LMFDB - Embedded newform 155.2.x.a.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(3,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 2]))

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

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

chi := DirichletCharacter("155.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.x (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:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			53.3
Character	$\chi$	$=$	155.53
Dual form			155.2.x.a.117.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.946511 - 1.85763i) q^{2} +(-0.762126 + 0.494930i) q^{3} +(-1.37935 + 1.89851i) q^{4} +(0.456638 - 2.18895i) q^{5} +(1.64076 + 0.947293i) q^{6} +(1.18794 - 3.09469i) q^{7} +(0.713889 + 0.113069i) q^{8} +(-0.884330 + 1.98624i) q^{9} +O(q^{10})$	\(q+(-0.946511 - 1.85763i) q^{2} +(-0.762126 + 0.494930i) q^{3} +(-1.37935 + 1.89851i) q^{4} +(0.456638 - 2.18895i) q^{5} +(1.64076 + 0.947293i) q^{6} +(1.18794 - 3.09469i) q^{7} +(0.713889 + 0.113069i) q^{8} +(-0.884330 + 1.98624i) q^{9} +(-4.49847 + 1.22360i) q^{10} +(-5.92368 - 0.622604i) q^{11} +(0.111607 - 2.12958i) q^{12} +(-0.0208725 - 0.398272i) q^{13} +(-6.87320 + 0.722402i) q^{14} +(0.735360 + 1.89426i) q^{15} +(0.984666 + 3.03049i) q^{16} +(0.0441159 - 0.0544786i) q^{17} +(4.52673 - 0.237236i) q^{18} +(4.60234 - 4.14397i) q^{19} +(3.52586 + 3.88624i) q^{20} +(0.626296 + 2.94649i) q^{21} +(4.45026 + 11.5933i) q^{22} +(0.734900 - 4.63998i) q^{23} +(-0.600035 + 0.267153i) q^{24} +(-4.58296 - 1.99911i) q^{25} +(-0.720086 + 0.415742i) q^{26} +(-0.735549 - 4.64407i) q^{27} +(4.23671 + 6.52396i) q^{28} +(-1.23801 + 3.81019i) q^{29} +(2.82280 - 3.15896i) q^{30} +(5.54061 - 0.549179i) q^{31} +(5.71972 - 5.71972i) q^{32} +(4.82274 - 2.45731i) q^{33} +(-0.142957 - 0.0303865i) q^{34} +(-6.23165 - 4.01349i) q^{35} +(-2.55109 - 4.41861i) q^{36} +(-4.52916 + 1.21358i) q^{37} +(-12.0541 - 4.62715i) q^{38} +(0.213024 + 0.293203i) q^{39} +(0.573491 - 1.51103i) q^{40} +(9.71922 - 2.06588i) q^{41} +(4.88070 - 3.95232i) q^{42} +(7.61760 + 0.399222i) q^{43} +(9.35282 - 10.3874i) q^{44} +(3.94395 + 2.84274i) q^{45} +(-9.31497 + 3.02662i) q^{46} +(3.28729 + 1.67496i) q^{47} +(-2.25032 - 1.82227i) q^{48} +(-2.96390 - 2.66870i) q^{49} +(0.624214 + 10.4056i) q^{50} +(-0.00665875 + 0.0633538i) q^{51} +(0.784912 + 0.509728i) q^{52} +(3.25195 - 1.24831i) q^{53} +(-7.93078 + 5.76205i) q^{54} +(-4.06782 + 12.6823i) q^{55} +(1.19797 - 2.07495i) q^{56} +(-1.45659 + 5.43606i) q^{57} +(8.24972 - 1.30663i) q^{58} +(2.25951 - 10.6302i) q^{59} +(-4.61057 - 1.21675i) q^{60} +4.79385i q^{61} +(-6.26443 - 9.77262i) q^{62} +(5.09626 + 5.09626i) q^{63} +(-9.97793 - 3.24203i) q^{64} +(-0.881326 - 0.136177i) q^{65} +(-9.12955 - 6.63300i) q^{66} +(-7.50670 - 2.01141i) q^{67} +(0.0425769 + 0.158899i) q^{68} +(1.73638 + 3.89997i) q^{69} +(-1.55726 + 15.3749i) q^{70} +(2.69492 + 1.19985i) q^{71} +(-0.855896 + 1.31796i) q^{72} +(-1.12036 - 1.38353i) q^{73} +(6.54129 + 7.26484i) q^{74} +(4.48222 - 0.744674i) q^{75} +(1.51913 + 14.4535i) q^{76} +(-8.96375 + 17.5923i) q^{77} +(0.343033 - 0.673240i) q^{78} +(-0.315564 - 3.00239i) q^{79} +(7.08321 - 0.771544i) q^{80} +(-1.50541 - 1.67193i) q^{81} +(-13.0370 - 16.0994i) q^{82} +(-6.74771 + 10.3906i) q^{83} +(-6.45781 - 2.87520i) q^{84} +(-0.0991056 - 0.121444i) q^{85} +(-6.46854 - 14.5286i) q^{86} +(-0.942262 - 3.51657i) q^{87} +(-4.15846 - 1.11425i) q^{88} +(6.05161 + 4.39675i) q^{89} +(1.54778 - 10.0171i) q^{90} +(-1.25732 - 0.408529i) q^{91} +(7.79535 + 7.79535i) q^{92} +(-3.95084 + 3.16076i) q^{93} -7.69194i q^{94} +(-6.96931 - 11.9666i) q^{95} +(-1.52828 + 7.19001i) q^{96} +(-10.7001 + 1.69473i) q^{97} +(-2.15211 + 8.03179i) q^{98} +(6.47513 - 11.2153i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8}+O(q^{10}) $ 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8	$ 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8} - 10 q^{10} - 28 q^{11} - 40 q^{12} - 14 q^{13} - 20 q^{15} + 24 q^{16} - 14 q^{17} - 40 q^{18} - 44 q^{20} - 44 q^{21} + 30 q^{22} - 30 q^{23} - 22 q^{25} - 48 q^{26} + 100 q^{27} - 48 q^{28} - 44 q^{31} + 28 q^{32} + 20 q^{33} - 72 q^{35} + 16 q^{36} + 30 q^{37} + 38 q^{38} - 4 q^{40} - 20 q^{41} - 130 q^{42} + 22 q^{43} - 34 q^{45} - 28 q^{47} - 156 q^{48} + 158 q^{50} - 36 q^{51} - 10 q^{52} + 26 q^{53} + 98 q^{55} - 48 q^{56} - 20 q^{58} + 260 q^{60} + 30 q^{62} + 152 q^{63} + 32 q^{65} - 152 q^{66} + 38 q^{67} - 126 q^{68} + 166 q^{70} - 128 q^{71} - 156 q^{72} - 30 q^{73} + 26 q^{75} + 128 q^{76} + 30 q^{78} + 154 q^{80} - 64 q^{81} + 8 q^{82} - 82 q^{83} + 60 q^{85} - 28 q^{86} - 24 q^{87} + 252 q^{88} + 38 q^{90} + 194 q^{93} - 74 q^{95} + 60 q^{96} - 38 q^{97} + 174 q^{98}+O(q^{100}) $ 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8 - 10 * q^10 - 28 * q^11 - 40 * q^12 - 14 * q^13 - 20 * q^15 + 24 * q^16 - 14 * q^17 - 40 * q^18 - 44 * q^20 - 44 * q^21 + 30 * q^22 - 30 * q^23 - 22 * q^25 - 48 * q^26 + 100 * q^27 - 48 * q^28 - 44 * q^31 + 28 * q^32 + 20 * q^33 - 72 * q^35 + 16 * q^36 + 30 * q^37 + 38 * q^38 - 4 * q^40 - 20 * q^41 - 130 * q^42 + 22 * q^43 - 34 * q^45 - 28 * q^47 - 156 * q^48 + 158 * q^50 - 36 * q^51 - 10 * q^52 + 26 * q^53 + 98 * q^55 - 48 * q^56 - 20 * q^58 + 260 * q^60 + 30 * q^62 + 152 * q^63 + 32 * q^65 - 152 * q^66 + 38 * q^67 - 126 * q^68 + 166 * q^70 - 128 * q^71 - 156 * q^72 - 30 * q^73 + 26 * q^75 + 128 * q^76 + 30 * q^78 + 154 * q^80 - 64 * q^81 + 8 * q^82 - 82 * q^83 + 60 * q^85 - 28 * q^86 - 24 * q^87 + 252 * q^88 + 38 * q^90 + 194 * q^93 - 74 * q^95 + 60 * q^96 - 38 * q^97 + 174 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{30}\right)$

Coefficient data

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

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

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

$2$	−0.946511	−	1.85763i	−0.669284	−	1.31354i	−0.936757	−	0.349979i	$-0.886189\pi$
$2$	−0.946511	−	1.85763i	−0.669284	−	1.31354i	0.267473	−	0.963565i	$-0.413811\pi$
$3$	−0.762126	+	0.494930i	−0.440014	+	0.285748i	−0.745572	−	0.666425i	$-0.767824\pi$
$3$	−0.762126	+	0.494930i	−0.440014	+	0.285748i	0.305558	+	0.952173i	$0.401157\pi$
$4$	−1.37935	+	1.89851i	−0.689673	+	0.949253i
$5$	0.456638	−	2.18895i	0.204215	−	0.978926i
$5$	0.456638	−	2.18895i	0.204215	−	0.978926i
$6$	1.64076	+	0.947293i	0.669837	+	0.386731i
$7$	1.18794	−	3.09469i	0.448999	−	1.16968i	−0.503190	−	0.864176i	$-0.667841\pi$
$7$	1.18794	−	3.09469i	0.448999	−	1.16968i	0.952190	−	0.305508i	$-0.0988261\pi$
$8$	0.713889	+	0.113069i	0.252398	+	0.0399759i
$9$	−0.884330	+	1.98624i	−0.294777	+	0.662079i
$10$	−4.49847	+	1.22360i	−1.42254	+	0.386935i
$11$	−5.92368	−	0.622604i	−1.78606	−	0.187722i	−0.847025	−	0.531553i	$-0.821609\pi$
$11$	−5.92368	−	0.622604i	−1.78606	−	0.187722i	−0.939032	+	0.343831i	$0.888275\pi$
$12$	0.111607	−	2.12958i	0.0322180	−	0.614757i
$13$	−0.0208725	−	0.398272i	−0.00578900	−	0.110461i	−0.999996	−	0.00297449i	$-0.999053\pi$
$13$	−0.0208725	−	0.398272i	−0.00578900	−	0.110461i	0.994207	−	0.107486i	$-0.0342801\pi$
$14$	−6.87320	+	0.722402i	−1.83694	+	0.193070i
$15$	0.735360	+	1.89426i	0.189869	+	0.489095i
$16$	0.984666	+	3.03049i	0.246166	+	0.757623i
$17$	0.0441159	−	0.0544786i	0.0106997	−	0.0132130i	−0.771768	−	0.635904i	$-0.780627\pi$
$17$	0.0441159	−	0.0544786i	0.0106997	−	0.0132130i	0.782468	+	0.622691i	$0.213961\pi$
$18$	4.52673	−	0.237236i	1.06696	−	0.0559170i
$19$	4.60234	−	4.14397i	1.05585	−	0.950691i	0.0569868	−	0.998375i	$-0.481851\pi$
$19$	4.60234	−	4.14397i	1.05585	−	0.950691i	0.998862	+	0.0476840i	$0.0151840\pi$
$20$	3.52586	+	3.88624i	0.788407	+	0.868990i
$21$	0.626296	+	2.94649i	0.136669	+	0.642977i
$22$	4.45026	+	11.5933i	0.948799	+	2.47171i
$23$	0.734900	−	4.63998i	0.153237	−	0.967503i	−0.784493	−	0.620138i	$-0.787077\pi$
$23$	0.734900	−	4.63998i	0.153237	−	0.967503i	0.937730	−	0.347365i	$-0.112923\pi$
$24$	−0.600035	+	0.267153i	−0.122482	+	0.0545323i
$25$	−4.58296	−	1.99911i	−0.916593	−	0.399822i
$26$	−0.720086	+	0.415742i	−0.141221	+	0.0815337i
$27$	−0.735549	−	4.64407i	−0.141556	−	0.893752i
$28$	4.23671	+	6.52396i	0.800663	+	1.23291i
$29$	−1.23801	+	3.81019i	−0.229892	+	0.707534i	0.767866	+	0.640610i	$0.221319\pi$
$29$	−1.23801	+	3.81019i	−0.229892	+	0.707534i	−0.997758	+	0.0669241i	$0.978681\pi$
$30$	2.82280	−	3.15896i	0.515371	−	0.576745i
$31$	5.54061	−	0.549179i	0.995124	−	0.0986354i
$31$	5.54061	−	0.549179i	0.995124	−	0.0986354i
$32$	5.71972	−	5.71972i	1.01111	−	1.01111i
$33$	4.82274	−	2.45731i	0.839530	−	0.427762i
$34$	−0.142957	−	0.0303865i	−0.0245170	−	0.00521125i
$35$	−6.23165	−	4.01349i	−1.05334	−	0.678404i
$36$	−2.55109	−	4.41861i	−0.425181	−	0.736436i
$37$	−4.52916	+	1.21358i	−0.744589	+	0.199512i	−0.611117	−	0.791541i	$-0.709279\pi$
$37$	−4.52916	+	1.21358i	−0.744589	+	0.199512i	−0.133472	+	0.991053i	$0.542613\pi$
$38$	−12.0541	−	4.62715i	−1.95544	−	0.750623i
$39$	0.213024	+	0.293203i	0.0341112	+	0.0469500i
$40$	0.573491	−	1.51103i	0.0906768	−	0.238915i
$41$	9.71922	−	2.06588i	1.51789	−	0.322637i	0.627781	−	0.778390i	$-0.283963\pi$
$41$	9.71922	−	2.06588i	1.51789	−	0.322637i	0.890106	+	0.455754i	$0.150630\pi$
$42$	4.88070	−	3.95232i	0.753109	−	0.609855i
$43$	7.61760	+	0.399222i	1.16167	+	0.0608807i	0.623409	−	0.781896i	$-0.285747\pi$
$43$	7.61760	+	0.399222i	1.16167	+	0.0608807i	0.538264	+	0.842776i	$0.319080\pi$
$44$	9.35282	−	10.3874i	1.40999	−	1.56595i
$45$	3.94395	+	2.84274i	0.587929	+	0.423771i
$46$	−9.31497	+	3.02662i	−1.37342	+	0.446250i
$47$	3.28729	+	1.67496i	0.479500	+	0.244318i	0.676997	−	0.735986i	$-0.263281\pi$
$47$	3.28729	+	1.67496i	0.479500	+	0.244318i	−0.197496	+	0.980304i	$0.563281\pi$
$48$	−2.25032	−	1.82227i	−0.324806	−	0.263023i
$49$	−2.96390	−	2.66870i	−0.423414	−	0.381243i
$50$	0.624214	+	10.4056i	0.0882772	+	1.47158i
$51$	−0.00665875	+	0.0633538i	−0.000932412	+	0.00887131i
$52$	0.784912	+	0.509728i	0.108848	+	0.0706865i
