−1.32197	−	1.25013i	−0.0646598	−	0.0611457i
$419$	31.7581	−	18.3355i	1.55148	−	0.895750i	0.553462	−	0.832874i	$-0.313306\pi$
$419$	31.7581	−	18.3355i	1.55148	−	0.895750i	0.998021	−	0.0628753i	$-0.0200270\pi$
$420$	−2.72050	+	3.39190i	−0.132747	+	0.165508i
$421$	−13.8751	−	27.2314i	−0.676230	−	1.32718i	−0.932710	−	0.360626i	$-0.882563\pi$
$421$	−13.8751	−	27.2314i	−0.676230	−	1.32718i	0.256481	−	0.966549i	$-0.417437\pi$
$422$	18.8669	−	0.538262i	0.918425	−	0.0262022i
$423$	−5.16249	−	4.18050i	−0.251009	−	0.203263i
$424$	10.3996	+	2.41959i	0.505051	+	0.117505i
$425$	−17.7568	−	3.77432i	−0.861329	−	0.183081i
$426$	−3.61812	−	1.27172i	−0.175298	−	0.0616148i
$427$	1.47604	+	1.82276i	0.0714307	+	0.0882096i
$428$	−16.2286	−	31.4850i	−0.784439	−	1.52188i
$429$	30.0378	−	3.17421i	1.45024	−	0.153252i
$430$	0.605851	+	0.369317i	0.0292167	+	0.0178101i
$431$	−16.2936	+	13.1943i	−0.784833	+	0.635545i	−0.935615	−	0.353022i	$-0.885154\pi$
$431$	−16.2936	+	13.1943i	−0.784833	+	0.635545i	0.150782	+	0.988567i	$0.451821\pi$
$432$	−3.52211	−	1.52877i	−0.169457	−	0.0735532i
$433$	3.16093	−	14.8710i	0.151905	−	0.714655i	−0.834591	−	0.550869i	$-0.814296\pi$
$433$	3.16093	−	14.8710i	0.151905	−	0.714655i	0.986496	−	0.163785i	$-0.0523704\pi$
$434$	−9.56009	−	8.12644i	−0.458899	−	0.390082i
$435$	2.34322	−	2.89364i	0.112349	−	0.138739i
$436$	11.6296	−	20.3628i	0.556958	−	0.975200i
$437$	3.04503	−	1.55152i	0.145663	−	0.0742192i
$438$	15.4157	+	1.99280i	0.736591	+	0.0952197i
$439$	−10.1589	−	17.5958i	−0.484859	−	0.839801i	0.514989	−	0.857197i	$-0.327796\pi$
$439$	−10.1589	−	17.5958i	−0.484859	−	0.839801i	−0.999849	+	0.0173954i	$0.994463\pi$
$440$	2.02790	+	1.37463i	0.0966764	+	0.0655328i
$441$			13.0534i			0.621591i
$442$	−10.5766	+	15.5051i	−0.503080	+	0.737505i
$443$	−21.4905	−	6.98268i	−1.02104	−	0.331757i	−0.249800	−	0.968297i	$-0.580365\pi$
$443$	−21.4905	−	6.98268i	−1.02104	−	0.331757i	−0.771244	+	0.636540i	$0.780365\pi$
$444$	−16.6362	−	28.5056i	−0.789519	−	1.35282i
$445$	3.62389	+	1.61346i	0.171789	+	0.0764854i
$446$	−26.0503	−	12.3505i	−1.23352	−	0.584815i
$447$	9.31696	−	18.2856i	0.440677	−	0.864878i
$448$	5.11889	−	25.8643i	0.241845	−	1.22197i
$449$	−28.3371	−	10.8776i	−1.33731	−	0.513345i	−0.418560	−	0.908189i	$-0.637465\pi$
$449$	−28.3371	−	10.8776i	−1.33731	−	0.513345i	−0.918748	+	0.394844i	$0.870798\pi$
$450$	22.9101	−	5.55699i	1.07999	−	0.261959i
$451$	5.03988	+	31.9438i	0.237319	+	1.50418i
$452$	29.6912	+	19.0846i	1.39655	+	0.897662i
$453$	−4.35026	+	3.52277i	−0.204393	+	0.165514i
$454$	−8.41186	−	9.80245i	−0.394788	−	0.460052i
$455$	−2.83652	−	1.25896i	−0.132978	−	0.0590209i
$456$	−2.35271	+	1.46458i	−0.110176	+	0.0685851i
$457$	−20.3735	+	7.82067i	−0.953034	+	0.365835i	−0.784687	−	0.619892i	$-0.787176\pi$
$457$	−20.3735	+	7.82067i	−0.953034	+	0.365835i	−0.168347	+	0.985728i	$0.553843\pi$
$458$	3.96509	+	13.2717i	0.185276	+	0.620146i
$459$	2.36423	+	2.62574i	0.110353	+	0.122559i
$460$	−3.71012	+	2.72220i	−0.172985	+	0.126923i
$461$	−3.20989	−	11.9795i	−0.149500	−	0.557940i	−0.999514	−	0.0311801i	$-0.990073\pi$
$461$	−3.20989	−	11.9795i	−0.149500	−	0.557940i	0.850014	−	0.526760i	$-0.176593\pi$
$462$	38.9202	−	3.13145i	1.81073	−	0.145688i
$463$	−10.7188	+	10.7188i	−0.498147	+	0.498147i	−0.910861	−	0.412714i	$-0.864581\pi$
$463$	−10.7188	+	10.7188i	−0.498147	+	0.498147i	0.412714	+	0.910861i	$0.364581\pi$
$464$	−4.48715	+	22.1276i	−0.208311	+	1.02725i
$465$	−0.369213	−	1.73701i	−0.0171219	−	0.0805520i
$466$	−2.09239	+	3.87532i	−0.0969280	+	0.179521i
$467$	10.2443	−	7.44294i	0.474051	−	0.344418i	−0.324967	−	0.945725i	$-0.605353\pi$
$467$	10.2443	−	7.44294i	0.474051	−	0.344418i	0.799018	+	0.601307i	$0.205353\pi$
$468$	3.67215	−	24.0955i	0.169745	−	1.11381i
$469$	−4.69939	−	14.4632i	−0.216998	−	0.667850i
$470$	0.654424	−	0.314028i	0.0301863	−	0.0144850i
$471$	−9.03916	−	0.950054i	−0.416503	−	0.0437762i
$472$	2.87517	−	4.24701i	0.132340	−	0.195484i
$473$	−1.32103	−	6.23323i	−0.0607410	−	0.286604i
$474$	−34.3193	−	10.0785i	−1.57634	−	0.462920i
$475$	0.685591	−	1.78603i	0.0314571	−	0.0819485i
$476$	−14.1691	+	19.6954i	−0.649440	+	0.902739i
$477$	12.4809	+	2.65289i	0.571459	+	0.121467i
$478$	19.0764	−	13.1768i	0.872536	−	0.602691i
$479$	0.831688	−	0.319255i	0.0380008	−	0.0145871i	−0.339293	−	0.940681i	$-0.610188\pi$
$479$	0.831688	−	0.319255i	0.0380008	−	0.0145871i	0.377294	+	0.926093i	$0.376855\pi$
$480$	2.80894	−	2.45652i	0.128210	−	0.112124i
$481$	16.6376	−	16.6763i	0.758610	−	0.760372i
$482$	26.0035	−	10.8424i	1.18443	−	0.493858i
$483$	−18.9819	+	70.8414i	−0.863707	+	3.22340i
$484$	−3.51739	−	21.7170i	−0.159881	−	0.987136i
$485$	1.46407	+	0.845279i	0.0664798	+	0.0383821i
$486$	29.2535	+	12.0370i	1.32697	+	0.546011i
$487$	−1.40097	+	26.7321i	−0.0634839	+	1.21135i	0.762249	+	0.647284i	$0.224095\pi$
$487$	−1.40097	+	26.7321i	−0.0634839	+	1.21135i	−0.825733	+	0.564061i	$0.809238\pi$
$488$	−0.972869	−	1.76216i	−0.0440397	−	0.0797695i
$489$	−31.8323	−	5.04174i	−1.43951	−	0.227995i
$490$	−1.28883	−	0.611042i	−0.0582236	−	0.0276040i
$491$	8.33481	−	9.25675i	0.376145	−	0.417751i	−0.525114	−	0.851032i	$-0.675977\pi$
$491$	8.33481	−	9.25675i	0.376145	−	0.417751i	0.901259	+	0.433281i	$0.142644\pi$
$492$	49.0111	+	4.91930i	2.20959	+	0.221779i
$493$	12.2123	−	16.8088i	0.550015	−	0.757030i
