LMFDB - Embedded newform 473.2.r.a.144.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [473,2,Mod(23,473)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(473, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("473.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 473 = 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	473.r (of order $21$, degree $12$, 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:	$3.77692401561$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			144.9
Character	$\chi$	$=$	473.144
Dual form			473.2.r.a.23.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.182040 - 0.228271i) q^{2} +(0.878059 - 2.23726i) q^{3} +(0.426073 + 1.86675i) q^{4} +(0.135358 + 1.80623i) q^{5} +(-0.350859 - 0.607706i) q^{6} +(-1.86992 + 3.23880i) q^{7} +(1.02980 + 0.495924i) q^{8} +(-2.03518 - 1.88837i) q^{9} +O(q^{10})$	\(q+(0.182040 - 0.228271i) q^{2} +(0.878059 - 2.23726i) q^{3} +(0.426073 + 1.86675i) q^{4} +(0.135358 + 1.80623i) q^{5} +(-0.350859 - 0.607706i) q^{6} +(-1.86992 + 3.23880i) q^{7} +(1.02980 + 0.495924i) q^{8} +(-2.03518 - 1.88837i) q^{9} +(0.436949 + 0.297907i) q^{10} +(-0.222521 + 0.974928i) q^{11} +(4.55051 + 0.685879i) q^{12} +(5.89166 - 4.01686i) q^{13} +(0.398923 + 1.01644i) q^{14} +(4.15984 + 1.28314i) q^{15} +(-3.14960 + 1.51677i) q^{16} +(-0.313558 + 4.18415i) q^{17} +(-0.801543 + 0.120813i) q^{18} +(-4.45026 + 4.12924i) q^{19} +(-3.31409 + 1.02226i) q^{20} +(5.60412 + 7.02735i) q^{21} +(0.182040 + 0.228271i) q^{22} +(4.81489 - 1.48520i) q^{23} +(2.01373 - 1.86847i) q^{24} +(1.70003 - 0.256238i) q^{25} +(0.155584 - 2.07612i) q^{26} +(0.484381 - 0.233265i) q^{27} +(-6.84274 - 2.11070i) q^{28} +(-1.15749 - 2.94922i) q^{29} +(1.05016 - 0.715988i) q^{30} +(-0.439561 - 0.0662532i) q^{31} +(-0.735797 + 3.22374i) q^{32} +(1.98578 + 1.35388i) q^{33} +(0.898039 + 0.833258i) q^{34} +(-6.10310 - 2.93910i) q^{35} +(2.65797 - 4.60374i) q^{36} +(-2.71780 - 4.70737i) q^{37} +(0.132460 + 1.76755i) q^{38} +(-3.81354 - 16.7082i) q^{39} +(-0.756360 + 1.92717i) q^{40} +(4.46857 - 5.60341i) q^{41} +2.62431 q^{42} +(-2.56713 - 6.03406i) q^{43} -1.91475 q^{44} +(3.13534 - 3.93159i) q^{45} +(0.537476 - 1.36947i) q^{46} +(0.978553 + 4.28732i) q^{47} +(0.627865 + 8.37827i) q^{48} +(-3.49320 - 6.05040i) q^{49} +(0.250981 - 0.434712i) q^{50} +(9.08569 + 4.37544i) q^{51} +(10.0087 + 9.28676i) q^{52} +(-4.29003 - 2.92489i) q^{53} +(0.0349289 - 0.153034i) q^{54} +(-1.79106 - 0.269959i) q^{55} +(-3.53184 + 2.40796i) q^{56} +(5.33058 + 13.5821i) q^{57} +(-0.883931 - 0.272656i) q^{58} +(12.8429 - 6.18480i) q^{59} +(-0.622905 + 8.31208i) q^{60} +(-13.4614 + 2.02898i) q^{61} +(-0.0951414 + 0.0882783i) q^{62} +(9.92166 - 3.06043i) q^{63} +(-3.75724 - 4.71143i) q^{64} +(8.05284 + 10.0979i) q^{65} +(0.670543 - 0.206835i) q^{66} +(-2.56145 + 2.37668i) q^{67} +(-7.94434 + 1.19742i) q^{68} +(0.904989 - 12.0762i) q^{69} +(-1.78192 + 0.858127i) q^{70} +(-3.39138 - 1.04610i) q^{71} +(-1.15933 - 2.95393i) q^{72} +(4.18989 - 2.85662i) q^{73} +(-1.56930 - 0.236535i) q^{74} +(0.919453 - 4.02839i) q^{75} +(-9.60438 - 6.54816i) q^{76} +(-2.74150 - 2.54374i) q^{77} +(-4.50821 - 2.17104i) q^{78} +(-4.91076 + 8.50568i) q^{79} +(-3.16594 - 5.48358i) q^{80} +(-0.718981 - 9.59414i) q^{81} +(-0.465637 - 2.04009i) q^{82} +(-4.32295 + 11.0147i) q^{83} +(-10.7305 + 13.4556i) q^{84} -7.59995 q^{85} +(-1.84472 - 0.512437i) q^{86} -7.61451 q^{87} +(-0.712642 + 0.893624i) q^{88} +(1.45769 - 3.71412i) q^{89} +(-0.326711 - 1.43141i) q^{90} +(1.99288 + 26.5931i) q^{91} +(4.82398 + 8.35538i) q^{92} +(-0.534186 + 0.925237i) q^{93} +(1.15681 + 0.557088i) q^{94} +(-8.06071 - 7.47925i) q^{95} +(6.56626 + 4.47680i) q^{96} +(2.73216 - 11.9704i) q^{97} +(-2.01703 - 0.304019i) q^{98} +(2.29389 - 1.56395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 2 q^{2} + 3 q^{3} - 44 q^{4} + 6 q^{5} - 2 q^{6} - 23 q^{7} - 6 q^{8} + q^{9}+O(q^{10}) $ 216 * q - 2 * q^2 + 3 * q^3 - 44 * q^4 + 6 * q^5 - 2 * q^6 - 23 * q^7 - 6 * q^8 + q^9	\( 216 q - 2 q^{2} + 3 q^{3} - 44 q^{4} + 6 q^{5} - 2 q^{6} - 23 q^{7} - 6 q^{8} + q^{9} - 40 q^{10} - 36 q^{11} - 32 q^{12} - 9 q^{13} + 6 q^{14} - 32 q^{16} - 21 q^{18} - 4 q^{19} + 168 q^{20} + 76 q^{21} - 2 q^{22} - 13 q^{23} - 6 q^{24} + 2 q^{25} - 13 q^{26} - 12 q^{27} + 18 q^{28} - 23 q^{29} - 150 q^{30} - 51 q^{31} - 54 q^{32} + 3 q^{33} + 30 q^{34} - 28 q^{35} - 74 q^{36} - 115 q^{37} + 28 q^{38} + 21 q^{39} - q^{40} + 36 q^{41} + 80 q^{42} + 44 q^{43} + 208 q^{44} - 22 q^{45} + 84 q^{46} + 14 q^{47} + 29 q^{48} - 99 q^{49} + 23 q^{50} - 72 q^{51} - 9 q^{52} - 47 q^{53} + 58 q^{54} + 6 q^{55} - 156 q^{56} - 52 q^{57} - 45 q^{58} + 14 q^{59} - 78 q^{60} + 25 q^{61} + 19 q^{62} + 203 q^{63} + 82 q^{64} + 46 q^{65} - 2 q^{66} - 31 q^{67} - 12 q^{68} + 2 q^{69} - 36 q^{70} + 51 q^{71} + 56 q^{72} - 51 q^{73} - 25 q^{74} + 4 q^{75} + 69 q^{76} + 5 q^{77} - 182 q^{78} + 43 q^{79} - 149 q^{80} - 152 q^{81} + 16 q^{82} + 127 q^{83} + 331 q^{84} + 298 q^{85} + 73 q^{86} - 210 q^{87} - 6 q^{88} + 52 q^{89} - 26 q^{90} + 19 q^{91} + 28 q^{92} - 75 q^{93} + 47 q^{94} + 13 q^{95} - 345 q^{96} - 51 q^{97} - 115 q^{98} + 15 q^{99}+O(q^{100}) \) 216 * q - 2 * q^2 + 3 * q^3 - 44 * q^4 + 6 * q^5 - 2 * q^6 - 23 * q^7 - 6 * q^8 + q^9 - 40 * q^10 - 36 * q^11 - 32 * q^12 - 9 * q^13 + 6 * q^14 - 32 * q^16 - 21 * q^18 - 4 * q^19 + 168 * q^20 + 76 * q^21 - 2 * q^22 - 13 * q^23 - 6 * q^24 + 2 * q^25 - 13 * q^26 - 12 * q^27 + 18 * q^28 - 23 * q^29 - 150 * q^30 - 51 * q^31 - 54 * q^32 + 3 * q^33 + 30 * q^34 - 28 * q^35 - 74 * q^36 - 115 * q^37 + 28 * q^38 + 21 * q^39 - q^40 + 36 * q^41 + 80 * q^42 + 44 * q^43 + 208 * q^44 - 22 * q^45 + 84 * q^46 + 14 * q^47 + 29 * q^48 - 99 * q^49 + 23 * q^50 - 72 * q^51 - 9 * q^52 - 47 * q^53 + 58 * q^54 + 6 * q^55 - 156 * q^56 - 52 * q^57 - 45 * q^58 + 14 * q^59 - 78 * q^60 + 25 * q^61 + 19 * q^62 + 203 * q^63 + 82 * q^64 + 46 * q^65 - 2 * q^66 - 31 * q^67 - 12 * q^68 + 2 * q^69 - 36 * q^70 + 51 * q^71 + 56 * q^72 - 51 * q^73 - 25 * q^74 + 4 * q^75 + 69 * q^76 + 5 * q^77 - 182 * q^78 + 43 * q^79 - 149 * q^80 - 152 * q^81 + 16 * q^82 + 127 * q^83 + 331 * q^84 + 298 * q^85 + 73 * q^86 - 210 * q^87 - 6 * q^88 + 52 * q^89 - 26 * q^90 + 19 * q^91 + 28 * q^92 - 75 * q^93 + 47 * q^94 + 13 * q^95 - 345 * q^96 - 51 * q^97 - 115 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/473\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$e\left(\frac{13}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	0.182040	−	0.228271i	0.128722	−	0.161412i	−0.713294	−	0.700865i	$-0.752798\pi$
$2$	0.182040	−	0.228271i	0.128722	−	0.161412i	0.842016	+	0.539453i	$0.181369\pi$
$3$	0.878059	−	2.23726i	0.506947	−	1.29168i	−0.416911	−	0.908947i	$-0.636887\pi$
$3$	0.878059	−	2.23726i	0.506947	−	1.29168i	0.923859	−	0.382734i	$-0.125017\pi$
$4$	0.426073	+	1.86675i	0.213036	+	0.933373i
$5$	0.135358	+	1.80623i	0.0605339	+	0.807768i	0.942020	+	0.335558i	$0.108925\pi$
$5$	0.135358	+	1.80623i	0.0605339	+	0.807768i	−0.881486	+	0.472211i	$0.843456\pi$
$6$	−0.350859	−	0.607706i	−0.143238	−	0.248095i
$7$	−1.86992	+	3.23880i	−0.706763	+	1.22415i	0.259288	+	0.965800i	$0.416512\pi$
$7$	−1.86992	+	3.23880i	−0.706763	+	1.22415i	−0.966051	+	0.258350i	$0.916821\pi$
$8$	1.02980	+	0.495924i	0.364088	+	0.175336i
$9$	−2.03518	−	1.88837i	−0.678392	−	0.629456i
$10$	0.436949	+	0.297907i	0.138175	+	0.0942064i
$11$	−0.222521	+	0.974928i	−0.0670926	+	0.293952i
$11$	−0.222521	+	0.974928i	−0.0670926	+	0.293952i
$12$	4.55051	+	0.685879i	1.31362	+	0.197996i
$13$	5.89166	−	4.01686i	1.63405	−	1.11408i	0.733138	−	0.680080i	$-0.238055\pi$
$13$	5.89166	−	4.01686i	1.63405	−	1.11408i	0.900914	−	0.433998i	$-0.142897\pi$
$14$	0.398923	+	1.01644i	0.106617	+	0.271655i
$15$	4.15984	+	1.28314i	1.07407	+	0.331306i
$16$	−3.14960	+	1.51677i	−0.787399	+	0.379192i
$17$	−0.313558	+	4.18415i	−0.0760491	+	1.01480i	0.820438	+	0.571735i	$0.193729\pi$
$17$	−0.313558	+	4.18415i	−0.0760491	+	1.01480i	−0.896487	+	0.443069i	$0.853890\pi$
$18$	−0.801543	+	0.120813i	−0.188926	+	0.0284759i
$19$	−4.45026	+	4.12924i	−1.02096	+	0.947313i	−0.998624	−	0.0524380i	$-0.983301\pi$
$19$	−4.45026	+	4.12924i	−1.02096	+	0.947313i	−0.0223359	+	0.999751i	$0.507110\pi$
$20$	−3.31409	+	1.02226i	−0.741054	+	0.228585i
$21$	5.60412	+	7.02735i	1.22292	+	1.53349i
$22$	0.182040	+	0.228271i	0.0388111	+	0.0486675i
$23$	4.81489	−	1.48520i	1.00397	−	0.309685i	0.251180	−	0.967940i	$-0.419181\pi$
$23$	4.81489	−	1.48520i	1.00397	−	0.309685i	0.752795	+	0.658255i	$0.228705\pi$
$24$	2.01373	−	1.86847i	0.411051	−	0.381400i
$25$	1.70003	−	0.256238i	0.340005	−	0.0512476i
$26$	0.155584	−	2.07612i	0.0305125	−	0.407161i
$27$	0.484381	−	0.233265i	0.0932191	−	0.0448919i
$28$	−6.84274	−	2.11070i	−1.29316	−	0.398886i
$29$	−1.15749	−	2.94922i	−0.214940	−	0.547657i	0.782218	−	0.623005i	$-0.214088\pi$
$29$	−1.15749	−	2.94922i	−0.214940	−	0.547657i	−0.997157	+	0.0753481i	$0.975993\pi$
$30$	1.05016	−	0.715988i	0.191732	−	0.130721i
$31$	−0.439561	−	0.0662532i	−0.0789475	−	0.0118994i	0.109450	−	0.993992i	$-0.465091\pi$
$31$	−0.439561	−	0.0662532i	−0.0789475	−	0.0118994i	−0.188397	+	0.982093i	$0.560329\pi$