$53$	3.25195	−	1.24831i	0.446690	−	0.171468i	−0.124617	−	0.992205i	$-0.539770\pi$
$53$	3.25195	−	1.24831i	0.446690	−	0.171468i	0.571306	+	0.820737i	$0.306437\pi$
$54$	−7.93078	+	5.76205i	−1.07924	+	0.784115i
$55$	−4.06782	+	12.6823i	−0.548505	+	1.71008i
$56$	1.19797	−	2.07495i	0.160086	−	0.277277i
$57$	−1.45659	+	5.43606i	−0.192930	+	0.720024i
$58$	8.24972	−	1.30663i	1.08324	−	0.171568i
$59$	2.25951	−	10.6302i	0.294164	−	1.38393i	−0.544262	−	0.838915i	$-0.683190\pi$
$59$	2.25951	−	10.6302i	0.294164	−	1.38393i	0.838426	−	0.545016i	$-0.183476\pi$
$60$	−4.61057	−	1.21675i	−0.595222	−	0.157081i
$61$			4.79385i			0.613790i	0.951743	+	0.306895i	$0.0992900\pi$
$61$			4.79385i			0.613790i	−0.951743	+	0.306895i	$0.900710\pi$
$62$	−6.26443	−	9.77262i	−0.795583	−	1.24112i
$63$	5.09626	+	5.09626i	0.642069	+	0.642069i
$64$	−9.97793	−	3.24203i	−1.24724	−	0.405253i
$65$	−0.881326	−	0.136177i	−0.109315	−	0.0168907i
$66$	−9.12955	−	6.63300i	−1.12377	−	0.816466i
$67$	−7.50670	−	2.01141i	−0.917089	−	0.245733i	−0.230748	−	0.973013i	$-0.574117\pi$
$67$	−7.50670	−	2.01141i	−0.917089	−	0.245733i	−0.686341	+	0.727280i	$0.740784\pi$
$68$	0.0425769	+	0.158899i	0.00516320	+	0.0192693i
$69$	1.73638	+	3.89997i	0.209036	+	0.469501i
$70$	−1.55726	+	15.3749i	−0.186128	+	1.83766i
$71$	2.69492	+	1.19985i	0.319828	+	0.142396i	0.560370	−	0.828242i	$-0.310659\pi$
$71$	2.69492	+	1.19985i	0.319828	+	0.142396i	−0.240543	+	0.970639i	$0.577325\pi$
$72$	−0.855896	+	1.31796i	−0.100868	+	0.155324i
$73$	−1.12036	−	1.38353i	−0.131129	−	0.161930i	0.707353	−	0.706861i	$-0.249889\pi$
$73$	−1.12036	−	1.38353i	−0.131129	−	0.161930i	−0.838481	+	0.544931i	$0.816556\pi$
$74$	6.54129	+	7.26484i	0.760409	+	0.844520i
$75$	4.48222	−	0.744674i	0.517562	−	0.0859876i
$76$	1.51913	+	14.4535i	0.174256	+	1.65793i
$77$	−8.96375	+	17.5923i	−1.02151	+	2.00483i
$78$	0.343033	−	0.673240i	0.0388408	−	0.0762295i
$79$	−0.315564	−	3.00239i	−0.0355037	−	0.337795i	−0.997827	−	0.0658876i	$-0.979012\pi$
$79$	−0.315564	−	3.00239i	−0.0355037	−	0.337795i	0.962323	−	0.271908i	$-0.0876545\pi$
$80$	7.08321	−	0.771544i	0.791927	−	0.0862612i
$81$	−1.50541	−	1.67193i	−0.167268	−	0.185770i
$82$	−13.0370	−	16.0994i	−1.43970	−	1.77788i
$83$	−6.74771	+	10.3906i	−0.740658	+	1.14051i	0.244631	+	0.969616i	$0.421333\pi$
$83$	−6.74771	+	10.3906i	−0.740658	+	1.14051i	−0.985289	+	0.170897i	$0.945333\pi$
$84$	−6.45781	−	2.87520i	−0.704605	−	0.313710i
$85$	−0.0991056	−	0.121444i	−0.0107495	−	0.0131725i
$86$	−6.46854	−	14.5286i	−0.697520	−	1.56666i
$87$	−0.942262	−	3.51657i	−0.101021	−	0.377016i
$88$	−4.15846	−	1.11425i	−0.443293	−	0.118780i
$89$	6.05161	+	4.39675i	0.641470	+	0.466055i	0.860355	−	0.509696i	$-0.170242\pi$
$89$	6.05161	+	4.39675i	0.641470	+	0.466055i	−0.218885	+	0.975751i	$0.570242\pi$
$90$	1.54778	−	10.0171i	0.163150	−	1.05589i
$91$	−1.25732	−	0.408529i	−0.131803	−	0.0428255i
$92$	7.79535	+	7.79535i	0.812721	+	0.812721i
$93$	−3.95084	+	3.16076i	−0.409683	+	0.327756i
$94$		−	7.69194i		−	0.793363i
$95$	−6.96931	−	11.9666i	−0.715036	−	1.22774i
$96$	−1.52828	+	7.19001i	−0.155980	+	0.733827i
$97$	−10.7001	+	1.69473i	−1.08643	+	0.172074i	−0.673866	−	0.738853i	$-0.735368\pi$
$97$	−10.7001	+	1.69473i	−1.08643	+	0.172074i	−0.412566	+	0.910927i	$0.635368\pi$
$98$	−2.15211	+	8.03179i	−0.217396	+	0.811333i
$99$	6.47513	−	11.2153i	0.650775	−	1.12718i
$100$	10.1168	−	5.94332i	1.01168	−	0.594332i
$101$	−7.07159	+	5.13781i	−0.703650	+	0.511231i	−0.881119	−	0.472895i	$-0.843209\pi$
$101$	−7.07159	+	5.13781i	−0.703650	+	0.511231i	0.177469	+	0.984126i	$0.443209\pi$
$102$	0.123991	−	0.0475956i	0.0122769	−	0.00471266i
$103$	−3.13244	−	2.03423i	−0.308649	−	0.200439i	0.381014	−	0.924569i	$-0.375575\pi$
$103$	−3.13244	−	2.03423i	−0.308649	−	0.200439i	−0.689663	+	0.724130i	$0.742241\pi$
$104$	0.0301315	−	0.286682i	0.00295464	−	0.0281115i
$105$	6.73570	−	0.0254488i	0.657337	−	0.00248354i
$106$	−5.39690	−	4.85939i	−0.524193	−	0.471986i
$107$	−6.37044	−	5.15868i	−0.615853	−	0.498708i	0.269885	−	0.962893i	$-0.413014\pi$
$107$	−6.37044	−	5.15868i	−0.615853	−	0.498708i	−0.885739	+	0.464184i	$0.846348\pi$
$108$	9.83138	+	5.00934i	0.946025	+	0.482024i
$109$	6.36957	−	2.06960i	0.610094	−	0.198231i	0.0123567	−	0.999924i	$-0.496067\pi$
$109$	6.36957	−	2.06960i	0.610094	−	0.198231i	0.597737	+	0.801692i	$0.296067\pi$
$110$	27.4093	−	4.44743i	2.61338	−	0.424046i
$111$	2.85115	−	3.16652i	0.270619	−	0.300553i
$112$	10.5482	+	0.552805i	0.996707	+	0.0522352i
$113$	3.93926	−	3.18995i	0.370574	−	0.300085i	−0.425885	−	0.904777i	$-0.640037\pi$
$113$	3.93926	−	3.18995i	0.370574	−	0.300085i	0.796459	+	0.604692i	$0.206704\pi$
$114$	11.4769	−	2.43949i	1.07491	−	0.228479i
$115$	−9.82108	−	3.72745i	−0.915820	−	0.347586i
$116$	−5.52603	−	7.60593i	−0.513079	−	0.706193i
$117$	0.809521	+	0.310746i	0.0748402	+	0.0287285i
$118$	−21.8856	+	5.86423i	−2.01473	+	0.539846i
$119$	−0.116187	−	0.201242i	−0.0106509	−	0.0184479i
$120$	0.310784	+	1.43544i	0.0283706	+	0.131037i
$121$	23.9427	+	5.08919i	2.17661	+	0.462653i
$122$	8.90521	−	4.53743i	0.806240	−	0.410800i
$123$	−6.38480	+	6.38480i	−0.575698	+	0.575698i
$124$	−6.59980	+	11.2764i	−0.592680	+	1.01265i
$125$	−6.46870	+	9.11899i	−0.578578	+	0.815627i
$126$	4.64331	−	14.2906i	0.413659	−	1.27311i
$127$	5.36494	+	8.26128i	0.476061	+	0.733070i	0.992365	−	0.123335i	$-0.0393591\pi$
$127$	5.36494	+	8.26128i	0.476061	+	0.733070i	−0.516304	+	0.856406i	$0.672692\pi$
$128$	0.890962	+	5.62531i	0.0787507	+	0.497212i
$129$	−6.00316	+	3.46592i	−0.528548	+	0.305158i
$130$	0.581218	+	1.76607i	0.0509762	+	0.154895i
$131$	3.72498	−	1.65847i	0.325453	−	0.144901i	−0.237505	−	0.971386i	$-0.576330\pi$
$131$	3.72498	−	1.65847i	0.325453	−	0.144901i	0.562959	+	0.826485i	$0.309663\pi$
$132$	−1.98701	+	12.5455i	−0.172947	+	1.09194i
$133$	−7.35699	−	19.1656i	−0.637932	−	1.66187i
$134$	3.36871	+	15.8485i	0.291012	+	1.36910i
$135$	−10.5015	−	0.510583i	−0.903825	−	0.0439440i
$136$	0.0376537	−	0.0339035i	0.00322878	−	0.00290720i
$137$	9.77627	−	0.512352i	0.835243	−	0.0437732i	0.370082	−	0.928999i	$-0.379330\pi$
$137$	9.77627	−	0.512352i	0.835243	−	0.0437732i	0.465161	+	0.885226i	$0.345996\pi$
$138$	5.60121	−	6.91692i	0.476807	−	0.588808i
$139$	−3.79791	−	11.6888i	−0.322135	−	0.991428i	−0.972717	−	0.231993i	$-0.925475\pi$
$139$	−3.79791	−	11.6888i	−0.322135	−	0.991428i	0.650583	−	0.759435i	$-0.274525\pi$
$140$	16.2152	−	6.29484i	1.37044	−	0.532011i
$141$	−3.33431	+	0.350451i	−0.280800	+	0.0295133i
$142$	−0.321880	−	6.14184i	−0.0270116	−	0.515412i
$143$	−0.124323	+	2.37223i	−0.0103964	+	0.198376i
$144$	−6.89005	−	0.724173i	−0.574170	−	0.0603477i
$145$	7.77497	+	4.44980i	0.645677	+	0.369536i
$146$	−1.50966	+	3.39075i	−0.124940	+	0.280621i
$147$	3.57968	+	0.566966i	0.295247	+	0.0467626i
$148$	3.94327	−	10.2726i	0.324135	−	0.844401i
$149$	4.54835	+	2.62599i	0.372616	+	0.215130i	0.674601	−	0.738183i	$-0.264316\pi$
$149$	4.54835	+	2.62599i	0.372616	+	0.215130i	−0.301985	+	0.953313i	$0.597649\pi$
$150$	−5.62580	−	7.62147i	−0.459344	−	0.622290i
$151$	−12.7622	+	17.5657i	−1.03858	+	1.42948i	−0.140267	+	0.990114i	$0.544796\pi$
$151$	−12.7622	+	17.5657i	−1.03858	+	1.42948i	−0.898309	+	0.439364i	$0.855204\pi$
$152$	3.75412	−	2.43795i	0.304499	−	0.197744i
$153$	0.0691944	+	0.135802i	0.00559404	+	0.0109789i
$154$	41.1644			3.31712
$155$	1.32793	−	12.3789i	0.106662	−	0.994295i
$156$	−0.850481			−0.0680930
$157$	2.24962	+	4.41513i	0.179539	+	0.352366i	0.963184	−	0.268844i	$-0.0866416\pi$
$157$	2.24962	+	4.41513i	0.179539	+	0.352366i	−0.783645	+	0.621210i	$0.786642\pi$
$158$	−5.27865	+	3.42800i	−0.419947	+	0.272717i
$159$	−1.86057	+	2.56086i	−0.147553	+	0.203089i
$160$	−9.90831	−	15.1320i	−0.783321	−	1.19629i
$161$	−13.4863	−	7.78631i	−1.06287	−	0.613647i
$162$	−1.68094	+	4.37901i	−0.132067	+	0.344047i
$163$	1.21504	+	0.192444i	0.0951693	+	0.0150733i	0.203837	−	0.979005i	$-0.434659\pi$
$163$	1.21504	+	0.192444i	0.0951693	+	0.0150733i	−0.108668	+	0.994078i	$0.534659\pi$
$164$	−9.48406	+	21.3016i	−0.740581	+	1.66337i
$165$	−3.17667	−	11.6788i	−0.247303	−	0.909194i
$166$	25.6886	+	2.69999i	1.99383	+	0.209560i
$167$	−0.149708	+	2.85660i	−0.0115848	+	0.221050i	0.986702	+	0.162540i	$0.0519685\pi$
$167$	−0.149708	+	2.85660i	−0.0115848	+	0.221050i	−0.998287	+	0.0585107i	$0.981365\pi$
$168$	0.113949	+	2.17428i	0.00879138	+	0.167750i
$169$	12.7706	−	1.34224i	0.982354	−	0.103250i
$170$	−0.131794	+	0.299050i	−0.0101081	+	0.0229361i
$171$	4.16091	+	12.8060i	0.318193	+	0.979298i
$172$	−11.2652	+	13.9114i	−0.858965	+	1.06073i
$173$	−0.0454644	+	0.00238269i	−0.00345659	+	0.000181152i	−0.0540642	−	0.998537i	$-0.517218\pi$
$173$	−0.0454644	+	0.00238269i	−0.00345659	+	0.000181152i	0.0506076	+	0.998719i	$0.483884\pi$
$174$	−5.64063	+	5.07885i	−0.427615	+	0.385027i
$175$	−11.6309	+	11.8080i	−0.879215	+	0.892603i
$176$	−3.94605	−	18.5647i	−0.297445	−	1.39937i
$177$	3.53916	+	9.21983i	0.266020	+	0.693005i
$178$	2.43964	−	15.4033i	0.182858	−	1.15452i
$179$	−18.6785	+	8.31619i	−1.39609	+	0.621581i	−0.960428	−	0.278527i	$-0.910154\pi$
$179$	−18.6785	+	8.31619i	−1.39609	+	0.621581i	−0.435666	+	0.900109i	$0.643487\pi$
$180$	−10.8370	+	3.56649i	−0.807744	+	0.265830i
$181$	3.79559	−	2.19138i	0.282124	−	0.162884i	−0.352261	−	0.935902i	$-0.614587\pi$
$181$	3.79559	−	2.19138i	0.282124	−	0.162884i	0.634385	+	0.773018i	$0.281254\pi$
$182$	0.431173	+	2.72232i	0.0319607	+	0.201792i
$183$	−2.37262	−	3.65352i	−0.175389	−	0.270076i
$184$	1.04928	−	3.22934i	0.0773536	−	0.238070i
$185$	0.588285	+	10.4682i	0.0432516	+	0.769641i
$186$	9.61105	+	4.34751i	0.704716	+	0.318775i
$187$	−0.295247	+	0.295247i	−0.0215906	+	0.0215906i
$188$	−7.71422	+	3.93059i	−0.562617	+	0.286668i
$189$	−15.2458	−	3.24059i	−1.10897	−	0.235718i
$190$	−15.6329	+	24.2729i	−1.13413	+	1.76094i
$191$	−0.664513	−	1.15097i	−0.0480824	−	0.0832812i	0.840983	−	0.541062i	$-0.181978\pi$
