LMFDB - Embedded newform 572.2.bm.a.35.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(35,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 3, 20]))

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

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

chi := DirichletCharacter("572.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bm (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			35.20
Character	$\chi$	$=$	572.35
Dual form			572.2.bm.a.523.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05823 - 0.938168i) q^{2} +(-0.852202 + 0.0895701i) q^{3} +(0.239682 + 1.98559i) q^{4} +(0.526525 + 1.62048i) q^{5} +(0.985854 + 0.704723i) q^{6} +(0.121128 - 1.15246i) q^{7} +(1.60917 - 2.32606i) q^{8} +(-2.21622 + 0.471071i) q^{9} +O(q^{10})$	\(q+(-1.05823 - 0.938168i) q^{2} +(-0.852202 + 0.0895701i) q^{3} +(0.239682 + 1.98559i) q^{4} +(0.526525 + 1.62048i) q^{5} +(0.985854 + 0.704723i) q^{6} +(0.121128 - 1.15246i) q^{7} +(1.60917 - 2.32606i) q^{8} +(-2.21622 + 0.471071i) q^{9} +(0.963098 - 2.20880i) q^{10} +(-2.13156 - 2.54096i) q^{11} +(-0.382107 - 1.67065i) q^{12} +(1.66527 - 3.19795i) q^{13} +(-1.20938 + 1.10592i) q^{14} +(-0.593852 - 1.33381i) q^{15} +(-3.88510 + 0.951820i) q^{16} +(2.53721 + 2.28451i) q^{17} +(2.78720 + 1.58068i) q^{18} +(4.56020 + 2.03033i) q^{19} +(-3.09140 + 1.43386i) q^{20} +0.992976i q^{21} +(-0.128173 + 4.68866i) q^{22} +(3.84394 + 2.21930i) q^{23} +(-1.16300 + 2.12641i) q^{24} +(1.69636 - 1.23248i) q^{25} +(-4.76244 + 1.82185i) q^{26} +(4.29134 - 1.39434i) q^{27} +(2.31733 - 0.0357133i) q^{28} +(3.94016 + 8.84975i) q^{29} +(-0.622912 + 1.96861i) q^{30} +(-3.60971 - 1.17287i) q^{31} +(5.00428 + 2.63764i) q^{32} +(2.04411 + 1.97448i) q^{33} +(-0.541683 - 4.79786i) q^{34} +(1.93131 - 0.410512i) q^{35} +(-1.46654 - 4.28758i) q^{36} +(4.14171 - 1.84401i) q^{37} +(-2.92093 - 6.42678i) q^{38} +(-1.13271 + 2.87446i) q^{39} +(4.61660 + 1.38290i) q^{40} +(5.40179 - 0.567751i) q^{41} +(0.931578 - 1.05079i) q^{42} +(0.317248 + 0.549489i) q^{43} +(4.53439 - 4.84142i) q^{44} +(-1.93026 - 3.34330i) q^{45} +(-1.98568 - 5.95478i) q^{46} +(-0.713180 - 0.981609i) q^{47} +(3.22564 - 1.15913i) q^{48} +(5.53355 + 1.17619i) q^{49} +(-2.95141 - 0.287232i) q^{50} +(-2.36684 - 1.71961i) q^{51} +(6.74894 + 2.54005i) q^{52} +(0.0275035 - 0.0846470i) q^{53} +(-5.84933 - 2.55047i) q^{54} +(2.99524 - 4.79202i) q^{55} +(-2.48577 - 2.13626i) q^{56} +(-4.06807 - 1.32180i) q^{57} +(4.13297 - 13.0616i) q^{58} +(-4.09856 - 0.430777i) q^{59} +(2.50607 - 1.49884i) q^{60} +(-3.08737 - 2.77988i) q^{61} +(2.71954 + 4.62767i) q^{62} +(0.274443 + 2.61115i) q^{63} +(-2.82111 - 7.48608i) q^{64} +(6.05901 + 1.01473i) q^{65} +(-0.310735 - 4.00717i) q^{66} +(-0.593376 - 0.342586i) q^{67} +(-3.92797 + 5.58541i) q^{68} +(-3.47460 - 1.54699i) q^{69} +(-2.42889 - 1.37748i) q^{70} +(7.27972 + 6.55469i) q^{71} +(-2.47054 + 5.91309i) q^{72} +(0.282493 - 0.388818i) q^{73} +(-6.11285 - 1.93424i) q^{74} +(-1.33525 + 1.20227i) q^{75} +(-2.93840 + 9.54130i) q^{76} +(-3.18653 + 2.14875i) q^{77} +(3.89538 - 1.97915i) q^{78} +(2.78905 - 8.58380i) q^{79} +(-3.58801 - 5.79457i) q^{80} +(2.67734 - 1.19203i) q^{81} +(-6.24896 - 4.46698i) q^{82} +(1.67712 + 5.16163i) q^{83} +(-1.97164 + 0.237999i) q^{84} +(-2.36610 + 5.31435i) q^{85} +(0.179793 - 0.879115i) q^{86} +(-4.15049 - 7.18886i) q^{87} +(-9.34047 + 0.869292i) q^{88} +(7.05491 - 12.2195i) q^{89} +(-1.09393 + 5.34887i) q^{90} +(-3.48379 - 2.30651i) q^{91} +(-3.48528 + 8.16440i) q^{92} +(3.18126 + 0.676197i) q^{93} +(-0.166208 + 1.70785i) q^{94} +(-0.889048 + 8.45872i) q^{95} +(-4.50092 - 1.79957i) q^{96} +(7.40965 - 1.57497i) q^{97} +(-4.75228 - 6.43607i) q^{98} +(5.92097 + 4.62719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 5 q^{2} - 3 q^{4} - 24 q^{5} - 5 q^{6} - 20 q^{8} - 78 q^{9}+O(q^{10}) $ 640 * q - 5 * q^2 - 3 * q^4 - 24 * q^5 - 5 * q^6 - 20 * q^8 - 78 * q^9	$ 640 q - 5 q^{2} - 3 q^{4} - 24 q^{5} - 5 q^{6} - 20 q^{8} - 78 q^{9} - 36 q^{12} - 20 q^{13} - 28 q^{14} - 11 q^{16} - 10 q^{17} - 20 q^{18} - 29 q^{20} + 25 q^{22} - 65 q^{24} - 152 q^{25} + 40 q^{26} - 5 q^{28} - 10 q^{29} + 5 q^{30} + 4 q^{33} - 132 q^{34} - 24 q^{36} - 6 q^{37} - 10 q^{38} - 20 q^{40} - 50 q^{41} - 49 q^{42} - 4 q^{44} + 28 q^{45} - 25 q^{46} + 35 q^{48} + 62 q^{49} + 20 q^{50} + 15 q^{52} - 8 q^{53} - 2 q^{56} - 40 q^{57} + 41 q^{58} - 68 q^{60} - 10 q^{61} - 5 q^{62} - 36 q^{64} - 66 q^{66} + 60 q^{68} - 58 q^{69} + 118 q^{70} - 5 q^{72} - 40 q^{73} + 45 q^{74} - 76 q^{77} + 12 q^{78} - 41 q^{80} + 30 q^{81} - 37 q^{82} + 50 q^{84} - 10 q^{85} - 120 q^{86} + 89 q^{88} - 40 q^{89} - 250 q^{90} - 46 q^{92} - 2 q^{93} - 5 q^{94} + 110 q^{96} - 10 q^{97}+O(q^{100}) $ 640 * q - 5 * q^2 - 3 * q^4 - 24 * q^5 - 5 * q^6 - 20 * q^8 - 78 * q^9 - 36 * q^12 - 20 * q^13 - 28 * q^14 - 11 * q^16 - 10 * q^17 - 20 * q^18 - 29 * q^20 + 25 * q^22 - 65 * q^24 - 152 * q^25 + 40 * q^26 - 5 * q^28 - 10 * q^29 + 5 * q^30 + 4 * q^33 - 132 * q^34 - 24 * q^36 - 6 * q^37 - 10 * q^38 - 20 * q^40 - 50 * q^41 - 49 * q^42 - 4 * q^44 + 28 * q^45 - 25 * q^46 + 35 * q^48 + 62 * q^49 + 20 * q^50 + 15 * q^52 - 8 * q^53 - 2 * q^56 - 40 * q^57 + 41 * q^58 - 68 * q^60 - 10 * q^61 - 5 * q^62 - 36 * q^64 - 66 * q^66 + 60 * q^68 - 58 * q^69 + 118 * q^70 - 5 * q^72 - 40 * q^73 + 45 * q^74 - 76 * q^77 + 12 * q^78 - 41 * q^80 + 30 * q^81 - 37 * q^82 + 50 * q^84 - 10 * q^85 - 120 * q^86 + 89 * q^88 - 40 * q^89 - 250 * q^90 - 46 * q^92 - 2 * q^93 - 5 * q^94 + 110 * q^96 - 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.05823	−	0.938168i	−0.748278	−	0.663385i
$2$	−1.05823	−	0.938168i	−0.748278	−	0.663385i
$3$	−0.852202	+	0.0895701i	−0.492019	+	0.0517133i	−0.347290	−	0.937758i	$-0.612898\pi$
$3$	−0.852202	+	0.0895701i	−0.492019	+	0.0517133i	−0.144730	+	0.989471i	$0.546231\pi$
$4$	0.239682	+	1.98559i	0.119841	+	0.992793i
$5$	0.526525	+	1.62048i	0.235469	+	0.724700i	0.997059	+	0.0766402i	$0.0244193\pi$
$5$	0.526525	+	1.62048i	0.235469	+	0.724700i	−0.761590	+	0.648060i	$0.775581\pi$
$6$	0.985854	+	0.704723i	0.402473	+	0.287702i
$7$	0.121128	−	1.15246i	0.0457821	−	0.435588i	−0.947490	−	0.319785i	$-0.896389\pi$
$7$	0.121128	−	1.15246i	0.0457821	−	0.435588i	0.993272	−	0.115803i	$-0.0369440\pi$
$8$	1.60917	−	2.32606i	0.568929	−	0.822386i
$9$	−2.21622	+	0.471071i	−0.738739	+	0.157024i
$10$	0.963098	−	2.20880i	0.304558	−	0.698484i
$11$	−2.13156	−	2.54096i	−0.642689	−	0.766127i
$11$	−2.13156	−	2.54096i	−0.642689	−	0.766127i
$12$	−0.382107	−	1.67065i	−0.110305	−	0.482276i
$13$	1.66527	−	3.19795i	0.461863	−	0.886951i
$13$	1.66527	−	3.19795i	0.461863	−	0.886951i
$14$	−1.20938	+	1.10592i	−0.323220	+	0.295570i
$15$	−0.593852	−	1.33381i	−0.153332	−	0.344389i
$16$	−3.88510	+	0.951820i	−0.971276	+	0.237955i
$17$	2.53721	+	2.28451i	0.615364	+	0.554076i	0.916768	−	0.399421i	$-0.130789\pi$
$17$	2.53721	+	2.28451i	0.615364	+	0.554076i	−0.301404	+	0.953496i	$0.597455\pi$
$18$	2.78720	+	1.58068i	0.656950	+	0.372571i
$19$	4.56020	+	2.03033i	1.04618	+	0.465790i	0.856549	−	0.516065i	$-0.172604\pi$
$19$	4.56020	+	2.03033i	1.04618	+	0.465790i	0.189632	+	0.981855i	$0.439270\pi$
$20$	−3.09140	+	1.43386i	−0.691258	+	0.320621i
$21$			0.992976i			0.216685i
$22$	−0.128173	+	4.68866i	−0.0273265	+	0.999627i
$23$	3.84394	+	2.21930i	0.801516	+	0.462756i	0.844001	−	0.536341i	$-0.180194\pi$
$23$	3.84394	+	2.21930i	0.801516	+	0.462756i	−0.0424847	+	0.999097i	$0.513527\pi$
$24$	−1.16300	+	2.12641i	−0.237396	+	0.434051i
$25$	1.69636	−	1.23248i	0.339273	−	0.246496i
$26$	−4.76244	+	1.82185i	−0.933992	+	0.357294i
$27$	4.29134	−	1.39434i	0.825869	−	0.268341i
$28$	2.31733	−	0.0357133i	0.437935	−	0.00674919i
$29$	3.94016	+	8.84975i	0.731670	+	1.64336i	0.765095	+	0.643917i	$0.222692\pi$
$29$	3.94016	+	8.84975i	0.731670	+	1.64336i	−0.0334252	+	0.999441i	$0.510642\pi$
$30$	−0.622912	+	1.96861i	−0.113728	+	0.359417i
$31$	−3.60971	−	1.17287i	−0.648323	−	0.210653i	−0.0336484	−	0.999434i	$-0.510713\pi$
$31$	−3.60971	−	1.17287i	−0.648323	−	0.210653i	−0.614675	+	0.788781i	$0.710713\pi$
$32$	5.00428	+	2.63764i	0.884641	+	0.466273i
$33$	2.04411	+	1.97448i	0.355834	+	0.343714i
$34$	−0.541683	−	4.79786i	−0.0928978	−	0.822826i
$35$	1.93131	−	0.410512i	0.326451	−	0.0693892i
$36$	−1.46654	−	4.28758i	−0.244424	−	0.714597i
$37$	4.14171	−	1.84401i	0.680893	−	0.303153i	−0.0369914	−	0.999316i	$-0.511777\pi$
$37$	4.14171	−	1.84401i	0.680893	−	0.303153i	0.717884	+	0.696163i	$0.245111\pi$
$38$	−2.92093	−	6.42678i	−0.473837	−	1.04256i
$39$	−1.13271	+	2.87446i	−0.181378	+	0.460282i
$40$	4.61660	+	1.38290i	0.729949	+	0.218656i
$41$	5.40179	−	0.567751i	0.843618	−	0.0886678i	0.327148	−	0.944973i	$-0.393912\pi$
$41$	5.40179	−	0.567751i	0.843618	−	0.0886678i	0.516470	+	0.856305i	$0.327246\pi$
$42$	0.931578	−	1.05079i	0.143746	−	0.162141i
$43$	0.317248	+	0.549489i	0.0483798	+	0.0837963i	0.889201	−	0.457516i	$-0.151261\pi$
$43$	0.317248	+	0.549489i	0.0483798	+	0.0837963i	−0.840821	+	0.541313i	$0.817928\pi$
$44$	4.53439	−	4.84142i	0.683585	−	0.729871i
$45$	−1.93026	−	3.34330i	−0.287745	−	0.498390i
$46$	−1.98568	−	5.95478i	−0.292772	−	0.877984i
$47$	−0.713180	−	0.981609i	−0.104028	−	0.143182i	0.753829	−	0.657070i	$-0.228205\pi$
$47$	−0.713180	−	0.981609i	−0.104028	−	0.143182i	−0.857857	+	0.513888i	$0.828205\pi$
$48$	3.22564	−	1.15913i	0.465581	−	0.167306i
$49$	5.53355	+	1.17619i	0.790507	+	0.168027i
$50$	−2.95141	−	0.287232i	−0.417392	−	0.0406207i
$51$	−2.36684	−	1.71961i	−0.331424	−	0.240794i
$52$	6.74894	+	2.54005i	0.935909	+	0.352241i
$53$	0.0275035	−	0.0846470i	0.00377789	−	0.0116272i	−0.949150	−	0.314825i	$-0.898054\pi$
$53$	0.0275035	−	0.0846470i	0.00377789	−	0.0116272i	0.952928	+	0.303198i	$0.0980542\pi$
$54$	−5.84933	−	2.55047i	−0.795994	−	0.347075i
$55$	2.99524	−	4.79202i	0.403879	−	0.646156i
$56$	−2.48577	−	2.13626i	−0.332175	−	0.285469i