$32$	−0.735797	+	3.22374i	−0.130072	+	0.569881i
$33$	1.98578	+	1.35388i	0.345680	+	0.235680i
$34$	0.898039	+	0.833258i	0.154012	+	0.142903i
$35$	−6.10310	−	2.93910i	−1.03161	−	0.496799i
$36$	2.65797	−	4.60374i	0.442995	−	0.767291i
$37$	−2.71780	−	4.70737i	−0.446804	−	0.773887i	0.551372	−	0.834260i	$-0.314105\pi$
$37$	−2.71780	−	4.70737i	−0.446804	−	0.773887i	−0.998176	+	0.0603723i	$0.980771\pi$
$38$	0.132460	+	1.76755i	0.0214878	+	0.286735i
$39$	−3.81354	−	16.7082i	−0.610655	−	2.67545i
$40$	−0.756360	+	1.92717i	−0.119591	+	0.304713i
$41$	4.46857	−	5.60341i	0.697873	−	0.875105i	−0.298990	−	0.954256i	$-0.596650\pi$
$41$	4.46857	−	5.60341i	0.697873	−	0.875105i	0.996863	+	0.0791514i	$0.0252211\pi$
$42$	2.62431			0.404940
$43$	−2.56713	−	6.03406i	−0.391484	−	0.920185i
$43$	−2.56713	−	6.03406i	−0.391484	−	0.920185i
$44$	−1.91475			−0.288660
$45$	3.13534	−	3.93159i	0.467389	−	0.586087i
$46$	0.537476	−	1.36947i	0.0792464	−	0.201917i
$47$	0.978553	+	4.28732i	0.142737	+	0.625370i	0.994793	+	0.101919i	$0.0324984\pi$
$47$	0.978553	+	4.28732i	0.142737	+	0.625370i	−0.852056	+	0.523450i	$0.824645\pi$
$48$	0.627865	+	8.37827i	0.0906244	+	1.20930i
$49$	−3.49320	−	6.05040i	−0.499029	−	0.864343i
$50$	0.250981	−	0.434712i	0.0354941	−	0.0614776i
$51$	9.08569	+	4.37544i	1.27225	+	0.612684i
$52$	10.0087	+	9.28676i	1.38796	+	1.28784i
$53$	−4.29003	−	2.92489i	−0.589281	−	0.401765i	0.231644	−	0.972801i	$-0.425590\pi$
$53$	−4.29003	−	2.92489i	−0.589281	−	0.401765i	−0.820925	+	0.571035i	$0.806542\pi$
$54$	0.0349289	−	0.153034i	0.00475322	−	0.0208252i
$55$	−1.79106	−	0.269959i	−0.241506	−	0.0364012i
$56$	−3.53184	+	2.40796i	−0.471961	+	0.321778i
$57$	5.33058	+	13.5821i	0.706053	+	1.79899i
$58$	−0.883931	−	0.272656i	−0.116066	−	0.0358015i
$59$	12.8429	−	6.18480i	1.67200	−	0.805193i	0.674225	−	0.738526i	$-0.264478\pi$
$59$	12.8429	−	6.18480i	1.67200	−	0.805193i	0.997775	−	0.0666669i	$-0.0212365\pi$
$60$	−0.622905	+	8.31208i	−0.0804166	+	1.07309i
$61$	−13.4614	+	2.02898i	−1.72355	+	0.259784i	−0.934863	−	0.355009i	$-0.884478\pi$
$61$	−13.4614	+	2.02898i	−1.72355	+	0.259784i	−0.788689	+	0.614792i	$0.789240\pi$
$62$	−0.0951414	+	0.0882783i	−0.0120830	+	0.0112114i
$63$	9.92166	−	3.06043i	1.25001	−	0.385578i
$64$	−3.75724	−	4.71143i	−0.469655	−	0.588928i
$65$	8.05284	+	10.0979i	0.998832	+	1.25250i
$66$	0.670543	−	0.206835i	0.0825381	−	0.0254596i
$67$	−2.56145	+	2.37668i	−0.312931	+	0.290358i	−0.820964	−	0.570980i	$-0.806563\pi$
$67$	−2.56145	+	2.37668i	−0.312931	+	0.290358i	0.508033	+	0.861338i	$0.330373\pi$
$68$	−7.94434	+	1.19742i	−0.963393	+	0.145208i
$69$	0.904989	−	12.0762i	0.108948	−	1.45381i
$70$	−1.78192	+	0.858127i	−0.212980	+	0.102566i
$71$	−3.39138	−	1.04610i	−0.402483	−	0.124150i	0.0869030	−	0.996217i	$-0.472303\pi$
$71$	−3.39138	−	1.04610i	−0.402483	−	0.124150i	−0.489386	+	0.872067i	$0.662779\pi$
$72$	−1.15933	−	2.95393i	−0.136629	−	0.348124i
$73$	4.18989	−	2.85662i	0.490390	−	0.334342i	−0.292749	−	0.956189i	$-0.594570\pi$
$73$	4.18989	−	2.85662i	0.490390	−	0.334342i	0.783138	+	0.621847i	$0.213618\pi$
$74$	−1.56930	−	0.236535i	−0.182428	−	0.0274966i
$75$	0.919453	−	4.02839i	0.106169	−	0.465158i
$76$	−9.60438	−	6.54816i	−1.10170	−	0.751125i
$77$	−2.74150	−	2.54374i	−0.312423	−	0.289886i
$78$	−4.50821	−	2.17104i	−0.510454	−	0.245822i
$79$	−4.91076	+	8.50568i	−0.552503	+	0.956964i	0.445590	+	0.895237i	$0.352994\pi$
$79$	−4.91076	+	8.50568i	−0.552503	+	0.956964i	−0.998093	+	0.0617265i	$0.980339\pi$
$80$	−3.16594	−	5.48358i	−0.353963	−	0.613083i
$81$	−0.718981	−	9.59414i	−0.0798868	−	1.06602i
$82$	−0.465637	−	2.04009i	−0.0514210	−	0.225290i
$83$	−4.32295	+	11.0147i	−0.474505	+	1.20902i	0.470627	+	0.882332i	$0.344028\pi$
$83$	−4.32295	+	11.0147i	−0.474505	+	1.20902i	−0.945132	+	0.326688i	$0.894067\pi$
$84$	−10.7305	+	13.4556i	−1.17079	+	1.46813i
$85$	−7.59995			−0.824331
$86$	−1.84472	−	0.512437i	−0.198921	−	0.0552575i
$87$	−7.61451			−0.816361
$88$	−0.712642	+	0.893624i	−0.0759679	+	0.0952607i
$89$	1.45769	−	3.71412i	0.154514	−	0.393696i	−0.832565	−	0.553927i	$-0.813129\pi$
$89$	1.45769	−	3.71412i	0.154514	−	0.393696i	0.987080	+	0.160231i	$0.0512238\pi$
$90$	−0.326711	−	1.43141i	−0.0344384	−	0.150884i
$91$	1.99288	+	26.5931i	0.208910	+	2.78771i
$92$	4.82398	+	8.35538i	0.502935	+	0.871109i
$93$	−0.534186	+	0.925237i	−0.0553925	+	0.0959427i
$94$	1.15681	+	0.557088i	0.119315	+	0.0574593i
$95$	−8.06071	−	7.47925i	−0.827012	−	0.767355i
$96$	6.56626	+	4.47680i	0.670166	+	0.456911i
$97$	2.73216	−	11.9704i	0.277409	−	1.21541i	−0.623648	−	0.781705i	$-0.714350\pi$
$97$	2.73216	−	11.9704i	0.277409	−	1.21541i	0.901057	−	0.433701i	$-0.142793\pi$
$98$	−2.01703	−	0.304019i	−0.203751	−	0.0307105i
$99$	2.29389	−	1.56395i	0.230545	−	0.157183i
$100$	1.20267	+	3.06434i	0.120267	+	0.306434i
$101$	3.27514	+	1.01025i	0.325888	+	0.100523i	0.453382	−	0.891316i	$-0.350217\pi$
$101$	3.27514	+	1.01025i	0.325888	+	0.100523i	−0.127494	+	0.991839i	$0.540693\pi$
$102$	2.65274	−	1.27749i	0.262661	−	0.126491i
$103$	0.470642	−	6.28027i	0.0463737	−	0.618814i	−0.924802	−	0.380449i	$-0.875770\pi$
$103$	0.470642	−	6.28027i	0.0463737	−	0.618814i	0.971176	−	0.238365i	$-0.0766115\pi$
$104$	8.05927	−	1.21474i	0.790277	−	0.119115i
$105$	−11.9344	+	11.0735i	−1.16468	+	1.08066i
$106$	−1.44863	+	0.446842i	−0.140703	+	0.0434011i
$107$	9.74450	+	12.2192i	0.942036	+	1.18128i	0.983275	+	0.182127i	$0.0582982\pi$
$107$	9.74450	+	12.2192i	0.942036	+	1.18128i	−0.0412385	+	0.999149i	$0.513130\pi$
$108$	0.641829	+	0.804828i	0.0617600	+	0.0774446i
$109$	8.29685	−	2.55924i	0.794694	−	0.245131i	0.129283	−	0.991608i	$-0.458732\pi$
$109$	8.29685	−	2.55924i	0.794694	−	0.245131i	0.665411	+	0.746477i	$0.268256\pi$
$110$	−0.387668	+	0.359703i	−0.0369627	+	0.0342964i
$111$	−12.9180	+	1.94707i	−1.22612	+	0.184808i
$112$	0.976998	−	13.0371i	0.0923177	−	1.23189i
$113$	9.97127	−	4.80191i	0.938018	−	0.451726i	0.0985486	−	0.995132i	$-0.468580\pi$
$113$	9.97127	−	4.80191i	0.938018	−	0.451726i	0.839470	+	0.543406i	$0.182866\pi$
$114$	4.07078	+	1.25567i	0.381263	+	0.117604i
$115$	3.33434	+	8.49575i	0.310928	+	0.792233i
$116$	5.01228	−	3.41732i	0.465379	−	0.317290i
$117$	−19.5759	−	2.95059i	−1.80979	−	0.272782i
$118$	0.926106	−	4.05754i	0.0852550	−	0.373527i
$119$	−12.9653	−	8.83957i	−1.18852	−	0.810322i
$120$	3.64745	+	3.38434i	0.332965	+	0.308947i
$121$	−0.900969	−	0.433884i	−0.0819063	−	0.0394440i
$122$	−1.98735	+	3.44219i	−0.179926	+	0.311642i
$123$	−8.61260	−	14.9175i	−0.776572	−	1.34506i
$124$	−0.0636071	−	0.848778i	−0.00571209	−	0.0762225i
$125$	2.70818	+	11.8653i	0.242227	+	1.06127i
$126$	1.10753	−	2.82195i	0.0986668	−	0.251399i
$127$	2.54650	−	3.19321i	0.225965	−	0.283352i	−0.655905	−	0.754843i	$-0.727713\pi$
$127$	2.54650	−	3.19321i	0.225965	−	0.283352i	0.881870	+	0.471492i	$0.156284\pi$
$128$	−8.37273			−0.740052
$129$	−15.7538	+	0.445083i	−1.38705	+	0.0391874i
$130$	3.77101			0.330739
$131$	−4.78317	+	5.99790i	−0.417907	+	0.524039i	−0.945572	−	0.325414i	$-0.894496\pi$
$131$	−4.78317	+	5.99790i	−0.417907	+	0.524039i	0.527664	+	0.849453i	$0.323068\pi$
$132$	−1.68127	+	4.28380i	−0.146335	+	0.372857i
$133$	−5.05213	−	22.1348i	−0.438075	−	1.91933i
$134$	0.0762403	+	1.01736i	0.00658616	+	0.0878862i
$135$	0.486895	+	0.843326i	0.0419052	+	0.0725820i
$136$	−2.39792	+	4.15332i	−0.205620	+	0.356144i
$137$	0.200516	+	0.0965636i	0.0171313	+	0.00824998i	0.442430	−	0.896803i	$-0.354117\pi$
$137$	0.200516	+	0.0965636i	0.0171313	+	0.00824998i	−0.425298	+	0.905053i	$0.639831\pi$
$138$	−2.59191	−	2.40494i	−0.220638	−	0.204722i
$139$	−11.3287	−	7.72376i	−0.960886	−	0.655121i	−0.0221486	−	0.999755i	$-0.507051\pi$
$139$	−11.3287	−	7.72376i	−0.960886	−	0.655121i	−0.938737	+	0.344634i	$0.888003\pi$
$140$	2.88619	−	12.6452i	0.243928	−	1.06872i
$141$	10.4511	+	1.57524i	0.880138	+	0.132660i
$142$	−0.856163	+	0.583722i	−0.0718476	+	0.0489848i
$143$	2.60514	+	6.63778i	0.217852	+	0.555079i
$144$	9.27420	+	2.86071i	0.772850	+	0.238393i
$145$	5.17029	−	2.48988i	0.429369	−	0.206773i
$146$	0.110645	−	1.47645i	0.00915701	−	0.122192i
$147$	−16.6035	+	2.50258i	−1.36944	+	0.206409i
$148$	7.62949	−	7.07913i	0.627140	−	0.581901i
$149$	12.0225	−	3.70846i	0.984924	−	0.303809i	0.239864	−	0.970806i	$-0.422897\pi$
$149$	12.0225	−	3.70846i	0.984924	−	0.303809i	0.745060	+	0.666998i	$0.232421\pi$
$150$	−0.752187	−	0.943212i	−0.0614158	−	0.0770130i
$151$	−4.16978	−	5.22873i	−0.339332	−	0.425508i	0.582661	−	0.812715i	$-0.302011\pi$
$151$	−4.16978	−	5.22873i	−0.339332	−	0.425508i	−0.921993	+	0.387207i	$0.873440\pi$
$152$	−6.63066	+	2.04529i	−0.537817	+	0.165895i
$153$	8.53936	−	7.92336i	0.690366	−	0.640566i
$154$	−1.07972	+	0.162742i	−0.0870066	+	0.0131141i
$155$	0.0601701	−	0.802914i	0.00483298	−	0.0644916i
$156$	29.5651	−	14.2378i	2.36711	−	1.13994i
$157$	−8.90561	−	2.74702i	−0.710745	−	0.219236i	−0.0817585	−	0.996652i	$-0.526054\pi$
$157$	−8.90561	−	2.74702i	−0.710745	−	0.219236i	−0.628986	+	0.777416i	$0.716530\pi$
$158$	1.04765	+	2.66936i	0.0833462	+	0.212363i
$159$	−10.3106	+	7.02968i	−0.817687	+	0.557490i
$160$	−5.92239	−	0.892657i	−0.468206	−	0.0705707i