$494$	−1.43952	−	1.35651i	−0.0647671	−	0.0610321i
$495$	2.45440	+	1.59599i	0.110317	+	0.0717343i
$496$	6.85471	+	8.30458i	0.307786	+	0.372887i
$497$	0.369862	−	3.51900i	0.0165906	−	0.157849i
$498$	−11.0351	−	58.7714i	−0.494493	−	2.63361i
$499$	5.46446	−	10.7246i	0.244623	−	0.480099i	−0.735750	−	0.677254i	$-0.763170\pi$
$499$	5.46446	−	10.7246i	0.244623	−	0.480099i	0.980372	+	0.197154i	$0.0631700\pi$
$500$	−1.05478	+	5.07920i	−0.0471711	+	0.227149i
$501$	28.3569	−	35.0178i	1.26689	−	1.56448i
$502$	−7.60191	+	4.68298i	−0.339290	+	0.209012i
$503$	−13.3598	+	12.0292i	−0.595683	+	0.536355i	−0.910880	−	0.412671i	$-0.864596\pi$
$503$	−13.3598	+	12.0292i	−0.595683	+	0.536355i	0.315197	+	0.949026i	$0.397929\pi$
$504$	5.52406	−	31.0198i	0.246061	−	1.38173i
$505$	0.688662	−	2.57012i	0.0306451	−	0.114369i
$506$	40.6440	+	7.45956i	1.80685	+	0.331618i
$507$	32.6484	−	3.50806i	1.44997	−	0.155799i
$508$	38.3835	+	5.89521i	1.70299	+	0.261557i
$509$	3.88009	−	5.97481i	0.171982	−	0.264829i	−0.742161	−	0.670222i	$-0.766199\pi$
$509$	3.88009	−	5.97481i	0.171982	−	0.264829i	0.914142	+	0.405393i	$0.132865\pi$
$510$	−3.29019	+	0.982985i	−0.145692	+	0.0435273i
$511$	1.49908	+	14.2628i	0.0663153	+	0.630948i
$512$	−8.21665	+	21.0829i	−0.363128	+	0.931739i
$513$	−0.312282	+	0.202798i	−0.0137876	+	0.00895375i
$514$	−4.80392	−	3.28511i	−0.211892	−	0.144900i
$515$	−1.38537	+	0.219421i	−0.0610468	+	0.00966886i
$516$	−9.69404	−	0.462526i	−0.426756	−	0.0203616i
$517$	−6.08394	−	2.33957i	−0.267571	−	0.102894i
$518$	22.0395	−	21.0130i	0.968361	−	0.923260i
$519$	44.2670	+	32.1618i	1.94310	+	1.41175i
$520$	2.20718	+	1.49050i	0.0967914	+	0.0653629i
$521$	−5.97053	−	18.3754i	−0.261574	−	0.805041i	−0.992463	−	0.122545i	$-0.960894\pi$
$521$	−5.97053	−	18.3754i	−0.261574	−	0.805041i	0.730889	−	0.682496i	$-0.239106\pi$
$522$	−4.85478	+	26.5408i	−0.212488	+	1.16166i
$523$	−10.1609	+	22.8217i	−0.444305	+	0.997925i	0.543094	+	0.839672i	$0.317253\pi$
$523$	−10.1609	+	22.8217i	−0.444305	+	0.997925i	−0.987399	+	0.158253i	$0.949414\pi$
$524$	10.5095	+	38.4997i	0.459109	+	1.68187i
$525$	18.6387	+	36.5806i	0.813461	+	1.59651i
$526$	19.8008	−	15.2675i	0.863358	−	0.665696i
$527$	−2.56467	−	9.57149i	−0.111719	−	0.416940i
$528$	−33.3553	−	3.21027i	−1.45160	−	0.139709i
$529$	−27.3086	+	47.2999i	−1.18733	+	2.05652i
$530$	−0.846174	+	1.10812i	−0.0367554	+	0.0481336i
$531$	3.33804	−	5.14013i	0.144859	−	0.223063i
$532$	−1.81645	−	1.79952i	−0.0787532	−	0.0780189i
$533$	5.53990	+	34.7169i	0.239960	+	1.50376i
$534$	−54.0808	+	4.38371i	−2.34031	+	0.189702i
$535$	4.61897	−	0.242070i	0.199696	−	0.0104656i
$536$	1.79439	+	12.9273i	0.0775057	+	0.558373i
$537$	−1.10671	−	2.48572i	−0.0477582	−	0.107267i
$538$	−8.93475	−	36.8357i	−0.385204	−	1.58810i
$539$	3.95080	+	12.1840i	0.170173	+	0.524803i
$540$	0.371017	−	0.337225i	0.0159660	−	0.0145118i
$541$	3.91617	+	24.7257i	0.168369	+	1.06304i	0.916659	+	0.399670i	$0.130875\pi$
$541$	3.91617	+	24.7257i	0.168369	+	1.06304i	−0.748290	+	0.663372i	$0.769125\pi$
$542$	−4.91469	−	26.1751i	−0.211104	−	1.12431i
$543$	6.66439	−	7.40155i	0.285996	−	0.317631i
$544$	14.9351	−	14.5090i	0.640338	−	0.622069i
$545$	1.79984	+	2.47726i	0.0770965	+	0.106114i
$546$	42.3046	−	3.47854i	1.81047	−	0.148868i
$547$	2.95165	+	0.959051i	0.126204	+	0.0410061i	0.371438	−	0.928458i	$-0.378865\pi$
$547$	2.95165	+	0.959051i	0.126204	+	0.0410061i	−0.245234	+	0.969464i	$0.578865\pi$
$548$	8.79140	−	19.9973i	0.375550	−	0.854244i
$549$	−1.20272	−	2.08317i	−0.0513307	−	0.0889074i
$550$	19.7023	−	12.1209i	0.840109	−	0.516838i
$551$	1.54825	+	1.54825i	0.0659576	+	0.0659576i
$552$	26.6971	−	56.9988i	1.13630	−	2.42603i
$553$	1.72715	−	32.9559i	0.0734457	−	1.40143i
$554$	−2.91095	−	4.72537i	−0.123675	−	0.200762i
$555$	4.28618	−	0.450496i	0.181938	−	0.0191225i
$556$	−0.518541	−	9.08041i	−0.0219910	−	0.385095i
$557$	−22.5813	+	1.18344i	−0.956802	+	0.0501439i	−0.524341	−	0.851509i	$-0.675688\pi$
$557$	−22.5813	+	1.18344i	−0.956802	+	0.0501439i	−0.432461	+	0.901652i	$0.642355\pi$
$558$	8.38009	+	9.76542i	0.354758	+	0.413403i
$559$	−1.44801	−	6.77370i	−0.0612442	−	0.286497i
$560$	2.80417	+	1.99748i	0.118498	+	0.0844091i
$561$	26.6958	+	15.4341i	1.12710	+	0.651626i
$562$	−20.9781	−	0.500172i	−0.884906	−	0.0210985i
$563$	26.1341	−	11.6357i	1.10142	−	0.490385i	0.226187	−	0.974084i	$-0.427374\pi$
$563$	26.1341	−	11.6357i	1.10142	−	0.490385i	0.875234	+	0.483699i	$0.160707\pi$
$564$	−5.79806	+	8.05946i	−0.244142	+	0.339364i
$565$	−3.86535	+	2.51019i	−0.162617	+	0.105604i
$566$	−36.1513	+	12.8972i	−1.51955	+	0.542110i
$567$	−3.97787	+	25.1153i	−0.167055	+	1.05474i
$568$	−0.841982	+	2.91760i	−0.0353288	+	0.122420i
$569$	−4.88310	−	22.9732i	−0.204710	−	0.963085i	−0.953759	−	0.300571i	$-0.902823\pi$
$569$	−4.88310	−	22.9732i	−0.204710	−	0.963085i	0.749049	−	0.662514i	$-0.230511\pi$
$570$	−0.0480748	−	0.358671i	−0.00201363	−	0.0150231i
$571$	−9.19354			−0.384737			−0.192369	−	0.981323i	$-0.561617\pi$
$571$	−9.19354			−0.384737			−0.192369	+	0.981323i	$0.561617\pi$
$572$	−3.86526	−	23.6021i	−0.161615	−	0.986854i
$573$	−13.0875			−0.546738
$574$	6.03743	+	45.0434i	0.251997	+	1.88008i
$575$	9.03364	+	42.5000i	0.376729	+	1.77237i
$576$	−9.33470	+	25.3779i	−0.388946	+	1.05741i
$577$	−1.69470	+	10.6999i	−0.0705515	+	0.445444i	0.926973	+	0.375127i	$0.122401\pi$