$191$	−0.664513	−	1.15097i	−0.0480824	−	0.0832812i	−0.889065	+	0.457781i	$0.848644\pi$
$192$	9.20901	−	2.46755i	0.664603	−	0.178080i
$193$	8.56097	+	3.28625i	0.616232	+	0.236549i	0.646404	−	0.762995i	$-0.276272\pi$
$193$	8.56097	+	3.28625i	0.616232	+	0.236549i	−0.0301719	+	0.999545i	$0.509605\pi$
$194$	13.2760	+	18.2728i	0.953159	+	1.31191i
$195$	0.739080	−	0.332411i	0.0529266	−	0.0238044i
$196$	9.15478	−	1.94591i	0.653913	−	0.138994i
$197$	17.2796	−	13.9928i	1.23112	−	0.996943i	0.231412	−	0.972856i	$-0.425666\pi$
$197$	17.2796	−	13.9928i	1.23112	−	0.996943i	0.999710	−	0.0240866i	$-0.00766776\pi$
$198$	−26.9626	−	1.41305i	−1.91615	−	0.100421i
$199$	0.523094	−	0.580955i	0.0370812	−	0.0411828i	−0.724319	−	0.689465i	$-0.757846\pi$
$199$	0.523094	−	0.580955i	0.0370812	−	0.0411828i	0.761400	+	0.648282i	$0.224512\pi$
$200$	−3.04569	−	1.94533i	−0.215363	−	0.137556i
$201$	6.71656	−	2.18234i	0.473750	−	0.153931i
$202$	16.2375	+	8.27342i	1.14247	+	0.582116i
$203$	10.3207	+	8.35752i	0.724370	+	0.586583i
$204$	−0.111093	−	0.100028i	−0.00777806	−	0.00700339i
$205$	−0.0839446	−	22.2182i	−0.00586294	−	1.55179i
$206$	−0.813965	+	7.74436i	−0.0567116	+	0.539575i
$207$	8.56621	+	5.56296i	0.595393	+	0.386653i
$208$	1.18641	−	0.455419i	0.0822625	−	0.0315776i
$209$	−29.8428	+	21.6821i	−2.06427	+	1.49978i
$210$	−6.42269	−	12.4884i	−0.443208	−	0.861779i
$211$	10.1298	−	17.5453i	0.697362	−	1.20787i	−0.272016	−	0.962293i	$-0.587690\pi$
$211$	10.1298	−	17.5453i	0.697362	−	1.20787i	0.969378	−	0.245573i	$-0.0789762\pi$
$212$	−2.11564	+	7.89569i	−0.145303	+	0.542278i
$213$	−2.64771	+	0.419356i	−0.181418	+	0.0287338i
$214$	−3.55324	+	16.7167i	−0.242895	+	1.14273i
$215$	4.35236	−	16.4922i	0.296828	−	1.12476i
$216$		−	3.39852i		−	0.231240i
$217$	4.88238	−	17.7989i	0.331438	−	1.20827i
$218$	−9.87342	−	9.87342i	−0.668712	−	0.668712i
$219$	1.53861	+	0.499925i	0.103970	+	0.0337818i
$220$	−18.4665	−	25.2161i	−1.24501	−	1.70007i
$221$	−0.0226181	−	0.0164330i	−0.00152146	−	0.00110540i
$222$	−8.58087	−	2.29924i	−0.575910	−	0.154315i
$223$	−6.41600	−	23.9448i	−0.429647	−	1.60347i	−0.753560	−	0.657379i	$-0.771665\pi$
$223$	−6.41600	−	23.9448i	−0.429647	−	1.60347i	0.323913	−	0.946087i	$-0.395002\pi$
$224$	−10.9061	−	24.4954i	−0.728693	−	1.63667i
$225$	8.02356	−	7.33498i	0.534904	−	0.488999i
$226$	−9.65430	−	4.29837i	−0.642194	−	0.285923i
$227$	−9.04619	+	13.9299i	−0.600417	+	0.924561i	0.399552	+	0.916710i	$0.369166\pi$
$227$	−9.04619	+	13.9299i	−0.600417	+	0.924561i	−0.999969	+	0.00785041i	$0.997501\pi$
$228$	−8.31126	−	10.2635i	−0.550426	−	0.679720i
$229$	−8.32011	−	9.24042i	−0.549808	−	0.610624i	0.402627	−	0.915364i	$-0.368097\pi$
$229$	−8.32011	−	9.24042i	−0.549808	−	0.610624i	−0.952436	+	0.304740i	$0.901430\pi$
$230$	2.37153	+	21.7720i	0.156374	+	1.43560i
$231$	−1.87548	−	17.8440i	−0.123398	−	1.17405i
$232$	−1.31461	+	2.58007i	−0.0863086	+	0.169390i
$233$	−1.40349	+	2.75450i	−0.0919455	+	0.180453i	−0.932399	−	0.361430i	$-0.882289\pi$
$233$	−1.40349	+	2.75450i	−0.0919455	+	0.180453i	0.840454	+	0.541883i	$0.182289\pi$
$234$	−0.188969	−	1.79792i	−0.0123533	−	0.117533i
$235$	5.16749	−	6.43085i	0.337090	−	0.419502i
$236$	17.0648	+	18.9524i	1.11082	+	1.23370i
$237$	1.72647	+	2.13202i	0.112146	+	0.138489i
$238$	−0.263862	+	0.406311i	−0.0171036	+	0.0263373i
$239$	20.9632	+	9.33342i	1.35600	+	0.603729i	0.950602	−	0.310413i	$-0.100467\pi$
$239$	20.9632	+	9.33342i	1.35600	+	0.603729i	0.405395	+	0.914141i	$0.367134\pi$
$240$	−5.01644	+	4.09371i	−0.323810	+	0.264248i
$241$	−2.41657	−	5.42770i	−0.155665	−	0.349629i	0.818831	−	0.574035i	$-0.194623\pi$
$241$	−2.41657	−	5.42770i	−0.155665	−	0.349629i	−0.974496	+	0.224406i	$0.927956\pi$
$242$	−13.2082	−	49.2938i	−0.849057	−	3.16872i
$243$	15.6000	+	4.18002i	1.00074	+	0.268148i
$244$	−9.10115	−	6.61238i	−0.582642	−	0.423314i
$245$	−7.19507	+	5.26917i	−0.459676	+	0.336635i
$246$	17.9039	+	5.81733i	1.14151	+	0.370899i
$247$	−1.74649	−	1.74649i	−0.111126	−	0.111126i
$248$	4.01748	+	0.234419i	0.255110	+	0.0148856i
$249$		−	11.2586i		−	0.713483i
$250$	23.0624	+	3.38524i	1.45860	+	0.214101i
$251$	−0.821485	+	3.86478i	−0.0518517	+	0.243943i	−0.996439	−	0.0843174i	$-0.973129\pi$
$251$	−0.821485	+	3.86478i	−0.0518517	+	0.243943i	0.944587	+	0.328260i	$0.106462\pi$
$252$	−16.7048	+	2.64578i	−1.05230	+	0.166668i
$253$	−7.24218	+	27.0282i	−0.455312	+	1.69925i
$254$	10.2685	−	17.7855i	0.644300	−	1.11596i
$255$	0.135637	+	0.0435054i	0.00849394	+	0.00272441i
$256$	−7.36901	+	5.35390i	−0.460563	+	0.334619i
$257$	−9.94310	+	3.81680i	−0.620234	+	0.238085i	−0.648135	−	0.761525i	$-0.724451\pi$
$257$	−9.94310	+	3.81680i	−0.620234	+	0.238085i	0.0279016	+	0.999611i	$0.491118\pi$
$258$	12.1205	+	7.87112i	0.754587	+	0.490035i
$259$	−1.62470	+	15.4580i	−0.100954	+	0.960514i
$260$	1.47419	−	1.48537i	0.0914251	−	0.0921186i
$261$	−6.47314	−	5.82844i	−0.400677	−	0.360771i
$262$	−6.60657	−	5.34989i	−0.408155	−	0.330517i
$263$	−0.821978	−	0.418819i	−0.0506853	−	0.0258255i	0.428464	−	0.903559i	$-0.359055\pi$
$263$	−0.821978	−	0.418819i	−0.0506853	−	0.0258255i	−0.479149	+	0.877733i	$0.659055\pi$
$264$	3.72074	−	1.20894i	0.228996	−	0.0744053i
$265$	−1.24751	−	7.68837i	−0.0766341	−	0.472293i
$266$	−28.6392	+	31.8070i	−1.75598	+	1.95021i
$267$	−6.78818	−	0.355753i	−0.415430	−	0.0217717i
$268$	14.1730	−	11.4771i	0.865755	−	0.701074i
$269$	16.8891	−	3.58989i	1.02975	−	0.218879i	0.338096	−	0.941112i	$-0.390217\pi$
$269$	16.8891	−	3.58989i	1.02975	−	0.218879i	0.691651	+	0.722232i	$0.256884\pi$
$270$	8.99131	+	19.9912i	0.547194	+	1.21663i
$271$	8.26401	+	11.3744i	0.502003	+	0.690948i	0.982545	−	0.186024i	$-0.0595602\pi$
$271$	8.26401	+	11.3744i	0.502003	+	0.690948i	−0.480542	+	0.876972i	$0.659560\pi$
$272$	0.208536	+	0.0800495i	0.0126444	+	0.00485372i
$273$	1.16043	−	0.310937i	0.0702325	−	0.0188187i
$274$	−10.2051	−	17.6758i	−0.616513	−	1.06783i
$275$	25.9034	+	14.6955i	1.56203	+	0.886170i
$276$	−9.79919	−	2.08288i	−0.589842	−	0.125375i
$277$	−27.9520	+	14.2423i	−1.67948	+	0.855735i	−0.687959	+	0.725749i	$0.741493\pi$
$277$	−27.9520	+	14.2423i	−1.67948	+	0.855735i	−0.991516	+	0.129986i	$0.958507\pi$
$278$	−18.1187	+	18.1187i	−1.08669	+	1.08669i
$279$	−3.80893	+	11.4906i	−0.228035	+	0.687926i
$280$	−3.99491	−	3.56979i	−0.238741	−	0.213336i
$281$	−6.97498	+	21.4668i	−0.416092	+	1.28060i	0.495178	+	0.868792i	$0.335103\pi$
$281$	−6.97498	+	21.4668i	−0.416092	+	1.28060i	−0.911270	+	0.411809i	$0.864897\pi$
$282$	3.80697	+	5.86223i	0.226702	+	0.349090i
$283$	3.59958	+	22.7268i	0.213973	+	1.35097i	0.827575	+	0.561355i	$0.189720\pi$
$283$	3.59958	+	22.7268i	0.213973	+	1.35097i	−0.613603	+	0.789615i	$0.710280\pi$
$284$	−5.99515	+	3.46130i	−0.355747	+	0.205390i
$285$	11.2341	+	5.67070i	0.665451	+	0.335903i
$286$	4.52440	−	2.01439i	0.267534	−	0.119114i
$287$	5.15258	−	32.5321i	0.304147	−	1.92031i
$288$	6.30260	+	16.4188i	0.371384	+	0.967489i
$289$	3.53348	+	16.6237i	0.207852	+	0.977865i
$290$	0.906997	−	18.6548i	0.0532607	−	1.09545i
$291$	7.31606	−	6.58741i	0.428875	−	0.386161i
$292$	4.17201	−	0.218646i	0.244149	−	0.0127953i
$293$	−1.46232	+	1.80581i	−0.0854295	+	0.105497i	−0.818069	−	0.575121i	$-0.804955\pi$
$293$	−1.46232	+	1.80581i	−0.0854295	+	0.105497i	0.732639	+	0.680617i	$0.238288\pi$
$294$	−2.33500	−	7.18638i	−0.136180	−	0.419118i
$295$	−22.2371	−	9.80009i	−1.29469	−	0.570583i
$296$	−3.37053	+	0.354257i	−0.195908	+	0.0205908i
$297$	1.46574	+	27.9680i	0.0850508	+	1.62287i
$298$	0.573063	−	10.9347i	0.0331967	−	0.633430i
$299$	−1.86331	−	0.195842i	−0.107758	−	0.0113258i
$300$	−4.76875	+	9.53668i	−0.275324	+	0.550600i
$301$	10.2847	−	23.0999i	0.592802	−	1.33145i
$302$	44.7103	+	7.08141i	2.57279	+	0.407489i
$303$	2.84658	−	7.41560i	0.163532	−	0.426015i
$304$	17.0900	+	9.86693i	0.980180	+	0.565907i
$305$	10.4935	+	2.18905i	0.600855	+	0.125345i
$306$	0.186776	−	0.257076i	0.0106773	−	0.0146960i
$307$	6.36797	−	4.13541i	0.363439	−	0.236020i	−0.349981	−	0.936757i	$-0.613812\pi$
$307$	6.36797	−	4.13541i	0.363439	−	0.236020i	0.713420	+	0.700737i	$0.247145\pi$
$308$	−21.0351	−	41.2836i	−1.19858	−	2.35235i
$309$	3.39412			0.193085
$310$	−24.2523	+	9.24994i	−1.37744	+	0.525361i
$311$	−6.44227			−0.365307			−0.182654	−	0.983177i	$-0.558469\pi$
$311$	−6.44227			−0.365307			−0.182654	+	0.983177i	$0.558469\pi$
$312$	0.118924	+	0.233401i	0.00673272	+	0.0132137i
$313$	−15.5109	+	10.0729i	−0.876730	+	0.569355i	−0.902682	−	0.430308i	$-0.858405\pi$
$313$	−15.5109	+	10.0729i	−0.876730	+	0.569355i	0.0259519	+	0.999663i	$0.491738\pi$
$314$	6.07240	−	8.35794i	0.342685	−	0.471666i
$315$	13.4826	−	8.82829i	0.759657	−	0.497418i
$316$	6.13533	+	3.54223i	0.345139	+	0.199266i
$317$	−1.74855	+	4.55513i	−0.0982083	+	0.255841i	−0.973879	−	0.227067i	$-0.927086\pi$
$317$	−1.74855	+	4.55513i	−0.0982083	+	0.255841i	0.875671	+	0.482909i	$0.160420\pi$
$318$	6.51818	+	1.03238i	0.365521	+	0.0578929i
$319$	9.70579	−	21.7996i	0.543420	−	1.22054i
$320$	−11.6529	+	20.3607i	−0.651418	+	1.13820i
$321$	7.40826	+	0.778640i	0.413489	+	0.0434594i
$322$	−1.69919	+	32.4224i	−0.0946919	+	1.80683i
$323$	−0.0227211	−	0.433544i	−0.00126423	−	0.0241230i
$324$	5.25066	−	0.551867i	0.291703	−	0.0306593i
$325$	−0.700531	+	1.86699i	−0.0388585	+	0.103562i
$326$	−0.792560	−	2.43925i	−0.0438959	−	0.135098i
$327$	−3.83010	+	4.72978i	−0.211805	+	0.261558i
$328$	7.17203	−	0.375870i	0.396009	−	0.0207540i
$329$	9.08858	−	8.18339i	0.501069	−	0.451165i
$330$	−18.6882	+	16.9552i	−1.02875	+	0.933353i
$331$	−0.930864	−	4.37937i	−0.0511649	−	0.240712i	0.945132	−	0.326688i	$-0.105933\pi$
$331$	−0.930864	−	4.37937i	−0.0511649	−	0.240712i	−0.996297	+	0.0859758i	$0.972599\pi$
$332$	−10.4191	−	27.1428i	−0.571824	−	1.48965i
$333$	1.59480	−	10.0692i	0.0873947	−	0.551788i
$334$	5.44821	−	2.42570i	0.298113	−	0.132728i
$335$	−7.83072	+	15.5133i	−0.427838	+	0.847580i
$336$	−8.31262	+	4.79929i	−0.453491	+	0.261823i
$337$	−3.76417	−	23.7661i	−0.205048	−	1.29462i	−0.848525	−	0.529155i	$-0.822509\pi$