$161$	−4.19321	+	18.3717i	−0.330471	+	1.44789i
$162$	−2.32095	−	1.58239i	−0.182351	−	0.124325i
$163$	10.5560	+	9.79457i	0.826813	+	0.767170i	0.975098	−	0.221775i	$-0.0711849\pi$
$163$	10.5560	+	9.79457i	0.826813	+	0.767170i	−0.148285	+	0.988945i	$0.547375\pi$
$164$	12.3641	+	5.95422i	0.965472	+	0.464947i
$165$	−2.17662	+	3.77002i	−0.169450	+	0.293496i
$166$	1.72738	+	2.99192i	0.134071	+	0.232218i
$167$	0.0361063	+	0.481805i	0.00279399	+	0.0372832i	0.998427	−	0.0560754i	$-0.0178587\pi$
$167$	0.0361063	+	0.481805i	0.00279399	+	0.0372832i	−0.995633	+	0.0933586i	$0.970240\pi$
$168$	2.28608	+	10.0160i	0.176375	+	0.772748i
$169$	13.8270	−	35.2306i	1.06362	−	2.71005i
$170$	−1.38350	+	1.73485i	−0.106109	+	0.133057i
$171$	16.8546			1.28890
$172$	10.1703	−	7.36314i	0.775476	−	0.561434i
$173$	−25.0636			−1.90555			−0.952776	−	0.303675i	$-0.901786\pi$
$173$	−25.0636			−1.90555			−0.952776	+	0.303675i	$0.901786\pi$
$174$	−1.38615	+	1.73817i	−0.105083	+	0.131770i
$175$	−2.34901	+	5.98518i	−0.177569	+	0.452437i
$176$	−0.777886	−	3.40814i	−0.0586354	−	0.256898i
$177$	−2.56020	−	34.1634i	−0.192436	−	2.56788i
$178$	−0.582469	−	1.00887i	−0.0436579	−	0.0756177i
$179$	−9.55699	+	16.5532i	−0.714323	+	1.23724i	0.248897	+	0.968530i	$0.419932\pi$
$179$	−9.55699	+	16.5532i	−0.714323	+	1.23724i	−0.963220	+	0.268714i	$0.913401\pi$
$180$	8.67517	+	4.17774i	0.646609	+	0.311391i
$181$	−8.43549	−	7.82699i	−0.627005	−	0.581775i	0.301330	−	0.953520i	$-0.402569\pi$
$181$	−8.43549	−	7.82699i	−0.627005	−	0.581775i	−0.928335	+	0.371744i	$0.878760\pi$
$182$	6.43321	+	4.38609i	0.476862	+	0.325119i
$183$	−7.28054	+	31.8981i	−0.538193	+	2.35798i
$184$	5.69491	+	0.858369i	0.419834	+	0.0632798i
$185$	8.13470	−	5.54614i	0.598075	−	0.407761i
$186$	0.113962	+	0.290369i	0.00835607	+	0.0212909i
$187$	−4.00947	−	1.23676i	−0.293201	−	0.0904406i
$188$	−7.58641	+	3.65342i	−0.553296	+	0.266453i
$189$	−0.150254	+	2.00500i	−0.0109294	+	0.145842i
$190$	−3.17467	+	0.478504i	−0.230315	+	0.0347143i
$191$	10.4153	−	9.66402i	0.753627	−	0.699264i	−0.206618	−	0.978422i	$-0.566246\pi$
$191$	10.4153	−	9.66402i	0.753627	−	0.699264i	0.960245	+	0.279158i	$0.0900553\pi$
$192$	−13.8398	+	4.26900i	−0.998798	+	0.308088i
$193$	−6.21995	−	7.79957i	−0.447722	−	0.561425i	0.505838	−	0.862628i	$-0.331183\pi$
$193$	−6.21995	−	7.79957i	−0.447722	−	0.561425i	−0.953560	+	0.301203i	$0.902612\pi$
$194$	−2.23512	−	2.80276i	−0.160473	−	0.201226i
$195$	29.6626	−	9.14969i	2.12418	−	0.655223i
$196$	9.80621	−	9.09884i	0.700444	−	0.649917i
$197$	1.66977	−	0.251678i	0.118966	−	0.0179313i	−0.0892891	−	0.996006i	$-0.528460\pi$
$197$	1.66977	−	0.251678i	0.118966	−	0.0179313i	0.208256	+	0.978074i	$0.433221\pi$
$198$	0.0605760	−	0.808330i	0.00430495	−	0.0574455i
$199$	19.8089	−	9.53945i	1.40421	−	0.676234i	0.430203	−	0.902732i	$-0.358442\pi$
$199$	19.8089	−	9.53945i	1.40421	−	0.676234i	0.974012	+	0.226498i	$0.0727278\pi$
$200$	1.87776	+	0.579211i	0.132777	+	0.0409564i
$201$	3.06814	+	7.81750i	0.216410	+	0.551404i
$202$	0.826816	−	0.563714i	0.0581746	−	0.0396627i
$203$	11.7163	+	1.76595i	0.822326	+	0.123946i
$204$	−4.29667	+	18.8249i	−0.300827	+	1.31801i
$205$	10.7259	+	7.31277i	0.749127	+	0.510746i
$206$	−1.34793	−	1.25069i	−0.0939146	−	0.0871400i
$207$	−12.6038	−	6.06965i	−0.876022	−	0.421870i
$208$	−12.4637	+	21.5878i	−0.864203	+	1.49684i
$209$	−3.03543	−	5.25753i	−0.209965	−	0.363671i
$210$	0.355221	+	4.74010i	0.0245126	+	0.327098i
$211$	1.71372	+	7.50830i	0.117977	+	0.516893i	0.999037	+	0.0438865i	$0.0139740\pi$
$211$	1.71372	+	7.50830i	0.117977	+	0.516893i	−0.881059	+	0.473006i	$0.843169\pi$
$212$	3.63217	−	9.25462i	0.249459	−	0.635610i
$213$	−5.31824	+	6.66886i	−0.364400	+	0.456943i
$214$	4.56318			0.311933
$215$	10.5514	−	5.45358i	0.719598	−	0.371931i
$216$	0.614496			0.0418111
$217$	1.03653	−	1.29976i	0.0703639	−	0.0882335i
$218$	0.926158	−	2.35981i	0.0627274	−	0.159827i
$219$	−2.71202	−	11.8821i	−0.183261	−	0.802921i
$220$	−0.259177	−	3.45848i	−0.0174737	−	0.233170i
$221$	14.9598	+	25.9111i	1.00630	+	1.74297i
$222$	−1.90713	+	3.30325i	−0.127998	+	0.221699i
$223$	5.76485	+	2.77620i	0.386043	+	0.185908i	0.616831	−	0.787096i	$-0.288416\pi$
$223$	5.76485	+	2.77620i	0.386043	+	0.185908i	−0.230788	+	0.973004i	$0.574130\pi$
$224$	−9.06515	−	8.41123i	−0.605690	−	0.561999i
$225$	−3.94373	−	2.68879i	−0.262915	−	0.179253i
$226$	0.719033	−	3.15029i	0.0478294	−	0.209554i
$227$	−8.82585	−	1.33028i	−0.585793	−	0.0882940i	−0.150542	−	0.988604i	$-0.548102\pi$
$227$	−8.82585	−	1.33028i	−0.585793	−	0.0882940i	−0.435250	+	0.900310i	$0.643340\pi$
$228$	−23.0831	+	15.7378i	−1.52872	+	1.04226i
$229$	−3.23456	−	8.24153i	−0.213746	−	0.544615i	0.783281	−	0.621667i	$-0.213544\pi$
$229$	−3.23456	−	8.24153i	−0.213746	−	0.544615i	−0.997027	+	0.0770521i	$0.975449\pi$
$230$	2.54631	+	0.785434i	0.167899	+	0.0517900i
$231$	−8.09819	+	3.89988i	−0.532822	+	0.256593i
$232$	0.270617	−	3.61113i	0.0177668	−	0.237082i
$233$	11.9018	−	1.79391i	0.779716	−	0.117523i	0.252888	−	0.967496i	$-0.418620\pi$
$233$	11.9018	−	1.79391i	0.779716	−	0.117523i	0.526827	+	0.849972i	$0.323381\pi$
$234$	−4.23713	+	3.93148i	−0.276990	+	0.257009i
$235$	−7.61141	+	2.34781i	−0.496514	+	0.153154i
$236$	17.0175	+	21.3392i	1.10774	+	1.38907i
$237$	14.7175	+	18.4551i	0.956002	+	1.19879i
$238$	−4.37801	+	1.35044i	−0.283784	+	0.0875359i
$239$	6.77815	−	6.28921i	0.438442	−	0.406815i	−0.429825	−	0.902912i	$-0.641425\pi$
$239$	6.77815	−	6.28921i	0.438442	−	0.406815i	0.868267	+	0.496097i	$0.165234\pi$
$240$	−15.0481	+	2.26813i	−0.971348	+	0.146407i
$241$	0.792816	−	10.5794i	0.0510698	−	0.681479i	−0.911648	−	0.410972i	$-0.865190\pi$
$241$	0.792816	−	10.5794i	0.0510698	−	0.681479i	0.962718	−	0.270507i	$-0.0871914\pi$
$242$	−0.263055	+	0.126681i	−0.0169098	+	0.00814335i
$243$	−20.5547	−	6.34027i	−1.31858	−	0.406729i
$244$	−9.52311	−	24.2645i	−0.609655	−	1.55337i
$245$	10.4556	−	7.12848i	0.667981	−	0.455422i
$246$	−4.97306	−	0.749568i	−0.317071	−	0.0477907i
$247$	−9.63283	+	42.2042i	−0.612922	+	2.68539i
$248$	−0.419802	−	0.286216i	−0.0266575	−	0.0181748i
$249$	20.8469	+	19.3431i	1.32112	+	1.22582i
$250$	3.20151	+	1.54177i	0.202481	+	0.0975098i
$251$	2.48287	−	4.30046i	0.156717	−	0.271443i	−0.776966	−	0.629543i	$-0.783242\pi$
$251$	2.48287	−	4.30046i	0.156717	−	0.271443i	0.933683	+	0.358100i	$0.116575\pi$
$252$	9.94039	+	17.2173i	0.626186	+	1.08459i
$253$	0.376546	+	5.02466i	0.0236733	+	0.315898i
$254$	−0.265352	−	1.16258i	−0.0166497	−	0.0729470i
$255$	−6.67320	+	17.0030i	−0.417892	+	1.06477i
$256$	5.99030	−	7.51160i	0.374394	−	0.469475i
$257$	5.19992			0.324362			0.162181	−	0.986761i	$-0.448147\pi$
$257$	5.19992			0.324362			0.162181	+	0.986761i	$0.448147\pi$
$258$	−2.76623	+	3.67716i	−0.172218	+	0.228930i
$259$	20.3283			1.26314
$260$	−15.4192	+	19.3351i	−0.956259	+	1.19911i
$261$	−3.21353	+	8.18795i	−0.198913	+	0.506821i
$262$	0.498419	+	2.18372i	0.0307924	+	0.134910i
$263$	−1.19029	−	15.8833i	−0.0733963	−	0.979406i	−0.905379	−	0.424604i	$-0.860413\pi$
$263$	−1.19029	−	15.8833i	−0.0733963	−	0.979406i	0.831983	−	0.554802i	$-0.187206\pi$
$264$	1.37353	+	2.37902i	0.0845347	+	0.146418i
$265$	4.70233	−	8.14467i	0.288862	−	0.500323i
$266$	−5.97243	−	2.87617i	−0.366193	−	0.176349i
$267$	−7.02952	−	6.52244i	−0.430199	−	0.399167i
$268$	−5.52803	−	3.76895i	−0.337678	−	0.230225i
$269$	−6.12498	+	26.8353i	−0.373447	+	1.63618i	0.343575	+	0.939125i	$0.388362\pi$
$269$	−6.12498	+	26.8353i	−0.373447	+	1.63618i	−0.717022	+	0.697051i	$0.754495\pi$
$270$	0.281141	+	0.0423752i	0.0171097	+	0.00257887i
$271$	−2.23431	+	1.52332i	−0.135724	+	0.0925354i	−0.629279	−	0.777179i	$-0.716650\pi$
$271$	−2.23431	+	1.52332i	−0.135724	+	0.0925354i	0.493555	+	0.869715i	$0.335697\pi$
$272$	−5.35879	−	13.6540i	−0.324924	−	0.827894i
$273$	61.2455	+	18.8917i	3.70674	+	1.14338i
$274$	0.0585446	−	0.0281936i	0.00353681	−	0.00170324i
$275$	−0.128478	+	1.71442i	−0.00774752	+	0.103384i
$276$	22.9289	−	3.45597i	1.38016	−	0.208025i
$277$	−19.0523	+	17.6779i	−1.14474	+	1.06216i	−0.147415	+	0.989075i	$0.547095\pi$
$277$	−19.0523	+	17.6779i	−1.14474	+	1.06216i	−0.997325	+	0.0730889i	$0.976714\pi$
$278$	−3.82538	+	1.17997i	−0.229431	+	0.0707701i
$279$	0.769475	+	0.964891i	0.0460672	+	0.0577665i
$280$	−4.82739	−	6.05335i	−0.288492	−	0.361757i
$281$	8.74604	−	2.69780i	0.521745	−	0.160937i	−0.0226860	−	0.999743i	$-0.507222\pi$
$281$	8.74604	−	2.69780i	0.521745	−	0.160937i	0.544431	+	0.838806i	$0.316746\pi$
$282$	2.26209	−	2.09892i	0.134706	−	0.124989i
$283$	−12.2324	+	1.84373i	−0.727139	+	0.109599i	−0.502172	−	0.864768i	$-0.667466\pi$
$283$	−12.2324	+	1.84373i	−0.727139	+	0.109599i	−0.224967	+	0.974366i	$0.572228\pi$
$284$	0.507834	−	6.77657i	0.0301344	−	0.402116i
$285$	−23.8108	+	11.4667i	−1.41043	+	0.679227i
$286$	1.98945	+	0.613664i	0.117639	+	0.0362867i
$287$	9.79243	+	24.9507i	0.578029	+	1.47279i
$288$	7.58508	−	5.17142i	0.446955	−	0.304729i
$289$	−0.598632	−	0.0902293i	−0.0352137	−	0.00530761i
$290$	0.372832	−	1.63348i	0.0218934	−	0.0959215i
$291$	−24.3818	−	16.6232i	−1.42929	−	0.974471i
$292$	7.11778	+	6.60434i	0.416537	+	0.386490i