$577$	−1.69470	+	10.6999i	−0.0705515	+	0.445444i	−0.997525	+	0.0703169i	$0.977599\pi$
$578$	4.59664	−	1.63988i	0.191195	−	0.0682100i
$579$	−20.7285	+	13.4612i	−0.861447	+	0.559430i
$580$	−2.39326	−	1.72173i	−0.0993745	−	0.0714911i
$581$	50.4019	−	22.4404i	2.09102	−	0.930984i
$582$	−23.1167	−	0.551164i	−0.958220	−	0.0228465i
$583$	12.4525	−	1.30131i	0.515731	−	0.0538946i
$584$	0.879436	−	12.2764i	0.0363913	−	0.507999i
$585$	2.67126	+	1.73033i	0.110443	+	0.0715405i
$586$	9.53093	+	11.1065i	0.393719	+	0.458806i
$587$	41.0451	−	2.15108i	1.69411	−	0.0887847i	0.819337	−	0.573312i	$-0.194342\pi$
$587$	41.0451	−	2.15108i	1.69411	−	0.0887847i	0.874776	+	0.484527i	$0.161008\pi$
$588$	19.4777	−	1.11228i	0.803248	−	0.0458698i
$589$	1.03855	−	0.109156i	0.0427926	−	0.00449769i
$590$	0.351257	+	0.570197i	0.0144610	+	0.0234746i
$591$	−2.84467	+	54.2795i	−0.117014	+	2.23276i
$592$	−21.7832	+	14.4380i	−0.895283	+	0.593400i
$593$	−7.27826	−	7.27826i	−0.298882	−	0.298882i	0.541694	−	0.840576i	$-0.317783\pi$
$593$	−7.27826	−	7.27826i	−0.298882	−	0.298882i	−0.840576	+	0.541694i	$0.817783\pi$
$594$	−4.48904	−	0.345412i	−0.184188	−	0.0141724i
$595$	−1.58410	−	2.74375i	−0.0649419	−	0.112483i
$596$	−14.8757	−	6.53976i	−0.609331	−	0.267879i
$597$	−5.65848	−	1.83855i	−0.231586	−	0.0752469i
$598$	44.1988	+	8.03180i	1.80742	+	0.328445i
$599$	−11.4618	−	15.7759i	−0.468318	−	0.644585i	0.507889	−	0.861422i	$-0.330426\pi$
$599$	−11.4618	−	15.7759i	−0.468318	−	0.644585i	−0.976208	+	0.216837i	$0.930426\pi$
$600$	−10.2441	−	33.7119i	−0.418212	−	1.37628i
$601$	−22.7610	+	25.2786i	−0.928440	+	1.03114i	0.0709938	+	0.997477i	$0.477383\pi$
$601$	−22.7610	+	25.2786i	−0.928440	+	1.03114i	−0.999433	+	0.0336598i	$0.989284\pi$
$602$	−1.65238	−	8.80040i	−0.0673461	−	0.358677i
$603$	2.43982	+	15.4044i	0.0993572	+	0.627317i
$604$	2.98120	+	3.27993i	0.121303	+	0.133459i
$605$	2.77398	+	0.746833i	0.112778	+	0.0303631i
$606$	8.57887	+	35.3685i	0.348493	+	1.43675i
$607$	−5.73418	−	12.8792i	−0.232743	−	0.522750i	0.758984	−	0.651109i	$-0.225696\pi$
$607$	−5.73418	−	12.8792i	−0.232743	−	0.522750i	−0.991728	+	0.128359i	$0.959029\pi$
$608$	1.26398	+	1.79375i	0.0512613	+	0.0727460i
$609$	−46.9239	+	2.45918i	−1.90145	+	0.0996508i
$610$	0.261983	−	0.0212359i	0.0106074	−	0.000859817i
$611$	−6.61840	−	2.53176i	−0.267752	−	0.102424i
$612$	17.5124	−	17.6772i	0.707897	−	0.714559i
$613$	−21.0152	+	32.3606i	−0.848797	+	1.30703i	0.101229	+	0.994863i	$0.467723\pi$
$613$	−21.0152	+	32.3606i	−0.848797	+	1.30703i	−0.950026	+	0.312170i	$0.898944\pi$
$614$	−3.07700	+	4.02953i	−0.124178	+	0.162619i
$615$	−3.21601	+	5.57029i	−0.129682	+	0.224616i
$616$	−4.23244	−	30.6257i	−0.170530	−	1.23395i
$617$	−0.767809	−	2.86550i	−0.0309108	−	0.115361i	0.948747	−	0.316038i	$-0.102353\pi$
$617$	−0.767809	−	2.86550i	−0.0309108	−	0.115361i	−0.979658	+	0.200677i	$0.935686\pi$
$618$	15.1933	−	11.7148i	0.611163	−	0.471240i
$619$	4.31312	+	8.46498i	0.173359	+	0.340236i	0.961295	−	0.275521i	$-0.0888503\pi$
$619$	4.31312	+	8.46498i	0.173359	+	0.340236i	−0.787936	+	0.615757i	$0.788850\pi$
$620$	−1.35647	+	0.370284i	−0.0544773	+	0.0148710i
$621$	3.43967	−	7.72562i	0.138029	−	0.310018i
$622$	−6.84231	+	37.4065i	−0.274352	+	1.49986i
$623$	−15.4694	−	47.6101i	−0.619770	−	1.90746i
$624$	−36.2671	−	3.42624i	−1.45185	−	0.137160i
$625$	19.4015	+	14.0960i	0.776060	+	0.563841i
$626$	−18.4443	+	17.5852i	−0.737181	+	0.702847i
$627$	−2.04659	+	2.52424i	−0.0817328	+	0.100809i
$628$	−0.342981	+	7.18851i	−0.0136864	+	0.286853i
$629$	23.7527	−	3.76206i	0.947082	−	0.150003i
$630$	3.39614	+	2.32241i	0.135305	+	0.0925271i
$631$	−36.3430	+	23.6014i	−1.44679	+	0.939557i	−0.447823	+	0.894122i	$0.647801\pi$
$631$	−36.3430	+	23.6014i	−1.44679	+	0.939557i	−0.998967	+	0.0454344i	$0.985533\pi$
$632$	−6.41795	+	27.5850i	−0.255292	+	1.09727i
$633$	−3.52377	−	33.5264i	−0.140057	−	1.33256i
$634$	23.0758	−	6.89420i	0.916459	−	0.273804i
$635$	−2.76180	+	4.25280i	−0.109599	+	0.168767i
$636$	2.89503	−	18.8494i	0.114795	−	0.747429i
$637$	4.31822	+	13.2379i	0.171094	+	0.524503i
$638$	3.50149	+	26.2424i	0.138625	+	1.03895i
$639$	−0.939220	+	3.50522i	−0.0371550	+	0.138664i
$640$	−2.06873	−	2.10963i	−0.0817737	−	0.0833903i
$641$	−8.71855	+	7.85022i	−0.344362	+	0.310065i	−0.823104	−	0.567891i	$-0.807760\pi$
$641$	−8.71855	+	7.85022i	−0.344362	+	0.310065i	0.478742	+	0.877956i	$0.341093\pi$
$642$	−53.8644	+	33.1819i	−2.12586	+	1.30959i
$643$	−15.7278	+	19.4222i	−0.620244	+	0.765938i	−0.986355	−	0.164633i	$-0.947356\pi$
$643$	−15.7278	+	19.4222i	−0.620244	+	0.765938i	0.366110	+	0.930571i	$0.380689\pi$
$644$	56.8583	+	11.8076i	2.24053	+	0.465283i
$645$	0.575336	−	1.12916i	0.0226538	−	0.0444606i
$646$	−0.372636	−	1.98462i	−0.0146612	−	0.0780837i
$647$	0.895688	−	8.52190i	0.0352131	−	0.335031i	−0.962706	−	0.270550i	$-0.912794\pi$
$647$	0.895688	−	8.52190i	0.0352131	−	0.335031i	0.997919	−	0.0644803i	$-0.0205390\pi$
$648$	7.13988	−	20.6217i	0.280481	−	0.810097i
$649$	1.55999	−	5.80810i	0.0612349	−	0.227988i
$650$	21.3955	−	13.2144i	0.839200	−	0.518313i
$651$	−13.1724	+	18.1302i	−0.516267	+	0.710580i
$652$	−2.54859	+	25.3916i	−0.0998103	+	0.994412i
$653$	22.6888	−	25.1985i	0.887883	−	0.986094i	−0.112088	−	0.993698i	$-0.535754\pi$
$653$	22.6888	−	25.1985i	0.887883	−	0.986094i	0.999971	+	0.00760442i	$0.00242058\pi$