$57$	−4.06807	−	1.32180i	−0.538829	−	0.175076i
$58$	4.13297	−	13.0616i	0.542686	−	1.71507i
$59$	−4.09856	−	0.430777i	−0.533588	−	0.0560823i	−0.166097	−	0.986109i	$-0.553116\pi$
$59$	−4.09856	−	0.430777i	−0.533588	−	0.0560823i	−0.367491	+	0.930027i	$0.619783\pi$
$60$	2.50607	−	1.49884i	0.323532	−	0.193499i
$61$	−3.08737	−	2.77988i	−0.395297	−	0.355927i	0.447383	−	0.894343i	$-0.352356\pi$
$61$	−3.08737	−	2.77988i	−0.395297	−	0.355927i	−0.842679	+	0.538416i	$0.819023\pi$
$62$	2.71954	+	4.62767i	0.345382	+	0.587715i
$63$	0.274443	+	2.61115i	0.0345766	+	0.328974i
$64$	−2.82111	−	7.48608i	−0.352639	−	0.935759i
$65$	6.05901	+	1.01473i	0.751528	+	0.125862i
$66$	−0.310735	−	4.00717i	−0.0382488	−	0.493249i
$67$	−0.593376	−	0.342586i	−0.0724925	−	0.0418535i	0.463316	−	0.886193i	$-0.346660\pi$
$67$	−0.593376	−	0.342586i	−0.0724925	−	0.0418535i	−0.535808	+	0.844340i	$0.679993\pi$
$68$	−3.92797	+	5.58541i	−0.476337	+	0.677330i
$69$	−3.47460	−	1.54699i	−0.418292	−	0.186236i
$70$	−2.42889	−	1.37748i	−0.290308	−	0.164640i
$71$	7.27972	+	6.55469i	0.863944	+	0.777899i	0.976448	−	0.215753i	$-0.0692205\pi$
$71$	7.27972	+	6.55469i	0.863944	+	0.777899i	−0.112504	+	0.993651i	$0.535887\pi$
$72$	−2.47054	+	5.91309i	−0.291156	+	0.696864i
$73$	0.282493	−	0.388818i	0.0330633	−	0.0455078i	−0.792165	−	0.610307i	$-0.791046\pi$
$73$	0.282493	−	0.388818i	0.0330633	−	0.0455078i	0.825229	+	0.564799i	$0.191046\pi$
$74$	−6.11285	−	1.93424i	−0.710604	−	0.224851i
$75$	−1.33525	+	1.20227i	−0.154182	+	0.138826i
$76$	−2.93840	+	9.54130i	−0.337057	+	1.09446i
$77$	−3.18653	+	2.14875i	−0.363139	+	0.244873i
$78$	3.89538	−	1.97915i	0.441065	−	0.224095i
$79$	2.78905	−	8.58380i	0.313792	−	0.965753i	−0.662457	−	0.749100i	$-0.730486\pi$
$79$	2.78905	−	8.58380i	0.313792	−	0.965753i	0.976249	−	0.216653i	$-0.0695139\pi$
$80$	−3.58801	−	5.79457i	−0.401152	−	0.647853i
$81$	2.67734	−	1.19203i	0.297482	−	0.132448i
$82$	−6.24896	−	4.46698i	−0.690082	−	0.493295i
$83$	1.67712	+	5.16163i	0.184087	+	0.566563i	0.999931	−	0.0117092i	$-0.00372724\pi$
$83$	1.67712	+	5.16163i	0.184087	+	0.566563i	−0.815844	+	0.578272i	$0.803727\pi$
$84$	−1.97164	+	0.237999i	−0.215123	+	0.0259678i
$85$	−2.36610	+	5.31435i	−0.256640	+	0.576422i
$86$	0.179793	−	0.879115i	0.0193876	−	0.0947974i
$87$	−4.15049	−	7.18886i	−0.444979	−	0.770727i
$88$	−9.34047	+	0.869292i	−0.995697	+	0.0926669i
$89$	7.05491	−	12.2195i	0.747819	−	1.29526i	−0.201047	−	0.979582i	$-0.564434\pi$
$89$	7.05491	−	12.2195i	0.747819	−	1.29526i	0.948866	−	0.315679i	$-0.102232\pi$
$90$	−1.09393	+	5.34887i	−0.115310	+	0.563820i
$91$	−3.48379	−	2.30651i	−0.365200	−	0.241788i
$92$	−3.48528	+	8.16440i	−0.363366	+	0.851197i
$93$	3.18126	+	0.676197i	0.329881	+	0.0701183i
$94$	−0.166208	+	1.70785i	−0.0171430	+	0.176151i
$95$	−0.889048	+	8.45872i	−0.0912144	+	0.867847i
$96$	−4.50092	−	1.79957i	−0.459373	−	0.183668i
$97$	7.40965	−	1.57497i	0.752336	−	0.159914i	0.184246	−	0.982880i	$-0.441016\pi$
$97$	7.40965	−	1.57497i	0.752336	−	0.159914i	0.568090	+	0.822966i	$0.307683\pi$
$98$	−4.75228	−	6.43607i	−0.480052	−	0.650142i
$99$	5.92097	+	4.62719i	0.595080	+	0.465050i
$100$	2.85379	+	3.07287i	0.285379	+	0.307287i
$101$	−3.69335	+	3.32551i	−0.367502	+	0.330900i	−0.832104	−	0.554619i	$-0.812864\pi$
$101$	−3.69335	+	3.32551i	−0.367502	+	0.330900i	0.464602	+	0.885519i	$0.346197\pi$
$102$	0.891368	+	4.04023i	0.0882585	+	0.400042i
$103$	−9.14914	+	12.5927i	−0.901491	+	1.24080i	0.0684989	+	0.997651i	$0.478179\pi$
$103$	−9.14914	+	12.5927i	−0.901491	+	1.24080i	−0.969990	+	0.243145i	$0.921821\pi$
$104$	−4.75891	−	9.01958i	−0.466649	−	0.884442i
$105$	−1.60910	+	0.522827i	−0.157032	+	0.0510227i
$106$	−0.108518	+	0.0637727i	−0.0105402	+	0.00619416i
$107$	−0.00253874	−	0.0241545i	−0.000245429	−	0.00233510i	0.994398	−	0.105696i	$-0.0337070\pi$
$107$	−0.00253874	−	0.0241545i	−0.000245429	−	0.00233510i	−0.994644	+	0.103361i	$0.967040\pi$
$108$	3.79714	+	8.18663i	0.365380	+	0.787759i
$109$		−	17.1415i		−	1.64186i	−0.571027	−	0.820931i	$-0.693455\pi$
$109$		−	17.1415i		−	1.64186i	0.571027	−	0.820931i	$-0.306545\pi$
$110$	−7.66536	+	2.26100i	−0.730864	+	0.215578i
$111$	−3.36441	+	1.94244i	−0.319335	+	0.184368i
$112$	0.626336	+	4.59271i	0.0591832	+	0.433970i
$113$	−0.888900	−	0.395764i	−0.0836206	−	0.0372303i	0.364500	−	0.931203i	$-0.381240\pi$
$113$	−0.888900	−	0.395764i	−0.0836206	−	0.0372303i	−0.448121	+	0.893973i	$0.647907\pi$
$114$	3.06487	+	5.21529i	0.287051	+	0.488457i
$115$	−1.57239	+	7.39753i	−0.146627	+	0.689824i
$116$	−16.6276	+	9.94467i	−1.54383	+	0.923339i
$117$	−2.18414	+	7.87181i	−0.201924	+	0.727749i
$118$	3.93307	+	4.30100i	0.362068	+	0.395939i
$119$	2.94013	−	2.64730i	0.269521	−	0.242678i
$120$	−4.05814	−	0.765004i	−0.370456	−	0.0698350i
$121$	−1.91291	+	10.8324i	−0.173901	+	0.984763i
$122$	0.659138	+	5.83820i	0.0596756	+	0.528566i
$123$	−4.55256	+	0.967677i	−0.410491	+	0.0872525i
$124$	1.46364	−	7.44850i	0.131439	−	0.668895i
$125$	9.78269	+	7.10754i	0.874991	+	0.635718i
$126$	2.15928	−	3.02066i	0.192364	−	0.269102i
$127$	14.5280	+	3.08802i	1.28915	+	0.274018i	0.800960	−	0.598718i	$-0.204323\pi$
$127$	14.5280	+	3.08802i	1.28915	+	0.274018i	0.488192	+	0.872736i	$0.337656\pi$
$128$	−4.03782	+	10.5686i	−0.356896	+	0.934144i
$129$	−0.319577	−	0.439860i	−0.0281372	−	0.0387275i
$130$	−5.45981	−	6.75819i	−0.478857	−	0.592732i
$131$	−20.9426			−1.82976			−0.914880	−	0.403726i	$-0.867715\pi$
$131$	−20.9426			−1.82976			−0.914880	+	0.403726i	$0.867715\pi$
$132$	−3.43057	+	4.53201i	−0.298593	+	0.394461i
$133$	2.89224	−	5.00950i	0.250789	−	0.434379i
$134$	0.306523	+	0.919220i	0.0264795	+	0.0794085i
$135$	4.51900	+	6.21987i	0.388934	+	0.535321i
$136$	9.39673	−	2.22552i	0.805763	−	0.190837i
$137$	−7.64187	+	8.48716i	−0.652889	+	0.725107i	−0.975150	−	0.221544i	$-0.928890\pi$
$137$	−7.64187	+	8.48716i	−0.652889	+	0.725107i	0.322261	+	0.946651i	$0.395557\pi$
$138$	2.22557	+	4.89682i	0.189453	+	0.416845i
$139$	1.04422	−	9.93508i	0.0885695	−	0.842682i	−0.856573	−	0.516025i	$-0.827411\pi$
$139$	1.04422	−	9.93508i	0.0885695	−	0.842682i	0.945143	−	0.326657i	$-0.105922\pi$
$140$	1.27801	+	3.73639i	0.108011	+	0.315782i
$141$	0.695697	+	0.772649i	0.0585882	+	0.0650688i
$142$	−1.55419	−	13.7659i	−0.130424	−	1.15521i
$143$	−11.6755	+	2.58524i	−0.976352	+	0.216188i
$144$	8.16186	−	3.93960i	0.680155	−	0.328300i
$145$	−12.2662	+	11.0446i	−1.01866	+	0.917202i
$146$	−0.663718	+	0.146432i	−0.0549297	+	0.0121188i
$147$	−4.82105	−	0.506713i	−0.397634	−	0.0417930i
$148$	4.65413	+	7.78174i	0.382567	+	0.639655i
$149$	2.30019	+	2.07110i	0.188439	+	0.169671i	0.757950	−	0.652312i	$-0.226201\pi$
$149$	2.30019	+	2.07110i	0.188439	+	0.169671i	−0.569512	+	0.821983i	$0.692868\pi$
$150$	2.54093	−	0.0195784i	0.207466	−	0.00159857i
$151$	10.1534	−	7.37685i	0.826269	−	0.600319i	−0.0922324	−	0.995738i	$-0.529400\pi$
$151$	10.1534	−	7.37685i	0.826269	−	0.600319i	0.918501	+	0.395418i	$0.129400\pi$
$152$	12.0608	−	7.34014i	0.978263	−	0.595364i
$153$	−6.69918	−	3.86777i	−0.541596	−	0.312691i
$154$	5.38796	+	0.715642i	0.434174	+	0.0576681i
$155$		−	6.46700i		−	0.519442i
$156$	−5.97897	−	1.56013i	−0.478701	−	0.124910i
$157$	−4.05432	+	2.94564i	−0.323570	+	0.235088i	−0.737697	−	0.675131i	$-0.764087\pi$
$157$	−4.05432	+	2.94564i	−0.323570	+	0.235088i	0.414127	+	0.910219i	$0.364087\pi$
$158$	−11.0045	+	6.46700i	−0.875470	+	0.514487i
$159$	−0.0158567	+	0.0745999i	−0.00125752	+	0.00591615i
$160$	−1.63936	+	9.49812i	−0.129602	+	0.750892i
$161$	3.02325	−	4.16115i	0.238266	−	0.327945i
$162$	−3.95155	−	1.25036i	−0.310463	−	0.0982374i
$163$	−1.89159	−	8.89925i	−0.148161	−	0.697043i	−0.988031	−	0.154256i	$-0.950702\pi$
$163$	−1.89159	−	8.89925i	−0.148161	−	0.697043i	0.839870	−	0.542788i	$-0.182631\pi$
$164$	2.42203	+	10.5896i	0.189129	+	0.826912i
$165$	−2.12333	+	4.35206i	−0.165301	+	0.338807i
$166$	3.06771	−	7.03559i	0.238101	−	0.546068i
$167$	12.2368	+	13.5904i	0.946916	+	1.05166i	0.998595	+	0.0529929i	$0.0168761\pi$
$167$	12.2368	+	13.5904i	0.946916	+	1.05166i	−0.0516790	+	0.998664i	$0.516457\pi$
$168$	2.30972	+	1.59787i	0.178199	+	0.123278i
$169$	−7.45374	−	10.6509i	−0.573365	−	0.819300i
$170$	7.48962	−	3.40398i	0.574427	−	0.261073i
$171$	−11.0628	−	2.35148i	−0.845995	−	0.179822i
$172$	−1.01502	+	0.761626i	−0.0773945	+	0.0580734i
$173$	−3.76815	+	8.46341i	−0.286487	+	0.643461i	−0.998261	−	0.0589479i	$-0.981225\pi$
$173$	−3.76815	+	8.46341i	−0.286487	+	0.643461i	0.711774	+	0.702409i	$0.247892\pi$
$174$	−2.35220	+	11.5013i	−0.178320	+	0.871911i
$175$	−1.21490	−	2.10427i	−0.0918381	−	0.159068i
$176$	10.6999	+	7.84302i	0.806532	+	0.591190i
$177$	3.53139			0.265436
$178$	−18.9296	+	6.31226i	−1.41883	+	0.473124i
$179$	−25.2368	+	2.65249i	−1.88629	+	0.198257i	−0.976306	−	0.216394i	$-0.930571\pi$
$179$	−25.2368	+	2.65249i	−1.88629	+	0.198257i	−0.909981	+	0.414650i	$0.863904\pi$
$180$	6.17576	−	4.63402i	0.460314	−	0.345399i
$181$	−7.70785	−	23.7223i	−0.572920	−	1.76327i	−0.643154	−	0.765737i	$-0.722375\pi$
$181$	−7.70785	−	23.7223i	−0.572920	−	1.76327i	0.0702338	−	0.997531i	$-0.477625\pi$
$182$	1.52273	+	5.70919i	0.112873	+	0.423193i
$183$	2.88005	+	2.09248i	0.212900	+	0.154681i
$184$	11.3478	−	5.36999i	0.836570	−	0.395881i
$185$	5.16889	+	5.74063i	0.380024	+	0.422060i
$186$	−2.73210	−	3.70012i	−0.200327	−	0.271306i
$187$	0.396636	−	11.3165i	0.0290049	−	0.827545i
$188$	1.77813	−	1.65136i	0.129684	−	0.120437i
$189$	−1.08712	−	5.11448i	−0.0790761	−	0.372024i
$190$	8.87652	−	8.11716i	0.643970	−	0.588881i
$191$	−13.4363	−	1.41222i	−0.972219	−	0.102184i	−0.394918	−	0.918716i	$-0.629227\pi$
$191$	−13.4363	−	1.41222i	−0.972219	−	0.102184i	−0.577300	+	0.816532i	$0.695894\pi$
$192$	3.07469	+	6.12696i	0.221896	+	0.442175i
$193$	1.04190	−	4.90174i	0.0749973	−	0.352835i	−0.924608	−	0.380919i	$-0.875608\pi$
$193$	1.04190	−	4.90174i	0.0749973	−	0.352835i	0.999606	+	0.0280848i	$0.00894084\pi$
$194$	−9.31866	−	5.28482i	−0.669041	−	0.379428i