$337$	−3.76417	−	23.7661i	−0.205048	−	1.29462i	0.643478	−	0.765465i	$-0.277491\pi$
$338$	−14.5809	−	22.4526i	−0.793097	−	1.22126i
$339$	−1.42341	+	4.38080i	−0.0773089	+	0.237932i
$340$	0.367263	−	0.0206391i	0.0199177	−	0.00111931i
$341$	−33.1627	−	0.196449i	−1.79586	−	0.0106383i
$342$	19.8505	−	19.8505i	1.07339	−	1.07339i
$343$	8.89521	−	4.53233i	0.480296	−	0.244723i
$344$	5.39298	+	1.14631i	0.290770	+	0.0618051i
$345$	9.32972	−	2.01997i	0.502295	−	0.108751i
$346$	0.0474587	+	0.0822009i	0.00255140	+	0.00441915i
$347$	19.9558	−	5.34715i	1.07129	−	0.287050i	0.320265	−	0.947328i	$-0.396228\pi$
$347$	19.9558	−	5.34715i	1.07129	−	0.287050i	0.751021	+	0.660278i	$0.229562\pi$
$348$	7.97593	+	3.06167i	0.427555	+	0.164123i
$349$	1.15187	+	1.58542i	0.0616583	+	0.0848654i	0.838733	−	0.544544i	$-0.183297\pi$
$349$	1.15187	+	1.58542i	0.0616583	+	0.0848654i	−0.777074	+	0.629409i	$0.783297\pi$
$350$	32.9438	+	10.4295i	1.76092	+	0.557482i
$351$	−1.83425	+	0.389882i	−0.0979050	+	0.0208104i
$352$	−37.4429	+	30.3207i	−1.99571	+	1.61610i
$353$	35.6230	+	1.86692i	1.89602	+	0.0993662i	0.964461	−	0.264224i	$-0.0851159\pi$
$353$	35.6230	+	1.86692i	1.89602	+	0.0993662i	0.931559	+	0.363590i	$0.118449\pi$
$354$	13.7772	−	15.3011i	0.732250	−	0.813246i
$355$	3.85701	−	5.35112i	0.204709	−	0.284008i
$356$	−16.6945	+	5.42438i	−0.884808	+	0.287492i
$357$	0.188150	+	0.0958673i	0.00995797	+	0.00507384i
$358$	33.1278	+	26.8264i	1.75086	+	1.41782i
$359$	−15.1411	−	13.6331i	−0.799115	−	0.719526i	0.164629	−	0.986356i	$-0.447357\pi$
$359$	−15.1411	−	13.6331i	−0.799115	−	0.719526i	−0.963744	+	0.266829i	$0.914024\pi$
$360$	2.49412	+	2.47534i	0.131451	+	0.130462i
$361$	2.02304	−	19.2480i	0.106476	−	1.01305i
$362$	−7.66336	−	4.97664i	−0.402777	−	0.261566i
$363$	−20.7662	+	7.97138i	−1.08994	+	0.418389i
$364$	2.50988	−	1.82353i	0.131553	−	0.0955791i
$365$	−3.54008	+	1.82064i	−0.185296	+	0.0952967i
$366$	−4.54118	+	7.86555i	−0.237371	+	0.411139i
$367$	−0.724289	+	2.70308i	−0.0378076	+	0.141100i	−0.982250	−	0.187578i	$-0.939936\pi$
$367$	−0.724289	+	2.70308i	−0.0378076	+	0.141100i	0.944442	+	0.328678i	$0.106603\pi$
$368$	14.7850	−	2.34172i	0.770724	−	0.122071i
$369$	−4.49166	+	21.1316i	−0.233827	+	1.10007i
$370$	18.8893	−	11.0011i	0.982010	−	0.571921i
$371$		−	11.5467i		−	0.599474i
$372$	−0.551151	−	11.8605i	−0.0285759	−	0.614937i
$373$	−2.48209	−	2.48209i	−0.128518	−	0.128518i	0.639922	−	0.768440i	$-0.278967\pi$
$373$	−2.48209	−	2.48209i	−0.128518	−	0.128518i	−0.768440	+	0.639922i	$0.778967\pi$
$374$	0.827915	+	0.269006i	0.0428105	+	0.0139100i
$375$	0.416697	−	10.1514i	0.0215182	−	0.524215i
$376$	2.15737	+	1.56742i	0.111258	+	0.0808337i
$377$	1.54333	+	0.413534i	0.0794856	+	0.0212981i
$378$	8.41046	+	31.3883i	0.432588	+	1.61444i
$379$	−9.05735	−	20.3431i	−0.465245	−	1.04496i	−0.982010	−	0.188830i	$-0.939531\pi$
$379$	−9.05735	−	20.3431i	−0.465245	−	1.04496i	0.516765	−	0.856127i	$-0.327136\pi$
$380$	32.3317	+	3.27474i	1.65858	+	0.167991i
$381$	−8.17752	−	3.64087i	−0.418947	−	0.186527i
$382$	−1.50911	+	2.32383i	−0.0772128	+	0.118897i
$383$	19.5559	+	24.1495i	0.999260	+	1.23398i	0.972152	+	0.234351i	$0.0752965\pi$
$383$	19.5559	+	24.1495i	0.999260	+	1.23398i	0.0271082	+	0.999633i	$0.491370\pi$
$384$	−3.46316	−	3.84623i	−0.176729	−	0.196277i
$385$	34.4155	+	27.6545i	1.75398	+	1.40940i
$386$	−1.99841	−	19.0136i	−0.101716	−	0.967767i
$387$	−7.52942	+	14.7773i	−0.382742	+	0.751174i
$388$	11.5417	−	22.6519i	0.585941	−	1.14997i
$389$	−1.93994	−	18.4572i	−0.0983586	−	0.935820i	−0.926752	−	0.375673i	$-0.877412\pi$
$389$	−1.93994	−	18.4572i	−0.0983586	−	0.935820i	0.828394	−	0.560146i	$-0.189255\pi$
$390$	−1.31704	−	1.05831i	−0.0666911	−	0.0535895i
$391$	−0.220359	−	0.244733i	−0.0111440	−	0.0123767i
$392$	−1.81415	−	2.24028i	−0.0916282	−	0.113151i
$393$	−2.01808	+	3.10757i	−0.101799	+	0.156756i
$394$	−42.3487	−	18.8549i	−2.13350	−	0.949895i
$395$	−6.71617	−	0.680252i	−0.337927	−	0.0342272i
$396$	12.3608	+	27.7628i	0.621153	+	1.39513i
$397$	−5.32514	−	19.8737i	−0.267261	−	0.997432i	−0.960852	−	0.277063i	$-0.910639\pi$
$397$	−5.32514	−	19.8737i	−0.267261	−	0.997432i	0.693591	−	0.720369i	$-0.256028\pi$
$398$	−1.57432	−	0.421836i	−0.0789133	−	0.0211447i
$399$	15.0926	+	10.9654i	0.755574	+	0.548957i
$400$	1.54560	−	15.8571i	0.0772798	−	0.792854i
$401$	11.7337	+	3.81250i	0.585951	+	0.190387i	0.586965	−	0.809612i	$-0.300323\pi$
$401$	11.7337	+	3.81250i	0.585951	+	0.190387i	−0.00101355	+	0.999999i	$0.500323\pi$
$402$	−10.4113	−	10.4113i	−0.519268	−	0.519268i
$403$	−0.334369	−	2.19521i	−0.0166561	−	0.109351i
$404$		−	20.5123i		−	1.02052i
$405$	−4.34720	+	2.53180i	−0.216014	+	0.125806i
$406$	5.75657	−	27.0825i	0.285694	−	1.34408i
$407$	27.5849	−	4.36901i	1.36733	−	0.216564i
$408$	−0.0119170	+	0.0444747i	−0.000589978	+	0.00220183i
$409$	−3.81972	+	6.61595i	−0.188873	+	0.327137i	−0.944875	−	0.327432i	$-0.893817\pi$
$409$	−3.81972	+	6.61595i	−0.188873	+	0.327137i	0.756002	+	0.654569i	$0.227150\pi$
$410$	−41.1938	+	21.1857i	−2.03442	+	1.04629i
$411$	−7.19717	+	5.22905i	−0.355010	+	0.257930i
$412$	8.18273	−	3.14106i	0.403134	−	0.154749i
$413$	−30.2129	−	19.6205i	−1.48668	−	0.965462i
$414$	2.22593	−	21.1783i	0.109398	−	1.04086i
$415$	19.6631	+	19.5151i	0.965225	+	0.957959i
$416$	−2.39739	−	2.15862i	−0.117542	−	0.105835i
$417$	8.67961	+	7.02861i	0.425042	+	0.344193i
$418$	68.5240	+	34.9147i	3.35162	+	1.70773i
$419$	−28.7818	+	9.35177i	−1.40608	+	0.456864i	−0.911152	−	0.412070i	$-0.864806\pi$
$419$	−28.7818	+	9.35177i	−1.40608	+	0.456864i	−0.494929	+	0.868933i	$0.664806\pi$
$420$	−9.24254	+	12.8229i	−0.450990	+	0.625692i
$421$	13.3467	−	14.8231i	0.650481	−	0.722432i	−0.324211	−	0.945985i	$-0.605099\pi$
$421$	13.3467	−	14.8231i	0.650481	−	0.722432i	0.974692	+	0.223553i	$0.0717655\pi$
$422$	−42.1806	−	2.21059i	−2.05332	−	0.107610i
$423$	−6.23391	+	5.04812i	−0.303103	+	0.245448i
$424$	2.46268	−	0.523458i	0.119598	−	0.0254214i
$425$	−0.311090	+	0.161481i	−0.0150901	+	0.00783297i
$426$	3.28509	+	4.52154i	0.159163	+	0.219070i
$427$	14.8355	+	5.69481i	0.717939	+	0.275591i
$428$	18.5808	−	4.97872i	0.898138	−	0.240655i
$429$	−1.07934	−	1.86947i	−0.0521109	−	0.0902588i
$430$	−34.7560	+	7.52498i	−1.67608	+	0.362887i
$431$	−8.14645	−	1.73158i	−0.392401	−	0.0834074i	0.00748583	−	0.999972i	$-0.497617\pi$
$431$	−8.14645	−	1.73158i	−0.392401	−	0.0834074i	−0.399887	+	0.916565i	$0.630950\pi$
$432$	13.3495	−	6.80194i	0.642281	−	0.327258i
$433$	25.0839	−	25.0839i	1.20545	−	1.20545i	0.232969	−	0.972484i	$-0.425156\pi$
$433$	25.0839	−	25.0839i	1.20545	−	1.20545i	0.972484	−	0.232969i	$-0.0748442\pi$
$434$	−37.6850	+	7.77717i	−1.80894	+	0.373316i
$435$	−8.12785	+	0.456762i	−0.389701	+	0.0219000i
$436$	−4.85669	+	14.9473i	−0.232593	+	0.715848i
$437$	−15.8457	−	24.4002i	−0.758000	−	1.16722i
$438$	−0.527635	−	3.33136i	−0.0252114	−	0.159178i
$439$	17.6786	−	10.2067i	0.843754	−	0.487142i	−0.0147845	−	0.999891i	$-0.504706\pi$
$439$	17.6786	−	10.2067i	0.843754	−	0.487142i	0.858538	+	0.512749i	$0.171373\pi$
$440$	−4.33795	+	8.59382i	−0.206804	+	0.409694i
$441$	7.92174	−	3.52699i	0.377226	−	0.167952i
$442$	−0.00911821	+	0.0575701i	−0.000433709	+	0.00273833i
$443$	−4.14605	−	10.8008i	−0.196985	−	0.513163i	0.799137	−	0.601149i	$-0.205290\pi$
$443$	−4.14605	−	10.8008i	−0.196985	−	0.513163i	−0.996122	+	0.0879862i	$0.971957\pi$
$444$	2.07894	+	9.78064i	0.0986621	+	0.464169i
$445$	12.3876	−	11.2389i	0.587231	−	0.532776i
$446$	−38.4079	+	34.5826i	−1.81867	+	1.63754i
$447$	−4.76610	+	0.249781i	−0.225429	+	0.0118142i
$448$	−21.8863	+	27.0273i	−1.03403	+	1.27692i
$449$	−12.9835	−	39.9592i	−0.612730	−	1.88579i	−0.430694	−	0.902498i	$-0.641731\pi$
$449$	−12.9835	−	39.9592i	−0.612730	−	1.88579i	−0.182036	−	0.983292i	$-0.558269\pi$
$450$	−21.2201	−	7.96219i	−1.00032	−	0.375341i
$451$	−58.8598	+	6.18641i	−2.77160	+	0.291307i
$452$	0.622538	+	11.8787i	0.0292817	+	0.558729i
$453$	1.03263	−	19.7037i	0.0485171	−	0.925761i
$454$	34.4390	+	3.61968i	1.61630	+	0.169880i
$455$	−1.46839	+	2.56566i	−0.0688391	+	0.120280i
$456$	−1.65449	+	3.71605i	−0.0774787	+	0.174020i
$457$	−2.36622	−	0.374773i	−0.110687	−	0.0175311i	0.100845	−	0.994902i	$-0.467845\pi$
$457$	−2.36622	−	0.374773i	−0.110687	−	0.0175311i	−0.211532	+	0.977371i	$0.567845\pi$
$458$	−9.29023	+	24.2019i	−0.434104	+	1.13088i
$459$	−0.285452	−	0.164806i	−0.0133238	−	0.00769247i
$460$	20.6232	−	13.5039i	0.961563	−	0.629624i
$461$	5.69872	−	7.84361i	0.265416	−	0.365313i	−0.655420	−	0.755265i	$-0.727508\pi$
$461$	5.69872	−	7.84361i	0.265416	−	0.365313i	0.920835	+	0.389951i	$0.127508\pi$
$462$	−31.3725	+	20.3735i	−1.45958	+	0.947861i
$463$	10.1470	+	19.9145i	0.471569	+	0.925507i	0.997199	+	0.0747932i	$0.0238297\pi$
$463$	10.1470	+	19.9145i	0.471569	+	0.925507i	−0.525630	+	0.850713i	$0.676170\pi$
$464$	−12.7658			−0.592636
$465$	5.11463	+	10.0915i	0.237185	+	0.467982i
$466$	6.44526			0.298571
$467$	16.1220	+	31.6412i	0.746036	+	1.46418i	0.880894	+	0.473313i	$0.156942\pi$
$467$	16.1220	+	31.6412i	0.746036	+	1.46418i	−0.134858	+	0.990865i	$0.543058\pi$
$468$	−1.70656	+	1.10825i	−0.0788858	+	0.0512291i
$469$	−15.1422	+	20.8415i	−0.699203	+	0.962370i
$470$	−16.8372	−	3.51243i	−0.776644	−	0.162016i
$471$	−3.89967	−	2.25148i	−0.179688	−	0.103743i
$472$	2.81499	−	7.33329i	0.129570	−	0.337542i
$473$	−44.8757	−	7.10761i	−2.06339	−	0.326808i
$474$	2.32638	−	5.22513i	0.106854	−	0.239998i
$475$	−29.3766	+	9.79106i	−1.34789	+	0.449245i
$476$	0.542322	+	0.0570004i	0.0248573	+	0.00261261i
$477$	−0.396363	+	7.56306i	−0.0181482	+	0.346289i
$478$	−2.50384	−	47.7761i	−0.114523	−	2.18523i
$479$	8.50119	−	0.893512i	0.388429	−	0.0408256i	0.0916988	−	0.995787i	$-0.470770\pi$
$479$	8.50119	−	0.893512i	0.388429	−	0.0408256i	0.296731	+	0.954961i	$0.404104\pi$
$480$	15.0407	+	6.62856i	0.686509	+	0.302551i
$481$	0.577871	+	1.77850i	0.0263486	+	0.0810928i
$482$	−7.79537	+	9.62648i	−0.355069	+	0.438474i
$483$	14.1319	−	0.740623i	0.643025	−	0.0336995i