$654$	−37.8448	−	17.9424i	−1.47985	−	0.701603i
$655$	−5.14707	−	0.815216i	−0.201113	−	0.0318531i
$656$	1.67629	−	38.9662i	0.0654483	−	1.52137i
$657$	0.769761	−	14.6879i	0.0300312	−	0.573030i
$658$	−8.47110	−	3.48563i	−0.330238	−	0.135884i
$659$	37.3327	+	21.5541i	1.45428	+	0.839627i	0.998720	−	0.0505800i	$-0.0161070\pi$
$659$	37.3327	+	21.5541i	1.45428	+	0.839627i	0.455556	+	0.890207i	$0.349440\pi$
$660$	2.17232	−	3.79834i	0.0845576	−	0.147850i
$661$	12.2974	−	45.8945i	0.478313	−	1.78509i	−0.130136	−	0.991496i	$-0.541542\pi$
$661$	12.2974	−	45.8945i	0.478313	−	1.78509i	0.608449	−	0.793593i	$-0.291792\pi$
$662$	−32.3737	+	13.4985i	−1.25824	+	0.524635i
$663$	29.0508	+	16.7276i	1.12824	+	0.649646i
$664$	−45.9617	+	11.3765i	−1.78366	+	0.441495i
$665$	0.311704	−	0.119652i	0.0120874	−	0.00463990i
$666$	−25.6961	+	17.7492i	−0.995703	+	0.687766i
$667$	−48.6416	−	10.3391i	−1.88341	−	0.400332i
$668$	−28.9623	−	20.8358i	−1.12059	−	0.806162i
$669$	−18.4529	+	48.0715i	−0.713432	+	1.85855i
$670$	−1.63517	−	0.480198i	−0.0631723	−	0.0185517i
$671$	−1.75311	−	1.58040i	−0.0676782	−	0.0610108i
$672$	−46.7571	−	5.59955i	−1.80369	−	0.216007i
$673$	−19.3592	−	2.03473i	−0.746242	−	0.0784331i	−0.276228	−	0.961092i	$-0.589084\pi$
$673$	−19.3592	−	2.03473i	−0.746242	−	0.0784331i	−0.470014	+	0.882659i	$0.655751\pi$
$674$	−6.38778	+	3.06520i	−0.246048	+	0.118067i
$675$	−1.46289	−	4.50231i	−0.0563066	−	0.173294i
$676$	−4.24703	−	25.6508i	−0.163347	−	0.986569i
$677$	30.5359	−	22.1857i	1.17359	−	0.852664i	0.182157	−	0.983269i	$-0.441692\pi$
$677$	30.5359	−	22.1857i	1.17359	−	0.852664i	0.991434	+	0.130605i	$0.0416920\pi$
$678$	29.9504	−	55.4711i	1.15024	−	2.13036i
$679$	−4.43564	−	20.8680i	−0.170224	−	0.800842i
$680$	0.925596	+	2.55658i	0.0354950	+	0.0980404i
$681$	−16.3133	+	16.3133i	−0.625126	+	0.625126i
$682$	10.7776	+	6.57867i	0.412696	+	0.251910i
$683$	−0.692827	−	2.58567i	−0.0265103	−	0.0989377i	0.951403	−	0.307948i	$-0.0996424\pi$
$683$	−0.692827	−	2.58567i	−0.0265103	−	0.0989377i	−0.977913	+	0.209011i	$0.932976\pi$
$684$	1.55126	+	2.11424i	0.0593140	+	0.0808398i
$685$	1.90866	+	2.11979i	0.0729263	+	0.0809928i
$686$	−4.18690	−	14.0141i	−0.159856	−	0.535062i
$687$	23.0962	−	8.86580i	0.881175	−	0.338251i
$688$	0.0719817	+	7.68419i	0.00274428	+	0.292957i
$689$	13.5348	−	1.43844i	0.515636	−	0.0548002i
$690$	5.35234	+	6.23715i	0.203760	+	0.237444i
$691$	31.0085	−	25.1102i	1.17962	−	0.955236i	0.180023	−	0.983662i	$-0.442383\pi$
$691$	31.0085	−	25.1102i	1.17962	−	0.955236i	0.999596	+	0.0284261i	$0.00904953\pi$
$692$	23.4262	−	36.4457i	0.890529	−	1.38546i
$693$	−5.75790	−	36.4948i	−0.218724	−	1.38632i
$694$	−5.88425	+	1.42727i	−0.223363	+	0.0541783i
$695$	1.10877	+	0.425616i	0.0420579	+	0.0161445i
$696$	40.0166	+	4.98254i	1.51683	+	0.188863i
$697$	−16.2941	+	31.9790i	−0.617183	+	1.21129i
$698$	−12.9998	−	6.16328i	−0.492051	−	0.233284i
$699$	7.18595	+	3.19939i	0.271798	+	0.121012i
$700$	28.0762	−	16.3856i	1.06118	−	0.619318i
$701$	41.7655	+	13.5704i	1.57746	+	0.512548i	0.961401	−	0.275150i	$-0.0887276\pi$
$701$	41.7655	+	13.5704i	1.57746	+	0.512548i	0.616061	+	0.787699i	$0.288728\pi$
$702$	−4.88075	−	0.366932i	−0.184212	−	0.0138490i
$703$			2.53437i			0.0955856i
$704$	−1.03202	+	26.5129i	−0.0388956	+	0.999243i
$705$	−0.648222	−	1.12275i	−0.0244134	−	0.0422853i
$706$	−20.2251	−	2.61452i	−0.761182	−	0.0983986i
$707$	−29.9184	+	15.2442i	−1.12520	+	0.573317i
$708$	−7.95432	−	4.54289i	−0.298942	−	0.170732i
$709$	−13.3998	+	16.5474i	−0.503239	+	0.621449i	−0.963944	−	0.266104i	$-0.914263\pi$
$709$	−13.3998	+	16.5474i	−0.503239	+	0.621449i	0.460705	+	0.887553i	$0.347597\pi$
$710$	−0.302123	−	0.256817i	−0.0113385	−	0.00963816i
$711$	−7.03679	+	33.1055i	−0.263900	+	1.24155i
$712$	5.90676	+	42.5540i	0.221365	+	1.59478i
$713$	−18.4316	+	14.9256i	−0.690269	+	0.558969i
$714$	37.0017	+	22.5556i	1.38475	+	0.844123i
$715$	3.01706	+	0.806596i	0.112831	+	0.0301650i
$716$	−1.91504	+	0.987088i	−0.0715685	+	0.0368892i
$717$	−26.0599	−	32.1813i	−0.973224	−	1.20183i
$718$	35.1580	+	12.3575i	1.31208	+	0.461178i
$719$	24.6250	+	5.23420i	0.918357	+	0.195203i	0.642757	−	0.766070i	$-0.277790\pi$
$719$	24.6250	+	5.23420i	0.918357	+	0.195203i	0.275600	+	0.961273i	$0.411124\pi$
$720$	−2.52000	−	2.47323i	−0.0939150	−	0.0921719i
$721$	13.7561	+	11.1395i	0.512305	+	0.414857i
$722$	−26.6464	+	0.760208i	−0.991677	+	0.0282920i
$723$	−22.8445	−	44.8348i	−0.849596	−	1.66743i
$724$	−6.15191	−	4.93419i	−0.228634	−	0.183378i
$725$	−24.1080	+	13.9187i	−0.895347	+	0.516929i
$726$	−38.1971	+	9.21674i	−1.41763	+	0.342065i
$727$	25.3313			0.939487			0.469743	−	0.882803i	$-0.344346\pi$
$727$	25.3313			0.939487			0.469743	+	0.882803i	$0.344346\pi$
$728$	−4.65960	−	33.2856i	−0.172696	−	1.23364i
$729$	10.3064	−	31.7199i	0.381720	−	1.17481i
$730$	1.41418	+	0.763557i	0.0523413	+	0.0282605i
$731$	2.87624	−	6.46014i	0.106382	−	0.238937i
$732$	−3.00593	+	1.97215i	−0.111102	+	0.0728927i
$733$	15.1274	+	7.70781i	0.558744	+	0.284694i	0.710469	−	0.703728i	$-0.248483\pi$
$733$	15.1274	+	7.70781i	0.558744	+	0.284694i	−0.151725	+	0.988423i	$0.548483\pi$
$734$	1.67370	+	1.14454i	0.0617772	+	0.0422457i
$735$	−0.912957	+	2.37834i	−0.0336749	+	0.0877262i
$736$	−46.2638	−	18.5315i	−1.70530	−	0.683079i
$737$	6.93969	+	13.6400i	0.255627	+	0.502436i