$195$	−5.25439	−	0.322053i	−0.376275	−	0.0230627i
$196$	−1.00914	+	11.2693i	−0.0720812	+	0.804946i
$197$	−17.0521	−	9.84504i	−1.21491	−	0.701430i	−0.251087	−	0.967964i	$-0.580788\pi$
$197$	−17.0521	−	9.84504i	−1.21491	−	0.701430i	−0.963825	+	0.266534i	$0.914122\pi$
$198$	−1.92464	−	10.4515i	−0.136778	−	0.742754i
$199$	13.5844	−	7.84297i	0.962974	−	0.555974i	0.0658872	−	0.997827i	$-0.479012\pi$
$199$	13.5844	−	7.84297i	0.962974	−	0.555974i	0.897087	+	0.441854i	$0.145679\pi$
$200$	−0.137078	−	5.92912i	−0.00969285	−	0.419252i
$201$	0.536362	+	0.238804i	0.0378321	+	0.0168439i
$202$	7.02828	−	0.0541546i	0.494508	−	0.00381030i
$203$	10.6762	−	3.46891i	0.749324	−	0.243470i
$204$	2.84714	−	5.11172i	0.199340	−	0.357892i
$205$	3.76421	+	8.45455i	0.262904	+	0.590491i
$206$	21.4959	−	4.74250i	1.49769	−	0.330425i
$207$	−9.56445	−	3.10768i	−0.664775	−	0.215999i
$208$	−3.42588	+	14.0094i	−0.237542	+	0.971377i
$209$	−4.56135	−	15.9150i	−0.315515	−	1.10087i
$210$	2.19328	+	0.956333i	0.151351	+	0.0659932i
$211$	10.2322	+	11.3640i	0.704412	+	0.782329i	0.984072	−	0.177770i	$-0.0568884\pi$
$211$	10.2322	+	11.3640i	0.704412	+	0.782329i	−0.279660	+	0.960099i	$0.590222\pi$
$212$	0.174666	+	0.0343221i	0.0119961	+	0.00235725i
$213$	−6.79090	−	4.93388i	−0.465305	−	0.338064i
$214$	−0.0199744	+	0.0279426i	−0.00136542	+	0.00191012i
$215$	−0.723397	+	0.803413i	−0.0493352	+	0.0547923i
$216$	3.66220	−	12.2257i	0.249181	−	0.831851i
$217$	−1.78891	+	4.01797i	−0.121439	+	0.272757i
$218$	−16.0816	+	18.1396i	−1.08919	+	1.22857i
$219$	−0.205915	+	0.356655i	−0.0139144	+	0.0241005i
$220$	10.2329	+	4.79875i	0.689901	+	0.323532i
$221$	11.5309	−	4.30953i	0.775652	−	0.289890i
$222$	5.38264	+	1.10084i	0.361259	+	0.0738833i
$223$	6.84614	−	0.719558i	0.458451	−	0.0481852i	0.127512	−	0.991837i	$-0.459301\pi$
$223$	6.84614	−	0.719558i	0.458451	−	0.0481852i	0.330940	+	0.943652i	$0.392634\pi$
$224$	3.64592	−	5.44773i	0.243604	−	0.363992i
$225$	−3.17892	+	3.53055i	−0.211928	+	0.235370i
$226$	0.569364	+	1.25274i	0.0378735	+	0.0833313i
$227$	−2.27076	+	21.6048i	−0.150716	+	1.43396i	0.613853	+	0.789421i	$0.289619\pi$
$227$	−2.27076	+	21.6048i	−0.150716	+	1.43396i	−0.764568	+	0.644543i	$0.777048\pi$
$228$	1.64949	−	8.39431i	0.109240	−	0.555927i
$229$	−5.15825	+	15.8754i	−0.340867	+	1.04908i	0.622893	+	0.782307i	$0.285957\pi$
$229$	−5.15825	+	15.8754i	−0.340867	+	1.04908i	−0.963760	+	0.266772i	$0.914043\pi$
$230$	8.60408	−	6.35309i	0.567336	−	0.418910i
$231$	2.52311	−	2.11659i	0.166008	−	0.139261i
$232$	26.9255	+	5.07574i	1.76774	+	0.333239i
$233$	7.05126	+	2.29109i	0.461944	+	0.150095i	0.530737	−	0.847536i	$-0.321915\pi$
$233$	7.05126	+	2.29109i	0.461944	+	0.150095i	−0.0687938	+	0.997631i	$0.521915\pi$
$234$	9.69639	−	6.28106i	0.633873	−	0.410606i
$235$	1.21517	−	1.67254i	0.0792688	−	0.109104i
$236$	−0.127010	−	8.24130i	−0.00826764	−	0.536463i
$237$	−1.60798	+	7.56495i	−0.104449	+	0.491396i
$238$	−5.59494	+	0.0431103i	−0.362666	+	0.00279443i
$239$	22.1374	−	16.0837i	1.43195	−	1.04037i	0.442296	−	0.896869i	$-0.354164\pi$
$239$	22.1374	−	16.0837i	1.43195	−	1.04037i	0.989650	−	0.143501i	$-0.0458361\pi$
$240$	3.57673	+	4.61677i	0.230877	+	0.298011i
$241$	−16.5866	+	9.57630i	−1.06844	+	0.616863i	−0.927755	−	0.373191i	$-0.878264\pi$
$241$	−16.5866	+	9.57630i	−1.06844	+	0.616863i	−0.140684	+	0.990055i	$0.544930\pi$
$242$	12.1869	−	9.66848i	0.783403	−	0.621514i
$243$	−13.8979	+	8.02393i	−0.891548	+	0.514736i
$244$	4.77970	−	6.79652i	0.305989	−	0.435102i
$245$	1.00756	+	9.58629i	0.0643706	+	0.612446i
$246$	5.72548	+	3.24705i	0.365043	+	0.207024i
$247$	14.0869	−	11.2022i	0.896326	−	0.712781i
$248$	−8.53681	+	6.50906i	−0.542088	+	0.413325i
$249$	−1.89157	−	4.24854i	−0.119873	−	0.269240i
$250$	−3.68423	−	16.6992i	−0.233011	−	1.05615i
$251$	−1.96869	−	9.26194i	−0.124262	−	0.584609i	−0.995582	−	0.0938932i	$-0.970069\pi$
$251$	−1.96869	−	9.26194i	−0.124262	−	0.584609i	0.871320	−	0.490715i	$-0.163265\pi$
$252$	−5.11889	+	1.17078i	−0.322460	+	0.0737521i
$253$	−2.55444	−	14.4978i	−0.160596	−	0.911471i
$254$	−12.4768	−	16.8975i	−0.782865	−	1.06025i
$255$	1.54039	−	4.74083i	0.0964629	−	0.296882i
$256$	14.1881	−	7.39584i	0.886755	−	0.462240i
$257$	−4.25350	+	1.89378i	−0.265326	+	0.118131i	−0.535088	−	0.844796i	$-0.679722\pi$
$257$	−4.25350	+	1.89378i	−0.265326	+	0.118131i	0.269762	+	0.962927i	$0.413055\pi$
$258$	−0.0744780	+	0.765288i	−0.00463680	+	0.0476448i
$259$	−1.62346	−	4.99650i	−0.100877	−	0.310467i
$260$	−0.562605	+	12.2739i	−0.0348913	+	0.761195i
$261$	−12.9011	−	17.7569i	−0.798560	−	1.09912i
$262$	22.1619	+	19.6476i	1.36917	+	1.21383i
$263$	6.98625	−	12.1005i	0.430790	−	0.746151i	−0.566151	−	0.824301i	$-0.691568\pi$
$263$	6.98625	−	12.1005i	0.430790	−	0.746151i	0.996942	+	0.0781506i	$0.0249015\pi$
$264$	7.88210	−	1.57744i	0.485110	−	0.0970847i
$265$	0.151650			0.00931578
$266$	−7.76039	+	2.58778i	−0.475820	+	0.158667i
$267$	−4.91771	+	11.0454i	−0.300959	+	0.675965i
$268$	0.538012	−	1.26031i	0.0328643	−	0.0769858i
$269$	−12.4927	+	13.8746i	−0.761696	+	0.845949i	−0.991877	−	0.127199i	$-0.959401\pi$
$269$	−12.4927	+	13.8746i	−0.761696	+	0.845949i	0.230182	+	0.973148i	$0.426068\pi$
$270$	1.05316	−	10.8216i	0.0640933	−	0.658582i
$271$	−0.352716	+	0.157039i	−0.0214260	+	0.00953947i	−0.417422	−	0.908713i	$-0.637066\pi$
$271$	−0.352716	+	0.157039i	−0.0214260	+	0.00953947i	0.395996	+	0.918252i	$0.370400\pi$
$272$	−12.0318	−	6.46061i	−0.729533	−	0.391732i
$273$	3.17548	+	1.65357i	0.192189	+	0.100079i
$274$	16.0492	−	1.81197i	0.969568	−	0.109465i
$275$	−6.74758	−	1.68328i	−0.406894	−	0.101506i
$276$	2.23888	−	7.26989i	0.134765	−	0.437596i
$277$	3.10655	+	14.6152i	0.186654	+	0.878140i	0.967393	+	0.253281i	$0.0815099\pi$
$277$	3.10655	+	14.6152i	0.186654	+	0.878140i	−0.780738	+	0.624858i	$0.785157\pi$
$278$	−10.4258	+	9.53390i	−0.625297	+	0.571805i
$279$	8.55240	+	0.898894i	0.512019	+	0.0538154i
$280$	2.15294	−	5.15292i	0.128663	−	0.307946i
$281$	−3.28588	+	1.06765i	−0.196019	+	0.0636905i	−0.405381	−	0.914148i	$-0.632861\pi$
$281$	−3.28588	+	1.06765i	−0.196019	+	0.0636905i	0.209362	+	0.977838i	$0.432861\pi$
$282$	−0.0113291	−	1.47032i	−0.000674641	−	0.0875561i
$283$	2.05624	+	19.5638i	0.122231	+	1.16295i	0.867938	+	0.496673i	$0.165445\pi$
$283$	2.05624	+	19.5638i	0.122231	+	1.16295i	−0.745707	+	0.666274i	$0.767888\pi$
$284$	−11.2701	+	16.0256i	−0.668756	+	0.950942i
$285$		−	7.28818i		−	0.431714i
$286$	14.7807	+	8.21779i	0.873999	+	0.485928i
$287$		−	6.29410i		−	0.371529i
$288$	−12.3331	−	3.48821i	−0.726735	−	0.205545i
$289$	−0.558555	−	5.31429i	−0.0328562	−	0.312605i
$290$	23.3421	−	0.179856i	1.37070	−	0.0105615i
$291$	−6.17345	+	2.00587i	−0.361894	+	0.117586i
$292$	0.839741	+	0.467721i	0.0491421	+	0.0273713i
$293$	7.66952	+	0.806099i	0.448058	+	0.0470928i	0.325871	−	0.945414i	$-0.394343\pi$
$293$	7.66952	+	0.806099i	0.448058	+	0.0470928i	0.122187	+	0.992507i	$0.461009\pi$
$294$	4.62638	+	5.05918i	0.269816	+	0.295057i
$295$	−1.45993	−	6.86845i	−0.0850006	−	0.399897i
$296$	2.37546	−	12.6012i	0.138071	−	0.732430i
$297$	−12.6902	−	7.93199i	−0.736361	−	0.460261i
$298$	−0.491079	−	4.34965i	−0.0284474	−	0.251968i
$299$	13.4984	−	8.59698i	0.780633	−	0.497176i
$300$	−2.70724	−	2.36310i	−0.156303	−	0.136433i
$301$	0.671690	−	0.299056i	0.0387156	−	0.0172373i
$302$	−17.6653	−	1.71919i	−1.01652	−	0.0989281i
$303$	2.84962	−	3.16482i	0.163706	−	0.181814i
$304$	−19.6494	−	3.54756i	−1.12697	−	0.203467i
$305$	2.87915	−	6.46668i	0.164860	−	0.370281i
$306$	3.46062	+	10.3779i	0.197830	+	0.593266i
$307$	18.3341			1.04638			0.523192	−	0.852215i	$-0.324741\pi$
$307$	18.3341			1.04638			0.523192	+	0.852215i	$0.324741\pi$
$308$	−5.03028	−	5.81212i	−0.286627	−	0.331176i
$309$	6.66898	−	11.5510i	0.379385	−	0.657115i
$310$	−6.06713	+	6.84354i	−0.344590	+	0.388687i
$311$	12.1623	+	16.7400i	0.689660	+	0.949235i	0.999999	−	0.00139043i	$-0.000442589\pi$
$311$	12.1623	+	16.7400i	0.689660	+	0.949235i	−0.310339	+	0.950626i	$0.600443\pi$
$312$	4.86344	+	7.26025i	0.275338	+	0.411031i
$313$	0.598110	+	1.84079i	0.0338072	+	0.104048i	0.966536	−	0.256530i	$-0.0825794\pi$
$313$	0.598110	+	1.84079i	0.0338072	+	0.104048i	−0.932729	+	0.360578i	$0.882579\pi$
$314$	7.05389	+	0.686486i	0.398074	+	0.0387406i
$315$	−4.08682	+	1.81957i	−0.230266	+	0.102521i
$316$	17.7124	+	3.48050i	0.996398	+	0.195794i
$317$	10.5525	−	32.4773i	0.592689	−	1.82411i	0.0267777	−	0.999641i	$-0.491475\pi$
$317$	10.5525	−	32.4773i	0.592689	−	1.82411i	0.565911	−	0.824466i	$-0.308525\pi$
$318$	0.0867671	−	0.0640672i	0.00486566	−	0.00359271i
$319$	14.0881	−	28.8756i	0.788784	−	1.61672i
$320$	10.6456	−	8.51316i	0.595109	−	0.475900i
$321$	0.00432704	+	0.0203571i	0.000241512	+	0.00113622i
$322$	−7.10314	+	1.56712i	−0.395843	+	0.0873321i
$323$	6.93186	+	15.5692i	0.385699	+	0.866294i
$324$	3.00858	+	5.03038i	0.167144	+	0.279465i
$325$	−1.11650	−	7.47730i	−0.0619325	−	0.414766i
$326$	−6.34726	+	11.1921i	−0.351542	+	0.619870i
$327$	1.53537	+	14.6081i	0.0849061	+	0.807828i
$328$	7.37180	−	13.4785i	0.407040	−	0.744226i
$329$	−1.21765	+	0.703009i	−0.0671311	+	0.0387581i
$330$	6.32992	−	2.61342i	0.348451	−	0.143864i
$331$	−2.77212	+	1.60048i	−0.152370	+	0.0879706i	−0.574246	−	0.818683i	$-0.694705\pi$
$331$	−2.77212	+	1.60048i	−0.152370	+	0.0879706i	0.421877	+	0.906653i	$0.361371\pi$
$332$	−9.84689	+	4.56721i	−0.540418	+	0.250658i
$333$	−8.31027	+	6.03776i	−0.455400	+	0.330867i
$334$	−0.199272	−	25.8619i	−0.0109037	−	1.41510i
$335$	0.242725	−	1.14193i	0.0132615	−	0.0623905i
$336$	−0.945134	−	3.85781i	−0.0515613	−	0.210461i
$337$	−15.0996	+	20.7828i	−0.822526	+	1.13211i	0.166743	+	0.986000i	$0.446675\pi$
$337$	−15.0996	+	20.7828i	−0.822526	+	1.13211i	−0.989268	+	0.146109i	$0.953325\pi$
$338$	−2.10459	+	18.2639i	−0.114475	+	0.993426i
$339$	0.792971	+	0.257652i	0.0430683	+	0.0139937i
$340$	−11.1192	−	3.42434i	−0.603024	−	0.185711i