$293$	6.08052	+	2.92822i	0.355228	+	0.171069i	0.602983	−	0.797754i	$-0.293979\pi$
$293$	6.08052	+	2.92822i	0.355228	+	0.171069i	−0.247755	+	0.968823i	$0.579693\pi$
$294$	−2.45124	+	4.24568i	−0.142959	+	0.247613i
$295$	12.9095	+	22.3600i	0.751622	+	1.30185i
$296$	−0.464286	−	6.19546i	−0.0269861	−	0.360104i
$297$	0.119632	+	0.524143i	0.00694176	+	0.0304138i
$298$	1.34205	−	3.41948i	0.0777428	−	0.198085i
$299$	22.4019	−	28.0911i	1.29553	−	1.62455i
$300$	7.91174			0.456784
$301$	24.3434	+	2.96878i	1.40313	+	0.171117i
$302$	−1.95263			−0.112361
$303$	5.13594	−	6.44027i	0.295052	−	0.369984i
$304$	7.75344	−	19.7555i	0.444690	−	1.13305i
$305$	−5.48689	−	24.0396i	−0.314178	−	1.37651i
$306$	−0.254169	−	3.39166i	−0.0145299	−	0.193888i
$307$	−4.91083	−	8.50581i	−0.280276	−	0.485452i	0.691177	−	0.722686i	$-0.257093\pi$
$307$	−4.91083	−	8.50581i	−0.280276	−	0.485452i	−0.971453	+	0.237234i	$0.923759\pi$
$308$	3.58044	−	6.20150i	0.204014	−	0.353363i
$309$	−13.6373	−	6.56740i	−0.775801	−	0.373606i
$310$	−0.172329	−	0.159898i	−0.00978761	−	0.00908157i
$311$	−19.2613	−	13.1321i	−1.09221	−	0.744654i	−0.123372	−	0.992360i	$-0.539371\pi$
$311$	−19.2613	−	13.1321i	−1.09221	−	0.744654i	−0.968835	+	0.247706i	$0.920323\pi$
$312$	4.35883	−	19.0973i	0.246770	−	1.08117i
$313$	−0.395132	−	0.0595565i	−0.0223342	−	0.00336633i	0.137866	−	0.990451i	$-0.455976\pi$
$313$	−0.395132	−	0.0595565i	−0.0223342	−	0.00336633i	−0.160200	+	0.987085i	$0.551214\pi$
$314$	−2.24824	+	1.53282i	−0.126876	+	0.0865023i
$315$	6.87079	+	17.5065i	0.387125	+	0.986379i
$316$	−17.9703	−	5.54310i	−1.01091	−	0.311824i
$317$	11.6087	−	5.59047i	0.652011	−	0.313992i	−0.0784783	−	0.996916i	$-0.525006\pi$
$317$	11.6087	−	5.59047i	0.652011	−	0.313992i	0.730490	+	0.682924i	$0.239292\pi$
$318$	−0.272278	+	3.63330i	−0.0152686	+	0.203745i
$319$	3.13285	−	0.472200i	0.175406	−	0.0264381i
$320$	8.00133	−	7.42415i	0.447288	−	0.415022i
$321$	35.8938	−	11.0718i	2.00340	−	0.617966i
$322$	3.43038	+	4.30156i	0.191168	+	0.239717i
$323$	−15.8819	−	19.9153i	−0.883694	−	1.10812i
$324$	17.6035	−	5.42996i	0.977972	−	0.301664i
$325$	8.98670	−	8.33844i	0.498493	−	0.462534i
$326$	4.15744	−	0.626633i	0.230259	−	0.0347060i
$327$	1.55944	−	20.8093i	0.0862375	−	1.15076i
$328$	7.38058	−	3.55430i	0.407524	−	0.196253i
$329$	−15.7156	−	4.84761i	−0.866427	−	0.267257i
$330$	0.464354	+	1.18315i	0.0255618	+	0.0651305i
$331$	−6.67625	+	4.55179i	−0.366960	+	0.250189i	−0.732735	−	0.680514i	$-0.761756\pi$
$331$	−6.67625	+	4.55179i	−0.366960	+	0.250189i	0.365775	+	0.930703i	$0.380804\pi$
$332$	−22.4035	−	3.37679i	−1.22955	−	0.185325i
$333$	−3.35804	+	14.7126i	−0.184020	+	0.806243i
$334$	0.116555	+	0.0794658i	0.00637760	+	0.00434817i
$335$	−4.63954	−	4.30486i	−0.253485	−	0.235200i
$336$	−28.3096	−	13.6332i	−1.54441	−	0.743750i
$337$	−2.68973	+	4.65874i	−0.146519	+	0.253778i	−0.929939	−	0.367715i	$-0.880140\pi$
$337$	−2.68973	+	4.65874i	−0.146519	+	0.253778i	0.783420	+	0.621493i	$0.213474\pi$
$338$	−5.52506	−	9.56968i	−0.300524	−	0.520522i
$339$	−1.98775	−	26.5247i	−0.107960	−	1.44062i
$340$	−3.23813	−	14.1872i	−0.175612	−	0.769408i
$341$	0.162404	−	0.413798i	0.00879465	−	0.0224084i
$342$	3.06821	−	3.84741i	0.165910	−	0.208044i
$343$	−0.0508511			−0.00274570
$344$	0.348807	−	7.48696i	0.0188064	−	0.403670i
$345$	21.9349			1.18094
$346$	−4.56258	+	5.72129i	−0.245286	+	0.307579i
$347$	−9.07857	+	23.1318i	−0.487363	+	1.24178i	0.449875	+	0.893092i	$0.351469\pi$
$347$	−9.07857	+	23.1318i	−0.487363	+	1.24178i	−0.937238	+	0.348690i	$0.886627\pi$
$348$	−3.24434	−	14.2144i	−0.173915	−	0.761970i
$349$	1.23089	+	16.4250i	0.0658879	+	0.879212i	0.928020	+	0.372529i	$0.121509\pi$
$349$	1.23089	+	16.4250i	0.0658879	+	0.879212i	−0.862133	+	0.506683i	$0.830872\pi$
$350$	0.938629	+	1.62575i	0.0501719	+	0.0869002i
$351$	1.91681	−	3.32001i	0.102312	−	0.177209i
$352$	−2.97918	−	1.43470i	−0.158791	−	0.0764696i
$353$	17.7739	+	16.4917i	0.946007	+	0.877766i	0.992635	−	0.121146i	$-0.0386569\pi$
$353$	17.7739	+	16.4917i	0.946007	+	0.877766i	−0.0466276	+	0.998912i	$0.514847\pi$
$354$	−8.26458	−	5.63469i	−0.439257	−	0.299481i
$355$	1.43045	−	6.26720i	0.0759203	−	0.332629i
$356$	7.55441	+	1.13864i	0.400383	+	0.0603480i
$357$	−31.1607	+	21.2450i	−1.64920	+	1.12440i
$358$	2.03886	+	5.19493i	0.107757	+	0.274560i
$359$	25.9425	+	8.00220i	1.36919	+	0.422340i	0.890237	−	0.455498i	$-0.150539\pi$
$359$	25.9425	+	8.00220i	1.36919	+	0.422340i	0.478957	+	0.877839i	$0.341015\pi$
$360$	5.17854	−	2.49385i	0.272933	−	0.131438i
$361$	1.33434	−	17.8055i	0.0702284	−	0.937133i
$362$	−3.32227	+	0.500752i	−0.174615	+	0.0263189i
$363$	−1.76181	+	1.63472i	−0.0924712	+	0.0858007i
$364$	−48.7935	+	15.0508i	−2.55747	+	0.788876i
$365$	5.72683	+	7.18122i	0.299756	+	0.375882i
$366$	5.95606	+	7.46867i	0.311328	+	0.390393i
$367$	−25.6403	+	7.90898i	−1.33841	+	0.412845i	−0.879611	−	0.475693i	$-0.842197\pi$
$367$	−25.6403	+	7.90898i	−1.33841	+	0.412845i	−0.458801	+	0.888539i	$0.651721\pi$
$368$	−12.9123	+	11.9808i	−0.673099	+	0.624545i
$369$	−19.6756	+	2.96562i	−1.02427	+	0.154384i
$370$	0.214817	−	2.86653i	0.0111678	−	0.149024i
$371$	17.4952	−	8.42522i	0.908303	−	0.437416i
$372$	−1.95479	−	0.602972i	−0.101351	−	0.0312626i
$373$	−9.55382	−	24.3427i	−0.494678	−	1.26042i	−0.932439	−	0.361328i	$-0.882324\pi$
$373$	−9.55382	−	24.3427i	−0.494678	−	1.26042i	0.437761	−	0.899091i	$-0.355772\pi$
$374$	−1.01220	+	0.690106i	−0.0523396	+	0.0356845i
$375$	28.9237	+	4.35955i	1.49362	+	0.225126i
$376$	−1.11847	+	4.90036i	−0.0576809	+	0.252717i
$377$	−18.6661	−	12.7264i	−0.961355	−	0.655441i
$378$	0.430330	+	0.399288i	0.0221338	+	0.0205372i
$379$	14.7663	+	7.11107i	0.758494	+	0.365271i	0.772819	−	0.634626i	$-0.218846\pi$
$379$	14.7663	+	7.11107i	0.758494	+	0.365271i	−0.0143256	+	0.999897i	$0.504560\pi$
$380$	10.5274	−	18.2340i	0.540045	−	0.935385i
$381$	−4.90806	−	8.50100i	−0.251447	−	0.435520i
$382$	−0.310007	−	4.13676i	−0.0158613	−	0.211655i
$383$	1.23662	+	5.41797i	0.0631881	+	0.276845i	0.996645	−	0.0818439i	$-0.0260809\pi$
$383$	1.23662	+	5.41797i	0.0631881	+	0.276845i	−0.933457	+	0.358689i	$0.883224\pi$
$384$	−7.35175	+	18.7320i	−0.375167	+	0.955911i
$385$	4.22348	−	5.29608i	0.215248	−	0.269913i
$386$	−2.91269			−0.148252
$387$	−6.16995	+	17.1281i	−0.313636	+	0.870669i
$388$	23.5097			1.19353
$389$	−8.82051	+	11.0606i	−0.447218	+	0.560793i	−0.953429	−	0.301616i	$-0.902474\pi$
$389$	−8.82051	+	11.0606i	−0.447218	+	0.560793i	0.506212	+	0.862409i	$0.331045\pi$
$390$	3.31117	−	8.43671i	0.167667	−	0.427210i
$391$	4.70453	+	20.6119i	0.237919	+	1.04239i
$392$	−0.596748	−	7.96305i	−0.0301403	−	0.402195i
$393$	9.21895	+	15.9677i	0.465035	+	0.805463i
$394$	0.246515	−	0.426976i	0.0124192	−	0.0215107i
$395$	−16.0279	−	7.71862i	−0.806450	−	0.388366i
$396$	3.89686	+	3.61576i	0.195825	+	0.181699i
$397$	12.9294	+	8.81509i	0.648906	+	0.442417i	0.842523	−	0.538661i	$-0.181070\pi$
$397$	12.9294	+	8.81509i	0.648906	+	0.442417i	−0.193617	+	0.981077i	$0.562022\pi$
$398$	1.42843	−	6.25835i	0.0716006	−	0.313703i
$399$	−53.9574	−	8.13277i	−2.70125	−	0.407148i
$400$	−4.96575	+	3.38559i	−0.248287	+	0.169279i
$401$	−8.63262	−	21.9956i	−0.431093	−	1.09841i	−0.967146	−	0.254222i	$-0.918181\pi$
$401$	−8.63262	−	21.9956i	−0.431093	−	1.09841i	0.536053	−	0.844184i	$-0.319915\pi$
$402$	2.34303	+	0.722730i	0.116860	+	0.0360465i
$403$	−2.85587	+	1.37532i	−0.142261	+	0.0685094i
$404$	−0.490427	+	6.54429i	−0.0243997	+	0.325591i
$405$	17.2319	−	2.59728i	0.856258	−	0.129060i
$406$	2.53596	−	2.35303i	0.125857	−	0.116779i
$407$	5.19412	−	1.60217i	0.257463	−	0.0794168i
$408$	7.18653	+	9.01162i	0.355786	+	0.446142i
$409$	0.886791	+	1.11200i	0.0438490	+	0.0549849i	0.803272	−	0.595612i	$-0.203090\pi$
$409$	0.886791	+	1.11200i	0.0438490	+	0.0549849i	−0.759423	+	0.650597i	$0.774519\pi$
$410$	3.62183	−	1.11719i	0.178869	−	0.0551739i
$411$	0.392103	−	0.363818i	0.0193410	−	0.0179458i
$412$	11.9242	−	1.79729i	0.587464	−	0.0885459i
$413$	−3.98383	+	53.1606i	−0.196032	+	2.61586i
$414$	−3.67991	+	1.77215i	−0.180858	+	0.0870966i
$415$	−20.4802	−	6.31729i	−1.00533	−	0.310104i
$416$	8.61425	+	21.9487i	0.422348	+	1.07613i
$417$	−27.2273	+	18.5632i	−1.33333	+	0.909046i
$418$	−1.75271	−	0.264179i	−0.0857279	−	0.0129214i
$419$	5.56408	−	24.3778i	0.271823	−	1.19094i	−0.636036	−	0.771659i	$-0.719427\pi$
$419$	5.56408	−	24.3778i	0.271823	−	1.19094i	0.907859	−	0.419276i	$-0.137716\pi$
$420$	−25.7564	−	17.5604i	−1.25678	−	0.856860i
$421$	1.40797	+	1.30641i	0.0686203	+	0.0636703i	0.713737	−	0.700413i	$-0.247001\pi$
$421$	1.40797	+	1.30641i	0.0686203	+	0.0636703i	−0.645117	+	0.764084i	$0.723191\pi$
$422$	2.02589	+	0.975618i	0.0986189	+	0.0474923i
$423$	6.10451	−	10.5733i	0.296811	−	0.514093i
$424$	−2.96734	−	5.13958i	−0.144107	−	0.249600i
$425$	0.539079	+	7.19350i	0.0261492	+	0.348936i
$426$	0.554175	+	2.42800i	0.0268498	+	0.117637i
$427$	18.6003	−	47.3927i	0.900129	−	2.29349i
$428$	−18.6583	+	23.3968i	−0.901884	+	1.13093i
$429$	17.1379			0.827425
$430$	0.675880	−	3.40134i	0.0325938	−	0.164027i
$431$	24.2298			1.16711			0.583554	−	0.812075i	$-0.301662\pi$
$431$	24.2298			1.16711			0.583554	+	0.812075i	$0.301662\pi$