$738$	1.11095	−	46.5952i	0.0408947	−	1.71519i
$739$	3.30787	+	4.08488i	0.121682	+	0.150265i	0.834347	−	0.551240i	$-0.185845\pi$
$739$	3.30787	+	4.08488i	0.121682	+	0.150265i	−0.712665	+	0.701505i	$0.752512\pi$
$740$	−0.549616	−	3.36797i	−0.0202043	−	0.123809i
$741$	−2.22005	+	2.74805i	−0.0815556	+	0.100952i
$742$	17.5374	−	1.42156i	0.643820	−	0.0521871i
$743$	−12.9678	−	33.7822i	−0.475741	−	1.23935i	−0.936137	−	0.351635i	$-0.885626\pi$
$743$	−12.9678	−	33.7822i	−0.475741	−	1.23935i	0.460396	−	0.887714i	$-0.347707\pi$
$744$	13.8575	−	13.3365i	0.508039	−	0.488940i
$745$	1.57687	−	1.41982i	0.0577721	−	0.0520182i
$746$	−2.21491	+	5.38288i	−0.0810935	+	0.197081i
$747$	−54.6547	+	14.6447i	−1.99971	+	0.535820i
$748$	10.9958	−	21.8002i	0.402045	−	0.797096i
$749$	−41.2737	−	41.2737i	−1.50811	−	1.50811i
$750$	9.18885	+	1.18785i	0.335529	+	0.0433742i
$751$	−22.2109	+	4.72107i	−0.810487	+	0.172274i	−0.594472	−	0.804116i	$-0.702639\pi$
$751$	−22.2109	+	4.72107i	−0.810487	+	0.172274i	−0.216014	+	0.976390i	$0.569306\pi$
$752$	6.63289	+	4.21965i	0.241877	+	0.153875i
$753$	9.37339	+	12.9014i	0.341585	+	0.470152i
$754$	3.85662	+	28.5218i	0.140450	+	1.03870i
$755$	−0.550445	+	0.178850i	−0.0200327	+	0.00650903i
$756$	−6.29551	−	0.631887i	−0.228965	−	0.0229815i
$757$	−5.34136	+	50.8197i	−0.194135	+	1.84707i	0.271925	+	0.962319i	$0.412340\pi$
$757$	−5.34136	+	50.8197i	−0.194135	+	1.84707i	−0.466060	+	0.884753i	$0.654327\pi$
$758$	14.7021	+	26.9274i	0.534006	+	0.978047i
$759$	7.75851	−	73.3962i	0.281616	−	2.66411i
$760$	−0.281366	+	0.0541954i	−0.0102062	+	0.00196587i
$761$	−10.2556	−	3.93677i	−0.371766	−	0.142708i	0.165309	−	0.986242i	$-0.447138\pi$
$761$	−10.2556	−	3.93677i	−0.371766	−	0.142708i	−0.537076	+	0.843534i	$0.680471\pi$
$762$	5.27992	−	69.1579i	0.191271	−	2.50533i
$763$	8.03416	−	37.7978i	0.290856	−	1.36837i
$764$	0.590808	+	10.3459i	0.0213747	+	0.374302i
$765$	1.16442	+	3.03342i	0.0420997	+	0.109673i
$766$	9.30739	+	2.21147i	0.336290	+	0.0799035i
$767$	1.68479	−	6.31703i	0.0608344	−	0.228095i
$768$	38.6631	+	11.7664i	1.39514	+	0.424582i
$769$	−7.82464	−	2.09661i	−0.282164	−	0.0756056i	0.114962	−	0.993370i	$-0.463326\pi$
$769$	−7.82464	−	2.09661i	−0.282164	−	0.0756056i	−0.397125	+	0.917764i	$0.629992\pi$
$770$	3.87286	+	1.13984i	0.139568	+	0.0410771i
$771$	−5.19722	+	9.00186i	−0.187173	+	0.324194i
$772$	11.5771	+	15.7786i	0.416669	+	0.567883i
$773$	−21.9406	−	1.14986i	−0.789147	−	0.0413575i	−0.346496	−	0.938051i	$-0.612629\pi$
$773$	−21.9406	−	1.14986i	−0.789147	−	0.0413575i	−0.442651	+	0.896694i	$0.645962\pi$
$774$	0.261884	+	9.17943i	0.00941324	+	0.329948i
$775$	−2.07692	+	13.1131i	−0.0746050	+	0.471038i
$776$	0.607851	+	18.2991i	0.0218206	+	0.656899i
$777$	−40.4182	−	36.3927i	−1.44999	−	1.30558i
$778$	−5.28376	+	2.53543i	−0.189432	+	0.0908995i
$779$	−3.05998	−	2.22320i	−0.109635	−	0.0796546i
$780$	2.35431	−	4.13338i	0.0842978	−	0.147999i
$781$	0.184237	+	3.55603i	0.00659253	+	0.127245i
$782$	31.6468	+	33.1927i	1.13169	+	1.18697i
$783$	5.38844	+	0.566348i	0.192567	+	0.0202396i
$784$	−1.75856	−	15.3473i	−0.0628058	−	0.548117i
$785$	−0.837316	−	0.426634i	−0.0298851	−	0.0152272i
$786$	67.1345	−	23.9506i	2.39461	−	0.854291i
$787$	5.19982	+	4.21073i	0.185353	+	0.150096i	0.717506	−	0.696552i	$-0.245283\pi$
$787$	5.19982	+	4.21073i	0.185353	+	0.150096i	−0.532153	+	0.846648i	$0.678617\pi$
$788$	43.0373	−	0.201572i	1.53314	−	0.00718069i
$789$	−29.8818	−	33.1871i	−1.06382	−	1.18149i
$790$	−2.93928	−	2.24448i	−0.104575	−	0.0798549i
$791$	56.1809	+	15.0536i	1.99756	+	0.535245i
$792$	−0.626209	+	31.7013i	−0.0222514	+	1.12646i
$793$	−1.90885	−	1.71473i	−0.0677852	−	0.0608919i
$794$	−1.89685	+	0.790908i	−0.0673165	+	0.0280683i
$795$	2.08847	+	1.35627i	0.0740705	+	0.0481019i
$796$	−1.19797	+	4.55613i	−0.0424608	+	0.161488i
$797$	−27.4112	+	2.88103i	−0.970955	+	0.102051i	−0.576706	−	0.816952i	$-0.695662\pi$
$797$	−27.4112	+	2.88103i	−0.970955	+	0.102051i	−0.394249	+	0.919004i	$0.628995\pi$
$798$	−2.95775	+	3.47955i	−0.104703	+	0.123175i
$799$	−3.94003	−	6.06711i	−0.139388	−	0.214639i
$800$	−26.1874	+	9.61998i	−0.925864	+	0.340117i
$801$	8.03140	+	50.7083i	0.283776	+	1.79169i
$802$	0.916841	+	1.67922i	0.0323748	+	0.0592954i
$803$	−3.72701	−	13.9427i	−0.131523	−	0.492025i
$804$	22.7779	−	4.95321i	0.803315	−	0.174686i
$805$	−4.45715	+	6.13474i	−0.157094	+	0.216221i
$806$	11.7290	+	7.13119i	0.413137	+	0.251185i
$807$	−64.3851	+	20.9200i	−2.26646	+	0.736418i
$808$	27.5721	−	8.37838i	0.969985	−	0.294751i
$809$	11.0812	+	4.93366i	0.389593	+	0.173458i	0.592179	−	0.805806i	$-0.298268\pi$
$809$	11.0812	+	4.93366i	0.389593	+	0.173458i	−0.202586	+	0.979265i	$0.564934\pi$
$810$	2.07162	+	1.95670i	0.0727894	+	0.0687513i
$811$	27.5694	−	14.0473i	0.968094	−	0.493268i	0.102892	−	0.994693i	$-0.467190\pi$
$811$	27.5694	−	14.0473i	0.968094	−	0.493268i	0.865202	+	0.501424i	$0.167190\pi$
$812$	4.06230	+	36.9832i	0.142559	+	1.29785i
$813$	−45.9464	+	12.3113i	−1.61141	+	0.431776i
$814$	−18.6126	+	24.3443i	−0.652372	+	0.853268i
$815$	−2.88585	−	1.66615i	−0.101087	−	0.0583625i
$816$	−27.8694	−	24.6249i	−0.975624	−	0.862046i
$817$	0.625000	+	0.405880i	0.0218660	+	0.0141999i
$818$	1.50369	−	6.32856i	0.0525752	−	0.221273i
$819$	−6.32915	−	39.6629i	−0.221158	−	1.38594i
$820$	4.54859	+	2.29085i	0.158844	+	0.0800000i