$341$	4.71411	+	11.6721i	0.255283	+	0.632082i
$342$	9.50088	+	12.8672i	0.513749	+	0.695777i
$343$	4.53241	−	13.9493i	0.244727	−	0.753193i
$344$	1.78865	+	0.146287i	0.0964377	+	0.00788727i
$345$	0.677400	−	6.44503i	0.0364700	−	0.346989i
$346$	11.9276	−	5.42103i	0.641234	−	0.291437i
$347$	−3.94868	+	4.38545i	−0.211976	+	0.235423i	−0.839751	−	0.542972i	$-0.817299\pi$
$347$	−3.94868	+	4.38545i	−0.211976	+	0.235423i	0.627775	+	0.778395i	$0.283966\pi$
$348$	13.2793	−	9.96420i	0.711845	−	0.534137i
$349$	−13.1630	+	1.38348i	−0.704597	+	0.0740561i	−0.450049	−	0.893004i	$-0.648593\pi$
$349$	−13.1630	+	1.38348i	−0.704597	+	0.0740561i	−0.254548	+	0.967060i	$0.581927\pi$
$350$	−0.688521	+	3.36658i	−0.0368030	+	0.179951i
$351$	2.68722	−	16.0454i	0.143433	−	0.856443i
$352$	−3.96480	−	18.3379i	−0.211325	−	0.977416i
$353$	16.7890	−	29.0793i	0.893587	−	1.54774i	0.0580423	−	0.998314i	$-0.481514\pi$
$353$	16.7890	−	29.0793i	0.893587	−	1.54774i	0.835544	−	0.549423i	$-0.185153\pi$
$354$	−3.73701	−	3.31304i	−0.198620	−	0.176086i
$355$	−6.78878	+	15.2478i	−0.360311	+	0.809271i
$356$	25.9537	+	11.0793i	1.37555	+	0.587204i
$357$	−2.26847	+	2.51939i	−0.120060	+	0.133340i
$358$	29.1947	+	20.8694i	1.54299	+	1.10298i
$359$	13.4843	+	9.79695i	0.711676	+	0.517063i	0.883714	−	0.468027i	$-0.155035\pi$
$359$	13.4843	+	9.79695i	0.711676	+	0.517063i	−0.172038	+	0.985090i	$0.555035\pi$
$360$	−10.8828	−	0.890065i	−0.573576	−	0.0469105i
$361$	3.95969	+	4.39768i	0.208405	+	0.231457i
$362$	−14.0989	+	32.3348i	−0.741021	+	1.69948i
$363$	0.659930	−	9.40273i	0.0346373	−	0.493515i
$364$	3.74478	−	7.47019i	0.196280	−	0.391544i
$365$	0.778812	+	0.253051i	0.0407649	+	0.0132453i
$366$	−1.08465	−	4.91629i	−0.0566954	−	0.256979i
$367$	−13.7927	−	30.9789i	−0.719973	−	1.61708i	−0.785221	−	0.619216i	$-0.787451\pi$
$367$	−13.7927	−	30.9789i	−0.719973	−	1.61708i	0.0652484	−	0.997869i	$-0.479216\pi$
$368$	−17.0465	−	4.96347i	−0.888609	−	0.258739i
$369$	−11.7041	+	3.80289i	−0.609290	+	0.197970i
$370$	−0.0841733	−	10.9242i	−0.00437596	−	0.567920i
$371$	−0.0942206	−	0.0419497i	−0.00489169	−	0.00217792i
$372$	−0.580156	+	6.47873i	−0.0300797	+	0.335907i
$373$	−14.9080	+	8.60713i	−0.771906	+	0.445660i	−0.833554	−	0.552438i	$-0.813698\pi$
$373$	−14.9080	+	8.60713i	−0.771906	+	0.445660i	0.0616482	+	0.998098i	$0.480364\pi$
$374$	−11.0365	+	11.6033i	−0.570685	+	0.599993i
$375$	−8.97346	−	5.18083i	−0.463387	−	0.267537i
$376$	−3.43091	+	0.0793205i	−0.176936	+	0.00409064i
$377$	34.8625	+	2.13680i	1.79551	+	0.110051i
$378$	−3.64783	+	6.43217i	−0.187624	+	0.330835i
$379$	−4.36238	+	20.5234i	−0.224081	+	1.05422i	0.711932	+	0.702249i	$0.247821\pi$
$379$	−4.36238	+	20.5234i	−0.224081	+	1.05422i	−0.936012	+	0.351968i	$0.885513\pi$
$380$	−17.0086	+	0.262126i	−0.872524	+	0.0134468i
$381$	−12.6574	−	1.33035i	−0.648458	−	0.0681557i
$382$	12.8938	+	14.1000i	0.659703	+	0.721417i
$383$	−3.28840	−	15.4707i	−0.168029	−	0.790515i	−0.978746	−	0.205077i	$-0.934256\pi$
$383$	−3.28840	−	15.4707i	−0.168029	−	0.790515i	0.810717	−	0.585439i	$-0.199078\pi$
$384$	2.49441	−	9.36828i	0.127292	−	0.478073i
$385$	−5.15979	−	4.03234i	−0.262967	−	0.205507i
$386$	−5.70121	+	4.20967i	−0.290184	+	0.214267i
$387$	−0.961939	−	1.06834i	−0.0488981	−	0.0543068i
$388$	4.90320	+	14.3350i	0.248922	+	0.727749i
$389$	19.0197	+	13.8186i	0.964338	+	0.700632i	0.954154	−	0.299316i	$-0.0967584\pi$
$389$	19.0197	+	13.8186i	0.964338	+	0.700632i	0.0101836	+	0.999948i	$0.496758\pi$
$390$	5.25819	+	5.27031i	0.266259	+	0.266872i
$391$	4.68286	+	14.4124i	0.236822	+	0.728864i
$392$	11.6403	−	10.9787i	0.587926	−	0.554507i
$393$	17.8473	−	1.87583i	0.900277	−	0.0946229i
$394$	8.80868	+	26.4160i	0.443775	+	1.33082i
$395$	15.3784			0.773769
$396$	−7.76854	+	12.8657i	−0.390384	+	0.646523i
$397$	4.89710	+	8.48202i	0.245778	+	0.425700i	0.962350	−	0.271813i	$-0.0876232\pi$
$397$	4.89710	+	8.48202i	0.245778	+	0.425700i	−0.716572	+	0.697513i	$0.754290\pi$
$398$	−21.7334	−	4.44484i	−1.08940	−	0.222800i
$399$	−2.01607	+	4.52817i	−0.100930	+	0.226692i
$400$	−5.41745	+	6.40295i	−0.270873	+	0.320148i
$401$	−35.5836	−	7.56352i	−1.77696	−	0.377704i	−0.801518	−	0.597971i	$-0.795974\pi$
$401$	−35.5836	−	7.56352i	−1.77696	−	0.377704i	−0.975440	+	0.220266i	$0.929307\pi$
$402$	−0.343554	−	0.755906i	−0.0171349	−	0.0377012i
$403$	−9.76191	+	9.59052i	−0.486275	+	0.477738i
$404$	−7.48831	−	6.53640i	−0.372557	−	0.325198i
$405$	3.34134	+	3.71094i	0.166033	+	0.184398i
$406$	−14.5523	−	6.34519i	−0.722217	−	0.314907i
$407$	−13.5138	−	6.59329i	−0.669856	−	0.326817i
$408$	−7.80857	+	2.73826i	−0.386582	+	0.135564i
$409$	1.93465	+	9.10179i	0.0956621	+	0.450055i	0.999742	+	0.0226923i	$0.00722379\pi$
$409$	1.93465	+	9.10179i	0.0956621	+	0.450055i	−0.904080	+	0.427362i	$0.859443\pi$
$410$	3.94840	−	12.4783i	0.194998	−	0.616258i
$411$	5.75222	−	7.91726i	0.283736	−	0.390530i
$412$	−27.1968	−	15.1481i	−1.33989	−	0.746296i
$413$	−0.992903	+	4.67124i	−0.0488575	+	0.229857i
$414$	7.20582	+	12.2617i	0.354147	+	0.602629i
$415$	−7.48127	+	5.43546i	−0.367241	+	0.266816i
$416$	16.7685	−	11.6111i	0.822145	−	0.569279i
$417$			8.56023i			0.419196i
$418$	−10.1040	+	21.1210i	−0.494205	+	1.03306i
$419$	−3.31223	−	1.91232i	−0.161813	−	0.0934228i	0.416907	−	0.908949i	$-0.363114\pi$
$419$	−3.31223	−	1.91232i	−0.161813	−	0.0934228i	−0.578720	+	0.815526i	$0.696447\pi$
$420$	−1.42379	−	3.06968i	−0.0694738	−	0.149785i
$421$	3.79029	−	2.75380i	0.184727	−	0.134212i	−0.491578	−	0.870833i	$-0.663580\pi$
$421$	3.79029	−	2.75380i	0.184727	−	0.134212i	0.676306	+	0.736621i	$0.263580\pi$
$422$	−0.166627	−	21.6252i	−0.00811127	−	1.05270i
$423$	2.04297	+	1.83950i	0.0993326	+	0.0894395i
$424$	−0.152636	−	0.200187i	−0.00741267	−	0.00972192i
$425$	7.11965	+	0.748305i	0.345354	+	0.0362981i
$426$	2.55750	+	11.5922i	0.123911	+	0.561642i
$427$	−3.57765	+	3.22133i	−0.173135	+	0.155891i
$428$	0.0473523	−	0.0108303i	0.00228886	−	0.000523502i
$429$	9.71830	−	3.24892i	0.469204	−	0.156859i
$430$	1.51925	−	0.171525i	0.0732649	−	0.00827167i
$431$	11.4557	+	12.7229i	0.551804	+	0.612840i	0.952933	−	0.303181i	$-0.0980488\pi$
$431$	11.4557	+	12.7229i	0.551804	+	0.612840i	−0.401129	+	0.916021i	$0.631382\pi$
$432$	−15.3452	+	9.50175i	−0.738294	+	0.457153i
$433$	2.07674	−	19.7589i	0.0998018	−	0.949551i	−0.823977	−	0.566624i	$-0.808249\pi$
$433$	2.07674	−	19.7589i	0.0998018	−	0.949551i	0.923779	−	0.382927i	$-0.125084\pi$
$434$	5.66260	−	2.57361i	0.271814	−	0.123537i
$435$	9.46405	−	10.5109i	0.453767	−	0.503959i
$436$	34.0360	−	4.10853i	1.63003	−	0.196763i
$437$	13.0232	+	17.9249i	0.622985	+	0.857465i
$438$	0.552506	−	0.184239i	0.0263998	−	0.00880326i
$439$	3.74396	−	6.48472i	0.178689	−	0.309499i	−0.762743	−	0.646702i	$-0.776148\pi$
$439$	3.74396	−	6.48472i	0.178689	−	0.309499i	0.941432	+	0.337203i	$0.109481\pi$
$440$	−6.32666	−	14.6783i	−0.301612	−	0.699761i
$441$	−12.8176			−0.610363
$442$	−16.2454	−	6.25746i	−0.772713	−	0.297637i
$443$	−2.01143	−	2.76850i	−0.0955660	−	0.131535i	0.758556	−	0.651607i	$-0.225905\pi$
$443$	−2.01143	−	2.76850i	−0.0955660	−	0.131535i	−0.854122	+	0.520072i	$0.825905\pi$
$444$	−4.66327	−	6.21475i	−0.221309	−	0.294939i
$445$	23.5160	+	4.99847i	1.11476	+	0.236950i
$446$	−7.91982	−	5.66137i	−0.375014	−	0.268074i
$447$	−2.14573	−	1.55897i	−0.101490	−	0.0737365i
$448$	−8.96909	+	2.34444i	−0.423750	+	0.110764i
$449$	−7.29839	+	1.55132i	−0.344432	+	0.0732114i	−0.376880	−	0.926262i	$-0.623003\pi$
$449$	−7.29839	+	1.55132i	−0.344432	+	0.0732114i	0.0324476	+	0.999473i	$0.489670\pi$
$450$	6.67627	−	0.753757i	0.314722	−	0.0355324i
$451$	−12.9569	−	12.5155i	−0.610115	−	0.589333i
$452$	0.572769	−	1.85984i	0.0269408	−	0.0874797i
$453$	−7.99197	+	7.19600i	−0.375496	+	0.338098i
$454$	22.6719	−	20.7324i	1.06405	−	0.973021i
$455$	1.90335	−	6.85984i	0.0892306	−	0.321594i
$456$	−9.62081	+	7.33557i	−0.450536	+	0.343520i
$457$	−7.04602	+	33.1489i	−0.329599	+	1.55064i	0.431565	+	0.902082i	$0.357961\pi$
$457$	−7.04602	+	33.1489i	−0.329599	+	1.55064i	−0.761164	+	0.648559i	$0.775372\pi$
$458$	20.3524	−	11.9605i	0.951006	−	0.558878i
$459$	14.0734	+	6.26589i	0.656891	+	0.292467i
$460$	−15.0653	−	1.34907i	−0.702424	−	0.0629005i
$461$	17.0366	−	9.83608i	0.793473	−	0.458112i	−0.0477110	−	0.998861i	$-0.515193\pi$
$461$	17.0366	−	9.83608i	0.793473	−	0.458112i	0.841184	+	0.540749i	$0.181859\pi$
$462$	−4.65573	−	0.127272i	−0.216604	−	0.00592125i
$463$			21.4046i			0.994754i	0.867534	+	0.497377i	$0.165703\pi$
$463$			21.4046i			0.994754i	−0.867534	+	0.497377i	$0.834297\pi$
$464$	−23.7313	−	30.6319i	−1.10170	−	1.42205i
$465$	0.579250	+	5.51119i	0.0268621	+	0.255575i
$466$	−5.31240	−	9.03976i	−0.246092	−	0.418759i
$467$	−13.8461	+	4.49889i	−0.640723	+	0.208184i	−0.611319	−	0.791384i	$-0.709361\pi$
$467$	−13.8461	+	4.49889i	−0.640723	+	0.208184i	−0.0294040	+	0.999568i	$0.509361\pi$
$468$	−16.1537	−	2.45006i	−0.746703	−	0.113254i
$469$	−0.466690	+	0.642344i	−0.0215497	+	0.0296607i
$470$	−2.85504	+	0.629888i	−0.131693	+	0.0290546i
$471$	3.19126	−	2.87343i	0.147046	−	0.132400i
$472$	−7.59732	+	8.84031i	−0.349695	+	0.406908i
$473$	0.719996	−	1.97738i	0.0331054	−	0.0909201i
$474$	8.79880	−	6.49687i	0.404142	−	0.298411i
$475$	10.2381	−	2.17618i	0.469756	−	0.0998498i
$476$	5.96115	+	5.20337i	0.273229	+	0.238496i
$477$	−0.0210789	+	0.200552i	−0.000965136	+	0.00918266i
$478$	−38.5156	−	3.74834i	−1.76166	−	0.171445i
$479$	−3.40178	−	0.723072i	−0.155431	−	0.0330380i	0.129539	−	0.991574i	$-0.458650\pi$
$479$	−3.40178	−	0.723072i	−0.155431	−	0.0330380i	−0.284970	+	0.958536i	$0.591984\pi$
$480$	0.546316	−	8.24115i	0.0249358	−	0.376155i
$481$	1.00003	−	16.3157i	0.0455973	−	0.743934i
$482$	26.5366	+	5.42716i	1.20871	+	0.247200i
$483$	−2.20371	+	3.81694i	−0.100272	+	0.173677i
$484$	−21.9671	−	1.20192i	−0.998507	−	0.0546326i
$485$	6.45357	+	11.1779i	0.293041	+	0.507563i
$486$	22.2349	+	4.54739i	1.00859	+	0.206274i