$432$	−1.17180	+	1.46938i	−0.0563780	+	0.0706958i
$433$	−4.59839	+	11.7165i	−0.220985	+	0.563060i	−0.997773	−	0.0667021i	$-0.978752\pi$
$433$	−4.59839	+	11.7165i	−0.220985	+	0.563060i	0.776788	+	0.629762i	$0.216848\pi$
$434$	−0.108009	−	0.473217i	−0.00518458	−	0.0227151i
$435$	−1.03068	−	13.7535i	−0.0494175	−	0.659431i
$436$	8.31251	+	14.3977i	0.398097	+	0.689525i
$437$	−15.2948	+	26.4914i	−0.731649	+	1.26725i
$438$	−3.20604	−	1.54395i	−0.153191	−	0.0737728i
$439$	−26.3484	−	24.4478i	−1.25754	−	1.16683i	−0.978432	−	0.206570i	$-0.933770\pi$
$439$	−26.3484	−	24.4478i	−1.25754	−	1.16683i	−0.279111	−	0.960259i	$-0.590040\pi$
$440$	−1.71055	−	1.16623i	−0.0815472	−	0.0555979i
$441$	−4.31611	+	18.9101i	−0.205529	+	0.900481i
$442$	8.63802	+	1.30197i	0.410869	+	0.0619285i
$443$	1.64714	−	1.12300i	0.0782582	−	0.0533555i	−0.523559	−	0.851989i	$-0.675396\pi$
$443$	1.64714	−	1.12300i	0.0782582	−	0.0533555i	0.601817	+	0.798634i	$0.294444\pi$
$444$	−9.13870	−	23.2850i	−0.433704	−	1.10506i
$445$	6.90585	+	2.13017i	0.327369	+	0.100980i
$446$	1.68316	−	0.810567i	0.0796999	−	0.0383814i
$447$	2.25971	−	30.1537i	0.106881	−	1.42622i
$448$	22.2851	−	3.35894i	1.05287	−	0.158695i
$449$	−27.9946	+	25.9752i	−1.32115	+	1.22585i	−0.365682	+	0.930740i	$0.619164\pi$
$449$	−27.9946	+	25.9752i	−1.32115	+	1.22585i	−0.955465	+	0.295105i	$0.904645\pi$
$450$	−1.33169	+	0.410771i	−0.0627764	+	0.0193639i
$451$	4.46857	+	5.60341i	0.210417	+	0.263854i
$452$	13.2124	+	16.5679i	0.621461	+	0.779287i
$453$	−15.3593	+	4.73773i	−0.721644	+	0.222598i
$454$	−1.91032	+	1.77252i	−0.0896559	+	0.0831885i
$455$	−47.7634	+	7.19917i	−2.23918	+	0.337502i
$456$	−1.24627	+	16.6304i	−0.0583621	+	0.778788i
$457$	−3.75321	+	1.80745i	−0.175568	+	0.0845490i	−0.519603	−	0.854408i	$-0.673920\pi$
$457$	−3.75321	+	1.80745i	−0.175568	+	0.0845490i	0.344035	+	0.938957i	$0.388206\pi$
$458$	−2.47012	−	0.761931i	−0.115421	−	0.0356027i
$459$	0.824135	+	2.09986i	0.0384673	+	0.0980131i
$460$	−14.4387	+	9.84417i	−0.673210	+	0.458987i
$461$	3.77112	+	0.568405i	0.175639	+	0.0264733i	0.236273	−	0.971687i	$-0.424074\pi$
$461$	3.77112	+	0.568405i	0.175639	+	0.0264733i	−0.0606340	+	0.998160i	$0.519312\pi$
$462$	−0.583965	+	2.55852i	−0.0271685	+	0.119033i
$463$	−8.50662	−	5.79971i	−0.395336	−	0.269536i	0.349294	−	0.937013i	$-0.386422\pi$
$463$	−8.50662	−	5.79971i	−0.395336	−	0.269536i	−0.744630	+	0.667478i	$0.767374\pi$
$464$	8.11890	+	7.53323i	0.376910	+	0.349722i
$465$	−1.74349	−	0.839622i	−0.0808526	−	0.0389365i
$466$	1.75711	−	3.04341i	0.0813967	−	0.140983i
$467$	−17.2568	−	29.8897i	−0.798551	−	1.38313i	−0.920559	−	0.390602i	$-0.872267\pi$
$467$	−17.2568	−	29.8897i	−0.798551	−	1.38313i	0.122008	−	0.992529i	$-0.461067\pi$
$468$	−2.83275	−	37.8004i	−0.130944	−	1.74732i
$469$	−2.90787	−	12.7402i	−0.134273	−	0.588289i
$470$	−0.849644	+	2.16486i	−0.0391912	+	0.0998575i
$471$	−13.9654	+	17.5121i	−0.643493	+	0.806914i
$472$	16.2928			0.749935
$473$	6.45401	−	1.16007i	0.296756	−	0.0533399i
$474$	6.89193			0.316557
$475$	−6.50750	+	8.16014i	−0.298584	+	0.374413i
$476$	10.9771	−	27.9692i	0.503134	−	1.28196i
$477$	3.20770	+	14.0538i	0.146870	+	0.643481i
$478$	−0.201748	−	2.69214i	−0.00922775	−	0.123136i
$479$	−2.59911	−	4.50179i	−0.118756	−	0.205692i	0.800519	−	0.599308i	$-0.204557\pi$
$479$	−2.59911	−	4.50179i	−0.118756	−	0.205692i	−0.919275	+	0.393616i	$0.871224\pi$
$480$	−7.19731	+	12.4661i	−0.328511	+	0.568997i
$481$	−34.9212	−	16.8172i	−1.59227	−	0.766798i
$482$	−2.27064	−	2.10685i	−0.103425	−	0.0959644i
$483$	37.4202	+	25.5127i	1.70268	+	1.16087i
$484$	0.426073	−	1.86675i	0.0193669	−	0.0848521i
$485$	21.9910	+	3.31461i	0.998560	+	0.150509i
$486$	−5.18907	+	3.53785i	−0.235381	+	0.160480i
$487$	9.23175	+	23.5221i	0.418331	+	1.06589i	0.972380	+	0.233405i	$0.0749868\pi$
$487$	9.23175	+	23.5221i	0.418331	+	1.06589i	−0.554049	+	0.832484i	$0.686918\pi$
$488$	−14.8687	−	4.58639i	−0.673074	−	0.207616i
$489$	31.1818	−	15.0164i	1.41009	−	0.679063i
$490$	0.276105	−	3.68437i	0.0124732	−	0.166443i
$491$	5.60190	−	0.844350i	0.252810	−	0.0381050i	−0.0214144	−	0.999771i	$-0.506817\pi$
$491$	5.60190	−	0.844350i	0.252810	−	0.0381050i	0.274225	+	0.961666i	$0.411579\pi$
$492$	24.1775	−	22.4335i	1.09001	−	1.01138i
$493$	12.7029	−	3.91833i	0.572111	−	0.176473i
$494$	7.88042	+	9.88174i	0.354557	+	0.444600i
$495$	3.13534	+	3.93159i	0.140923	+	0.176712i
$496$	1.48493	−	0.458041i	0.0666754	−	0.0205666i
$497$	9.72973	−	9.02787i	0.436438	−	0.404955i
$498$	8.21044	−	1.23752i	0.367918	−	0.0554548i
$499$	0.139524	−	1.86182i	0.00624595	−	0.0833465i	−0.993210	−	0.116338i	$-0.962884\pi$
$499$	0.139524	−	1.86182i	0.00624595	−	0.0833465i	0.999456	+	0.0329916i	$0.0105035\pi$
$500$	−20.9957	+	10.1110i	−0.938956	+	0.452177i
$501$	1.10963	+	0.342274i	0.0495744	+	0.0152917i
$502$	−0.529688	−	1.34962i	−0.0236411	−	0.0602366i
$503$	−18.4991	+	12.6125i	−0.824834	+	0.562363i	−0.900543	−	0.434767i	$-0.856831\pi$
$503$	−18.4991	+	12.6125i	−0.824834	+	0.562363i	0.0757084	+	0.997130i	$0.475878\pi$
$504$	11.7350	+	1.76877i	0.522720	+	0.0787874i
$505$	−1.38142	+	6.05238i	−0.0614722	+	0.269327i
$506$	1.21553	+	0.828735i	0.0540369	+	0.0368417i
$507$	−66.6791	−	61.8691i	−2.96132	−	2.74770i
$508$	7.04591	+	3.39313i	0.312612	+	0.150546i
$509$	−19.2605	+	33.3601i	−0.853705	+	1.47866i	0.0241356	+	0.999709i	$0.492317\pi$
$509$	−19.2605	+	33.3601i	−0.853705	+	1.47866i	−0.877841	+	0.478952i	$0.841017\pi$
$510$	2.66651	+	4.61853i	0.118075	+	0.204512i
$511$	1.41725	+	18.9119i	0.0626953	+	0.836611i
$512$	−4.35042	−	19.0604i	−0.192263	−	0.842361i
$513$	−1.19241	+	3.03822i	−0.0526463	+	0.134140i
$514$	0.946594	−	1.18699i	0.0417525	−	0.0523559i
$515$	11.4073			0.502665
$516$	−7.54314	−	29.2188i	−0.332068	−	1.28628i
$517$	−4.39758			−0.193405
$518$	3.70056	−	4.64036i	0.162593	−	0.203886i
$519$	−22.0073	+	56.0738i	−0.966014	+	2.46136i
$520$	3.28498	+	14.3924i	0.144056	+	0.631150i
$521$	−1.89325	−	25.2637i	−0.0829449	−	1.10682i	−0.871021	−	0.491245i	$-0.836542\pi$
$521$	−1.89325	−	25.2637i	−0.0829449	−	1.10682i	0.788076	−	0.615577i	$-0.211077\pi$
$522$	1.28408	+	2.22409i	0.0562026	+	0.0973458i
$523$	1.39567	−	2.41737i	0.0610283	−	0.105704i	−0.833897	−	0.551920i	$-0.813895\pi$
$523$	1.39567	−	2.41737i	0.0610283	−	0.105704i	0.894925	+	0.446216i	$0.147229\pi$
$524$	−13.2345	−	6.37342i	−0.578154	−	0.278424i
$525$	11.3278	+	10.5107i	0.494387	+	0.458724i
$526$	−3.84237	−	2.61969i	−0.167535	−	0.114224i
$527$	0.415041	−	1.81841i	0.0180795	−	0.0792114i
$528$	−8.30792	−	1.25222i	−0.361556	−	0.0544958i
$529$	1.97389	−	1.34578i	0.0858213	−	0.0585120i
$530$	−1.00318	−	2.55606i	−0.0435753	−	0.111028i
$531$	−37.8167	−	11.6649i	−1.64111	−	0.506214i
$532$	39.1676	−	18.8621i	1.69813	−	0.817776i
$533$	3.81915	−	50.9630i	0.165426	−	2.20745i
$534$	−2.76854	+	0.417290i	−0.119806	+	0.0180579i
$535$	−20.7517	+	19.2547i	−0.897173	+	0.832455i
$536$	−3.81643	+	1.17721i	−0.164845	+	0.0508479i
$537$	28.6422	+	35.9161i	1.23600	+	1.54990i
$538$	5.01072	+	6.28325i	0.216028	+	0.270890i
$539$	6.67602	−	2.05928i	0.287556	−	0.0886994i
$540$	−1.36682	+	1.26823i	−0.0588187	+	0.0545758i
$541$	−5.68440	+	0.856785i	−0.244391	+	0.0368361i	−0.270096	−	0.962834i	$-0.587055\pi$
$541$	−5.68440	+	0.856785i	−0.244391	+	0.0368361i	0.0257042	+	0.999670i	$0.491817\pi$
$542$	−0.0590025	+	0.787333i	−0.00253437	+	0.0338189i
$543$	−24.9178	+	11.9998i	−1.06933	+	0.514961i
$544$	−13.2579	−	4.08951i	−0.568426	−	0.175336i
$545$	5.74561	+	14.6396i	0.246115	+	0.627090i
$546$	15.4616	−	10.5415i	0.661693	−	0.451135i
$547$	1.59267	+	0.240056i	0.0680976	+	0.0102641i	0.183003	−	0.983112i	$-0.441418\pi$
$547$	1.59267	+	0.240056i	0.0680976	+	0.0102641i	−0.114905	+	0.993376i	$0.536656\pi$
$548$	−0.0948252	+	0.415456i	−0.00405073	+	0.0177474i
$549$	31.2277	+	21.2907i	1.33277	+	0.908665i
$550$	0.367964	+	0.341421i	0.0156901	+	0.0145582i
$551$	17.3292	+	8.34528i	0.738247	+	0.355521i
$552$	6.92086	−	11.9873i	0.294571	−	0.510212i
$553$	−18.3654	−	31.8099i	−0.780978	−	1.35269i
$554$	0.567081	+	7.56717i	0.0240930	+	0.321498i
$555$	−5.26541	−	23.0693i	−0.223504	−	0.979235i
$556$	9.59147	−	24.4387i	0.406769	−	1.03643i
$557$	−18.2654	+	22.9041i	−0.773931	+	0.970479i	−0.999993	−	0.00363392i	$-0.998843\pi$
$557$	−18.2654	+	22.9041i	−0.773931	+	0.970479i	0.226062	+	0.974113i	$0.427415\pi$
$558$	0.360332			0.0152541
$559$	−39.3627	−	25.2388i	−1.66486	−	1.06749i
$560$	23.6803			1.00067
$561$	−6.28749	+	7.88426i	−0.265458	+	0.332874i
$562$	0.976301	−	2.48757i	0.0411828	−	0.104932i
$563$	0.252808	+	1.10762i	0.0106546	+	0.0466808i	0.979976	−	0.199117i	$-0.0638073\pi$
$563$	0.252808	+	1.10762i	0.0106546	+	0.0466808i	−0.969321	+	0.245798i	$0.920950\pi$
$564$	1.51233	+	20.1807i	0.0636806	+	0.849759i
$565$	10.0230	+	17.3604i	0.421672	+	0.730357i
$566$	−1.80591	+	3.12793i	−0.0759081	+	0.131477i
$567$	32.4179	+	15.6116i	1.36142	+	0.655627i
$568$	−2.97365	−	2.75914i	−0.124772	−	0.115771i
$569$	16.5318	+	11.2712i	0.693047	+	0.472512i	0.857907	−	0.513805i	$-0.171765\pi$
$569$	16.5318	+	11.2712i	0.693047	+	0.472512i	−0.164859	+	0.986317i	$0.552717\pi$
$570$	−1.71701	+	7.52270i	−0.0719175	+	0.315091i