$484$	−42.6871	+	38.4357i	−1.94032	+	1.74708i
$485$	−1.17640	+	24.1959i	−0.0534176	+	1.09868i
$486$	−7.00068	−	32.9356i	−0.317557	−	1.49399i
$487$	−5.56314	−	14.4925i	−0.252090	−	0.656716i	0.747885	−	0.663828i	$-0.231069\pi$
$487$	−5.56314	−	14.4925i	−0.252090	−	0.656716i	−0.999975	+	0.00711209i	$0.997736\pi$
$488$	−0.542036	+	3.42228i	−0.0245368	+	0.154919i
$489$	−1.02126	+	0.454694i	−0.0461830	+	0.0205620i
$490$	16.5984	+	8.37847i	0.749840	+	0.378501i
$491$	16.0294	−	9.25457i	0.723396	−	0.417653i	−0.0926055	−	0.995703i	$-0.529520\pi$
$491$	16.0294	−	9.25457i	0.723396	−	0.417653i	0.816001	+	0.578050i	$0.196186\pi$
$492$	−3.31474	−	20.9284i	−0.149440	−	0.943526i
$493$	0.152958	+	0.235535i	0.00688888	+	0.0106079i
$494$	−1.59126	+	4.89740i	−0.0715942	+	0.220344i
$495$	−21.5928	−	19.2950i	−0.970524	−	0.867246i
$496$	7.11993	+	16.2500i	0.319695	+	0.729647i
$497$	6.91457	−	6.91457i	0.310161	−	0.310161i
$498$	−20.9143	+	10.6564i	−0.937192	+	0.477523i
$499$	11.4408	+	2.43181i	0.512159	+	0.108863i	0.456740	−	0.889600i	$-0.349017\pi$
$499$	11.4408	+	2.43181i	0.512159	+	0.108863i	0.0554192	+	0.998463i	$0.482350\pi$
$500$	−8.38989	−	24.8591i	−0.375207	−	1.11173i
$501$	−1.29972	−	2.25118i	−0.0580673	−	0.100575i
$502$	7.95689	−	2.13204i	0.355134	−	0.0951577i
$503$	36.6654	+	14.0745i	1.63483	+	0.627553i	0.990540	−	0.137227i	$-0.0438189\pi$
$503$	36.6654	+	14.0745i	1.63483	+	0.627553i	0.644292	+	0.764780i	$0.277152\pi$
$504$	3.06194	+	4.21440i	0.136390	+	0.187724i
$505$	8.01723	+	17.8254i	0.356762	+	0.793222i
$506$	57.0633	−	12.1292i	2.53677	−	0.539208i
$507$	−9.06849	+	7.34352i	−0.402746	+	0.326137i
$508$	−23.0842	−	1.20979i	−1.02420	−	0.0536758i
$509$	−0.0398311	+	0.0442369i	−0.00176548	+	0.00196077i	−0.744027	−	0.668150i	$-0.767087\pi$
$509$	−0.0398311	+	0.0442369i	−0.00176548	+	0.00196077i	0.742261	+	0.670110i	$0.233753\pi$
$510$	−0.0475653	−	0.293143i	−0.00210623	−	0.0129806i
$511$	−5.61253	+	1.82362i	−0.248284	+	0.0806723i
$512$	27.0698	+	13.7927i	1.19633	+	0.609558i
$513$	−22.6301	−	18.3255i	−0.999145	−	0.809091i
$514$	16.5015	+	14.8580i	0.727848	+	0.655358i
$515$	−5.88322	+	5.92784i	−0.259246	+	0.261212i
$516$	1.70035	−	16.1777i	0.0748537	−	0.712185i
$517$	−18.4300	−	11.9686i	−0.810551	−	0.526378i
$518$	30.2531	−	11.6131i	1.32924	−	0.510249i
$519$	0.0334703	−	0.0243176i	0.00146918	−	0.00106742i
$520$	−0.613772	−	0.196866i	−0.0269157	−	0.00863314i
$521$	−3.41052	+	5.90719i	−0.149418	+	0.258799i	−0.931012	−	0.364988i	$-0.881073\pi$
$521$	−3.41052	+	5.90719i	−0.149418	+	0.258799i	0.781595	+	0.623787i	$0.214407\pi$
$522$	−4.70020	+	17.5414i	−0.205722	+	0.767766i
$523$	−37.6271	+	5.95955i	−1.64532	+	0.260593i	−0.909231	−	0.416293i	$-0.863329\pi$
$523$	−37.6271	+	5.95955i	−1.64532	+	0.260593i	−0.736088	+	0.676886i	$0.763329\pi$
$524$	−1.98943	+	9.35951i	−0.0869084	+	0.408872i
$525$	3.02007	−	14.7557i	0.131807	−	0.643992i
$526$			1.92335i			0.0838620i
$527$	0.214511	−	0.326072i	0.00934423	−	0.0142039i
$528$	12.1956	+	12.1956i	0.530747	+	0.530747i
$529$	0.884973	+	0.287545i	0.0384771	+	0.0125020i
$530$	−13.1014	+	9.59454i	−0.569087	+	0.416760i
$531$	19.1159	+	13.8885i	0.829560	+	0.602710i
$532$	46.5338	+	12.4687i	2.01750	+	0.540587i
$533$	−1.02565	−	3.82777i	−0.0444257	−	0.165799i
$534$	5.76423	+	12.9467i	0.249442	+	0.560257i
$535$	−14.2010	+	11.5889i	−0.613965	+	0.501032i
$536$	−5.13152	−	2.28470i	−0.221648	−	0.0986841i
$537$	10.1194	−	15.5825i	0.436685	−	0.672435i
$538$	−22.6544	−	27.9759i	−0.976701	−	1.20613i
$539$	15.8956	+	17.6539i	0.684673	+	0.760406i
$540$	15.4545	−	19.2329i	0.665058	−	0.827652i
$541$	4.56321	+	43.4160i	0.196188	+	1.86660i	0.441640	+	0.897192i	$0.354397\pi$
$541$	4.56321	+	43.4160i	0.196188	+	1.86660i	−0.245452	+	0.969409i	$0.578937\pi$
$542$	13.3075	−	26.1175i	0.571608	−	1.12184i
$543$	−1.80813	+	3.54866i	−0.0775945	+	0.152288i
$544$	−0.0592717	−	0.563932i	−0.00254125	−	0.0241784i
$545$	−1.62165	−	14.8877i	−0.0694639	−	0.637719i
$546$	−1.67597	−	1.86135i	−0.0717248	−	0.0796585i
$547$	−7.01545	−	8.66336i	−0.299959	−	0.370419i	0.604774	−	0.796397i	$-0.293263\pi$
$547$	−7.01545	−	8.66336i	−0.299959	−	0.370419i	−0.904733	+	0.425978i	$0.859930\pi$
$548$	−12.5121	+	19.2670i	−0.534492	+	0.823046i
$549$	−9.52173	−	4.23935i	−0.406377	−	0.180931i
$550$	2.78095	−	62.0283i	0.118580	−	2.64490i
$551$	10.0916	+	22.6660i	0.429915	+	0.965606i
$552$	0.798617	+	2.98048i	0.0339914	+	0.126858i
$553$	−9.66634	−	2.59009i	−0.411055	−	0.110142i
$554$	52.9138	+	38.4441i	2.24809	+	1.63334i
$555$	−5.62940	−	7.68696i	−0.238955	−	0.326293i
$556$	27.4298	+	8.91249i	1.16328	+	0.377974i
$557$	−14.5641	−	14.5641i	−0.617099	−	0.617099i	0.327687	−	0.944786i	$-0.393731\pi$
$557$	−14.5641	−	14.5641i	−0.617099	−	0.617099i	−0.944786	+	0.327687i	$0.893731\pi$
$558$	24.9506	−	3.80042i	1.05624	−	0.160884i
$559$		−	3.04221i		−	0.128672i
$560$	6.02675	−	22.8369i	0.254677	−	0.965035i
$561$	0.0788887	−	0.371142i	0.00333068	−	0.0156696i
$562$	46.4793	−	7.36159i	1.96061	−	0.310530i
$563$	−2.96681	+	11.0723i	−0.125036	+	0.466641i	−0.999841	−	0.0178345i	$-0.994323\pi$
$563$	−2.96681	+	11.0723i	−0.125036	+	0.466641i	0.874805	+	0.484475i	$0.160989\pi$
$564$	3.93384	−	6.81361i	0.165644	−	0.286905i
$565$	−5.18381	−	10.0795i	−0.218084	−	0.424046i
$566$	38.8111	−	28.1979i	1.63135	−	1.18525i
$567$	−6.96246	+	2.67264i	−0.292396	+	0.112240i
$568$	1.78821	+	1.16127i	0.0750314	+	0.0487260i
$569$	−1.23878	+	11.7862i	−0.0519323	+	0.494103i	0.937382	+	0.348303i	$0.113242\pi$
$569$	−1.23878	+	11.7862i	−0.0519323	+	0.494103i	−0.989314	+	0.145799i	$0.953425\pi$
$570$	−0.0991255	−	26.2362i	−0.00415191	−	1.09891i
$571$	−21.4768	−	19.3378i	−0.898774	−	0.809260i	0.0835390	−	0.996505i	$-0.473378\pi$
$571$	−21.4768	−	19.3378i	−0.898774	−	0.809260i	−0.982313	+	0.187244i	$0.940044\pi$
$572$	−4.33221	−	3.50815i	−0.181139	−	0.146683i
$573$	1.07609	+	0.548296i	0.0449544	+	0.0229054i
$574$	−65.3097	+	21.2204i	−2.72597	+	0.885723i
$575$	−12.6439	+	19.7957i	−0.527285	+	0.825538i
$576$	15.2632	−	16.9515i	0.635967	−	0.706313i
$577$	19.9492	+	1.04550i	0.830498	+	0.0435245i	0.462846	−	0.886439i	$-0.346828\pi$
$577$	19.9492	+	1.04550i	0.830498	+	0.0435245i	0.367652	+	0.929963i	$0.380162\pi$
$578$	27.5363	−	22.2984i	1.14536	−	0.927492i
$579$	−8.15100	+	1.73255i	−0.338744	+	0.0720022i
$580$	−19.1724	+	8.62302i	−0.796089	+	0.358052i
$581$	24.1397	+	33.2255i	1.00148	+	1.37842i
$582$	−19.1617	−	7.35550i	−0.794279	−	0.304895i
$583$	−20.0407	+	5.36989i	−0.830002	+	0.222398i
$584$	−0.643381	−	1.11437i	−0.0266233	−	0.0461129i
$585$	1.04986	−	1.63010i	0.0434065	−	0.0673963i
$586$	4.73863	+	1.00723i	0.195751	+	0.0416082i
$587$	27.8790	−	14.2051i	1.15069	−	0.586306i	0.228692	−	0.973499i	$-0.426555\pi$
$587$	27.8790	−	14.2051i	1.15069	−	0.586306i	0.921999	+	0.387193i	$0.126555\pi$
$588$	−6.01401	+	6.01401i	−0.248013	+	0.248013i
$589$	23.2240	−	25.4876i	0.956929	−	1.05020i
$590$	2.84269	+	50.5842i	0.117032	+	2.08252i
$591$	−6.24380	+	19.2164i	−0.256836	+	0.790459i
$592$	−8.13746	−	12.5306i	−0.334448	−	0.515004i
$593$	−1.34479	−	8.49068i	−0.0552240	−	0.348671i	−0.999793	−	0.0203570i	$-0.993520\pi$
$593$	−1.34479	−	8.49068i	−0.0552240	−	0.348671i	0.944569	−	0.328314i	$-0.106480\pi$
$594$	50.5669	−	29.1948i	2.07478	−	1.19788i
$595$	−0.493564	+	0.162433i	−0.0202341	+	0.00665910i
$596$	−11.2592	+	5.01292i	−0.461195	+	0.205337i
$597$	−0.111131	+	0.701656i	−0.00454830	+	0.0287169i
$598$	1.39984	+	3.64671i	0.0572438	+	0.149125i
$599$	3.80203	+	17.8871i	0.155347	+	0.730849i	0.984998	+	0.172567i	$0.0552060\pi$
$599$	3.80203	+	17.8871i	0.155347	+	0.730849i	−0.829651	+	0.558282i	$0.811461\pi$
$600$	3.28401	−	0.0248156i	0.134069	−	0.00101309i
$601$	22.5148	−	20.2724i	0.918398	−	0.826930i	−0.0669021	−	0.997760i	$-0.521312\pi$
$601$	22.5148	−	20.2724i	0.918398	−	0.826930i	0.985301	+	0.170830i	$0.0546449\pi$
$602$	−52.6457	+	2.75904i	−2.14568	+	0.112450i
$603$	10.6335	−	13.1313i	0.433032	−	0.534749i
$604$	−15.7451	−	48.4584i	−0.640658	−	1.97174i
$605$	22.0731	−	50.0854i	0.897399	−	2.03626i
$606$	−16.4698	+	1.73104i	−0.669039	+	0.0703189i
$607$	1.22395	+	23.3544i	0.0496786	+	0.947925i	0.903828	+	0.427897i	$0.140745\pi$
$607$	1.22395	+	23.3544i	0.0496786	+	0.947925i	−0.854149	+	0.520028i	$0.825921\pi$
$608$	2.62177	−	50.0264i	0.106327	−	2.02884i
$609$	−12.0020	−	1.26147i	−0.486347	−	0.0511172i
$610$	−5.86574	−	21.5650i	−0.237497	−	0.873141i
$611$	0.598474	−	1.34419i	0.0242117	−	0.0543803i
$612$	−0.353263	−	0.0559514i	−0.0142798	−	0.00226170i
$613$	−14.4163	+	37.5558i	−0.582270	+	1.51687i	0.253247	+	0.967402i	$0.418501\pi$
$613$	−14.4163	+	37.5558i	−0.582270	+	1.51687i	−0.835517	+	0.549464i	$0.814832\pi$
$614$	−13.7094	−	7.91514i	−0.553267	−	0.319429i
$615$	11.0604	+	16.8915i	0.446000	+	0.681132i
$616$	−8.38827	+	11.5455i	−0.337973	+	0.465180i
$617$	−4.37293	+	2.83982i	−0.176048	+	0.114327i	−0.629655	−	0.776875i	$-0.716804\pi$
$617$	−4.37293	+	2.83982i	−0.176048	+	0.114327i	0.453607	+	0.891202i	$0.350137\pi$
$618$	−3.21257	−	6.30503i	−0.129229	−	0.253625i
$619$	29.7961			1.19761			0.598803	−	0.800897i	$-0.295643\pi$
$619$	29.7961			1.19761			0.598803	+	0.800897i	$0.295643\pi$
$620$	21.6697	+	19.5958i	0.870276	+	0.786988i
$621$	−22.0890			−0.886399
$622$	6.09768	+	11.9674i	0.244495	+	0.479848i
$623$	20.7956	−	13.5048i	0.833156	−	0.541058i
$624$	−0.678790	+	0.934274i	−0.0271734	+	0.0374009i
$625$	17.0071	+	18.3237i	0.680285	+	0.732948i
$626$	33.3931	+	19.2795i	1.33466	+	0.770564i
$627$	12.0129	−	31.2946i	0.479748	−	1.24979i
$628$	−11.4852	−	1.81907i	−0.458307	−	0.0725888i
$629$	−0.133693	+	0.300280i	−0.00533070	+	0.0119730i
$630$	−29.1611	−	16.6896i	−1.16181	−	0.664930i
$631$	−25.9244	−	2.72477i	−1.03204	−	0.108471i	−0.426661	−	0.904412i	$-0.640310\pi$
$631$	−25.9244	−	2.72477i	−1.03204	−	0.108471i	−0.605375	+	0.795940i	$0.706977\pi$
$632$	0.114199	−	2.17905i	0.00454261	−	0.0866781i
$633$	0.963529	+	18.3852i	0.0382968	+	0.730747i