$487$	−13.8689	+	31.1501i	−0.628460	+	1.41154i	0.265814	+	0.964024i	$0.414359\pi$
$487$	−13.8689	+	31.1501i	−0.628460	+	1.41154i	−0.894274	+	0.447520i	$0.852307\pi$
$488$	−11.4343	+	2.70809i	−0.517605	+	0.122589i
$489$	2.40913	+	7.41453i	0.108945	+	0.335297i
$490$	7.92732	−	11.0897i	0.358120	−	0.500982i
$491$	−32.2139	+	14.3425i	−1.45379	+	0.647270i	−0.973260	−	0.229707i	$-0.926223\pi$
$491$	−32.2139	+	14.3425i	−1.45379	+	0.647270i	−0.480532	+	0.876977i	$0.659556\pi$
$492$	−3.01258	−	8.80757i	−0.135817	−	0.397076i
$493$	−10.2204	+	31.4550i	−0.460302	+	1.41666i
$494$	−25.4166	−	1.36136i	−1.14355	−	0.0612504i
$495$	−4.38072	+	12.0311i	−0.196899	+	0.540759i
$496$	15.1405	+	1.12091i	0.679827	+	0.0503304i
$497$	8.43577	−	7.59561i	0.378396	−	0.340709i
$498$	−1.98413	+	6.27052i	−0.0889111	+	0.280989i
$499$	−5.80447	+	7.98917i	−0.259844	+	0.357644i	−0.918928	−	0.394424i	$-0.870944\pi$
$499$	−5.80447	+	7.98917i	−0.259844	+	0.357644i	0.659084	+	0.752069i	$0.270944\pi$
$500$	−11.7679	+	21.1279i	−0.526276	+	0.944870i
$501$	−11.6456	−	10.4857i	−0.520285	−	0.468467i
$502$	−6.60594	+	11.6482i	−0.294838	+	0.519884i
$503$	−28.8608	−	12.8497i	−1.28684	−	0.572938i	−0.354681	−	0.934987i	$-0.615411\pi$
$503$	−28.8608	−	12.8497i	−1.28684	−	0.572938i	−0.932159	+	0.362049i	$0.882077\pi$
$504$	6.51533	+	3.56343i	0.290216	+	0.158728i
$505$	−7.33355	−	4.23403i	−0.326339	−	0.188412i
$506$	−10.8982	+	17.7385i	−0.484486	+	0.788572i
$507$	7.30610	+	8.40909i	0.324475	+	0.373461i
$508$	−2.64943	+	29.5867i	−0.117549	+	1.31270i
$509$	−0.389191	−	3.70291i	−0.0172506	−	0.164129i	0.982505	−	0.186236i	$-0.0596290\pi$
$509$	−0.389191	−	3.70291i	−0.0172506	−	0.164129i	−0.999756	+	0.0221077i	$0.992962\pi$
$510$	−6.07777	+	3.57172i	−0.269128	+	0.158159i
$511$	−0.413879	−	0.372658i	−0.0183089	−	0.0164854i
$512$	−21.9527	−	5.48433i	−0.970183	−	0.242375i
$513$	22.4004	+	2.35437i	0.989000	+	0.103948i
$514$	6.27785	+	1.98645i	0.276904	+	0.0876186i
$515$	−25.2235	−	8.19560i	−1.11148	−	0.361141i
$516$	0.796783	−	0.739975i	0.0350764	−	0.0325756i
$517$	−0.974038	+	3.90452i	−0.0428381	+	0.171720i
$518$	−2.96957	+	6.81050i	−0.130475	+	0.299236i
$519$	2.45316	−	7.55005i	0.107682	−	0.331410i
$520$	12.1103	−	12.4607i	0.531074	−	0.546440i
$521$	12.1324	+	8.81467i	0.531528	+	0.386178i	0.820929	−	0.571030i	$-0.193456\pi$
$521$	12.1324	+	8.81467i	0.531528	+	0.386178i	−0.289401	+	0.957208i	$0.593456\pi$
$522$	−3.00663	+	30.8942i	−0.131597	+	1.35220i
$523$	−10.0042	−	2.12647i	−0.437455	−	0.0929839i	−0.0160806	−	0.999871i	$-0.505119\pi$
$523$	−10.0042	−	2.12647i	−0.437455	−	0.0929839i	−0.421374	+	0.906887i	$0.638452\pi$
$524$	−5.01956	−	41.5833i	−0.219281	−	1.81657i
$525$	1.22382	+	1.68445i	0.0534120	+	0.0735153i
$526$	−18.7454	+	6.25082i	−0.817336	+	0.272549i
$527$	−6.47916	−	11.2222i	−0.282237	−	0.488848i
$528$	−9.82095	−	5.72545i	−0.427402	−	0.249168i
$529$	−1.64943	−	2.85689i	−0.0717143	−	0.124213i
$530$	−0.160480	−	0.142273i	−0.00697080	−	0.00617995i
$531$	9.28624	−	0.976023i	0.402988	−	0.0423558i
$532$	10.6400	+	4.54210i	0.461303	+	0.196925i
$533$	7.17981	−	18.2201i	0.310992	−	0.789200i
$534$	15.5665	−	7.07485i	0.673626	−	0.306158i
$535$	0.0378051	−	0.0168319i	0.00163446	−	0.000727707i
$536$	−1.75172	+	0.828948i	−0.0756629	+	0.0358051i
$537$	21.2693	−	4.52092i	0.917837	−	0.195092i
$538$	26.2368	−	2.96216i	1.13115	−	0.127708i
$539$	−8.80643	−	16.5676i	−0.379320	−	0.713618i
$540$	−11.2670	+	10.4637i	−0.484853	+	0.450284i
$541$	−17.2884	−	5.61734i	−0.743286	−	0.241508i	−0.0871962	−	0.996191i	$-0.527791\pi$
$541$	−17.2884	−	5.61734i	−0.743286	−	0.241508i	−0.656090	+	0.754683i	$0.727791\pi$
$542$	0.520583	+	0.164724i	0.0223610	+	0.00707550i
$543$	8.69346	+	19.5258i	0.373072	+	0.837934i
$544$	6.67119	+	18.1246i	0.286025	+	0.777086i
$545$	27.7775	−	9.02546i	1.18986	−	0.386608i
$546$	−1.80905	−	4.72899i	−0.0774202	−	0.202382i
$547$	−18.5640	+	13.4875i	−0.793739	+	0.576685i	−0.909071	−	0.416642i	$-0.863207\pi$
$547$	−18.5640	+	13.4875i	−0.793739	+	0.576685i	0.115332	+	0.993327i	$0.463207\pi$
$548$	−18.6836	−	13.1394i	−0.798124	−	0.561286i
$549$	8.15179	+	4.70644i	0.347910	+	0.200866i
$550$	5.56126	+	8.11165i	0.237133	+	0.345882i
$551$			48.3565i			2.06006i
$552$	−9.18962	+	5.59274i	−0.391136	+	0.238043i
$553$	−9.55462	−	4.25399i	−0.406304	−	0.180898i
$554$	10.4240	−	18.3806i	0.442875	−	0.780917i
$555$	−4.91913	−	4.42920i	−0.208805	−	0.188009i
$556$	19.9772	−	0.307877i	0.847223	−	0.0130569i
$557$	−8.21956	−	18.4614i	−0.348274	−	0.782236i	−0.999723	−	0.0235437i	$-0.992505\pi$
$557$	−8.21956	−	18.4614i	−0.348274	−	0.782236i	0.651449	−	0.758693i	$-0.274162\pi$
$558$	−8.20706	−	8.97482i	−0.347432	−	0.379934i
$559$	2.28554	−	0.0994934i	0.0966681	−	0.00420812i
$560$	−7.11260	+	3.43314i	−0.300562	+	0.145077i
$561$	0.675606	+	9.67948i	0.0285241	+	0.408668i
$562$	4.47883	+	1.95289i	0.188928	+	0.0823779i
$563$	34.9040	−	7.41908i	1.47103	−	0.312677i	0.598455	−	0.801157i	$-0.295782\pi$
$563$	34.9040	−	7.41908i	1.47103	−	0.312677i	0.872575	+	0.488480i	$0.162448\pi$
$564$	−1.36742	+	1.56656i	−0.0575786	+	0.0659639i
$565$	0.173298	−	1.64882i	0.00729071	−	0.0693665i
$566$	16.1782	−	22.6320i	0.680018	−	0.951294i
$567$	−1.04946	−	3.22990i	−0.0440731	−	0.135643i
$568$	26.9609	−	6.38543i	1.13126	−	0.267926i
$569$	18.4048	−	1.93442i	0.771570	−	0.0810952i	0.289441	−	0.957196i	$-0.406531\pi$
$569$	18.4048	−	1.93442i	0.771570	−	0.0810952i	0.482128	+	0.876101i	$0.339864\pi$
$570$	−6.83753	+	7.71253i	−0.286393	+	0.323043i
$571$	−37.8573			−1.58428			−0.792139	−	0.610340i	$-0.791033\pi$
$571$	−37.8573			−1.58428			−0.792139	+	0.610340i	$0.791033\pi$
$572$	−7.93161	−	22.5630i	−0.331637	−	0.943407i
$573$	11.5770			0.483635
$574$	−5.90492	+	6.66058i	−0.246467	+	0.278007i
$575$	9.25596	−	0.972841i	0.386000	−	0.0405703i
$576$	9.77867	+	15.2618i	0.407445	+	0.635909i
$577$	−6.88335	−	21.1848i	−0.286558	−	0.881934i	−0.985927	−	0.167174i	$-0.946536\pi$
$577$	−6.88335	−	21.1848i	−0.286558	−	0.881934i	0.699370	−	0.714760i	$-0.253464\pi$
$578$	−4.39462	+	6.14774i	−0.182792	+	0.255712i
$579$	−0.448857	+	4.27059i	−0.0186539	+	0.177480i
$580$	−24.8699	−	21.7085i	−1.03267	−	0.901396i
$581$	6.15170	−	1.30758i	0.255216	−	0.0542478i
$582$	8.41475	+	3.66906i	0.348802	+	0.152087i
$583$	−0.273710	+	0.110545i	−0.0113359	+	0.00457831i
$584$	−0.449834	−	1.28277i	−0.0186143	−	0.0530815i
$585$	−13.9061	+	0.605355i	−0.574946	+	0.0250284i
$586$	−7.35982	−	8.04833i	−0.304032	−	0.332473i
$587$	−2.88755	−	6.48554i	−0.119182	−	0.267687i	0.844097	−	0.536191i	$-0.180137\pi$
$587$	−2.88755	−	6.48554i	−0.119182	−	0.267687i	−0.963279	+	0.268504i	$0.913471\pi$
$588$	−0.149399	−	9.69407i	−0.00616111	−	0.399777i
$589$	−14.0797	−	12.6774i	−0.580143	−	0.522364i
$590$	−4.89882	+	8.63803i	−0.201681	+	0.355622i
$591$	15.4137	+	6.86261i	0.634034	+	0.282290i
$592$	−14.3358	+	11.1063i	−0.589198	+	0.456467i
$593$			25.7786i			1.05860i	0.848435	+	0.529299i	$0.177545\pi$
$593$			25.7786i			1.05860i	−0.848435	+	0.529299i	$0.822455\pi$
$594$	5.98757	+	20.2994i	0.245673	+	0.832894i
$595$	5.83795	+	3.37054i	0.239333	+	0.138179i
$596$	−3.56103	+	5.06362i	−0.145865	+	0.207414i
$597$	−10.8742	+	7.90056i	−0.445051	+	0.323348i
$598$	−22.3498	−	3.56622i	−0.913950	−	0.145834i
$599$	10.4076	−	3.38164i	0.425244	−	0.138170i	−0.0885737	−	0.996070i	$-0.528231\pi$
$599$	10.4076	−	3.38164i	0.425244	−	0.138170i	0.513817	+	0.857900i	$0.328231\pi$
$600$	0.647890	+	5.04053i	0.0264500	+	0.205779i
$601$	12.8089	+	28.7692i	0.522485	+	1.17352i	0.961441	+	0.275012i	$0.0886817\pi$
$601$	12.8089	+	28.7692i	0.522485	+	1.17352i	−0.438956	+	0.898508i	$0.644652\pi$
$602$	−0.991364	−	0.313690i	−0.0404050	−	0.0127850i
$603$	1.47643	+	0.479722i	0.0601250	+	0.0195358i
$604$	17.0810	+	18.3923i	0.695014	+	0.748371i
$605$	−18.5609	+	2.60370i	−0.754606	+	0.105855i
$606$	−5.98467	+	0.675674i	−0.243110	+	0.0274474i
$607$	39.9458	−	8.49075i	1.62135	−	0.344629i	0.694335	−	0.719652i	$-0.255698\pi$
$607$	39.9458	−	8.49075i	1.62135	−	0.344629i	0.927016	+	0.375023i	$0.122365\pi$
$608$	17.4652	+	22.1885i	0.708309	+	0.899863i
$609$	−8.78759	+	3.91249i	−0.356091	+	0.158542i
$610$	−9.11363	+	4.14208i	−0.369000	+	0.167708i
$611$	−4.32677	+	0.646070i	−0.175042	+	0.0261372i
$612$	6.07412	−	14.2288i	0.245532	−	0.575166i
$613$	29.5630	−	3.10719i	1.19404	−	0.125498i	0.513419	−	0.858138i	$-0.328379\pi$
$613$	29.5630	−	3.10719i	1.19404	−	0.125498i	0.680617	+	0.732640i	$0.261712\pi$
$614$	−19.4017	−	17.2005i	−0.782987	−	0.694156i
$615$	−3.96514	−	6.86782i	−0.159890	−	0.276937i
$616$	−0.129571	+	10.8698i	−0.00522057	+	0.437956i
$617$	−14.6740	−	25.4161i	−0.590752	−	1.02321i	−0.994131	−	0.108180i	$-0.965498\pi$
$617$	−14.6740	−	25.4161i	−0.590752	−	1.02321i	0.403379	−	0.915033i	$-0.367836\pi$
$618$	−17.8941	+	5.96696i	−0.719806	+	0.240026i
$619$	−13.7355	−	18.9052i	−0.552075	−	0.759865i	0.438217	−	0.898869i	$-0.355610\pi$
$619$	−13.7355	−	18.9052i	−0.552075	−	0.759865i	−0.990292	+	0.139004i	$0.955610\pi$
$620$	12.8408	−	1.55003i	0.515698	−	0.0622505i
$621$	19.5901	+	4.16401i	0.786124	+	0.167096i
$622$	2.83444	−	29.1249i	0.113651	−	1.16780i
$623$	−13.2279	−	9.61060i	−0.529963	−	0.385040i
$624$	1.66472	−	12.2457i	0.0666422	−	0.490220i
$625$	−3.12701	+	9.62396i	−0.125081	+	0.384958i
$626$	1.09404	−	2.50910i	0.0437266	−	0.100284i
$627$	5.31270	+	13.1543i	0.212169	+	0.525331i
$628$	−6.82057	−	7.34419i	−0.272170	−	0.293065i
$629$	14.7210	+	4.78316i	0.586966	+	0.190717i
$630$	6.03183	+	1.90861i	0.240314	+	0.0760407i
$631$	−7.81346	−	0.821227i	−0.311049	−	0.0326925i	−0.0522820	−	0.998632i	$-0.516649\pi$
$631$	−7.81346	−	0.821227i	−0.311049	−	0.0326925i	−0.258767	+	0.965940i	$0.583316\pi$
$632$	−15.4784	−	20.3003i	−0.615697	−	0.807503i
$633$	−9.73775	−	8.76791i	−0.387041	−	0.348493i
$634$	−41.6361	+	24.4683i	−1.65358	+	0.971760i
$635$	2.64529	+	25.1682i	0.104975	+	0.998771i