$571$	3.40811	+	0.513691i	0.142625	+	0.0214973i	0.219967	−	0.975507i	$-0.429405\pi$
$571$	3.40811	+	0.513691i	0.142625	+	0.0214973i	−0.0773416	+	0.997005i	$0.524643\pi$
$572$	−11.2811	+	7.69131i	−0.471685	+	0.321590i
$573$	−12.4756	−	31.7874i	−0.521177	−	1.32794i
$574$	7.47813	+	2.30670i	0.312131	+	0.0962797i
$575$	7.80488	−	3.75863i	0.325486	−	0.156746i
$576$	−1.25027	+	16.6836i	−0.0520944	+	0.695152i
$577$	−34.5858	+	5.21296i	−1.43982	+	0.217019i	−0.822085	−	0.569365i	$-0.807189\pi$
$577$	−34.5858	+	5.21296i	−1.43982	+	0.217019i	−0.617739	+	0.786383i	$0.711951\pi$
$578$	−0.129572	+	0.120225i	−0.00538947	+	0.00500070i
$579$	−22.9111	+	7.06714i	−0.952153	+	0.293700i
$580$	6.85089	+	8.59075i	0.284468	+	0.356711i
$581$	−27.5908	−	34.5978i	−1.14466	−	1.43536i
$582$	−8.23306	+	2.53956i	−0.341271	+	0.105268i
$583$	3.80618	−	3.53162i	0.157636	−	0.146265i
$584$	5.73140	−	0.863870i	0.237167	−	0.0357472i
$585$	2.67968	−	35.7578i	0.110791	−	1.47841i
$586$	1.77533	−	0.854952i	0.0733380	−	0.0353177i
$587$	−18.9907	−	5.85786i	−0.783831	−	0.241780i	−0.123092	−	0.992395i	$-0.539281\pi$
$587$	−18.9907	−	5.85786i	−0.783831	−	0.241780i	−0.660739	+	0.750616i	$0.729757\pi$
$588$	−11.7460	−	29.9283i	−0.484397	−	1.23422i
$589$	2.22974	−	1.52021i	0.0918748	−	0.0626391i
$590$	7.45418	+	1.12354i	0.306884	+	0.0462553i
$591$	0.903091	−	3.95670i	0.0371482	−	0.162757i
$592$	15.7000	+	10.7041i	0.645265	+	0.439934i
$593$	31.4712	+	29.2010i	1.29237	+	1.19914i	0.967353	+	0.253434i	$0.0815599\pi$
$593$	31.4712	+	29.2010i	1.29237	+	1.19914i	0.325015	+	0.945709i	$0.394631\pi$
$594$	0.141424	+	0.0681064i	0.00580271	+	0.00279444i
$595$	14.2113	−	24.6147i	0.582607	−	1.00910i
$596$	12.0452	+	20.8630i	0.493392	+	0.854580i
$597$	−3.94885	−	52.6938i	−0.161616	−	2.15661i
$598$	−2.33433	−	10.2274i	−0.0954580	−	0.418229i
$599$	−13.3210	+	33.9414i	−0.544282	+	1.38681i	0.348920	+	0.937152i	$0.386548\pi$
$599$	−13.3210	+	33.9414i	−0.544282	+	1.38681i	−0.893202	+	0.449655i	$0.851547\pi$
$600$	2.94463	−	3.69244i	0.120214	−	0.150743i
$601$	41.7920			1.70473			0.852366	−	0.522946i	$-0.175167\pi$
$601$	41.7920			1.70473			0.852366	+	0.522946i	$0.175167\pi$
$602$	5.10916	−	5.01646i	0.208234	−	0.204456i
$603$	9.70106			0.395058
$604$	7.98409	−	10.0117i	0.324868	−	0.407372i
$605$	0.661738	−	1.68608i	0.0269035	−	0.0685490i
$606$	−0.535179	−	2.34477i	−0.0217402	−	0.0952499i
$607$	1.45963	+	19.4774i	0.0592446	+	0.790565i	0.945137	+	0.326674i	$0.105928\pi$
$607$	1.45963	+	19.4774i	0.0592446	+	0.790565i	−0.885892	+	0.463891i	$0.846453\pi$
$608$	−10.0371	−	17.3848i	−0.407058	−	0.705045i
$609$	14.2385	−	24.6619i	0.576974	−	0.999349i
$610$	−6.48638	−	3.12368i	−0.262626	−	0.126474i
$611$	22.9869	+	21.3287i	0.929950	+	0.862867i
$612$	18.4293	+	12.5649i	0.744960	+	0.507905i
$613$	−6.32687	+	27.7198i	−0.255540	+	1.11959i	0.670423	+	0.741979i	$0.266113\pi$
$613$	−6.32687	+	27.7198i	−0.255540	+	1.11959i	−0.925963	+	0.377614i	$0.876745\pi$
$614$	−2.83560	−	0.427397i	−0.114435	−	0.0172484i
$615$	25.7785	−	17.5755i	1.03949	−	0.708712i
$616$	−1.56168	−	3.97911i	−0.0629221	−	0.160323i
$617$	33.1576	+	10.2278i	1.33487	+	0.411754i	0.878376	−	0.477970i	$-0.158627\pi$
$617$	33.1576	+	10.2278i	1.33487	+	0.411754i	0.456498	+	0.889724i	$0.349104\pi$
$618$	−3.98169	+	1.91748i	−0.160167	+	0.0771323i
$619$	−0.521635	+	6.96073i	−0.0209663	+	0.279775i	0.976860	+	0.213879i	$0.0686098\pi$
$619$	−0.521635	+	6.96073i	−0.0209663	+	0.279775i	−0.997826	+	0.0658966i	$0.979009\pi$
$620$	1.52448	−	0.229778i	0.0612244	−	0.00922809i
$621$	1.98580	−	1.84255i	0.0796872	−	0.0739389i
$622$	−6.50401	+	2.00622i	−0.260787	+	0.0804421i
$623$	9.30353	+	11.6663i	0.372738	+	0.467399i
$624$	37.3535	+	46.8399i	1.49534	+	1.87510i
$625$	−12.8506	+	3.96390i	−0.514026	+	0.158556i
$626$	−0.0855248	+	0.0793554i	−0.00341826	+	0.00317168i
$627$	−14.4277	+	2.17463i	−0.576188	+	0.0868464i
$628$	1.33355	−	17.7949i	0.0532143	−	0.710095i
$629$	20.5485	−	9.89565i	0.819323	−	0.394565i
$630$	5.24698	+	1.61848i	0.209045	+	0.0644818i
$631$	−0.797782	−	2.03271i	−0.0317592	−	0.0809211i	0.914114	−	0.405456i	$-0.132887\pi$
$631$	−0.797782	−	2.03271i	−0.0317592	−	0.0809211i	−0.945874	+	0.324535i	$0.894792\pi$
$632$	−9.27525	+	6.32376i	−0.368950	+	0.251546i
$633$	18.3027	+	2.75869i	0.727469	+	0.109648i
$634$	0.837112	−	3.66763i	0.0332459	−	0.145660i
$635$	6.11235	+	4.16733i	0.242561	+	0.165375i
$636$	−17.5157	−	16.2522i	−0.694543	−	0.644442i
$637$	−44.8844	−	21.6152i	−1.77838	−	0.856425i
$638$	0.462513	−	0.801097i	0.0183111	−	0.0317157i
$639$	4.92664	+	8.53319i	0.194895	+	0.337568i
$640$	−1.13331	−	15.1230i	−0.0447982	−	0.597791i
$641$	2.14067	+	9.37890i	0.0845514	+	0.370444i	0.999447	−	0.0332461i	$-0.0105845\pi$
$641$	2.14067	+	9.37890i	0.0845514	+	0.370444i	−0.914896	+	0.403690i	$0.867727\pi$
$642$	4.00674	−	10.2090i	0.158133	−	0.402917i
$643$	−3.83093	+	4.80383i	−0.151077	+	0.189445i	−0.851611	−	0.524175i	$-0.824374\pi$
$643$	−3.83093	+	4.80383i	−0.151077	+	0.189445i	0.700534	+	0.713619i	$0.252945\pi$
$644$	−36.0819			−1.42182
$645$	−2.93632	−	28.3947i	−0.115618	−	1.11804i
$646$	−7.43723			−0.292614
$647$	6.75677	−	8.47272i	0.265636	−	0.333097i	−0.631068	−	0.775727i	$-0.717383\pi$
$647$	6.75677	−	8.47272i	0.265636	−	0.333097i	0.896704	+	0.442630i	$0.145955\pi$
$648$	4.01756	−	10.2366i	0.157825	−	0.402131i
$649$	3.17193	+	13.8971i	0.124509	+	0.545510i
$650$	−0.267485	−	3.56933i	−0.0104916	−	0.140001i
$651$	−1.99777	−	3.46024i	−0.0782988	−	0.135617i
$652$	−13.7863	+	23.8787i	−0.539915	+	0.935160i
$653$	3.76779	+	1.81447i	0.147445	+	0.0710058i	0.506151	−	0.862445i	$-0.331068\pi$
$653$	3.76779	+	1.81447i	0.147445	+	0.0710058i	−0.358706	+	0.933451i	$0.616782\pi$
$654$	−4.46629	−	4.14411i	−0.174646	−	0.162047i
$655$	−11.4810	−	7.82762i	−0.448600	−	0.305850i
$656$	−5.57513	+	24.4262i	−0.217672	+	0.953685i
$657$	−13.9215	−	2.09833i	−0.543130	−	0.0818637i
$658$	−3.96743	+	2.70495i	−0.154667	+	0.105450i
$659$	−5.90619	−	15.0487i	−0.230072	−	0.586215i	0.768487	−	0.639865i	$-0.221010\pi$
$659$	−5.90619	−	15.0487i	−0.230072	−	0.586215i	−0.998560	+	0.0536499i	$0.982914\pi$
$660$	−7.96507	−	2.45690i	−0.310040	−	0.0956347i
$661$	−10.0597	+	4.84452i	−0.391279	+	0.188430i	−0.619171	−	0.785257i	$-0.712531\pi$
$661$	−10.0597	+	4.84452i	−0.391279	+	0.188430i	0.227892	+	0.973686i	$0.426817\pi$
$662$	−0.176303	+	2.35260i	−0.00685222	+	0.0914365i
$663$	71.1053	−	10.7174i	2.76150	−	0.416229i
$664$	−9.91421	+	9.19905i	−0.384746	+	0.356992i
$665$	39.2967	−	12.1214i	1.52386	−	0.470048i
$666$	2.74715	+	3.44482i	0.106450	+	0.133484i
$667$	−9.95335	−	12.4811i	−0.385395	−	0.483270i
$668$	−0.884024	+	0.272685i	−0.0342039	+	0.0105505i
$669$	11.2730	−	10.4598i	0.435838	−	0.404398i
$670$	−1.82726	+	0.275414i	−0.0705930	+	0.0106402i
$671$	1.01733	−	13.5754i	0.0392737	−	0.524071i
$672$	−26.7778	+	12.8955i	−1.03298	+	0.497455i
$673$	−4.90217	−	1.51212i	−0.188965	−	0.0582879i	0.198828	−	0.980034i	$-0.436286\pi$
$673$	−4.90217	−	1.51212i	−0.188965	−	0.0582879i	−0.387793	+	0.921746i	$0.626763\pi$
$674$	0.573818	+	1.46206i	0.0221026	+	0.0563166i
$675$	0.763689	−	0.520674i	0.0293944	−	0.0200408i
$676$	71.6580	+	10.8007i	2.75608	+	0.415412i
$677$	4.60343	−	20.1689i	0.176924	−	0.775156i	−0.806115	−	0.591759i	$-0.798434\pi$
$677$	4.60343	−	20.1689i	0.176924	−	0.775156i	0.983039	−	0.183396i	$-0.0587092\pi$
$678$	−6.41666	−	4.37480i	−0.246430	−	0.168013i
$679$	33.6607	+	31.2325i	1.29178	+	1.19859i
$680$	−7.82641	−	3.76900i	−0.300129	−	0.144535i
$681$	−10.7258	+	18.5776i	−0.411014	+	0.711897i
$682$	−0.0648940	−	0.112400i	−0.00248492	−	0.00430401i
$683$	1.19500	+	15.9462i	0.0457254	+	0.610163i	0.972252	+	0.233935i	$0.0751602\pi$
$683$	1.19500	+	15.9462i	0.0457254	+	0.610163i	−0.926527	+	0.376228i	$0.877221\pi$
$684$	7.18129	+	31.4633i	0.274583	+	1.20303i
$685$	−0.147274	+	0.375248i	−0.00562705	+	0.0143375i
$686$	−0.00925694	+	0.0116078i	−0.000353432	+	0.000443189i
$687$	−21.2785			−0.811827
$688$	17.2377	+	15.1111i	0.657181	+	0.576106i
$689$	−37.0243			−1.41051
$690$	3.99303	−	5.00710i	0.152012	−	0.190617i
$691$	−11.8548	+	30.2056i	−0.450979	+	1.14908i	0.506926	+	0.861989i	$0.330782\pi$
$691$	−11.8548	+	30.2056i	−0.450979	+	1.14908i	−0.957905	+	0.287086i	$0.907314\pi$
$692$	−10.6789	−	46.7874i	−0.405952	−	1.77859i
$693$	0.775918	+	10.3539i	0.0294747	+	0.393313i
$694$	3.62766	+	6.28329i	0.137704	+	0.238510i
$695$	12.4174	−	21.5076i	0.471020	−	0.815830i
$696$	−7.84140	−	3.77622i	−0.297228	−	0.143137i
$697$	22.0443	+	20.4541i	0.834988	+	0.774755i
$698$	3.97343	+	2.70904i	0.150397	+	0.102539i
$699$	6.43707	−	28.2026i	0.243472	−	1.06672i
$700$	−12.1737	−	1.83489i	−0.460122	−	0.0693522i
$701$	28.8029	−	19.6375i	1.08787	−	0.741698i	0.119907	−	0.992785i	$-0.461740\pi$
$701$	28.8029	−	19.6375i	1.08787	−	0.741698i	0.967964	+	0.251087i	$0.0807881\pi$
$702$	−0.408926	−	1.04193i	−0.0154339	−	0.0393250i
$703$	31.5328	+	9.72658i	1.18928	+	0.366845i
$704$	5.42937	−	2.61464i	0.204627	−	0.0985431i
$705$	−1.43061	+	19.0902i	−0.0538800	+	0.718978i
$706$	7.00014	−	1.05510i	0.263454	−	0.0397092i
$707$	−9.39623	+	8.71843i	−0.353382	+	0.327890i