$634$	10.1168	−	1.06332i	0.401788	−	0.0422297i
$635$	20.5333	−	7.97115i	0.814840	−	0.316325i
$636$	−2.29543	−	7.06461i	−0.0910197	−	0.280130i
$637$	−1.00100	+	1.23614i	−0.0396613	+	0.0489776i
$638$	−49.6822	+	2.60373i	−1.96694	+	0.103083i
$639$	−4.76639	+	4.29168i	−0.188555	+	0.169776i
$640$	12.7204	+	0.618463i	0.502816	+	0.0244469i
$641$	1.78401	+	8.39313i	0.0704643	+	0.331509i	0.999233	−	0.0391505i	$-0.0124652\pi$
$641$	1.78401	+	8.39313i	0.0704643	+	0.331509i	−0.928769	+	0.370659i	$0.879132\pi$
$642$	−5.56558	−	14.4988i	−0.219656	−	0.572223i
$643$	0.916968	−	5.78951i	0.0361617	−	0.228316i	−0.962988	−	0.269544i	$-0.913127\pi$
$643$	0.916968	−	5.78951i	0.0361617	−	0.228316i	0.999150	+	0.0412281i	$0.0131270\pi$
$644$	33.3846	−	14.8638i	1.31554	−	0.585715i
$645$	4.84545	+	14.7233i	0.190789	+	0.579728i
$646$	−0.783859	+	0.452561i	−0.0308405	+	0.0178058i
$647$	−0.528570	−	3.33726i	−0.0207802	−	0.131201i	0.975117	−	0.221690i	$-0.0711572\pi$
$647$	−0.528570	−	3.33726i	−0.0207802	−	0.131201i	−0.995898	+	0.0904885i	$0.971157\pi$
$648$	−0.885656	−	1.36379i	−0.0347918	−	0.0535747i
$649$	−20.0030	+	61.5630i	−0.785187	+	2.41656i
$650$	4.13124	−	0.465799i	0.162041	−	0.0182701i
$651$	5.08822	+	15.9814i	0.199423	+	0.626361i
$652$	−2.04132	+	2.04132i	−0.0799441	+	0.0799441i
$653$	35.8693	−	18.2763i	1.40368	−	0.715209i	0.422148	−	0.906527i	$-0.361276\pi$
$653$	35.8693	−	18.2763i	1.40368	−	0.715209i	0.981528	+	0.191318i	$0.0612763\pi$
$654$	12.4114	+	2.63813i	0.485326	+	0.103159i
$655$	−1.92933	−	8.91111i	−0.0753852	−	0.348186i
$656$	15.8308	+	27.4198i	0.618090	+	1.07056i
$657$	3.73880	−	1.00181i	0.145864	−	0.0390842i
$658$	−23.8042	−	9.13757i	−0.927983	−	0.356219i
$659$	−5.00761	−	6.89238i	−0.195069	−	0.268489i	0.700267	−	0.713881i	$-0.253064\pi$
$659$	−5.00761	−	6.89238i	−0.195069	−	0.268489i	−0.895336	+	0.445392i	$0.853064\pi$
$660$	26.5540	+	10.0782i	1.03361	+	0.392293i
$661$	−20.3932	+	4.33470i	−0.793202	+	0.168600i	−0.586656	−	0.809837i	$-0.699556\pi$
$661$	−20.3932	+	4.33470i	−0.793202	+	0.168600i	−0.206546	+	0.978437i	$0.566222\pi$
$662$	−7.25419	+	5.87432i	−0.281942	+	0.228312i
$663$	0.0253710	+	0.00132964i	0.000985328	+	5.16389e-5i
$664$	−5.99197	+	6.65476i	−0.232534	+	0.258255i
$665$	−45.3119	+	7.35230i	−1.75712	+	0.285110i
$666$	−20.2144	+	6.56804i	−0.783290	+	0.254506i
$667$	16.7694	+	8.54443i	0.649313	+	0.330842i
$668$	−5.21677	−	4.22446i	−0.201843	−	0.163449i
$669$	16.7408	+	15.0735i	0.647238	+	0.582776i
$670$	36.2298	−	0.136883i	1.39968	−	0.00528826i
$671$	2.98467	−	28.3972i	0.115222	−	1.09626i
$672$	20.4353	+	13.2709i	0.788310	+	0.511935i
$673$	12.1318	−	4.65697i	0.467648	−	0.179513i	−0.113122	−	0.993581i	$-0.536085\pi$
$673$	12.1318	−	4.65697i	0.467648	−	0.179513i	0.580770	+	0.814068i	$0.302752\pi$
$674$	−40.5858	+	29.4873i	−1.56331	+	1.13581i
$675$	−5.91302	+	22.7541i	−0.227592	+	0.875804i
$676$	−15.0668	+	26.0965i	−0.579493	+	1.00371i
$677$	−6.73168	+	25.1230i	−0.258720	+	0.965554i	0.707264	+	0.706950i	$0.249929\pi$
$677$	−6.73168	+	25.1230i	−0.258720	+	0.965554i	−0.965983	+	0.258605i	$0.916737\pi$
$678$	9.48518	−	1.50231i	0.364276	−	0.0576957i
$679$	−7.46643	+	35.1268i	−0.286535	+	1.34804i
$680$	−0.0570189	−	0.0979035i	−0.00218657	−	0.00375443i
$681$		−	15.0936i		−	0.578387i
$682$	31.0240	+	61.7901i	1.18797	+	2.36607i
$683$	13.1825	+	13.1825i	0.504415	+	0.504415i	0.912807	−	0.408392i	$-0.133910\pi$
$683$	13.1825	+	13.1825i	0.504415	+	0.504415i	−0.408392	+	0.912807i	$0.633910\pi$
$684$	−30.0516	−	9.76435i	−1.14905	−	0.373349i
$685$	3.34270	−	21.6337i	0.127718	−	0.826580i
$686$	−16.8388	−	12.2341i	−0.642909	−	0.467101i
$687$	10.9143	+	2.92449i	0.416408	+	0.111576i
$688$	6.29095	+	23.4782i	0.239840	+	0.895097i
$689$	−0.565042	−	1.26910i	−0.0215264	−	0.0483490i
$690$	−12.5830	−	15.4193i	−0.479028	−	0.587002i
$691$	−2.85391	−	1.27064i	−0.108568	−	0.0483375i	0.351734	−	0.936100i	$-0.385592\pi$
$691$	−2.85391	−	1.27064i	−0.108568	−	0.0483375i	−0.460302	+	0.887762i	$0.652259\pi$
$692$	0.0581875	−	0.0896009i	0.00221196	−	0.00340612i
$693$	−27.0157	−	33.3616i	−1.02624	−	1.26730i
$694$	−28.8215	−	32.0095i	−1.09405	−	1.21506i
$695$	−27.3203	+	2.97589i	−1.03632	+	0.112882i
$696$	−0.275056	−	2.61698i	−0.0104260	−	0.0991964i
$697$	0.316225	−	0.620627i	0.0119779	−	0.0235079i
$698$	1.85486	−	3.64037i	0.0702075	−	0.137790i
$699$	−0.293651	−	2.79390i	−0.0111069	−	0.105675i
$700$	−6.37457	−	38.3687i	−0.240936	−	1.45020i
$701$	20.9742	+	23.2942i	0.792183	+	0.879809i	0.995048	−	0.0993980i	$-0.0316917\pi$
$701$	20.9742	+	23.2942i	0.792183	+	0.879809i	−0.202864	+	0.979207i	$0.565025\pi$
$702$	2.46040	+	3.03834i	0.0928616	+	0.114675i
$703$	−15.8157	+	24.3540i	−0.596499	+	0.918528i
$704$	57.0876	+	25.4170i	2.15157	+	0.957940i
$705$	−0.755457	+	7.45866i	−0.0284521	+	0.280909i
$706$	−30.2495	−	67.9415i	−1.13845	−	2.55701i
$707$	7.49931	+	27.9878i	0.282041	+	1.05259i
$708$	−22.3856	−	5.99821i	−0.841304	−	0.225427i
$709$	3.07037	+	2.23076i	0.115310	+	0.0837779i	0.643946	−	0.765071i	$-0.277296\pi$
$709$	3.07037	+	2.23076i	0.115310	+	0.0837779i	−0.528636	+	0.848849i	$0.677296\pi$
$710$	−13.5911	−	2.10002i	−0.510066	−	0.0788122i
$711$	6.24252	+	2.02832i	0.234113	+	0.0760679i
$712$	3.82305	+	3.82305i	0.143275	+	0.143275i
$713$	1.52362	−	26.1119i	0.0570601	−	0.977899i
$714$		−	0.440254i		−	0.0164761i
$715$	5.13591	+	1.35539i	0.192072	+	0.0506886i
$716$	9.97572	−	46.9321i	0.372810	−	1.75393i
$717$	−20.5960	+	3.26209i	−0.769172	+	0.121825i
$718$	−10.9941	+	41.0304i	−0.410295	+	1.53124i
$719$	14.1714	−	24.5456i	0.528505	−	0.915397i	−0.470943	−	0.882164i	$-0.656086\pi$
$719$	14.1714	−	24.5456i	0.528505	−	0.915397i	0.999448	−	0.0332335i	$-0.0105805\pi$
$720$	−4.73143	+	14.7512i	−0.176330	+	0.549747i
$721$	−10.0165	+	7.27740i	−0.373033	+	0.271025i
$722$	−37.6705	+	14.4603i	−1.40195	+	0.538158i
$723$	4.52806	+	2.94056i	0.168400	+	0.109361i
$724$	−1.07507	+	10.2286i	−0.0399547	+	0.380144i
$725$	13.2907	−	14.9870i	0.493605	−	0.556605i
$726$	34.4633	+	31.0309i	1.27905	+	1.15166i
$727$	−13.3886	−	10.8419i	−0.496558	−	0.402104i	0.348062	−	0.937472i	$-0.386840\pi$
$727$	−13.3886	−	10.8419i	−0.496558	−	0.402104i	−0.844619	+	0.535367i	$0.820173\pi$
$728$	−0.851398	−	0.433809i	−0.0315549	−	0.0160780i
$729$	−7.53894	+	2.44955i	−0.279220	+	0.0907240i
$730$	6.73280	+	4.85291i	0.249192	+	0.179614i
$731$	0.357806	−	0.397384i	0.0132339	−	0.0146978i
$732$	10.2089	+	0.535025i	0.377331	+	0.0197751i
$733$	−28.4334	+	23.0249i	−1.05021	+	0.850443i	−0.989035	−	0.147684i	$-0.952818\pi$
$733$	−28.4334	+	23.0249i	−1.05021	+	0.850443i	−0.0611752	+	0.998127i	$0.519485\pi$
$734$	5.70688	−	1.21304i	0.210645	−	0.0447739i
$735$	2.87568	−	7.57683i	0.106071	−	0.279476i
$736$	−22.3359	−	30.7428i	−0.823314	−	1.13319i
$737$	43.2150	+	16.5887i	1.59184	+	0.611052i
$738$	43.5062	−	11.6574i	1.60148	−	0.429116i
$739$	6.50667	+	11.2699i	0.239352	+	0.414569i	0.960528	−	0.278182i	$-0.0897317\pi$
$739$	6.50667	+	11.2699i	0.239352	+	0.414569i	−0.721177	+	0.692751i	$0.756398\pi$
$740$	−20.6855	−	13.3225i	−0.760413	−	0.489743i
$741$	2.19543	+	0.466653i	0.0806512	+	0.0171429i
$742$	−21.4495	+	10.9291i	−0.787437	+	0.401219i
$743$	−34.0733	+	34.0733i	−1.25003	+	1.25003i	−0.294324	+	0.955706i	$0.595095\pi$
$743$	−34.0733	+	34.0733i	−1.25003	+	1.25003i	−0.955706	+	0.294324i	$0.904905\pi$
$744$	−3.17785	+	1.80972i	−0.116505	+	0.0663474i
$745$	7.82510	−	8.75697i	0.286690	−	0.320831i
$746$	−2.26149	+	6.96014i	−0.0827989	+	0.254829i
$747$	−14.6709	−	22.5913i	−0.536782	−	0.826571i
$748$	−0.153281	−	0.967776i	−0.00560449	−	0.0353854i
$749$	−23.5322	+	13.5863i	−0.859849	+	0.496434i
$750$	−19.2519	+	8.83431i	−0.702981	+	0.322584i
$751$	6.84947	−	3.04958i	0.249941	−	0.111281i	−0.277943	−	0.960598i	$-0.589653\pi$
$751$	6.84947	−	3.04958i	0.249941	−	0.111281i	0.527883	+	0.849317i	$0.322986\pi$
$752$	−1.83906	+	11.6114i	−0.0670636	+	0.423423i
$753$	−1.28672	−	3.35203i	−0.0468908	−	0.122155i
$754$	−0.692585	−	3.25836i	−0.0252225	−	0.118662i
$755$	32.6227	+	35.9570i	1.18726	+	1.30861i
$756$	27.1814	−	24.4743i	0.988580	−	0.890121i
$757$	−43.7461	+	2.29264i	−1.58998	+	0.0833273i	−0.826663	−	0.562697i	$-0.809764\pi$
$757$	−43.7461	+	2.29264i	−1.58998	+	0.0833273i	−0.763316	+	0.646025i	$0.776430\pi$
$758$	−29.2172	+	36.0802i	−1.06122	+	1.31049i
$759$	−7.85762	−	24.1833i	−0.285214	−	0.877797i
$760$	−3.62227	−	9.33081i	−0.131394	−	0.338464i
$761$	−1.82048	+	0.191340i	−0.0659924	+	0.00693608i	−0.137467	−	0.990506i	$-0.543896\pi$
$761$	−1.82048	+	0.191340i	−0.0659924	+	0.00693608i	0.0714747	+	0.997442i	$0.477229\pi$
$762$	0.976721	+	18.6369i	0.0353829	+	0.675145i
$763$	1.16190	−	22.1704i	0.0420636	−	0.802622i
$764$	3.10171	+	0.326003i	0.112216	+	0.0117944i
$765$	0.328859	−	0.0894506i	0.0118899	−	0.00323409i
$766$	26.3511	−	59.1855i	0.952103	−	2.13846i
$767$	−4.28086	−	0.678022i	−0.154573	−	0.0244819i
$768$	2.96630	−	7.72749i	0.107037	−	0.278842i
$769$	−12.1144	−	6.99424i	−0.436856	−	0.252219i	0.265407	−	0.964136i	$-0.414494\pi$
$769$	−12.1144	−	6.99424i	−0.436856	−	0.252219i	−0.702263	+	0.711918i	$0.747827\pi$
$770$	18.7972	−	90.1066i	0.677405	−	3.24722i
$771$	5.68884	−	7.83002i	0.204879	−	0.281991i
$772$	−18.0475	+	11.7202i	−0.649543	+	0.421818i
$773$	−11.7720	−	23.1039i	−0.423410	−	0.830988i	−0.999904	−	0.0138868i	$-0.995580\pi$
$773$	−11.7720	−	23.1039i	−0.423410	−	0.830988i	0.576494	−	0.817101i	$-0.304420\pi$
$774$	34.5775			1.24286
$775$	−26.4903	−	8.55943i	−0.951560	−	0.307464i
$776$	−7.83032			−0.281092
$777$	−6.41241	−	12.5851i	−0.230044	−	0.451486i
$778$	−32.4506	+	21.0737i	−1.16341	+	0.755528i
$779$	36.1702	−	49.7840i	1.29593	−	1.78370i
$780$	−0.388362	+	1.86166i	−0.0139056	+	0.0666580i
$781$	−15.2168	−	8.78541i	−0.544499	−	0.314367i
$782$	−0.246052	+	0.640988i	−0.00879881	+	0.0229217i
$783$	18.6054	+	2.94681i	0.664903	+	0.105310i
$784$	5.16903	−	11.6098i	0.184608	−	0.414637i
$785$	10.6917	−	2.90818i	0.381604	−	0.103797i