$636$	−0.151925	−	0.0136046i	−0.00602422	−	0.000539456i
$637$	12.9763	−	15.7373i	0.514138	−	0.623535i
$638$	−41.9985	+	17.3398i	−1.66274	+	0.686490i
$639$	−19.2212	−	11.0973i	−0.760378	−	0.439004i
$640$	−19.2523	−	0.978551i	−0.761012	−	0.0386806i
$641$	−31.9196	−	14.2115i	−1.26075	−	0.561322i	−0.335987	−	0.941867i	$-0.609070\pi$
$641$	−31.9196	−	14.2115i	−1.26075	−	0.561322i	−0.924763	+	0.380545i	$0.875737\pi$
$642$	0.0145194	−	0.0256019i	0.000573035	−	0.00101043i
$643$	−3.13566	−	2.82336i	−0.123658	−	0.111342i	0.604982	−	0.796240i	$-0.293180\pi$
$643$	−3.13566	−	2.82336i	−0.123658	−	0.111342i	−0.728640	+	0.684897i	$0.759847\pi$
$644$	8.98695	+	5.00558i	0.354135	+	0.197247i
$645$	0.544518	−	0.749465i	0.0214404	−	0.0295102i
$646$	7.27106	−	22.9790i	0.286076	−	0.904096i
$647$	24.2889	−	21.8698i	0.954893	−	0.859790i	−0.0353165	−	0.999376i	$-0.511244\pi$
$647$	24.2889	−	21.8698i	0.954893	−	0.859790i	0.990210	+	0.139586i	$0.0445773\pi$
$648$	1.53558	−	8.14583i	0.0603232	−	0.319998i
$649$	7.64175	+	11.3325i	0.299965	+	0.444839i
$650$	−5.83345	+	8.96014i	−0.228807	+	0.351445i
$651$	1.16463	−	3.58435i	0.0456453	−	0.140482i
$652$	17.2169	−	5.88892i	0.674264	−	0.230628i
$653$	35.5121	−	15.8110i	1.38970	−	0.618732i	0.430788	−	0.902453i	$-0.358236\pi$
$653$	35.5121	−	15.8110i	1.38970	−	0.618732i	0.958907	+	0.283721i	$0.0915688\pi$
$654$	12.0800	−	16.8991i	0.472367	−	0.660806i
$655$	−11.0268	−	33.9370i	−0.430852	−	1.32603i
$656$	−20.4461	+	7.34730i	−0.798287	+	0.286864i
$657$	−0.442905	+	0.994780i	−0.0172794	+	0.0388101i
$658$	1.94809	+	0.398415i	0.0759443	+	0.0155319i
$659$	0.926837	+	1.60533i	0.0361045	+	0.0625348i	0.883513	−	0.468407i	$-0.155172\pi$
$659$	0.926837	+	1.60533i	0.0361045	+	0.0625348i	−0.847409	+	0.530941i	$0.821838\pi$
$660$	−9.15031	−	3.17295i	−0.356175	−	0.123507i
$661$	−16.4678	+	28.5231i	−0.640523	+	1.10942i	0.344793	+	0.938679i	$0.387949\pi$
$661$	−16.4678	+	28.5231i	−0.640523	+	1.10942i	−0.985316	+	0.170740i	$0.945384\pi$
$662$	4.43505	+	0.907041i	0.172373	+	0.0352531i
$663$	−9.44065	+	4.70541i	−0.366645	+	0.182743i
$664$	14.7050	+	4.40490i	0.570666	+	0.170943i
$665$	9.64062	+	2.04918i	0.373847	+	0.0794637i
$666$	14.4586	+	1.40711i	0.560258	+	0.0545244i
$667$	−4.49450	+	42.7623i	−0.174028	+	1.65576i
$668$	−24.0519	+	27.5547i	−0.930598	+	1.06612i
$669$	−5.76984	+	1.22642i	−0.223075	+	0.0474161i
$670$	−1.32818	+	0.980706i	−0.0513122	+	0.0378880i
$671$	−0.482641	+	13.7703i	−0.0186321	+	0.531598i
$672$	−2.61911	+	4.96913i	−0.101034	+	0.191688i
$673$	33.4050	−	30.0780i	1.28767	−	1.15942i	0.309663	−	0.950846i	$-0.399784\pi$
$673$	33.4050	−	30.0780i	1.28767	−	1.15942i	0.978006	−	0.208576i	$-0.0668828\pi$
$674$	35.4765	−	7.82693i	1.36650	−	0.301482i
$675$	5.56118	−	7.65431i	0.214050	−	0.294614i
$676$	19.3617	−	17.3529i	0.744683	−	0.667419i
$677$	43.7247	−	14.2070i	1.68048	−	0.546021i	0.695474	−	0.718551i	$-0.255194\pi$
$677$	43.7247	−	14.2070i	1.68048	−	0.546021i	0.985004	+	0.172531i	$0.0551944\pi$
$678$	−0.597421	−	1.01659i	−0.0229438	−	0.0390420i
$679$	−0.917567	−	8.73007i	−0.0352130	−	0.335029i
$680$	8.55402	+	14.0554i	0.328032	+	0.539000i
$681$		−	18.6151i		−	0.713331i
$682$	5.96184	−	16.7744i	0.228291	−	0.642324i
$683$	−32.4110	+	18.7125i	−1.24017	+	0.716014i	−0.969129	−	0.246554i	$-0.920702\pi$
$683$	−32.4110	+	18.7125i	−1.24017	+	0.716014i	−0.271043	+	0.962567i	$0.587369\pi$
$684$	2.01749	−	22.5298i	0.0771408	−	0.861448i
$685$	−17.7769	−	7.91478i	−0.679220	−	0.302408i
$686$	−17.8831	+	10.5094i	−0.682781	+	0.401250i
$687$	2.97390	−	13.9911i	0.113462	−	0.533794i
$688$	−1.75556	−	1.83286i	−0.0669299	−	0.0698772i
$689$	−0.224896	−	0.228915i	−0.00856786	−	0.00872096i
$690$	−6.76337	+	6.18478i	−0.257477	+	0.235451i
$691$	27.4141	−	24.6838i	1.04288	−	0.939014i	0.0446821	−	0.999001i	$-0.485773\pi$
$691$	27.4141	−	24.6838i	1.04288	−	0.939014i	0.998199	+	0.0599868i	$0.0191059\pi$
$692$	−17.7080	−	5.45346i	−0.673156	−	0.207309i
$693$	6.04983	−	6.26318i	0.229814	−	0.237918i
$694$	8.29288	−	0.936273i	0.314793	−	0.0355404i
$695$	16.6494	−	3.53894i	0.631547	−	0.134239i
$696$	−23.4006	−	1.91384i	−0.886997	−	0.0725440i
$697$	15.0025	+	10.9000i	0.568260	+	0.412865i
$698$	15.2273	+	10.8850i	0.576362	+	0.412004i
$699$	−6.21432	−	1.32089i	−0.235047	−	0.0499608i
$700$	3.88703	−	2.91665i	0.146916	−	0.110239i
$701$	−1.87798	−	2.58482i	−0.0709304	−	0.0976273i	0.772078	−	0.635528i	$-0.219218\pi$
$701$	−1.87798	−	2.58482i	−0.0709304	−	0.0976273i	−0.843008	+	0.537901i	$0.819218\pi$
$702$	−17.8970	+	14.4586i	−0.675479	+	0.545706i
$703$	22.6310			0.853543
$704$	−13.0084	+	23.1253i	−0.490273	+	0.871569i
$705$	−0.885760	+	1.53418i	−0.0333596	+	0.0577806i
$706$	−45.0478	+	15.0216i	−1.69540	+	0.565347i
$707$	3.38513	+	4.65924i	0.127311	+	0.175229i
$708$	0.846412	+	7.01188i	0.0318101	+	0.263523i
$709$	21.0128	−	23.3371i	0.789152	−	0.876442i	−0.205613	−	0.978633i	$-0.565919\pi$
$709$	21.0128	−	23.3371i	0.789152	−	0.876442i	0.994765	+	0.102191i	$0.0325853\pi$
$710$	21.4891	−	9.76664i	0.806471	−	0.366536i
$711$	−2.13755	+	20.3374i	−0.0801643	+	0.762712i
$712$	−17.0706	−	36.0734i	−0.639749	−	1.35191i
$713$	−11.2726	−	12.5194i	−0.422161	−	0.468857i
$714$	4.76416	−	0.537878i	0.178294	−	0.0201296i
$715$	−10.3367	−	17.5587i	−0.386572	−	0.656656i
$716$	−11.3156	−	49.4741i	−0.422883	−	1.84893i
$717$	−17.4249	+	15.6894i	−0.650744	+	0.585933i
$718$	−5.07829	−	23.0180i	−0.189520	−	0.859023i
$719$	16.5694	+	1.74151i	0.617933	+	0.0649474i	0.408323	−	0.912838i	$-0.366114\pi$
$719$	16.5694	+	1.74151i	0.617933	+	0.0649474i	0.209611	+	0.977785i	$0.432780\pi$
$720$	10.6815	+	11.1518i	0.398075	+	0.415604i
$721$	13.4043	+	12.0693i	0.499203	+	0.449485i
$722$	−0.0644820	−	8.36859i	−0.00239977	−	0.311447i
$723$	13.2774	−	9.64661i	0.493792	−	0.358761i
$724$	45.2553	−	20.9904i	1.68190	−	0.780103i
$725$	17.5911	+	10.1562i	0.653317	+	0.377193i
$726$	−9.51969	+	9.33108i	−0.353309	+	0.346309i
$727$			4.30983i			0.159843i	0.996801	+	0.0799213i	$0.0254669\pi$
$727$			4.30983i			0.159843i	−0.996801	+	0.0799213i	$0.974533\pi$
$728$	−10.9711	+	4.39191i	−0.406616	+	0.162775i
$729$	4.01210	−	2.91496i	0.148596	−	0.107961i
$730$	−0.586754	−	0.998441i	−0.0217167	−	0.0369540i
$731$	−0.450392	+	2.11893i	−0.0166583	+	0.0783713i
$732$	−3.46450	+	6.22013i	−0.128052	+	0.229902i
$733$	8.83153	−	12.1556i	0.326200	−	0.448976i	−0.614148	−	0.789191i	$-0.710500\pi$
$733$	8.83153	−	12.1556i	0.326200	−	0.448976i	0.940347	+	0.340216i	$0.110500\pi$
$734$	−14.4676	+	45.7225i	−0.534010	+	1.68765i
$735$	−1.71729	−	8.07921i	−0.0633432	−	0.298006i
$736$	13.3824	+	21.2449i	0.493283	+	0.783098i
$737$	0.394321	+	2.23799i	0.0145250	+	0.0824372i
$738$	15.9533	+	6.95608i	0.587249	+	0.256057i
$739$	−15.7035	−	17.4405i	−0.577663	−	0.641560i	0.381515	−	0.924363i	$-0.375403\pi$
$739$	−15.7035	−	17.4405i	−0.577663	−	0.641560i	−0.959178	+	0.282803i	$0.908736\pi$
$740$	−10.1596	+	11.6392i	−0.373475	+	0.427866i
$741$	−11.0015	+	10.8083i	−0.404149	+	0.397054i
$742$	0.0603507	+	0.132787i	0.00221555	+	0.00487476i
$743$	0.344272	+	0.0731773i	0.0126301	+	0.00268462i	0.214222	−	0.976785i	$-0.431278\pi$
$743$	0.344272	+	0.0731773i	0.0126301	+	0.00268462i	−0.201592	+	0.979470i	$0.564612\pi$
$744$	6.69207	−	6.31167i	0.245343	−	0.231397i
$745$	−2.14506	+	4.81788i	−0.0785889	+	0.176514i
$746$	23.8509	+	4.87791i	0.873245	+	0.178593i
$747$	−6.14835	−	10.6493i	−0.224956	−	0.389636i
$748$	22.5650	−	1.92481i	0.825057	−	0.0703781i
$749$	−0.0281445			−0.00102838
$750$	4.63545	+	13.9011i	0.169263	+	0.507596i
$751$	−9.22155	+	0.969224i	−0.336499	+	0.0353675i	−0.271271	−	0.962503i	$-0.587444\pi$
$751$	−9.22155	+	0.969224i	−0.336499	+	0.0353675i	−0.0652278	+	0.997870i	$0.520777\pi$
$752$	3.70510	+	3.13483i	0.135111	+	0.114316i
$753$	2.50731	+	7.71671i	0.0913715	+	0.281213i
$754$	−34.8877	−	34.9681i	−1.27054	−	1.27346i
$755$	17.3000	+	12.5692i	0.629612	+	0.457440i
$756$	9.89468	−	3.38441i	0.359866	−	0.123090i
$757$	5.74352	+	6.37883i	0.208752	+	0.231843i	0.838424	−	0.545019i	$-0.183477\pi$
$757$	5.74352	+	6.37883i	0.208752	+	0.231843i	−0.629672	+	0.776861i	$0.716811\pi$
$758$	23.8708	−	17.6257i	0.867026	−	0.640196i
$759$	3.47547	+	12.1263i	0.126152	+	0.440157i
$760$	18.2449	+	15.6795i	0.661811	+	0.568757i
$761$	3.89450	+	18.3222i	0.141176	+	0.664179i	0.990636	+	0.136527i	$0.0435941\pi$
$761$	3.89450	+	18.3222i	0.141176	+	0.664179i	−0.849461	+	0.527652i	$0.823073\pi$
$762$	12.1463	+	13.2826i	0.440014	+	0.481176i
$763$	−19.7549	−	2.07632i	−0.715175	−	0.0751679i
$764$	−0.416377	−	27.0175i	−0.0150640	−	0.977458i
$765$	2.74035	−	12.8923i	0.0990777	−	0.466124i
$766$	−11.0342	+	19.4565i	−0.398683	+	0.702994i
$767$	−8.20282	+	12.3896i	−0.296187	+	0.447364i
$768$	−11.4287	+	7.57358i	−0.412396	+	0.273288i
$769$	18.5623	+	10.7169i	0.669373	+	0.386463i	0.795839	−	0.605508i	$-0.207030\pi$
$769$	18.5623	+	10.7169i	0.669373	+	0.386463i	−0.126466	+	0.991971i	$0.540363\pi$
$770$	1.67721	+	9.10787i	0.0604425	+	0.328225i
$771$	3.45522	−	1.99487i	0.124437	−	0.0718435i
$772$	9.98254	+	0.893915i	0.359280	+	0.0321727i
$773$	−7.71696	−	3.43581i	−0.277560	−	0.123578i	0.263236	−	0.964731i	$-0.415210\pi$
$773$	−7.71696	−	3.43581i	−0.277560	−	0.123578i	−0.540796	+	0.841154i	$0.681877\pi$
$774$	0.0156648	+	2.03301i	0.000563059	+	0.0730749i
$775$	−7.56892	+	2.45929i	−0.271883	+	0.0883403i
$776$	8.25994	−	19.7697i	0.296515	−	0.709690i
$777$	1.83105	+	4.11262i	0.0656887	+	0.147539i
$778$	−7.16295	−	32.4669i	−0.256804	−	1.16400i
$779$	25.7860	+	8.37837i	0.923878	+	0.300186i
$780$	−0.619921	−	10.5102i	−0.0221967	−	0.376327i
$781$	1.13802	−	32.4692i	0.0407217	−	1.16184i
$782$	8.56569	−	19.6448i	0.306308	−	0.702498i
$783$	29.2482	+	32.4834i	1.04524	+	1.16086i
$784$	−22.6179	+	0.697313i	−0.807784	+	0.0249040i
$785$	−6.90805	−	5.01899i	−0.246559	−	0.179135i
$786$	−20.6463	−	14.7587i	−0.736429	−	0.526426i
$787$	−15.2391	+	16.9247i	−0.543214	+	0.603301i	−0.950777	−	0.309877i	$-0.899712\pi$