$708$	62.6837	−	19.3354i	2.35580	−	0.726667i
$709$	25.0676	+	31.4338i	0.941433	+	1.18052i	0.983409	+	0.181401i	$0.0580633\pi$
$709$	25.0676	+	31.4338i	0.941433	+	1.18052i	−0.0419761	+	0.999119i	$0.513365\pi$
$710$	−1.17022	−	1.46741i	−0.0439176	−	0.0550710i
$711$	26.0561	−	8.03725i	0.977181	−	0.301420i
$712$	3.34304	−	3.10189i	0.125286	−	0.116248i
$713$	−2.21484	+	0.333833i	−0.0829464	+	0.0125022i
$714$	−0.822875	+	10.9805i	−0.0307953	+	0.410935i
$715$	−11.6367	+	5.60394i	−0.435188	+	0.209575i
$716$	−34.9726	−	10.7876i	−1.30699	−	0.403152i
$717$	−8.11896	−	20.6868i	−0.303208	−	0.772562i
$718$	6.54924	−	4.46520i	0.244416	−	0.166640i
$719$	−50.8937	−	7.67100i	−1.89802	−	0.286080i	−0.907137	−	0.420835i	$-0.861737\pi$
$719$	−50.8937	−	7.67100i	−1.89802	−	0.286080i	−0.990879	+	0.134755i	$0.956975\pi$
$720$	−3.91176	+	17.1385i	−0.145783	+	0.638715i
$721$	19.4605	+	13.2679i	0.724746	+	0.494123i
$722$	−3.82158	−	3.54591i	−0.142224	−	0.131965i
$723$	−22.9727	−	11.0631i	−0.854364	−	0.411440i
$724$	11.0169	−	19.0818i	0.409439	−	0.709169i
$725$	−2.72346	−	4.71717i	−0.101147	−	0.175191i
$726$	0.0524394	+	0.699756i	0.00194621	+	0.0259704i
$727$	7.15140	+	31.3323i	0.265231	+	1.16205i	0.915490	+	0.402340i	$0.131803\pi$
$727$	7.15140	+	31.3323i	0.265231	+	1.16205i	−0.650260	+	0.759712i	$0.725340\pi$
$728$	−11.1359	+	28.3738i	−0.412724	+	1.05160i
$729$	−14.2371	+	17.8528i	−0.527302	+	0.661215i
$730$	2.68178			0.0992570
$731$	26.0523	−	8.84923i	0.963580	−	0.327301i
$732$	−62.6477			−2.31553
$733$	−4.35426	+	5.46007i	−0.160828	+	0.201672i	−0.855716	−	0.517446i	$-0.826883\pi$
$733$	−4.35426	+	5.46007i	−0.160828	+	0.201672i	0.694887	+	0.719119i	$0.255454\pi$
$734$	−2.86217	+	7.29268i	−0.105645	+	0.269178i
$735$	−6.76765	−	29.6510i	−0.249628	−	1.09369i
$736$	1.24510	+	16.6148i	0.0458951	+	0.612428i
$737$	−1.74712	−	3.02609i	−0.0643559	−	0.111468i
$738$	−2.90478	+	5.03123i	−0.106927	+	0.185202i
$739$	−41.2918	−	19.8851i	−1.51894	−	0.731484i	−0.526045	−	0.850457i	$-0.676326\pi$
$739$	−41.2918	−	19.8851i	−1.51894	−	0.731484i	−0.992898	+	0.118973i	$0.962040\pi$
$740$	13.8192	+	12.8224i	0.508005	+	0.471359i
$741$	85.9634	+	58.6088i	3.15794	+	2.15305i
$742$	1.26158	−	5.52736i	0.0463142	−	0.202916i
$743$	−21.6770	−	3.26728i	−0.795251	−	0.119865i	−0.261164	−	0.965294i	$-0.584106\pi$
$743$	−21.6770	−	3.26728i	−0.795251	−	0.119865i	−0.534087	+	0.845430i	$0.679344\pi$
$744$	−1.00895	+	0.687891i	−0.0369899	+	0.0252193i
$745$	8.32566	+	21.2134i	0.305029	+	0.777200i
$746$	−7.29592	−	2.25049i	−0.267122	−	0.0823964i
$747$	29.5978	−	14.2535i	1.08293	−	0.521510i
$748$	0.600387	−	8.01161i	0.0219523	−	0.292933i
$749$	−57.7970	+	8.71150i	−2.11186	+	0.318311i
$750$	6.26044	−	5.80884i	0.228599	−	0.212109i
$751$	−35.1868	+	10.8537i	−1.28398	+	0.396057i	−0.860316	−	0.509760i	$-0.829734\pi$
$751$	−35.1868	+	10.8537i	−1.28398	+	0.396057i	−0.423668	+	0.905817i	$0.639258\pi$
$752$	−9.58491	−	12.0191i	−0.349526	−	0.438291i
$753$	−7.44113	−	9.33088i	−0.271170	−	0.340036i
$754$	−6.30304	+	1.94423i	−0.229543	+	0.0708047i
$755$	8.87986	−	8.23930i	0.323171	−	0.299859i
$756$	−3.80684	+	0.573789i	−0.138454	+	0.0208685i
$757$	−2.62781	+	35.0657i	−0.0955095	+	1.27449i	0.719277	+	0.694724i	$0.244473\pi$
$757$	−2.62781	+	35.0657i	−0.0955095	+	1.27449i	−0.814786	+	0.579762i	$0.803146\pi$
$758$	4.31131	−	2.07622i	0.156594	−	0.0754116i
$759$	11.5721	+	3.56952i	0.420040	+	0.129565i
$760$	−4.59176	−	11.6996i	−0.166561	−	0.424390i
$761$	37.5971	−	25.6333i	1.36289	−	0.929205i	0.362897	−	0.931829i	$-0.381788\pi$
$761$	37.5971	−	25.6333i	1.36289	−	0.929205i	0.999997	+	0.00262444i	$0.000835387\pi$
$762$	−2.83399	−	0.427156i	−0.102665	−	0.0154742i
$763$	−7.22559	+	31.6574i	−0.261584	+	1.14607i
$764$	22.4780	+	15.3252i	0.813224	+	0.554447i
$765$	15.4672	+	14.3515i	0.559220	+	0.518880i
$766$	1.46188	+	0.704004i	0.0528198	+	0.0254367i
$767$	50.8223	−	88.0269i	1.83509	−	3.17847i
$768$	−11.5456	−	19.9975i	−0.416614	−	0.721597i
$769$	3.21025	+	42.8377i	0.115764	+	1.54477i	0.688626	+	0.725117i	$0.258214\pi$
$769$	3.21025	+	42.8377i	0.115764	+	1.54477i	−0.572862	+	0.819652i	$0.694167\pi$
$770$	−0.440098	−	1.92819i	−0.0158600	−	0.0694873i
$771$	4.56584	−	11.6336i	0.164435	−	0.418973i
$772$	11.9097	−	14.9342i	0.428638	−	0.537495i
$773$	−23.6351			−0.850094			−0.425047	−	0.905171i	$-0.639742\pi$
$773$	−23.6351			−0.850094			−0.425047	+	0.905171i	$0.639742\pi$
$774$	2.78666	+	4.52641i	0.100165	+	0.162699i
$775$	−0.764242			−0.0274524
$776$	8.74996	−	10.9721i	0.314105	−	0.393876i
$777$	17.8494	−	45.4796i	0.640345	−	1.63157i
$778$	0.919121	+	4.02693i	0.0329521	+	0.144372i
$779$	3.25151	+	43.3884i	0.116497	+	1.55455i
$780$	29.7186	+	51.4741i	1.06410	+	1.84307i
$781$	1.77453	−	3.07358i	0.0634977	−	0.109981i
$782$	5.56151	+	2.67828i	0.198879	+	0.0957752i
$783$	−1.24862	−	1.15855i	−0.0446219	−	0.0414030i
$784$	20.1792	+	13.7580i	0.720687	+	0.491356i
$785$	3.75628	−	16.4574i	0.134068	−	0.587388i
$786$	5.32318	+	0.802340i	0.189871	+	0.0286185i
$787$	−21.3999	+	14.5902i	−0.762825	+	0.520086i	−0.881120	−	0.472893i	$-0.843210\pi$
$787$	−21.3999	+	14.5902i	−0.762825	+	0.520086i	0.118294	+	0.992979i	$0.462257\pi$
$788$	1.18126	+	3.00981i	0.0420808	+	0.107220i
$789$	−36.5802	−	11.2835i	−1.30229	−	0.401703i
$790$	−4.67965	+	2.25360i	−0.166495	+	0.0801795i
$791$	−3.09307	+	41.2741i	−0.109977	+	1.46754i
$792$	3.13784	−	0.472954i	0.111498	−	0.0168057i
$793$	−71.1597	+	66.0265i	−2.52695	+	2.34467i
$794$	4.36589	−	1.34670i	0.154940	−	0.0477925i
$795$	−14.0928	−	17.6718i	−0.499820	−	0.626755i
$796$	26.2478	+	32.9137i	0.930328	+	1.16659i
$797$	−35.8012	+	11.0432i	−1.26814	+	0.391171i	−0.854587	−	0.519308i	$-0.826190\pi$
$797$	−35.8012	+	11.0432i	−1.26814	+	0.391171i	−0.413557	+	0.910478i	$0.635714\pi$
$798$	−11.6789	+	10.8364i	−0.413428	+	0.383605i
$799$	−18.2456	+	2.75008i	−0.645483	+	0.0972909i
$800$	−0.424831	+	5.66898i	−0.0150200	+	0.200429i
$801$	−9.98028	+	4.80625i	−0.352636	+	0.169821i
$802$	−6.59243	−	2.03350i	−0.232787	−	0.0718052i
$803$	1.85266	+	4.72050i	0.0653789	+	0.166583i
$804$	−13.2860	+	9.05827i	−0.468562	+	0.319460i
$805$	−33.7509	−	5.08714i	−1.18956	−	0.179298i
$806$	−0.205939	+	0.902276i	−0.00725388	+	0.0317813i
$807$	54.6593	+	37.2661i	1.92410	+	1.31183i
$808$	2.87172	+	2.66457i	0.101027	+	0.0937392i
$809$	−14.2760	−	6.87494i	−0.501916	−	0.241710i	0.165754	−	0.986167i	$-0.446994\pi$
$809$	−14.2760	−	6.87494i	−0.501916	−	0.241710i	−0.667670	+	0.744457i	$0.732708\pi$
$810$	2.54400	−	4.40634i	0.0893871	−	0.154823i
$811$	2.36796	+	4.10143i	0.0831504	+	0.144021i	0.904602	−	0.426258i	$-0.140168\pi$
$811$	2.36796	+	4.10143i	0.0831504	+	0.144021i	−0.821451	+	0.570279i	$0.806835\pi$
$812$	1.69542	+	22.6239i	0.0594977	+	0.793942i
$813$	1.44622	+	6.33629i	0.0507210	+	0.222223i
$814$	0.579807	−	1.47733i	0.0203222	−	0.0517802i
$815$	−16.2624	+	20.3924i	−0.569646	+	0.714313i
$816$	−35.2528			−1.23409
$817$	36.3405	+	16.2528i	1.27139	+	0.568614i
$818$	0.415269			0.0145195
$819$	46.1617	−	57.8850i	1.61302	−	2.02266i
$820$	−9.08110	+	23.1383i	−0.317126	+	0.808023i
$821$	1.21370	+	5.31758i	0.0423585	+	0.185585i	0.991681	−	0.128718i	$-0.0410863\pi$
$821$	1.21370	+	5.31758i	0.0423585	+	0.185585i	−0.949323	+	0.314303i	$0.898229\pi$
$822$	−0.0116707	−	0.155735i	−0.000407063	−	0.00543188i
$823$	−19.1204	−	33.1176i	−0.666496	−	1.15441i	−0.978877	−	0.204449i	$-0.934460\pi$
$823$	−19.1204	−	33.1176i	−0.666496	−	1.15441i	0.312381	−	0.949957i	$-0.398873\pi$
$824$	3.59921	−	6.23401i	0.125384	−	0.217172i
$825$	3.72279	+	1.79280i	0.129611	+	0.0624173i
$826$	11.4098	+	10.5867i	0.396997	+	0.368360i
$827$	−12.2218	−	8.33268i	−0.424993	−	0.289756i	0.331874	−	0.943324i	$-0.392319\pi$
$827$	−12.2218	−	8.33268i	−0.424993	−	0.289756i	−0.756868	+	0.653568i	$0.773271\pi$
$828$	5.96038	−	26.1141i	0.207138	−	0.907529i
$829$	−15.3831	−	2.31863i	−0.534276	−	0.0805292i	−0.123638	−	0.992327i	$-0.539456\pi$
$829$	−15.3831	−	2.31863i	−0.534276	−	0.0805292i	−0.410639	+	0.911798i	$0.634694\pi$
$830$	−5.17026	+	3.52503i	−0.179462	+	0.122355i
$831$	22.8211	+	58.1471i	0.791654	+	2.01710i
$832$	−41.0615	−	12.6658i	−1.42355	−	0.439108i
$833$	26.4111	−	12.7189i	0.915090	−	0.440684i
$834$	−0.719005	+	9.59445i	−0.0248971	+	0.332229i
$835$	−0.865361	+	0.130432i	−0.0299471	+	0.00451379i
$836$	8.52116	−	7.90648i	0.294710	−	0.273451i
$837$	−0.228370	+	0.0704427i	−0.00789361	+	0.00243485i
$838$	−4.55186	−	5.70786i	−0.157242	−	0.197175i
$839$	29.4700	+	36.9542i	1.01742	+	1.27580i	0.960752	+	0.277409i	$0.0894756\pi$
$839$	29.4700	+	36.9542i	1.01742	+	1.27580i	0.0566661	+	0.998393i	$0.481953\pi$
$840$	−17.7816	+	5.48491i	−0.613525	+	0.189247i
$841$	13.9004	−	12.8976i	0.479323	−	0.444746i
$842$	0.554522	−	0.0835807i	0.0191101	−	0.00288038i
$843$	1.64387	−	21.9360i	0.0566180	−	0.755515i
$844$	−13.2859	+	6.39816i	−0.457320	+	0.220234i
$845$	65.5060	+	20.2059i	2.25348	+	0.695105i
$846$	−1.30232	−	3.31825i	−0.0447746	−	0.114084i
$847$	3.09000	−	2.10673i	0.106174	−	0.0723880i
$848$	17.9483	+	2.70526i	0.616346	+	0.0928992i
$849$	−6.61584	+	28.9859i	−0.227055	+	0.994793i
$850$	1.74020	+	1.18645i	0.0596884	+	0.0406949i