$786$	7.68286	+	0.807501i	0.274039	+	0.0288026i
$787$	−0.562227	+	10.7279i	−0.0200412	+	0.382410i	0.970133	+	0.242572i	$0.0779912\pi$
$787$	−0.562227	+	10.7279i	−0.0200412	+	0.382410i	−0.990175	+	0.139837i	$0.955342\pi$
$788$	2.73078	+	52.1063i	0.0972798	+	1.85621i
$789$	0.833737	−	0.0876292i	0.0296818	−	0.00311968i
$790$	5.09327	+	13.1200i	0.181210	+	0.466790i
$791$	−5.19230	−	15.9802i	−0.184617	−	0.568192i
$792$	5.89062	−	7.27431i	0.209314	−	0.258481i
$793$	1.90925	−	0.100060i	0.0677996	−	0.00355323i
$794$	−31.8777	+	28.7028i	−1.13130	+	1.01863i
$795$	4.75597	+	5.24207i	0.168677	+	0.185917i
$796$	0.381419	+	1.79443i	0.0135190	+	0.0636020i
$797$	6.68867	+	17.4246i	0.236925	+	0.617210i	0.999561	−	0.0296171i	$-0.00942880\pi$
$797$	6.68867	+	17.4246i	0.236925	+	0.617210i	−0.762637	+	0.646827i	$0.776095\pi$
$798$	6.08440	−	38.4154i	0.215385	−	1.35989i
$799$	0.236271	−	0.105195i	0.00835866	−	0.00372152i
$800$	−37.6476	+	14.7789i	−1.33104	+	0.522513i
$801$	−14.0846	+	8.13176i	−0.497656	+	0.287322i
$802$	−4.02382	−	25.4054i	−0.142086	−	0.897097i
$803$	5.77528	+	8.89315i	0.203805	+	0.313832i
$804$	−5.12126	+	15.7616i	−0.180613	+	0.555870i
$805$	−23.2022	+	25.9652i	−0.817768	+	0.915154i
$806$	−3.76140	+	2.69892i	−0.132490	+	0.0950655i
$807$	−11.0949	+	11.0949i	−0.390558	+	0.390558i
$808$	−5.62926	+	2.86825i	−0.198037	+	0.100905i
$809$	40.5581	+	8.62090i	1.42595	+	0.303095i	0.855314	−	0.518110i	$-0.173364\pi$
$809$	40.5581	+	8.62090i	1.42595	+	0.303095i	0.570634	+	0.821204i	$0.306697\pi$
$810$	8.81783	+	5.67912i	0.309827	+	0.199544i
$811$	−13.5781	−	23.5179i	−0.476791	−	0.825826i	0.522855	−	0.852422i	$-0.324867\pi$
$811$	−13.5781	−	23.5179i	−0.476791	−	0.825826i	−0.999646	+	0.0265951i	$0.991534\pi$
$812$	−30.1026	+	8.06596i	−1.05639	+	0.283060i
$813$	−11.9278	−	4.57864i	−0.418325	−	0.160580i
$814$	−34.2254	−	47.1072i	−1.19960	−	1.65111i
$815$	0.976082	−	2.57178i	0.0341907	−	0.0900856i
$816$	−0.198550	+	0.0422031i	−0.00695063	+	0.00147740i
$817$	36.7131	−	29.7297i	1.28443	−	1.04011i
$818$	15.9054	+	0.833567i	0.556119	+	0.0291450i
$819$	1.92332	−	2.13607i	0.0672064	−	0.0746403i
$820$	42.2972	+	30.4872i	1.47708	+	1.06466i
$821$	−15.1717	+	4.92959i	−0.529497	+	0.172044i	−0.561551	−	0.827442i	$-0.689795\pi$
$821$	−15.1717	+	4.92959i	−0.529497	+	0.172044i	0.0320542	+	0.999486i	$0.489795\pi$
$822$	16.5258	+	8.42034i	0.576405	+	0.293693i
$823$	9.23429	+	7.47778i	0.321887	+	0.260659i	0.776621	−	0.629968i	$-0.216932\pi$
$823$	9.23429	+	7.47778i	0.321887	+	0.260659i	−0.454734	+	0.890628i	$0.650266\pi$
$824$	−2.00621	−	1.80640i	−0.0698896	−	0.0629289i
$825$	−27.0148	+	1.62057i	−0.940536	+	0.0564209i
$826$	−7.85082	+	74.6956i	−0.273165	+	2.59899i
$827$	4.83027	+	3.13682i	0.167965	+	0.109078i	0.625884	−	0.779916i	$-0.284738\pi$
$827$	4.83027	+	3.13682i	0.167965	+	0.109078i	−0.457919	+	0.888994i	$0.651405\pi$
$828$	−22.3771	+	8.58975i	−0.777657	+	0.298515i
$829$	1.50573	−	1.09397i	0.0522960	−	0.0379953i	−0.561330	−	0.827592i	$-0.689710\pi$
$829$	1.50573	−	1.09397i	0.0522960	−	0.0379953i	0.613626	+	0.789597i	$0.289710\pi$
$830$	17.6405	−	54.9981i	0.612312	−	1.90901i
$831$	14.2540	−	24.6887i	0.494467	−	0.856442i
$832$	−1.08294	+	4.04160i	−0.0375443	+	0.140117i
$833$	−0.276142	+	0.0437366i	−0.00956775	+	0.00151538i
$834$	4.84123	−	22.7762i	0.167638	−	0.788675i
$835$	6.18458	+	1.63213i	0.214026	+	0.0564823i
$836$		−	86.5639i		−	2.99388i
$837$	−6.62582	−	25.3271i	−0.229022	−	0.875432i
$838$	44.6144	+	44.6144i	1.54118	+	1.54118i
$839$	7.27059	+	2.36236i	0.251009	+	0.0815577i	0.431819	−	0.901960i	$-0.357872\pi$
$839$	7.27059	+	2.36236i	0.251009	+	0.0815577i	−0.180810	+	0.983518i	$0.557872\pi$
$840$	4.81142	+	0.743431i	0.166010	+	0.0256508i
$841$	10.4766	+	7.61171i	0.361263	+	0.262473i
$842$	−40.1686	−	10.7632i	−1.38430	−	0.370923i
$843$	−5.30875	−	19.8125i	−0.182843	−	0.682379i
$844$	19.3373	+	43.4324i	0.665619	+	1.49500i
$845$	2.89344	−	28.5671i	0.0995373	−	0.982737i
$846$	15.2780	+	6.80221i	0.525269	+	0.233865i
$847$	44.1920	−	68.0497i	1.51846	−	2.33822i
$848$	6.98507	+	8.62584i	0.239868	+	0.296212i
$849$	−13.9915	−	15.5392i	−0.480188	−	0.533303i
$850$	0.594422	+	0.425048i	0.0203885	+	0.0145790i
$851$	2.30252	+	21.9071i	0.0789295	+	0.750964i
$852$	2.85595	−	5.60513i	0.0978434	−	0.192028i
$853$	18.8096	−	36.9159i	0.644028	−	1.26398i	−0.306065	−	0.952011i	$-0.599013\pi$
$853$	18.8096	−	36.9159i	0.644028	−	1.26398i	0.950093	−	0.311966i	$-0.100987\pi$
$854$	−3.46309	−	32.9491i	−0.118504	−	1.12749i
$855$	29.9316	−	3.26032i	1.02364	−	0.111501i
$856$	−3.96450	−	4.40302i	−0.135504	−	0.150492i
$857$	−30.7259	−	37.9434i	−1.04958	−	1.29612i	−0.953710	−	0.300727i	$-0.902771\pi$
$857$	−30.7259	−	37.9434i	−1.04958	−	1.29612i	−0.0958680	−	0.995394i	$-0.530563\pi$
$858$	−2.45118	+	3.77449i	−0.0836819	+	0.128859i
$859$	15.1802	+	6.75865i	0.517941	+	0.230602i	0.649022	−	0.760769i	$-0.275178\pi$
$859$	15.1802	+	6.75865i	0.517941	+	0.230602i	−0.131081	+	0.991372i	$0.541845\pi$
$860$	25.3072	+	31.0114i	0.862967	+	1.05748i
$861$	12.1742	+	27.3437i	0.414896	+	0.931872i
$862$	4.49406	+	16.7721i	0.153068	+	0.571259i
$863$	−29.0545	−	7.78514i	−0.989028	−	0.265009i	−0.272186	−	0.962245i	$-0.587746\pi$
$863$	−29.0545	−	7.78514i	−0.989028	−	0.265009i	−0.716842	+	0.697236i	$0.754413\pi$
$864$	−30.7699	−	22.3557i	−1.04681	−	0.760555i
$865$	−0.0155452	+	0.100607i	−0.000528552	+	0.00342074i
$866$	−70.3388	−	22.8544i	−2.39021	−	0.776626i
$867$	−10.9205	−	10.9205i	−0.370881	−	0.370881i
$868$	27.0568	+	33.8200i	0.918367	+	1.14793i
$869$			17.9817i			0.609986i
$870$	8.54160	+	14.6662i	0.289587	+	0.497232i
$871$	−0.644405	+	3.03169i	−0.0218348	+	0.102725i
$872$	4.78117	−	0.757263i	0.161911	−	0.0256442i
$873$	6.09630	−	22.7517i	0.206328	−	0.770028i
$874$	−30.3285	+	52.5304i	−1.02588	+	1.77687i
$875$	20.5360	+	30.8514i	0.694244	+	1.04297i
$876$	−3.07138	+	2.23149i	−0.103772	+	0.0753951i
$877$	−3.52437	+	1.35288i	−0.119009	+	0.0456835i	−0.417144	−	0.908840i	$-0.636969\pi$
$877$	−3.52437	+	1.35288i	−0.119009	+	0.0456835i	0.298135	+	0.954524i	$0.403636\pi$
$878$	−35.6934	−	23.1796i	−1.20459	−	0.782272i
$879$	0.220719	−	2.10000i	0.00744467	−	0.0708313i
$880$	−42.4391	+	0.160343i	−1.43062	+	0.00540516i
$881$	15.0056	+	13.5111i	0.505550	+	0.455199i	0.882008	−	0.471234i	$-0.156191\pi$
$881$	15.0056	+	13.5111i	0.505550	+	0.455199i	−0.376458	+	0.926434i	$0.622858\pi$
$882$	−14.0499	−	11.3774i	−0.473083	−	0.383095i
$883$	−8.14486	−	4.15001i	−0.274096	−	0.139659i	0.311540	−	0.950233i	$-0.399155\pi$
$883$	−8.14486	−	4.15001i	−0.274096	−	0.139659i	−0.585636	+	0.810574i	$0.699155\pi$
$884$	0.0623963	−	0.0202738i	0.00209861	−	0.000681881i
$885$	21.7978	−	3.53691i	0.732726	−	0.118892i
$886$	−16.1397	+	17.9249i	−0.542223	+	0.602200i
$887$	−25.0758	−	1.31417i	−0.841962	−	0.0441253i	−0.373523	−	0.927621i	$-0.621850\pi$
$887$	−25.0758	−	1.31417i	−0.841962	−	0.0441253i	−0.468439	+	0.883496i	$0.655183\pi$
$888$	2.39344	−	1.93817i	0.0803185	−	0.0650407i
$889$	31.9393	−	6.78892i	1.07121	−	0.227693i
$890$	−32.6028	−	12.3739i	−1.09285	−	0.414775i
$891$	7.87664	+	10.8413i	0.263877	+	0.363196i
$892$	54.3093	+	20.8474i	1.81841	+	0.698023i
$893$	22.0702	−	5.91369i	0.738551	−	0.197894i
$894$	4.97517	+	8.61724i	0.166395	+	0.288204i
$895$	9.67439	+	44.6836i	0.323379	+	1.49361i
$896$	18.4670	+	3.92529i	0.616940	+	0.131135i
$897$	1.51701	−	0.772953i	0.0506513	−	0.0258082i
$898$	−61.9404	+	61.9404i	−2.06698	+	2.06698i
$899$	−4.76684	+	21.7907i	−0.158983	+	0.726760i
$900$	2.85825	+	25.3503i	0.0952750	+	0.845009i
$901$	0.0754567	−	0.232232i	0.00251383	−	0.00773676i
$902$	67.2035	+	103.484i	2.23763	+	3.44565i
$903$	3.59457	+	22.6952i	0.119620	+	0.755250i
$904$	3.17288	−	1.83186i	0.105528	−	0.0609268i
$905$	−3.06361	−	9.30901i	−0.101838	−	0.309442i
$906$	−37.5796	+	16.7315i	−1.24850	+	0.555868i
$907$	−4.92367	+	31.0868i	−0.163488	+	1.03222i	0.760372	+	0.649488i	$0.225017\pi$
$907$	−4.92367	+	31.0868i	−0.163488	+	1.03222i	−0.923859	+	0.382732i	$0.874983\pi$
$908$	−13.9682	−	36.3884i	−0.463551	−	1.20759i
$909$	−3.95130	−	18.5894i	−0.131056	−	0.616571i
$910$	6.15590	+	0.299300i	0.204066	+	0.00992169i
$911$	−12.0601	+	10.8590i	−0.399570	+	0.359774i	−0.844282	−	0.535899i	$-0.819973\pi$
$911$	−12.0601	+	10.8590i	−0.399570	+	0.359774i	0.444712	+	0.895674i	$0.353306\pi$
$912$	−17.9082	+	0.938528i	−0.592999	+	0.0310778i
$913$	46.4405	−	57.3493i	1.53696	−	1.89798i
$914$	1.54347	+	4.75030i	0.0510533	+	0.157126i
$915$	−9.08078	+	3.52521i	−0.300201	+	0.116540i
$916$	29.0193	−	3.05005i	0.958825	−	0.100777i
$917$	−0.707392	−	13.4978i	−0.0233601	−	0.445738i
$918$	−0.0359651	+	0.686255i	−0.00118703	+	0.0226498i
$919$	4.56590	+	0.479896i	0.150615	+	0.0158303i	0.179536	−	0.983751i	$-0.442540\pi$
$919$	4.56590	+	0.479896i	0.150615	+	0.0158303i	−0.0289207	+	0.999582i	$0.509207\pi$
$920$	−6.58970	−	3.77144i	−0.217256	−	0.124341i
$921$	−2.80645	+	6.30340i	−0.0924758	+	0.207704i
$922$	−19.9645	−	3.16206i	−0.657494	−	0.104137i
$923$	0.421618	−	1.09835i	0.0138777	−	0.0361527i
$924$	36.4639	+	21.0524i	1.19957	+	0.692574i
$925$	23.1830	+	3.49247i	0.762254	+	0.114832i
$926$	27.3897	−	37.6986i	0.900080	−	1.23885i
$927$	6.81059	−	4.42285i	0.223689	−	0.145265i
$928$	14.7122	+	28.8742i	0.482950	+	0.947843i
$929$	29.3461			0.962815			0.481408	−	0.876497i	$-0.340126\pi$
$929$	29.3461			0.962815			0.481408	+	0.876497i	$0.340126\pi$
$930$	13.9052	−	19.0528i	0.455971	−	0.624766i
$931$	−24.6999			−0.809505
$932$	−3.29354	−	6.46393i	−0.107883	−	0.211733i
$933$	4.90982	−	3.18847i	0.160740	−	0.104386i
$934$	43.5180	−	59.8974i	1.42395	−	1.95990i
$935$	0.511459	+	0.781100i	0.0167265	+	0.0255447i
$936$	0.542772	+	0.313370i	0.0177411	+	0.0102428i
$937$	−8.87692	+	23.1252i	−0.289996	+	0.755467i	0.708752	+	0.705457i	$0.249258\pi$
$937$	−8.87692	+	23.1252i	−0.289996	+	0.755467i	−0.998749	+	0.0500091i	$0.984075\pi$
$938$	53.0481	+	8.40199i	1.73208	+	0.274335i