$787$	−15.2391	+	16.9247i	−0.543214	+	0.603301i	0.407562	+	0.913177i	$0.366379\pi$
$788$	15.4611	−	36.2181i	0.550779	−	1.29022i
$789$	−4.86985	+	10.9379i	−0.173371	+	0.389398i
$790$	−16.2738	−	14.4275i	−0.578995	−	0.513307i
$791$	−0.563771	+	0.976480i	−0.0200454	+	0.0347196i
$792$	20.2910	−	6.32657i	0.721009	−	0.224805i
$793$	−14.0312	+	5.24399i	−0.498263	+	0.186219i
$794$	2.77532	−	13.5702i	0.0984926	−	0.481588i
$795$	−0.129236	+	0.0135833i	−0.00458354	+	0.000481750i
$796$	18.8288	+	25.0932i	0.667371	+	0.889406i
$797$	16.3783	−	18.1900i	0.580151	−	0.644323i	−0.379608	−	0.925147i	$-0.623941\pi$
$797$	16.3783	−	18.1900i	0.580151	−	0.644323i	0.959759	+	0.280825i	$0.0906079\pi$
$798$	6.38164	−	2.90041i	0.225907	−	0.102673i
$799$	0.433010	−	4.11982i	0.0153188	−	0.145749i
$800$	11.7399	−	1.69329i	0.415069	−	0.0598667i
$801$	−9.87897	+	30.4043i	−0.349056	+	1.07428i
$802$	30.5596	+	41.3873i	1.07910	+	1.46143i
$803$	−1.59012	+	0.110987i	−0.0561142	+	0.00391664i
$804$	−0.345609	+	1.12223i	−0.0121887	+	0.0395780i
$805$	8.33488	+	2.70817i	0.293766	+	0.0954503i
$806$	19.3278	−	0.990629i	0.680793	−	0.0348934i
$807$	9.40359	−	12.9429i	0.331022	−	0.455613i
$808$	1.79208	+	13.9423i	0.0630453	+	0.490488i
$809$	−7.05439	+	33.1883i	−0.248019	+	1.16684i	0.661098	+	0.750299i	$0.270091\pi$
$809$	−7.05439	+	33.1883i	−0.248019	+	1.16684i	−0.909118	+	0.416540i	$0.863243\pi$
$810$	−0.0544124	−	7.06174i	−0.00191186	−	0.248124i
$811$	0.628410	−	0.456567i	0.0220665	−	0.0160322i	−0.576697	−	0.816958i	$-0.695659\pi$
$811$	0.628410	−	0.456567i	0.0220665	−	0.0160322i	0.598764	+	0.800926i	$0.295659\pi$
$812$	9.44673	+	20.3671i	0.331515	+	0.714746i
$813$	0.286520	−	0.165422i	0.0100487	−	0.00580161i
$814$	8.11508	+	19.6554i	0.284433	+	0.688923i
$815$	13.4251	−	7.75097i	0.470260	−	0.271505i
$816$	10.8322	+	4.42806i	0.379202	+	0.155013i
$817$	0.331068	+	3.14990i	0.0115826	+	0.110201i
$818$	6.49172	−	11.4468i	0.226978	−	0.400227i
$819$	8.80736	+	3.47062i	0.307754	+	0.121273i
$820$	−15.8850	+	9.50056i	−0.554729	+	0.331774i
$821$	−9.83276	−	22.0847i	−0.343166	−	0.770762i	−0.999862	−	0.0166075i	$-0.994713\pi$
$821$	−9.83276	−	22.0847i	−0.343166	−	0.770762i	0.656697	−	0.754155i	$-0.271953\pi$
$822$	−13.5149	+	2.98169i	−0.471385	+	0.103998i
$823$	6.68107	+	31.4320i	0.232888	+	1.09565i	0.926790	+	0.375581i	$0.122557\pi$
$823$	6.68107	+	31.4320i	0.232888	+	1.09565i	−0.693902	+	0.720069i	$0.744110\pi$
$824$	14.5688	+	41.5453i	0.507529	+	1.44730i
$825$	5.90107	+	0.830115i	0.205449	+	0.0289009i
$826$	5.43312	−	4.01172i	0.189042	−	0.139585i
$827$	14.7606	−	45.4285i	0.513277	−	1.57970i	−0.273119	−	0.961980i	$-0.588055\pi$
$827$	14.7606	−	45.4285i	0.513277	−	1.57970i	0.786396	−	0.617723i	$-0.211945\pi$
$828$	3.87813	−	19.7359i	0.134774	−	0.685870i
$829$	−29.1195	+	12.9648i	−1.01136	+	0.450287i	−0.844421	−	0.535680i	$-0.820055\pi$
$829$	−29.1195	+	12.9648i	−1.01136	+	0.450287i	−0.166940	+	0.985967i	$0.553389\pi$
$830$	13.0162	+	1.26674i	0.451800	+	0.0439693i
$831$	−3.95649	−	12.1768i	−0.137249	−	0.422409i
$832$	−28.6380	−	3.44458i	−0.992844	−	0.119419i
$833$	11.3527	+	15.6257i	0.393349	+	0.541399i
$834$	8.03093	−	9.05865i	0.278088	−	0.313675i
$835$	−15.5799	+	26.9852i	−0.539166	+	0.933863i
$836$	30.5074	−	12.8715i	1.05512	−	0.445170i
$837$	−17.1259			−0.591957
$838$	1.71101	+	5.13109i	0.0591059	+	0.177251i
$839$	−2.87078	+	6.44787i	−0.0991103	+	0.222605i	−0.956295	−	0.292404i	$-0.905545\pi$
$839$	−2.87078	+	6.44787i	−0.0991103	+	0.222605i	0.857185	+	0.515009i	$0.172211\pi$
$840$	−1.37319	+	4.58417i	−0.0473795	+	0.158169i
$841$	−43.3885	+	48.1878i	−1.49615	+	1.66165i
$842$	−6.59451	−	0.641779i	−0.227262	−	0.0221172i
$843$	2.70460	−	1.20417i	0.0931515	−	0.0414737i
$844$	−20.1117	+	23.0406i	−0.692273	+	0.793090i
$845$	13.3350	−	17.6866i	0.458737	−	0.608438i
$846$	−0.436165	−	3.86325i	−0.0149957	−	0.132821i
$847$	12.2522	+	3.51666i	0.420989	+	0.120834i
$848$	−0.0262852	+	0.355041i	−0.000902637	+	0.0121922i
$849$	−3.50466	−	16.4881i	−0.120280	−	0.565871i
$850$	−6.83216	−	7.47130i	−0.234341	−	0.256264i
$851$	20.0129	+	2.10344i	0.686033	+	0.0721049i
$852$	8.16898	−	14.6665i	0.279865	−	0.502465i
$853$	29.8783	−	9.70806i	1.02302	−	0.332398i	0.250990	−	0.967990i	$-0.419244\pi$
$853$	29.8783	−	9.70806i	1.02302	−	0.332398i	0.772025	+	0.635592i	$0.219244\pi$
$854$	6.80812	−	0.0524581i	0.232969	−	0.00179508i
$855$	−2.01434	−	19.1652i	−0.0688890	−	0.655435i
$856$	−0.0602700	−	0.0329635i	−0.00205999	−	0.00112667i
$857$			22.6416i			0.773422i	0.922201	+	0.386711i	$0.126389\pi$
$857$			22.6416i			0.773422i	−0.922201	+	0.386711i	$0.873611\pi$
$858$	−13.3322	−	5.67931i	−0.455153	−	0.193888i
$859$		−	49.0992i		−	1.67524i	−0.546251	−	0.837621i	$-0.683946\pi$
$859$		−	49.0992i		−	1.67524i	0.546251	−	0.837621i	$-0.316054\pi$
$860$	−1.76863	−	1.24380i	−0.0603098	−	0.0424133i
$861$	0.563763	+	5.36385i	0.0192130	+	0.182799i
$862$	−0.186552	−	24.2111i	−0.00635399	−	0.824633i
$863$	3.47404	−	1.12878i	0.118258	−	0.0384243i	−0.249290	−	0.968429i	$-0.580197\pi$
$863$	3.47404	−	1.12878i	0.118258	−	0.0384243i	0.367548	+	0.930005i	$0.380197\pi$
$864$	25.1529	+	4.34133i	0.855718	+	0.147695i
$865$	−15.6988	−	1.65001i	−0.533775	−	0.0561020i
$866$	−20.7348	+	18.9610i	−0.704597	+	0.644321i
$867$	0.952003	+	4.47882i	0.0323317	+	0.152109i
$868$	−8.40679	−	2.58901i	−0.285345	−	0.0878766i
$869$	−27.7561	+	11.2100i	−0.941560	+	0.380274i
$870$	−19.8761	+	2.24403i	−0.673862	+	0.0760797i
$871$	−2.08370	+	1.32709i	−0.0706036	+	0.0449667i
$872$	−39.8723	−	27.5837i	−1.35025	−	0.934104i
$873$	−15.6795	+	6.98095i	−0.530669	+	0.236269i
$874$	3.03508	−	31.1866i	0.102663	−	1.05490i
$875$	9.37609	−	10.4132i	0.316970	−	0.352031i
$876$	−0.757523	−	0.323378i	−0.0255943	−	0.0109259i
$877$	−12.0281	+	27.0155i	−0.406159	+	0.912248i	0.588448	+	0.808535i	$0.299739\pi$
$877$	−12.0281	+	27.0155i	−0.406159	+	0.912248i	−0.994607	+	0.103713i	$0.966928\pi$
$878$	−10.0457	+	3.34984i	−0.339026	+	0.113052i
$879$	−6.60818			−0.222889
$880$	−7.07569	+	21.4684i	−0.238522	+	0.723701i
$881$	−29.2741	+	50.7043i	−0.986271	+	1.70827i	−0.350122	+	0.936704i	$0.613860\pi$
$881$	−29.2741	+	50.7043i	−0.986271	+	1.70827i	−0.636148	+	0.771567i	$0.719473\pi$
$882$	13.5639	+	12.0251i	0.456721	+	0.404905i
$883$	23.2345	+	31.9795i	0.781903	+	1.07620i	0.995069	+	0.0991808i	$0.0316222\pi$
$883$	23.2345	+	31.9795i	0.781903	+	1.07620i	−0.213167	+	0.977016i	$0.568378\pi$
$884$	11.3207	+	21.8627i	0.380756	+	0.735321i
$885$	1.85937	+	5.72254i	0.0625019	+	0.192361i
$886$	−0.468768	+	4.81676i	−0.0157486	+	0.161822i
$887$	0.138560	−	0.0616907i	0.00465238	−	0.00207137i	−0.404409	−	0.914578i	$-0.632523\pi$
$887$	0.138560	−	0.0616907i	0.00465238	−	0.00207137i	0.409062	+	0.912507i	$0.365856\pi$
$888$	−0.895684	+	10.9515i	−0.0300572	+	0.367510i
$889$	5.31856	−	16.3688i	0.178379	−	0.548994i
$890$	−20.1958	−	27.3514i	−0.676964	−	0.916822i
$891$	−8.73579	−	4.26212i	−0.292660	−	0.142786i
$892$	3.06964	+	13.4211i	0.102779	+	0.449373i
$893$	−1.25925	−	5.92432i	−0.0421393	−	0.198250i
$894$	0.808097	+	3.66279i	0.0270268	+	0.122502i
$895$	−17.5861	−	39.4991i	−0.587839	−	1.32031i
$896$	11.6908	+	5.93357i	0.390562	+	0.198227i
$897$	−10.7333	+	8.53542i	−0.358376	+	0.284989i
$898$	9.17875	+	5.20547i	0.306299	+	0.173709i
$899$	−3.84328	−	36.5663i	−0.128180	−	1.21956i
$900$	−7.77215	−	5.46582i	−0.259072	−	0.182194i
$901$	0.263159	−	0.151935i	0.00876711	−	0.00506169i
$902$	1.96963	+	25.3999i	0.0655816	+	0.845726i
$903$	−0.545630	+	0.315019i	−0.0181574	+	0.0104832i
$904$	−2.35096	+	1.43078i	−0.0781919	+	0.0475871i
$905$	34.3831	−	24.9808i	1.14293	−	0.830391i
$906$	15.2084	−	0.117184i	0.505264	−	0.00389318i
$907$	−6.86412	+	32.2931i	−0.227919	+	1.07228i	0.704166	+	0.710036i	$0.251321\pi$
$907$	−6.86412	+	32.2931i	−0.227919	+	1.07228i	−0.932085	+	0.362240i	$0.882012\pi$
$908$	−43.4425	+	0.669510i	−1.44169	+	0.0222185i
$909$	6.61871	−	9.10988i	0.219529	−	0.302156i
$910$	−8.44986	+	5.47359i	−0.280110	+	0.181448i
$911$	5.46232	+	1.77481i	0.180975	+	0.0588022i	0.398102	−	0.917341i	$-0.369669\pi$
$911$	5.46232	+	1.77481i	0.180975	+	0.0588022i	−0.217128	+	0.976143i	$0.569669\pi$
$912$	17.0630	+	1.26325i	0.565012	+	0.0418302i
$913$	9.54061	−	15.2638i	0.315748	−	0.505158i
$914$	38.5555	−	28.4687i	1.27530	−	0.941660i
$915$	−1.87440	+	5.76881i	−0.0619657	+	0.190711i
$916$	−32.7584	−	6.43708i	−1.08237	−	0.212687i
$917$	−2.53673	+	24.1354i	−0.0837703	+	0.797021i
$918$	−9.01440	−	19.8340i	−0.297519	−	0.654618i
$919$	16.3108	−	18.1149i	0.538043	−	0.597557i	−0.411417	−	0.911447i	$-0.634966\pi$
$919$	16.3108	−	18.1149i	0.538043	−	0.597557i	0.949459	+	0.313891i	$0.101633\pi$
$920$	14.6769	+	15.5614i	0.483881	+	0.513045i
$921$	−15.6244	+	1.64219i	−0.514841	+	0.0541120i
$922$	−27.2564	−	5.57439i	−0.897643	−	0.183583i
$923$	33.0843	−	12.3648i	1.08898	−	0.406993i
$924$	4.80741	+	4.50254i	0.158152	+	0.148123i
$925$	4.75314	−	8.23269i	0.156282	−	0.270689i
$926$	20.0811	−	22.6508i	0.659905	−	0.744353i
$927$	14.3444	−	32.2181i	0.471132	−	1.05818i
$928$	−3.62476	+	54.6794i	−0.118989	+	1.79494i
$929$	−14.4271	+	16.0229i	−0.473337	+	0.525694i	−0.931777	−	0.363031i	$-0.881742\pi$
$929$	−14.4271	+	16.0229i	−0.473337	+	0.525694i	0.458440	+	0.888725i	$0.348408\pi$
$930$	4.55745	−	6.37552i	0.149445	−	0.209061i
$931$	22.8460	+	16.5986i	0.748748	+	0.543997i
$932$	−2.85910	+	14.5500i	−0.0936530	+	0.476602i
$933$	−11.8641	−	13.1764i	−0.388414	−	0.431378i
$934$	18.8731	+	8.22917i	0.617545	+	0.269267i
$935$	18.5470	−	5.31569i	0.606552	−	0.173842i
$936$	14.7956	+	17.7476i	0.483611	+	0.580097i
$937$	−17.2951	−	5.61952i	−0.565007	−	0.183582i	0.0125660	−	0.999921i	$-0.496000\pi$
$937$	−17.2951	−	5.61952i	−0.565007	−	0.183582i	−0.577573	+	0.816339i	$0.696000\pi$
$938$	1.09649	−	0.241911i	0.0358016	−	0.00789867i
$939$	−0.674591	−	1.51516i	−0.0220144	−	0.0494453i