$821$	−0.487563	−	9.30326i	−0.0170161	−	0.324686i	−0.993854	−	0.110703i	$-0.964690\pi$
$821$	−0.487563	−	9.30326i	−0.0170161	−	0.324686i	0.976837	−	0.213983i	$-0.0686436\pi$
$822$	−36.8081	−	12.9375i	−1.28383	−	0.451248i
$823$	−22.5354	+	10.0334i	−0.785536	+	0.349743i	−0.759994	−	0.649930i	$-0.774798\pi$
$823$	−22.5354	+	10.0334i	−0.785536	+	0.349743i	−0.0255426	+	0.999674i	$0.508131\pi$
$824$	−9.94666	−	11.4817i	−0.346508	−	0.399984i
$825$	−24.2647	−	33.4394i	−0.844788	−	1.16421i
$826$	2.38136	−	8.10902i	0.0828581	−	0.282149i
$827$	22.6871	−	3.59328i	0.788906	−	0.124951i	0.251036	−	0.967978i	$-0.419229\pi$
$827$	22.6871	−	3.59328i	0.788906	−	0.124951i	0.537871	+	0.843027i	$0.319229\pi$
$828$	−55.7001	−	21.0825i	−1.93571	−	0.732667i
$829$	32.9158	+	29.6376i	1.14321	+	1.02935i	0.999209	+	0.0397779i	$0.0126651\pi$
$829$	32.9158	+	29.6376i	1.14321	+	1.02935i	0.144006	+	0.989577i	$0.454002\pi$
$830$	1.11248	−	6.08188i	0.0386149	−	0.211105i
$831$	−8.01953	+	5.82653i	−0.278194	+	0.202120i
$832$	−1.07130	+	28.8245i	−0.0371408	+	0.999310i
$833$	−4.39279	+	13.5196i	−0.152201	+	0.468427i
$834$	−16.1006	+	2.15805i	−0.557518	+	0.0747273i
$835$	4.03471	−	2.32944i	0.139627	−	0.0806136i
$836$	2.08785	+	1.50391i	0.0722098	+	0.0520139i
$837$	1.82722	−	1.82722i	0.0631579	−	0.0631579i
$838$	−41.0698	+	31.6671i	−1.41873	+	1.09392i
$839$	0.533202	+	0.0279439i	0.0184082	+	0.000964731i	0.0615378	−	0.998105i	$-0.480400\pi$
$839$	0.533202	+	0.0279439i	0.0184082	+	0.000964731i	−0.0431296	+	0.999069i	$0.513733\pi$
$840$	3.17601	−	5.26546i	0.109583	−	0.181676i
$841$	−0.298981	−	2.84462i	−0.0103097	−	0.0980903i
$842$	24.5645	+	35.5629i	0.846548	+	1.22558i
$843$	1.96148	+	37.4274i	0.0675571	+	1.28907i
$844$	−26.3442	+	4.29908i	−0.906804	+	0.147980i
$845$	3.28142	+	0.871102i	0.112884	+	0.0299668i
$846$	8.02156	+	4.88982i	0.275787	+	0.168115i
$847$	−16.4201	−	32.3214i	−0.564200	−	1.11058i
$848$	−15.0315	−	1.43765i	−0.516184	−	0.0493692i
$849$	27.8836	+	62.6276i	0.956963	+	2.14937i
$850$	25.5984	+	1.95433i	0.878017	+	0.0670329i
$851$	−31.3492	−	48.2736i	−1.07464	−	1.65480i
$852$	5.31036	+	1.10278i	0.181930	+	0.0377807i
$853$	−25.3408	−	4.01358i	−0.867651	−	0.137422i	−0.293289	−	0.956024i	$-0.594750\pi$
$853$	−25.3408	−	4.01358i	−0.867651	−	0.137422i	−0.574362	+	0.818601i	$0.694750\pi$
$854$	−2.41139	−	2.27761i	−0.0825160	−	0.0779383i
$855$	−0.334936	+	0.0711928i	−0.0114546	+	0.00243474i
$856$	28.6625	+	41.0829i	0.979664	+	1.40418i
$857$			31.1659i			1.06461i	0.846554	+	0.532304i	$0.178673\pi$
$857$			31.1659i			1.06461i	−0.846554	+	0.532304i	$0.821327\pi$
$858$	−41.5070	+	10.0926i	−1.41702	+	0.344554i
$859$			9.58629i			0.327080i	0.986537	+	0.163540i	$0.0522913\pi$
$859$			9.58629i			0.327080i	−0.986537	+	0.163540i	$0.947709\pi$
$860$	−0.918594	−	0.403840i	−0.0313238	−	0.0137708i
$861$	79.3960	−	16.8761i	2.70581	−	0.575137i
$862$	20.3595	−	21.5553i	0.693446	−	0.734175i
$863$	−28.2363	−	4.47219i	−0.961176	−	0.152235i	−0.343921	−	0.938999i	$-0.611755\pi$
$863$	−28.2363	−	4.47219i	−0.961176	−	0.152235i	−0.617255	+	0.786763i	$0.711755\pi$
$864$	5.22408	+	1.48113i	0.177727	+	0.0503892i
$865$	3.08124	+	4.74469i	0.104765	+	0.161324i
$866$	−1.63672	+	21.4382i	−0.0556180	+	0.728501i
$867$	−3.54540	−	7.96309i	−0.120408	−	0.270441i
$868$	14.9269	+	9.59456i	0.506653	+	0.325661i
$869$	3.45172	+	33.0304i	0.117091	+	1.12048i
$870$	−2.74081	+	4.49619i	−0.0929220	+	0.152435i
$871$	7.57027	+	14.8150i	0.256509	+	0.501987i
$872$	−12.4754	+	30.7270i	−0.422469	+	1.04055i
$873$	1.14510	+	21.8498i	0.0387558	+	0.739505i
$874$	−3.97666	+	2.74681i	−0.134512	+	0.0929123i
$875$	0.893556	+	8.50162i	0.0302077	+	0.287407i
$876$	−21.9823	+	0.102957i	−0.742712	+	0.00347860i
$877$	−5.74771	−	0.301225i	−0.194087	−	0.0101716i	−0.0449550	−	0.998989i	$-0.514314\pi$
$877$	−5.74771	−	0.301225i	−0.194087	−	0.0101716i	−0.149132	+	0.988817i	$0.547648\pi$
$878$	17.5454	+	22.7550i	0.592128	+	0.767945i
$879$	18.4835	−	18.4835i	0.623433	−	0.623433i
$880$	−3.10072	−	1.54579i	−0.104525	−	0.0521087i
$881$	−35.4578	+	20.4715i	−1.19460	+	0.689704i	−0.959347	−	0.282230i	$-0.908926\pi$
$881$	−35.4578	+	20.4715i	−1.19460	+	0.689704i	−0.235255	+	0.971934i	$0.575593\pi$
$882$	−2.45241	−	18.2967i	−0.0825769	−	0.616081i
$883$	6.36110	−	19.5775i	0.214068	−	0.658834i	−0.785150	−	0.619305i	$-0.787414\pi$
$883$	6.36110	−	19.5775i	0.214068	−	0.658834i	0.999218	−	0.0395287i	$-0.0125856\pi$
$884$	11.9120	−	23.7203i	0.400645	−	0.797801i
$885$	0.967694	−	0.703071i	0.0325287	−	0.0236335i
$886$	31.4346	+	5.74996i	1.05607	+	0.193174i
$887$	6.52227	+	5.87268i	0.218996	+	0.197185i	0.771325	−	0.636441i	$-0.219594\pi$
$887$	6.52227	+	5.87268i	0.218996	+	0.197185i	−0.552329	+	0.833626i	$0.686261\pi$
$888$	28.6741	+	36.8301i	0.962240	+	1.23594i
$889$	63.2050	−	10.0107i	2.11983	−	0.335747i
$890$	−5.38266	−	1.58072i	−0.180427	−	0.0529857i
$891$	0.0152606	−	25.5894i	0.000511249	−	0.857278i
$892$	38.8344	+	12.4173i	1.30027	+	0.415762i
$893$	0.696462	−	0.310085i	0.0233062	−	0.0103766i
$894$	−9.62399	+	27.3809i	−0.321874	+	0.915755i
$895$	−0.0147237	−	0.280945i	−0.000492158	−	0.00939094i
$896$	−2.31580	+	37.2151i	−0.0773653	+	1.24327i
$897$	8.29426	−	79.8048i	0.276937	−	2.66460i
$898$	41.7631	+	9.92305i	1.39365	+	0.331136i
$899$	−12.7438	−	8.27589i	−0.425028	−	0.276017i