$939$	6.83589	−	15.3537i	0.223081	−	0.501048i
$940$	5.08125	+	18.6809i	0.165732	+	0.609303i
$941$	−14.8456	−	1.56034i	−0.483953	−	0.0508655i	−0.140589	−	0.990068i	$-0.544900\pi$
$941$	−14.8456	−	1.56034i	−0.483953	−	0.0508655i	−0.343364	+	0.939202i	$0.611566\pi$
$942$	−0.491334	+	9.37521i	−0.0160085	+	0.305461i
$943$	−2.44300	−	46.6152i	−0.0795550	−	1.51800i
$944$	34.4395	−	3.61974i	1.12091	−	0.117812i
$945$	−14.0553	+	31.8924i	−0.457218	+	1.03746i
$946$	29.2720	+	90.0900i	0.951715	+	2.92908i
$947$	9.52417	−	11.7614i	0.309494	−	0.382193i	−0.598538	−	0.801094i	$-0.704251\pi$
$947$	9.52417	−	11.7614i	0.309494	−	0.382193i	0.908032	+	0.418901i	$0.137585\pi$
$948$	−6.42905	+	0.336932i	−0.208806	+	0.0109430i
$949$	−0.527637	+	0.475087i	−0.0171278	+	0.0154220i
$950$	45.9935	+	45.3036i	1.49223	+	1.46984i
$951$	−0.921855	−	4.33699i	−0.0298932	−	0.140636i
$952$	−0.0601906	−	0.156802i	−0.00195079	−	0.00508198i
$953$	−6.49252	+	40.9922i	−0.210313	+	1.32787i	0.626089	+	0.779751i	$0.284655\pi$
$953$	−6.49252	+	40.9922i	−0.210313	+	1.32787i	−0.836403	+	0.548115i	$0.815345\pi$
$954$	14.4246	−	6.42223i	0.467012	−	0.207927i
$955$	−2.82285	+	0.929006i	−0.0913453	+	0.0300619i
$956$	−46.6351	+	26.9248i	−1.50829	+	0.870809i
$957$	3.39223	+	21.4177i	0.109655	+	0.692336i
$958$	−9.70629	−	14.9464i	−0.313596	−	0.482896i
$959$	10.0281	−	30.8632i	0.323823	−	0.996624i
$960$	−1.19614	−	21.2848i	−0.0386054	−	0.686964i
$961$	30.3968	−	6.08557i	0.980542	−	0.196309i
$962$	2.75685	−	2.75685i	0.0888843	−	0.0888843i
$963$	15.8799	−	8.09123i	0.511724	−	0.260736i
$964$	13.6378	+	2.89881i	0.439244	+	0.0933642i
$965$	11.1027	−	17.2389i	0.357408	−	0.554939i
$966$	−14.7518	−	25.5509i	−0.474632	−	0.822087i
$967$	−52.2097	+	13.9896i	−1.67895	+	0.449874i	−0.967502	−	0.252863i	$-0.918628\pi$
$967$	−52.2097	+	13.9896i	−1.67895	+	0.449874i	−0.711450	+	0.702737i	$0.751961\pi$
$968$	16.5170	+	6.34029i	0.530878	+	0.203785i
$969$	0.231890	+	0.319169i	0.00744939	+	0.0102532i
$970$	46.0605	−	20.7163i	1.47891	−	0.665161i
$971$	−35.6230	+	7.57190i	−1.14320	+	0.242994i	−0.740316	−	0.672259i	$-0.765324\pi$
$971$	−35.6230	+	7.57190i	−1.14320	+	0.242994i	−0.402880	+	0.915253i	$0.631991\pi$
$972$	−29.4536	+	23.8511i	−0.944726	+	0.765024i
$973$	−40.6848	−	2.13220i	−1.30430	−	0.0683552i
$974$	−21.6561	+	24.0515i	−0.693906	+	0.770661i
$975$	−0.390138	−	1.76960i	−0.0124944	−	0.0566724i
$976$	−14.5277	+	4.72034i	−0.465021	+	0.151094i
$977$	−41.7069	−	21.2507i	−1.33432	−	0.679870i	−0.366243	−	0.930519i	$-0.619356\pi$
$977$	−41.7069	−	21.2507i	−1.33432	−	0.679870i	−0.968078	+	0.250649i	$0.919356\pi$
$978$	1.81129	+	1.46675i	0.0579186	+	0.0469016i
$979$	−33.1104	−	29.8127i	−1.05821	−	0.952819i
$980$	−0.0790696	−	20.9279i	−0.00252579	−	0.668517i
$981$	−1.52209	+	14.4817i	−0.0485965	+	0.462365i
$982$	−32.3636	−	21.0171i	−1.03276	−	0.670684i
$983$	−44.1734	+	16.9566i	−1.40891	+	0.540830i	−0.939622	−	0.342214i	$-0.888823\pi$
$983$	−44.1734	+	16.9566i	−1.40891	+	0.540830i	−0.469289	+	0.883044i	$0.655490\pi$
$984$	−5.27996	+	3.83612i	−0.168319	+	0.122291i
$985$	−22.7389	−	44.2138i	−0.724520	−	1.40877i
$986$	0.292760	−	0.507076i	0.00932339	−	0.0161486i
$987$	−2.87643	+	10.7350i	−0.0915578	+	0.341698i
$988$	5.72472	−	0.906707i	0.182128	−	0.0288462i
$989$	7.45056	−	35.0521i	0.236914	−	1.11459i
$990$	−15.4052	+	58.3744i	−0.489610	+	1.85526i
$991$			7.44500i			0.236498i	0.992984	+	0.118249i	$0.0377281\pi$
$991$			7.44500i			0.236498i	−0.992984	+	0.118249i	$0.962272\pi$
$992$	28.5496	−	34.8319i	0.906451	−	1.10591i
$993$	2.87692	+	2.87692i	0.0912962	+	0.0912962i
$994$	−19.3895	−	6.30002i	−0.614996	−	0.199824i
$995$	−1.03281	−	1.41031i	−0.0327424	−	0.0447098i
$996$	21.3745	+	15.5295i	0.677276	+	0.492070i
$997$	18.7101	+	5.01336i	0.592556	+	0.158775i	0.542621	−	0.839978i	$-0.317432\pi$
$997$	18.7101	+	5.01336i	0.592556	+	0.158775i	0.0499346	+	0.998752i	$0.484099\pi$
$998$	−6.31140	−	23.5545i	−0.199784	−	0.745604i
$999$	8.96739	+	20.1411i	0.283716	+	0.637236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.x.a.53.3	yes	224
5.2	odd	4	inner	155.2.x.a.22.12	✓	224
5.3	odd	4		775.2.df.b.332.3		224
5.4	even	2		775.2.df.b.518.12		224
31.24	odd	30	inner	155.2.x.a.148.12	yes	224
155.24	odd	30		775.2.df.b.768.3		224
155.117	even	60	inner	155.2.x.a.117.3	yes	224
155.148	even	60		775.2.df.b.582.12		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.x.a.22.12	✓	224	5.2	odd	4	inner
155.2.x.a.53.3	yes	224	1.1	even	1	trivial
155.2.x.a.117.3	yes	224	155.117	even	60	inner
155.2.x.a.148.12	yes	224	31.24	odd	30	inner
775.2.df.b.332.3		224	5.3	odd	4
775.2.df.b.518.12		224	5.4	even	2
775.2.df.b.582.12		224	155.148	even	60
775.2.df.b.768.3		224	155.24	odd	30

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:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.946511 - 1.85763i) q^{2} +(-0.762126 + 0.494930i) q^{3} +(-1.37935 + 1.89851i) q^{4} +(0.456638 - 2.18895i) q^{5} +(1.64076 + 0.947293i) q^{6} +(1.18794 - 3.09469i) q^{7} +(0.713889 + 0.113069i) q^{8} +(-0.884330 + 1.98624i) q^{9} +O(q^{10})\)	\(q+(-0.946511 - 1.85763i) q^{2} +(-0.762126 + 0.494930i) q^{3} +(-1.37935 + 1.89851i) q^{4} +(0.456638 - 2.18895i) q^{5} +(1.64076 + 0.947293i) q^{6} +(1.18794 - 3.09469i) q^{7} +(0.713889 + 0.113069i) q^{8} +(-0.884330 + 1.98624i) q^{9} +(-4.49847 + 1.22360i) q^{10} +(-5.92368 - 0.622604i) q^{11} +(0.111607 - 2.12958i) q^{12} +(-0.0208725 - 0.398272i) q^{13} +(-6.87320 + 0.722402i) q^{14} +(0.735360 + 1.89426i) q^{15} +(0.984666 + 3.03049i) q^{16} +(0.0441159 - 0.0544786i) q^{17} +(4.52673 - 0.237236i) q^{18} +(4.60234 - 4.14397i) q^{19} +(3.52586 + 3.88624i) q^{20} +(0.626296 + 2.94649i) q^{21} +(4.45026 + 11.5933i) q^{22} +(0.734900 - 4.63998i) q^{23} +(-0.600035 + 0.267153i) q^{24} +(-4.58296 - 1.99911i) q^{25} +(-0.720086 + 0.415742i) q^{26} +(-0.735549 - 4.64407i) q^{27} +(4.23671 + 6.52396i) q^{28} +(-1.23801 + 3.81019i) q^{29} +(2.82280 - 3.15896i) q^{30} +(5.54061 - 0.549179i) q^{31} +(5.71972 - 5.71972i) q^{32} +(4.82274 - 2.45731i) q^{33} +(-0.142957 - 0.0303865i) q^{34} +(-6.23165 - 4.01349i) q^{35} +(-2.55109 - 4.41861i) q^{36} +(-4.52916 + 1.21358i) q^{37} +(-12.0541 - 4.62715i) q^{38} +(0.213024 + 0.293203i) q^{39} +(0.573491 - 1.51103i) q^{40} +(9.71922 - 2.06588i) q^{41} +(4.88070 - 3.95232i) q^{42} +(7.61760 + 0.399222i) q^{43} +(9.35282 - 10.3874i) q^{44} +(3.94395 + 2.84274i) q^{45} +(-9.31497 + 3.02662i) q^{46} +(3.28729 + 1.67496i) q^{47} +(-2.25032 - 1.82227i) q^{48} +(-2.96390 - 2.66870i) q^{49} +(0.624214 + 10.4056i) q^{50} +(-0.00665875 + 0.0633538i) q^{51} +(0.784912 + 0.509728i) q^{52} +(3.25195 - 1.24831i) q^{53} +(-7.93078 + 5.76205i) q^{54} +(-4.06782 + 12.6823i) q^{55} +(1.19797 - 2.07495i) q^{56} +(-1.45659 + 5.43606i) q^{57} +(8.24972 - 1.30663i) q^{58} +(2.25951 - 10.6302i) q^{59} +(-4.61057 - 1.21675i) q^{60} +4.79385i q^{61} +(-6.26443 - 9.77262i) q^{62} +(5.09626 + 5.09626i) q^{63} +(-9.97793 - 3.24203i) q^{64} +(-0.881326 - 0.136177i) q^{65} +(-9.12955 - 6.63300i) q^{66} +(-7.50670 - 2.01141i) q^{67} +(0.0425769 + 0.158899i) q^{68} +(1.73638 + 3.89997i) q^{69} +(-1.55726 + 15.3749i) q^{70} +(2.69492 + 1.19985i) q^{71} +(-0.855896 + 1.31796i) q^{72} +(-1.12036 - 1.38353i) q^{73} +(6.54129 + 7.26484i) q^{74} +(4.48222 - 0.744674i) q^{75} +(1.51913 + 14.4535i) q^{76} +(-8.96375 + 17.5923i) q^{77} +(0.343033 - 0.673240i) q^{78} +(-0.315564 - 3.00239i) q^{79} +(7.08321 - 0.771544i) q^{80} +(-1.50541 - 1.67193i) q^{81} +(-13.0370 - 16.0994i) q^{82} +(-6.74771 + 10.3906i) q^{83} +(-6.45781 - 2.87520i) q^{84} +(-0.0991056 - 0.121444i) q^{85} +(-6.46854 - 14.5286i) q^{86} +(-0.942262 - 3.51657i) q^{87} +(-4.15846 - 1.11425i) q^{88} +(6.05161 + 4.39675i) q^{89} +(1.54778 - 10.0171i) q^{90} +(-1.25732 - 0.408529i) q^{91} +(7.79535 + 7.79535i) q^{92} +(-3.95084 + 3.16076i) q^{93} -7.69194i q^{94} +(-6.96931 - 11.9666i) q^{95} +(-1.52828 + 7.19001i) q^{96} +(-10.7001 + 1.69473i) q^{97} +(-2.15211 + 8.03179i) q^{98} +(6.47513 - 11.2153i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8}+O(q^{10}) \) 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8	\( 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8} - 10 q^{10} - 28 q^{11} - 40 q^{12} - 14 q^{13} - 20 q^{15} + 24 q^{16} - 14 q^{17} - 40 q^{18} - 44 q^{20} - 44 q^{21} + 30 q^{22} - 30 q^{23} - 22 q^{25} - 48 q^{26} + 100 q^{27} - 48 q^{28} - 44 q^{31} + 28 q^{32} + 20 q^{33} - 72 q^{35} + 16 q^{36} + 30 q^{37} + 38 q^{38} - 4 q^{40} - 20 q^{41} - 130 q^{42} + 22 q^{43} - 34 q^{45} - 28 q^{47} - 156 q^{48} + 158 q^{50} - 36 q^{51} - 10 q^{52} + 26 q^{53} + 98 q^{55} - 48 q^{56} - 20 q^{58} + 260 q^{60} + 30 q^{62} + 152 q^{63} + 32 q^{65} - 152 q^{66} + 38 q^{67} - 126 q^{68} + 166 q^{70} - 128 q^{71} - 156 q^{72} - 30 q^{73} + 26 q^{75} + 128 q^{76} + 30 q^{78} + 154 q^{80} - 64 q^{81} + 8 q^{82} - 82 q^{83} + 60 q^{85} - 28 q^{86} - 24 q^{87} + 252 q^{88} + 38 q^{90} + 194 q^{93} - 74 q^{95} + 60 q^{96} - 38 q^{97} + 174 q^{98}+O(q^{100}) \) 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8 - 10 * q^10 - 28 * q^11 - 40 * q^12 - 14 * q^13 - 20 * q^15 + 24 * q^16 - 14 * q^17 - 40 * q^18 - 44 * q^20 - 44 * q^21 + 30 * q^22 - 30 * q^23 - 22 * q^25 - 48 * q^26 + 100 * q^27 - 48 * q^28 - 44 * q^31 + 28 * q^32 + 20 * q^33 - 72 * q^35 + 16 * q^36 + 30 * q^37 + 38 * q^38 - 4 * q^40 - 20 * q^41 - 130 * q^42 + 22 * q^43 - 34 * q^45 - 28 * q^47 - 156 * q^48 + 158 * q^50 - 36 * q^51 - 10 * q^52 + 26 * q^53 + 98 * q^55 - 48 * q^56 - 20 * q^58 + 260 * q^60 + 30 * q^62 + 152 * q^63 + 32 * q^65 - 152 * q^66 + 38 * q^67 - 126 * q^68 + 166 * q^70 - 128 * q^71 - 156 * q^72 - 30 * q^73 + 26 * q^75 + 128 * q^76 + 30 * q^78 + 154 * q^80 - 64 * q^81 + 8 * q^82 - 82 * q^83 + 60 * q^85 - 28 * q^86 - 24 * q^87 + 252 * q^88 + 38 * q^90 + 194 * q^93 - 74 * q^95 + 60 * q^96 - 38 * q^97 + 174 * q^98

Introduction

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