$940$	3.61222	+	2.01194i	0.117818	+	0.0656224i
$941$	−22.7883	+	7.40438i	−0.742879	+	0.241376i	−0.655914	−	0.754835i	$-0.727717\pi$
$941$	−22.7883	+	7.40438i	−0.742879	+	0.241376i	−0.0869646	+	0.996211i	$0.527717\pi$
$942$	−6.07283	+	0.0467926i	−0.197864	+	0.00152459i
$943$	22.0242	+	9.80578i	0.717205	+	0.319320i
$944$	16.3334	−	2.22748i	0.531606	−	0.0724984i
$945$	7.71551	−	4.45455i	0.250985	−	0.144907i
$946$	−2.61703	+	1.41704i	−0.0850871	+	0.0460719i
$947$	−14.8483	−	8.57268i	−0.482506	−	0.278575i	0.238955	−	0.971031i	$-0.423195\pi$
$947$	−14.8483	−	8.57268i	−0.482506	−	0.278575i	−0.721460	+	0.692456i	$0.756529\pi$
$948$	−15.4063	−	1.37960i	−0.500372	−	0.0448072i
$949$	−0.772994	−	1.55089i	−0.0250924	−	0.0503439i
$950$	−12.8758	−	7.30217i	−0.417747	−	0.236914i
$951$	−6.08389	+	28.6224i	−0.197284	+	0.928146i
$952$	−1.42661	−	11.0989i	−0.0462366	−	0.359717i
$953$	−33.1993	−	3.48939i	−1.07543	−	0.113032i	−0.449783	−	0.893138i	$-0.648499\pi$
$953$	−33.1993	−	3.48939i	−1.07543	−	0.113032i	−0.625648	+	0.780106i	$0.715165\pi$
$954$	0.210458	−	0.192454i	0.00681383	−	0.00623093i
$955$	−4.78610	−	22.5168i	−0.154875	−	0.728628i
$956$	37.2416	+	40.1006i	1.20448	+	1.29695i
$957$	−9.41956	+	25.8697i	−0.304491	+	0.836248i
$958$	2.92149	+	3.95662i	0.0943891	+	0.127832i
$959$	8.85544	+	9.83496i	0.285957	+	0.317587i
$960$	−8.30971	+	8.20846i	−0.268195	+	0.264927i
$961$	−13.4251	−	9.75393i	−0.433069	−	0.314643i
$962$	−16.3652	+	16.3275i	−0.527634	+	0.526421i
$963$	0.0170049	+	0.0523356i	0.000547974	+	0.00168649i
$964$	−22.9901	−	30.6389i	−0.740461	−	0.986813i
$965$	8.49174	−	0.892518i	0.273359	−	0.0287312i
$966$	5.91295	−	1.97173i	0.190246	−	0.0634394i
$967$	7.50877			0.241466			0.120733	−	0.992685i	$-0.461476\pi$
$967$	7.50877			0.241466			0.120733	+	0.992685i	$0.461476\pi$
$968$	22.1186	+	21.8808i	0.710918	+	0.703274i
$969$	−7.30188	−	12.6472i	−0.234570	−	0.406288i
$970$	3.65742	−	17.8833i	0.117433	−	0.574197i
$971$	2.06381	−	4.63539i	0.0662308	−	0.148757i	−0.877397	−	0.479765i	$-0.840722\pi$
$971$	2.06381	−	4.63539i	0.0662308	−	0.148757i	0.943628	+	0.331008i	$0.107389\pi$
$972$	−19.2633	−	25.6722i	−0.617870	−	0.823436i
$973$	−11.3233	−	2.40683i	−0.363007	−	0.0771595i
$974$	43.9004	−	19.9524i	1.40666	−	0.639317i
$975$	1.62123	+	6.27217i	0.0519209	+	0.200870i
$976$	14.6407	+	7.86149i	0.468637	+	0.251640i
$977$	−5.02081	−	5.57618i	−0.160630	−	0.178398i	0.657457	−	0.753492i	$-0.271632\pi$
$977$	−5.02081	−	5.57618i	−0.160630	−	0.178398i	−0.818087	+	0.575094i	$0.804965\pi$
$978$	4.40668	−	10.1064i	0.140910	−	0.323168i
$979$	−46.0871	+	8.12029i	−1.47295	+	0.259526i
$980$	−18.7929	+	4.29826i	−0.600318	+	0.137303i
$981$	8.07489	+	37.9894i	0.257812	+	1.21291i
$982$	47.5453	+	15.0444i	1.51723	+	0.480085i
$983$	−35.6222	+	49.0297i	−1.13617	+	1.56381i	−0.360392	+	0.932801i	$0.617357\pi$
$983$	−35.6222	+	49.0297i	−1.13617	+	1.56381i	−0.775779	+	0.631005i	$0.782643\pi$
$984$	−5.07500	+	12.1467i	−0.161785	+	0.387223i
$985$	6.97531	−	32.8162i	0.222252	−	1.04561i
$986$	40.3256	−	23.6981i	1.28423	−	0.754702i
$987$	0.974713	−	0.708171i	0.0310255	−	0.0225413i
$988$	25.6194	+	25.2857i	0.815061	+	0.804445i
$989$			2.81627i			0.0895522i
$990$	15.9230	−	8.62180i	0.506067	−	0.274019i
$991$	−20.4442	−	11.8034i	−0.649430	−	0.374949i	0.138808	−	0.990319i	$-0.455673\pi$
$991$	−20.4442	−	11.8034i	−0.649430	−	0.374949i	−0.788238	+	0.615371i	$0.789006\pi$
$992$	−14.9704	−	15.3905i	−0.475311	−	0.488648i
$993$	2.21905	−	1.61224i	0.0704195	−	0.0511628i
$994$	−16.0529	+	0.123691i	−0.509167	+	0.00392325i
$995$	19.8619	+	17.8837i	0.629665	+	0.566953i
$996$	7.98246	−	4.77417i	0.252934	−	0.151276i
$997$	−19.3787	−	2.03678i	−0.613728	−	0.0645054i	−0.207436	−	0.978249i	$-0.566512\pi$
$997$	−19.3787	−	2.03678i	−0.613728	−	0.0645054i	−0.406292	+	0.913743i	$0.633179\pi$
$998$	13.6376	−	3.00878i	0.431691	−	0.0952411i
$999$	15.2023	−	13.6882i	0.480980	−	0.433076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bm.a.35.20	✓	640
4.3	odd	2	inner	572.2.bm.a.35.57	yes	640
11.6	odd	10	inner	572.2.bm.a.347.3	yes	640
13.3	even	3	inner	572.2.bm.a.211.72	yes	640
44.39	even	10	inner	572.2.bm.a.347.72	yes	640
52.3	odd	6	inner	572.2.bm.a.211.3	yes	640
143.94	odd	30	inner	572.2.bm.a.523.57	yes	640
572.523	even	30	inner	572.2.bm.a.523.20	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bm.a.35.20	✓	640	1.1	even	1	trivial
572.2.bm.a.35.57	yes	640	4.3	odd	2	inner
572.2.bm.a.211.3	yes	640	52.3	odd	6	inner
572.2.bm.a.211.72	yes	640	13.3	even	3	inner
572.2.bm.a.347.3	yes	640	11.6	odd	10	inner
572.2.bm.a.347.72	yes	640	44.39	even	10	inner
572.2.bm.a.523.20	yes	640	572.523	even	30	inner
572.2.bm.a.523.57	yes	640	143.94	odd	30	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.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05823 - 0.938168i) q^{2} +(-0.852202 + 0.0895701i) q^{3} +(0.239682 + 1.98559i) q^{4} +(0.526525 + 1.62048i) q^{5} +(0.985854 + 0.704723i) q^{6} +(0.121128 - 1.15246i) q^{7} +(1.60917 - 2.32606i) q^{8} +(-2.21622 + 0.471071i) q^{9} +O(q^{10})\)	\(q+(-1.05823 - 0.938168i) q^{2} +(-0.852202 + 0.0895701i) q^{3} +(0.239682 + 1.98559i) q^{4} +(0.526525 + 1.62048i) q^{5} +(0.985854 + 0.704723i) q^{6} +(0.121128 - 1.15246i) q^{7} +(1.60917 - 2.32606i) q^{8} +(-2.21622 + 0.471071i) q^{9} +(0.963098 - 2.20880i) q^{10} +(-2.13156 - 2.54096i) q^{11} +(-0.382107 - 1.67065i) q^{12} +(1.66527 - 3.19795i) q^{13} +(-1.20938 + 1.10592i) q^{14} +(-0.593852 - 1.33381i) q^{15} +(-3.88510 + 0.951820i) q^{16} +(2.53721 + 2.28451i) q^{17} +(2.78720 + 1.58068i) q^{18} +(4.56020 + 2.03033i) q^{19} +(-3.09140 + 1.43386i) q^{20} +0.992976i q^{21} +(-0.128173 + 4.68866i) q^{22} +(3.84394 + 2.21930i) q^{23} +(-1.16300 + 2.12641i) q^{24} +(1.69636 - 1.23248i) q^{25} +(-4.76244 + 1.82185i) q^{26} +(4.29134 - 1.39434i) q^{27} +(2.31733 - 0.0357133i) q^{28} +(3.94016 + 8.84975i) q^{29} +(-0.622912 + 1.96861i) q^{30} +(-3.60971 - 1.17287i) q^{31} +(5.00428 + 2.63764i) q^{32} +(2.04411 + 1.97448i) q^{33} +(-0.541683 - 4.79786i) q^{34} +(1.93131 - 0.410512i) q^{35} +(-1.46654 - 4.28758i) q^{36} +(4.14171 - 1.84401i) q^{37} +(-2.92093 - 6.42678i) q^{38} +(-1.13271 + 2.87446i) q^{39} +(4.61660 + 1.38290i) q^{40} +(5.40179 - 0.567751i) q^{41} +(0.931578 - 1.05079i) q^{42} +(0.317248 + 0.549489i) q^{43} +(4.53439 - 4.84142i) q^{44} +(-1.93026 - 3.34330i) q^{45} +(-1.98568 - 5.95478i) q^{46} +(-0.713180 - 0.981609i) q^{47} +(3.22564 - 1.15913i) q^{48} +(5.53355 + 1.17619i) q^{49} +(-2.95141 - 0.287232i) q^{50} +(-2.36684 - 1.71961i) q^{51} +(6.74894 + 2.54005i) q^{52} +(0.0275035 - 0.0846470i) q^{53} +(-5.84933 - 2.55047i) q^{54} +(2.99524 - 4.79202i) q^{55} +(-2.48577 - 2.13626i) q^{56} +(-4.06807 - 1.32180i) q^{57} +(4.13297 - 13.0616i) q^{58} +(-4.09856 - 0.430777i) q^{59} +(2.50607 - 1.49884i) q^{60} +(-3.08737 - 2.77988i) q^{61} +(2.71954 + 4.62767i) q^{62} +(0.274443 + 2.61115i) q^{63} +(-2.82111 - 7.48608i) q^{64} +(6.05901 + 1.01473i) q^{65} +(-0.310735 - 4.00717i) q^{66} +(-0.593376 - 0.342586i) q^{67} +(-3.92797 + 5.58541i) q^{68} +(-3.47460 - 1.54699i) q^{69} +(-2.42889 - 1.37748i) q^{70} +(7.27972 + 6.55469i) q^{71} +(-2.47054 + 5.91309i) q^{72} +(0.282493 - 0.388818i) q^{73} +(-6.11285 - 1.93424i) q^{74} +(-1.33525 + 1.20227i) q^{75} +(-2.93840 + 9.54130i) q^{76} +(-3.18653 + 2.14875i) q^{77} +(3.89538 - 1.97915i) q^{78} +(2.78905 - 8.58380i) q^{79} +(-3.58801 - 5.79457i) q^{80} +(2.67734 - 1.19203i) q^{81} +(-6.24896 - 4.46698i) q^{82} +(1.67712 + 5.16163i) q^{83} +(-1.97164 + 0.237999i) q^{84} +(-2.36610 + 5.31435i) q^{85} +(0.179793 - 0.879115i) q^{86} +(-4.15049 - 7.18886i) q^{87} +(-9.34047 + 0.869292i) q^{88} +(7.05491 - 12.2195i) q^{89} +(-1.09393 + 5.34887i) q^{90} +(-3.48379 - 2.30651i) q^{91} +(-3.48528 + 8.16440i) q^{92} +(3.18126 + 0.676197i) q^{93} +(-0.166208 + 1.70785i) q^{94} +(-0.889048 + 8.45872i) q^{95} +(-4.50092 - 1.79957i) q^{96} +(7.40965 - 1.57497i) q^{97} +(-4.75228 - 6.43607i) q^{98} +(5.92097 + 4.62719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 5 q^{2} - 3 q^{4} - 24 q^{5} - 5 q^{6} - 20 q^{8} - 78 q^{9}+O(q^{10}) \) 640 * q - 5 * q^2 - 3 * q^4 - 24 * q^5 - 5 * q^6 - 20 * q^8 - 78 * q^9	\( 640 q - 5 q^{2} - 3 q^{4} - 24 q^{5} - 5 q^{6} - 20 q^{8} - 78 q^{9} - 36 q^{12} - 20 q^{13} - 28 q^{14} - 11 q^{16} - 10 q^{17} - 20 q^{18} - 29 q^{20} + 25 q^{22} - 65 q^{24} - 152 q^{25} + 40 q^{26} - 5 q^{28} - 10 q^{29} + 5 q^{30} + 4 q^{33} - 132 q^{34} - 24 q^{36} - 6 q^{37} - 10 q^{38} - 20 q^{40} - 50 q^{41} - 49 q^{42} - 4 q^{44} + 28 q^{45} - 25 q^{46} + 35 q^{48} + 62 q^{49} + 20 q^{50} + 15 q^{52} - 8 q^{53} - 2 q^{56} - 40 q^{57} + 41 q^{58} - 68 q^{60} - 10 q^{61} - 5 q^{62} - 36 q^{64} - 66 q^{66} + 60 q^{68} - 58 q^{69} + 118 q^{70} - 5 q^{72} - 40 q^{73} + 45 q^{74} - 76 q^{77} + 12 q^{78} - 41 q^{80} + 30 q^{81} - 37 q^{82} + 50 q^{84} - 10 q^{85} - 120 q^{86} + 89 q^{88} - 40 q^{89} - 250 q^{90} - 46 q^{92} - 2 q^{93} - 5 q^{94} + 110 q^{96} - 10 q^{97}+O(q^{100}) \) 640 * q - 5 * q^2 - 3 * q^4 - 24 * q^5 - 5 * q^6 - 20 * q^8 - 78 * q^9 - 36 * q^12 - 20 * q^13 - 28 * q^14 - 11 * q^16 - 10 * q^17 - 20 * q^18 - 29 * q^20 + 25 * q^22 - 65 * q^24 - 152 * q^25 + 40 * q^26 - 5 * q^28 - 10 * q^29 + 5 * q^30 + 4 * q^33 - 132 * q^34 - 24 * q^36 - 6 * q^37 - 10 * q^38 - 20 * q^40 - 50 * q^41 - 49 * q^42 - 4 * q^44 + 28 * q^45 - 25 * q^46 + 35 * q^48 + 62 * q^49 + 20 * q^50 + 15 * q^52 - 8 * q^53 - 2 * q^56 - 40 * q^57 + 41 * q^58 - 68 * q^60 - 10 * q^61 - 5 * q^62 - 36 * q^64 - 66 * q^66 + 60 * q^68 - 58 * q^69 + 118 * q^70 - 5 * q^72 - 40 * q^73 + 45 * q^74 - 76 * q^77 + 12 * q^78 - 41 * q^80 + 30 * q^81 - 37 * q^82 + 50 * q^84 - 10 * q^85 - 120 * q^86 + 89 * q^88 - 40 * q^89 - 250 * q^90 - 46 * q^92 - 2 * q^93 - 5 * q^94 + 110 * q^96 - 10 * q^97

Introduction

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