$900$	−31.0685	+	12.0933i	−1.03562	+	0.403111i
$901$	12.0339	+	6.94775i	0.400906	+	0.231463i
$902$	−13.0657	−	43.8281i	−0.435041	−	1.45932i
$903$	−15.4478	+	4.13922i	−0.514070	+	0.137745i
$904$	−45.2030	−	21.1722i	−1.50343	−	0.704176i
$905$	0.917540	−	0.467510i	0.0305001	−	0.0155406i
$906$	5.43583	−	5.75510i	0.180593	−	0.191200i
$907$	−21.5328	−	9.58701i	−0.714984	−	0.318331i	0.0168087	−	0.999859i	$-0.494649\pi$
$907$	−21.5328	−	9.58701i	−0.714984	−	0.318331i	−0.731793	+	0.681527i	$0.761316\pi$
$908$	13.6324	+	12.1595i	0.452406	+	0.403527i
$909$	32.7514	−	10.6416i	1.08630	−	0.352959i
$910$	4.21241	+	1.23175i	0.139640	+	0.0408320i
$911$	20.4380	−	28.1304i	0.677140	−	0.932003i	−0.322755	−	0.946483i	$-0.604609\pi$
$911$	20.4380	−	28.1304i	0.677140	−	0.932003i	0.999895	+	0.0144791i	$0.00460901\pi$
$912$	3.02259	−	2.49488i	0.100088	−	0.0826138i
$913$	−46.5821	+	30.2113i	−1.54164	+	0.999848i
$914$	27.0878	−	14.7897i	0.895986	−	0.489201i
$915$	−0.0734384	−	0.463672i	−0.00242780	−	0.0153285i
$916$	−8.05120	−	17.8577i	−0.266019	−	0.590036i
$917$	35.8176	+	55.1543i	1.18280	+	1.82135i
$918$	−3.80720	−	3.23626i	−0.125656	−	0.106813i
$919$	25.4776	−	2.67780i	0.840427	−	0.0883324i	0.325474	−	0.945551i	$-0.394476\pi$
$919$	25.4776	−	2.67780i	0.840427	−	0.0883324i	0.514953	+	0.857219i	$0.327809\pi$
$920$	4.68896	−	4.51268i	0.154590	−	0.148779i
$921$	7.59446	+	4.93190i	0.250246	+	0.162512i
$922$	6.74988	+	16.1883i	0.222295	+	0.533134i
$923$	0.207075	+	3.86546i	0.00681596	+	0.127233i
$924$	−53.9653	+	11.7014i	−1.77533	+	0.384948i
$925$	−31.1235	−	8.33950i	−1.02333	−	0.274201i
$926$	13.0106	−	17.0382i	0.427554	−	0.559909i
$927$	−12.1471	−	13.4907i	−0.398962	−	0.443092i
$928$	2.13232	−	31.8588i	0.0699969	−	1.04582i
$929$	27.7642	+	22.4830i	0.910913	+	0.737643i	0.965373	−	0.260873i	$-0.0840105\pi$
$929$	27.7642	+	22.4830i	0.910913	+	0.737643i	−0.0544603	+	0.998516i	$0.517344\pi$
$930$	0.843860	+	2.36537i	0.0276713	+	0.0775635i
$931$	−1.33480	−	0.680114i	−0.0437463	−	0.0222898i
$932$	2.20478	−	5.82505i	0.0722200	−	0.190806i
$933$	67.5467	+	7.09944i	2.21138	+	0.232425i
$934$	−12.9609	+	12.3573i	−0.424094	+	0.404342i
$935$	2.00497	+	2.47896i	0.0655696	+	0.0810705i
$936$	−0.620242	+	34.4641i	−0.0202732	+	1.12649i
$937$	−45.9816	−	33.4076i	−1.50215	−	1.09138i	−0.969513	−	0.245038i	$-0.921199\pi$
$937$	−45.9816	−	33.4076i	−1.50215	−	1.09138i	−0.532641	−	0.846341i	$-0.678801\pi$
$938$	9.30431	+	19.3899i	0.303797	+	0.633103i
$939$	33.8249	+	30.4560i	1.10383	+	0.993896i
$940$	−0.858294	+	0.563115i	−0.0279945	+	0.0183668i
$941$	4.58041	−	28.9196i	0.149317	−	0.942751i	−0.793289	−	0.608845i	$-0.791633\pi$
$941$	4.58041	−	28.9196i	0.149317	−	0.942751i	0.942606	−	0.333906i	$-0.108367\pi$
$942$	12.8485	−	0.366561i	0.418627	−	0.0119432i
$943$	85.7853	+	4.49582i	2.79355	+	0.146404i
$944$	−3.23215	+	6.49311i	−0.105198	+	0.211333i
$945$	0.413098	−	0.715507i	0.0134381	−	0.0232755i
$946$	3.02273	+	8.48880i	0.0982773	+	0.275995i
$947$	24.3642	+	6.52836i	0.791729	+	0.212143i	0.631949	−	0.775010i	$-0.282255\pi$
$947$	24.3642	+	6.52836i	0.791729	+	0.212143i	0.159779	+	0.987153i	$0.448922\pi$
$948$	49.9981	+	7.67906i	1.62386	+	0.249404i
$949$	−4.07830	−	15.1501i	−0.132387	−	0.491794i
$950$	−0.625429	+	2.63224i	−0.0202916	+	0.0854012i
$951$	−15.4152	−	40.1579i	−0.499871	−	1.30221i
$952$	16.1603	−	30.2687i	0.523757	−	0.981015i
$953$	−0.312126	+	1.46844i	−0.0101107	+	0.0475673i	−0.982914	−	0.184067i	$-0.941074\pi$
$953$	−0.312126	+	1.46844i	−0.0101107	+	0.0475673i	0.972803	+	0.231634i	$0.0744071\pi$
$954$	−17.9926	−	1.37366i	−0.582531	−	0.0444738i
$955$	−1.26329	−	0.484932i	−0.0408791	−	0.0156920i
$956$	−24.2635	+	22.0536i	−0.784736	+	0.713263i
$957$	46.2585	−	9.80372i	1.49533	−	0.316909i
$958$	−1.10578	+	0.603747i	−0.0357261	+	0.0195062i
$959$	3.76271	−	35.7998i	0.121504	−	1.15603i
$960$	−3.47572	+	3.97098i	−0.112178	+	0.128163i
$961$	22.5904	−	7.34006i	0.728722	−	0.236776i
$962$	−20.1876	+	26.5005i	−0.650873	+	0.854412i
$963$	35.1863	+	48.4298i	1.13386	+	1.56063i
$964$	−34.4115	+	20.0830i	−1.10832	+	0.646829i
$965$	−2.49963	+	0.531313i	−0.0804659	+	0.0171036i
$966$	13.2972	−	102.863i	0.427831	−	3.30957i
$967$	−28.0340	−	28.0340i	−0.901513	−	0.901513i	0.0940541	−	0.995567i	$-0.470017\pi$
$967$	−28.0340	−	28.0340i	−0.901513	−	0.901513i	−0.995567	+	0.0940541i	$0.970017\pi$
$968$	9.01033	+	29.7794i	0.289603	+	0.957147i
$969$	−3.48370	+	0.933454i	−0.111912	+	0.0299868i
$970$	−2.21096	−	0.909748i	−0.0709895	−	0.0292102i
$971$	37.0563	−	33.3657i	1.18919	−	1.07076i	0.193217	−	0.981156i	$-0.438108\pi$
$971$	37.0563	−	33.3657i	1.18919	−	1.07076i	0.995978	−	0.0895994i	$-0.0285587\pi$
$972$	−43.2655	−	11.3760i	−1.38774	−	0.364887i
$973$	−5.37112	−	13.9922i	−0.172190	−	0.448571i
$974$	−3.05858	−	37.7330i	−0.0980031	−	1.20904i
$975$	−26.4423	−	36.3061i	−0.846831	−	1.16272i
$976$	1.69472	+	2.28721i	0.0542465	+	0.0732118i
$977$	−24.5261	−	30.2872i	−0.784658	−	0.968972i	0.215313	−	0.976545i	$-0.430923\pi$
$977$	−24.5261	−	30.2872i	−0.784658	−	0.968972i	−0.999971	+	0.00757281i	$0.997589\pi$
$978$	45.5659	+	1.08641i	1.45704	+	0.0347396i
$979$	22.8441	+	44.9002i	0.730100	+	1.43502i
$980$	1.92133	+	0.614344i	0.0613747	+	0.0196245i
$981$	−14.2023	+	36.9981i	−0.453443	+	1.18126i
$982$	−9.94362	+	14.5409i	−0.317314	+	0.464018i
$983$	−19.1309	−	9.74770i	−0.610182	−	0.310903i	0.121456	−	0.992597i	$-0.461244\pi$
$983$	−19.1309	−	9.74770i	−0.610182	−	0.310903i	−0.731638	+	0.681694i	$0.761244\pi$
$984$	−69.6220	+	2.31267i	−2.21947	+	0.0737253i
$985$	−2.28581	+	5.13401i	−0.0728318	+	0.163583i
$986$	−13.9598	+	25.8549i	−0.444570	+	0.823388i
$987$	−5.05572	+	15.5599i	−0.160925	+	0.495278i
$988$	2.27260	+	1.63094i	0.0723010	+	0.0518870i
$989$	−16.9253			−0.538193
$990$	−3.74013	−	1.77594i	−0.118869	−	0.0564432i
$991$	−11.6188	+	6.70815i	−0.369085	+	0.213091i	−0.673059	−	0.739589i	$-0.735020\pi$
$991$	−11.6188	+	6.70815i	−0.369085	+	0.213091i	0.303974	+	0.952680i	$0.401687\pi$
$992$	−11.1683	−	10.3525i	−0.354595	−	0.328693i
$993$	28.4409	+	55.8183i	0.902543	+	1.77134i
$994$	0.142704	+	5.00199i	0.00452630	+	0.158654i
$995$	−0.478069	−	0.387133i	−0.0151558	−	0.0122729i
$996$	26.5093	+	80.3054i	0.839978	+	2.54457i
$997$	−56.9797	−	12.1114i	−1.80456	−	0.383572i	−0.821999	−	0.569489i	$-0.807141\pi$
$997$	−56.9797	−	12.1114i	−1.80456	−	0.383572i	−0.982565	+	0.185917i	$0.940474\pi$
$998$	−5.64453	+	16.0591i	−0.178675	+	0.508341i
$999$	3.94670	+	4.87377i	0.124868	+	0.154199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bs.a.15.5	✓	1280
4.3	odd	2	inner	572.2.bs.a.15.50	yes	1280
11.3	even	5	inner	572.2.bs.a.223.38	yes	1280
13.7	odd	12	inner	572.2.bs.a.59.19	yes	1280
44.3	odd	10	inner	572.2.bs.a.223.19	yes	1280
52.7	even	12	inner	572.2.bs.a.59.38	yes	1280
143.124	odd	60	inner	572.2.bs.a.267.50	yes	1280
572.267	even	60	inner	572.2.bs.a.267.5	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bs.a.15.5	✓	1280	1.1	even	1	trivial
572.2.bs.a.15.50	yes	1280	4.3	odd	2	inner
572.2.bs.a.59.19	yes	1280	13.7	odd	12	inner
572.2.bs.a.59.38	yes	1280	52.7	even	12	inner
572.2.bs.a.223.19	yes	1280	44.3	odd	10	inner
572.2.bs.a.223.38	yes	1280	11.3	even	5	inner
572.2.bs.a.267.5	yes	1280	572.267	even	60	inner
572.2.bs.a.267.50	yes	1280	143.124	odd	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40168 + 0.187875i) q^{2} +(0.525158 + 2.47067i) q^{3} +(1.92941 - 0.526680i) q^{4} +(-0.0408544 + 0.257944i) q^{5} +(-1.20028 - 3.36443i) q^{6} +(2.76404 - 1.79499i) q^{7} +(-2.60546 + 1.10072i) q^{8} +(-3.08781 + 1.37478i) q^{9} +O(q^{10})\)	\(q+(-1.40168 + 0.187875i) q^{2} +(0.525158 + 2.47067i) q^{3} +(1.92941 - 0.526680i) q^{4} +(-0.0408544 + 0.257944i) q^{5} +(-1.20028 - 3.36443i) q^{6} +(2.76404 - 1.79499i) q^{7} +(-2.60546 + 1.10072i) q^{8} +(-3.08781 + 1.37478i) q^{9} +(0.00880344 - 0.369231i) q^{10} +(-2.46606 + 2.21778i) q^{11} +(2.31450 + 4.49034i) q^{12} +(-2.67665 + 2.41569i) q^{13} +(-3.53707 + 3.03529i) q^{14} +(-0.658752 + 0.0345237i) q^{15} +(3.44522 - 2.03236i) q^{16} +(-3.66074 + 0.384759i) q^{17} +(4.06983 - 2.50712i) q^{18} +(0.0203016 - 0.387378i) q^{19} +(0.0570296 + 0.519197i) q^{20} +(5.88640 + 5.88640i) q^{21} +(3.03995 - 3.57193i) q^{22} +(4.40503 + 7.62974i) q^{23} +(-4.08781 - 5.85918i) q^{24} +(4.69042 + 1.52401i) q^{25} +(3.29795 - 3.88890i) q^{26} +(-0.564212 - 0.776572i) q^{27} +(4.38758 - 4.91903i) q^{28} +(-3.77690 + 4.19467i) q^{29} +(0.916872 - 0.172154i) q^{30} +(0.421128 + 2.65890i) q^{31} +(-4.44726 + 3.49599i) q^{32} +(-6.77449 - 4.92813i) q^{33} +(5.05889 - 1.22707i) q^{34} +(0.350084 + 0.786303i) q^{35} +(-5.23356 + 4.27880i) q^{36} +(-6.52444 + 0.341931i) q^{37} +(0.0443223 + 0.546794i) q^{38} +(-7.37405 - 5.34451i) q^{39} +(-0.177481 - 0.717032i) q^{40} +(5.31054 - 8.17751i) q^{41} +(-9.35675 - 7.14493i) q^{42} +(-0.960567 + 1.66375i) q^{43} +(-3.58996 + 5.57783i) q^{44} +(-0.228466 - 0.852648i) q^{45} +(-7.60787 - 9.86685i) q^{46} +(0.892243 + 1.75113i) q^{47} +(6.83059 + 7.44470i) q^{48} +(1.57079 - 3.52805i) q^{49} +(-6.86078 - 1.25496i) q^{50} +(-2.87308 - 8.84243i) q^{51} +(-3.89204 + 6.07059i) q^{52} +(-3.05406 - 2.21891i) q^{53} +(0.936743 + 0.982503i) q^{54} +(-0.471316 - 0.726711i) q^{55} +(-5.22581 + 7.71922i) q^{56} +(0.967748 - 0.153276i) q^{57} +(4.50593 - 6.58917i) q^{58} +(-1.52074 + 0.987579i) q^{59} +(-1.25282 + 0.413562i) q^{60} +(0.0743889 + 0.707763i) q^{61} +(-1.08983 - 3.64780i) q^{62} +(-6.06711 + 9.34254i) q^{63} +(5.57681 - 5.73578i) q^{64} +(-0.513761 - 0.789117i) q^{65} +(10.4215 + 5.63490i) q^{66} +(1.19427 - 4.45707i) q^{67} +(-6.86040 + 2.67040i) q^{68} +(-16.5373 + 14.8902i) q^{69} +(-0.638432 - 1.03637i) q^{70} +(0.675652 - 0.834361i) q^{71} +(6.53190 - 6.98075i) q^{72} +(-1.97553 + 3.87719i) q^{73} +(9.08093 - 1.70506i) q^{74} +(-1.30212 + 12.3888i) q^{75} +(-0.164855 - 0.758103i) q^{76} +(-2.83538 + 10.5566i) q^{77} +(11.3401 + 6.10588i) q^{78} +(5.88565 - 8.10090i) q^{79} +(0.383484 + 0.971705i) q^{80} +(-5.16268 + 5.73374i) q^{81} +(-5.90732 + 12.4600i) q^{82} +(16.5342 + 2.61876i) q^{83} +(14.4575 + 8.25700i) q^{84} +(0.0503107 - 0.959986i) q^{85} +(1.03383 - 2.51251i) q^{86} +(-12.3471 - 7.12863i) q^{87} +(3.98403 - 8.49279i) q^{88} +(3.93129 - 14.6718i) q^{89} +(0.480428 + 1.15222i) q^{90} +(-3.06223 + 11.4816i) q^{91} +(12.5175 + 12.4008i) q^{92} +(-6.34811 + 2.43681i) q^{93} +(-1.57963 - 2.28689i) q^{94} +(0.0990927 + 0.0210628i) q^{95} +(-10.9730 - 9.15178i) q^{96} +(2.31981 - 6.04332i) q^{97} +(-1.53891 + 5.24030i) q^{98} +(4.56574 - 10.2384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Introduction

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