$851$	−20.0773	−	18.6290i	−0.688241	−	0.638595i
$852$	−14.7150	−	7.08638i	−0.504129	−	0.242776i
$853$	24.4925	−	42.4223i	0.838608	−	1.45251i	−0.0524504	−	0.998624i	$-0.516703\pi$
$853$	24.4925	−	42.4223i	0.838608	−	1.45251i	0.891059	−	0.453888i	$-0.149964\pi$
$854$	−7.43238	−	12.8733i	−0.254331	−	0.440514i
$855$	2.28140	+	30.4432i	0.0780223	+	1.04114i
$856$	3.97505	+	17.4158i	0.135865	+	0.595261i
$857$	11.6922	−	29.7913i	0.399398	−	1.01765i	−0.579803	−	0.814757i	$-0.696870\pi$
$857$	11.6922	−	29.7913i	0.399398	−	1.01765i	0.979201	−	0.202893i	$-0.0650345\pi$
$858$	3.11978	−	3.91208i	0.106508	−	0.133556i
$859$	51.7041			1.76412			0.882060	−	0.471136i	$-0.156156\pi$
$859$	51.7041			1.76412			0.882060	+	0.471136i	$0.156156\pi$
$860$	14.6761	+	17.3731i	0.500451	+	0.592419i
$861$	64.4195			2.19541
$862$	4.41079	−	5.53095i	0.150232	−	0.188385i
$863$	−2.79132	+	7.11216i	−0.0950176	+	0.242101i	−0.970478	−	0.241188i	$-0.922463\pi$
$863$	−2.79132	+	7.11216i	−0.0950176	+	0.242101i	0.875461	+	0.483289i	$0.160558\pi$
$864$	0.395580	+	1.73315i	0.0134579	+	0.0589630i
$865$	−3.39256	−	45.2705i	−0.115350	−	1.53924i
$866$	1.83745	+	3.18255i	0.0624390	+	0.108148i
$867$	−0.727501	+	1.26007i	−0.0247072	+	0.0427942i
$868$	2.86796	+	1.38114i	0.0973449	+	0.0468788i
$869$	−7.19968	−	6.68033i	−0.244232	−	0.226615i
$870$	−3.32715	−	2.26842i	−0.112801	−	0.0769065i
$871$	−5.54440	+	24.2916i	−0.187865	+	0.823090i
$872$	9.81326	+	1.47911i	0.332319	+	0.0500890i
$873$	−28.1649	+	19.2025i	−0.953237	+	0.649906i
$874$	3.26294	+	8.31384i	0.110371	+	0.281220i
$875$	−43.4935	−	13.4160i	−1.47035	−	0.453542i
$876$	21.0254	−	10.1253i	0.710384	−	0.342103i
$877$	−0.579595	+	7.73416i	−0.0195715	+	0.261164i	0.978831	+	0.204669i	$0.0656117\pi$
$877$	−0.579595	+	7.73416i	−0.0195715	+	0.261164i	−0.998403	+	0.0564954i	$0.982007\pi$
$878$	−10.3772	+	1.56411i	−0.350213	+	0.0527861i
$879$	11.8902	−	11.0325i	0.401048	−	0.372118i
$880$	6.05058	−	1.86636i	0.203965	−	0.0629149i
$881$	−36.7976	−	46.1427i	−1.23974	−	1.55459i	−0.703979	−	0.710221i	$-0.748595\pi$
$881$	−36.7976	−	46.1427i	−1.23974	−	1.55459i	−0.535764	−	0.844368i	$-0.679976\pi$
$882$	3.53092	+	4.42763i	0.118892	+	0.149086i
$883$	29.0346	−	8.95598i	0.977091	−	0.301393i	0.235225	−	0.971941i	$-0.424417\pi$
$883$	29.0346	−	8.95598i	0.977091	−	0.301393i	0.741866	+	0.670548i	$0.233941\pi$
$884$	−41.9955	+	38.9661i	−1.41246	+	1.31057i
$885$	61.3603	−	9.24858i	2.06260	−	0.310888i
$886$	0.0434970	−	0.580427i	0.00146131	−	0.0194998i
$887$	7.54970	−	3.63574i	0.253494	−	0.122076i	−0.302822	−	0.953047i	$-0.597929\pi$
$887$	7.54970	−	3.63574i	0.253494	−	0.122076i	0.556316	+	0.830971i	$0.312214\pi$
$888$	−14.2685	−	4.40125i	−0.478820	−	0.147696i
$889$	5.58041	+	14.2186i	0.187161	+	0.476878i
$890$	1.74340	−	1.18863i	0.0584388	−	0.0398429i
$891$	9.51358	+	1.43394i	0.318717	+	0.0480388i
$892$	−2.72623	+	11.9444i	−0.0912808	+	0.399927i
$893$	−22.0582	−	15.0390i	−0.738149	−	0.503261i
$894$	−6.47187	−	6.00501i	−0.216452	−	0.200838i
$895$	−31.1924	−	15.0215i	−1.04265	−	0.502112i
$896$	15.6563	−	27.1176i	0.523042	−	0.905934i
$897$	−43.1768	−	74.7843i	−1.44163	−	2.49698i
$898$	0.833245	+	11.1189i	0.0278057	+	0.371042i
$899$	0.313390	+	1.37305i	0.0104521	+	0.0457938i
$900$	3.33897	−	8.50756i	0.111299	−	0.283585i
$901$	13.5834	−	17.0330i	0.452527	−	0.567451i
$902$	2.09255			0.0696744
$903$	28.0169	−	51.8557i	0.932343	−	1.72565i
$904$	12.6498			0.420725
$905$	12.9955	−	16.2958i	0.431985	−	0.541692i
$906$	−1.71453	+	4.36854i	−0.0569613	+	0.145135i
$907$	−0.881249	−	3.86101i	−0.0292614	−	0.128203i	0.958188	−	0.286141i	$-0.0923725\pi$
$907$	−0.881249	−	3.86101i	−0.0292614	−	0.128203i	−0.987449	+	0.157938i	$0.949515\pi$
$908$	−1.27715	−	17.0424i	−0.0423838	−	0.565573i
$909$	−4.75777	−	8.24070i	−0.157805	−	0.273327i
$910$	−7.05148	+	12.2135i	−0.233754	+	0.404874i
$911$	−10.8739	−	5.23658i	−0.360268	−	0.173496i	0.244990	−	0.969526i	$-0.421215\pi$
$911$	−10.8739	−	5.23658i	−0.360268	−	0.173496i	−0.605257	+	0.796030i	$0.706930\pi$
$912$	−37.3900	−	34.6929i	−1.23811	−	1.14880i
$913$	−9.77659	−	6.66556i	−0.323558	−	0.220598i
$914$	−0.270646	+	1.18578i	−0.00895217	+	0.0392220i
$915$	−58.6007	−	8.83263i	−1.93728	−	0.291998i
$916$	14.0067	−	9.54960i	0.462794	−	0.315528i
$917$	−10.4818	−	26.7073i	−0.346141	−	0.881953i
$918$	0.629363	+	0.194133i	0.0207721	+	0.00640733i
$919$	−29.7880	+	14.3451i	−0.982614	+	0.473202i	−0.855003	−	0.518622i	$-0.826445\pi$
$919$	−29.7880	+	14.3451i	−0.982614	+	0.473202i	−0.127611	+	0.991824i	$0.540731\pi$
$920$	−0.779558	+	10.4025i	−0.0257013	+	0.342959i
$921$	−23.3417	+	3.51819i	−0.769135	+	0.115928i
$922$	0.816245	−	0.757365i	0.0268816	−	0.0249425i
$923$	−24.1829	+	7.45945i	−0.795991	+	0.245531i
$924$	−10.7305	−	13.4556i	−0.353008	−	0.442658i
$925$	−5.82654	−	7.30625i	−0.191576	−	0.240228i
$926$	−2.87245	+	0.886033i	−0.0943946	+	0.0291169i
$927$	−12.8173	+	11.8927i	−0.420976	+	0.390608i
$928$	10.3592	−	1.56140i	0.340057	−	0.0512554i
$929$	−0.538194	+	7.18170i	−0.0176576	+	0.235624i	0.981391	+	0.192019i	$0.0615034\pi$
$929$	−0.538194	+	7.18170i	−0.0176576	+	0.235624i	−0.999049	+	0.0436052i	$0.986116\pi$
$930$	−0.509047	+	0.245144i	−0.0166923	+	0.00803859i
$931$	40.5292	+	12.5016i	1.32829	+	0.409724i
$932$	8.41983	+	21.4534i	0.275801	+	0.702729i
$933$	−46.2925	+	31.5617i	−1.51555	+	1.03328i
$934$	−9.96439	−	1.50189i	−0.326045	−	0.0491433i
$935$	1.69115	−	7.40941i	0.0553065	−	0.242313i
$936$	−18.6959	−	12.7467i	−0.611095	−	0.416638i
$937$	2.93110	+	2.71966i	0.0957547	+	0.0888474i	0.726598	−	0.687063i	$-0.241100\pi$
$937$	2.93110	+	2.71966i	0.0957547	+	0.0888474i	−0.630843	+	0.775910i	$0.717291\pi$
$938$	−3.43757	−	1.65545i	−0.112241	−	0.0540523i
$939$	−0.480192	+	0.831717i	−0.0156705	+	0.0271421i
$940$	−7.62578	−	13.2082i	−0.248726	−	0.430805i
$941$	−4.29093	−	57.2584i	−0.139880	−	1.86657i	−0.421213	−	0.906962i	$-0.638396\pi$
$941$	−4.29093	−	57.2584i	−0.139880	−	1.86657i	0.281333	−	0.959610i	$-0.409223\pi$
$942$	1.45523	+	6.37580i	0.0474141	+	0.207735i
$943$	13.1935	−	33.6165i	0.429640	−	1.09470i
$944$	−31.0690	+	38.9593i	−1.01121	+	1.26802i
$945$	−3.64182			−0.118468
$946$	0.910078	−	1.68444i	0.0295892	−	0.0547659i
$947$	12.1160			0.393717			0.196858	−	0.980432i	$-0.436926\pi$
$947$	12.1160			0.393717			0.196858	+	0.980432i	$0.436926\pi$
$948$	−28.1803	+	35.3370i	−0.915254	+	1.14769i
$949$	13.2108	−	33.6604i	0.428839	−	1.09266i
$950$	0.678099	+	2.97094i	0.0220004	+	0.0963902i
$951$	−2.31417	−	30.8805i	−0.0750422	−	1.00137i
$952$	−8.96784	−	15.5328i	−0.290649	−	0.503419i
$953$	21.3500	−	36.9793i	0.691594	−	1.19788i	−0.279721	−	0.960081i	$-0.590242\pi$
$953$	21.3500	−	36.9793i	0.691594	−	1.19788i	0.971315	−	0.237795i	$-0.0764247\pi$
$954$	3.79201	+	1.82614i	0.122771	+	0.0591234i
$955$	18.8652	+	17.5043i	0.610463	+	0.566427i
$956$	14.6283	+	9.97344i	0.473115	+	0.322564i
$957$	1.69439	−	7.42360i	0.0547718	−	0.239971i
$958$	−1.50077	−	0.226205i	−0.0484877	−	0.00730834i
$959$	−0.687699	+	0.468865i	−0.0222070	+	0.0151405i
$960$	−9.58409	−	24.4199i	−0.309325	−	0.788148i
$961$	−29.4339	−	9.07917i	−0.949482	−	0.292876i
$962$	−10.1959	+	4.91010i	−0.328730	+	0.158308i
$963$	3.24260	−	43.2695i	0.104491	−	1.39434i
$964$	20.0869	−	3.02761i	0.646954	−	0.0975126i
$965$	13.2459	−	12.2904i	0.426399	−	0.395641i
$966$	12.6358	−	3.89762i	0.406550	−	0.125404i
$967$	−13.9767	−	17.5262i	−0.449459	−	0.563604i	0.504550	−	0.863383i	$-0.331659\pi$
$967$	−13.9767	−	17.5262i	−0.449459	−	0.563604i	−0.954009	+	0.299779i	$0.903087\pi$
$968$	−0.712642	−	0.893624i	−0.0229052	−	0.0287222i
$969$	−58.5009	+	18.0451i	−1.87932	+	0.579693i
$970$	4.75987	−	4.41651i	0.152830	−	0.141806i
$971$	−45.5058	+	6.85889i	−1.46035	+	0.220112i	−0.830680	−	0.556751i	$-0.812048\pi$
$971$	−45.5058	+	6.85889i	−1.46035	+	0.220112i	−0.629670	+	0.776863i	$0.716810\pi$
$972$	3.07790	−	41.0717i	0.0987238	−	1.31738i
$973$	46.1994	−	22.2485i	1.48109	−	0.713253i
$974$	7.04997	+	2.17463i	0.225895	+	0.0696795i
$975$	−10.7644	−	27.4272i	−0.344736	−	0.878374i
$976$	39.3204	−	26.8082i	1.25862	−	0.858110i
$977$	21.6834	+	3.26825i	0.693714	+	0.104561i	0.486429	−	0.873720i	$-0.338299\pi$
$977$	21.6834	+	3.26825i	0.693714	+	0.104561i	0.207285	+	0.978281i	$0.433537\pi$
$978$	2.24854	−	9.85148i	0.0719002	−	0.315015i
$979$	3.29664	+	2.24761i	0.105361	+	0.0718339i
$980$	17.7619	+	16.4806i	0.567383	+	0.526454i
$981$	−21.7183	−	10.4590i	−0.693413	−	0.333930i
$982$	0.827029	−	1.43246i	0.0263916	−	0.0457115i
$983$	−11.3101	−	19.5896i	−0.360735	−	0.624811i	0.627347	−	0.778740i	$-0.284141\pi$
$983$	−11.3101	−	19.5896i	−0.360735	−	0.624811i	−0.988082	+	0.153928i	$0.950807\pi$
$984$	−1.47130	−	19.6331i	−0.0469034	−	0.625882i
$985$	0.680604	+	2.98192i	0.0216858	+	0.0950119i
$986$	1.41800	−	3.61300i	0.0451583	−	0.115061i
$987$	−24.6445	+	30.9033i	−0.784445	+	0.983662i
$988$	−82.8888			−2.63704
$989$	−21.3222	−	25.2406i	−0.678008	−	0.802605i
$990$	1.46823			0.0466633
$991$	10.4386	−	13.0896i	0.331592	−	0.415803i	−0.587886	−	0.808943i	$-0.700040\pi$
$991$	10.4386	−	13.0896i	0.331592	−	0.415803i	0.919479	+	0.393140i	$0.128611\pi$
$992$	0.537011	−	1.36828i	0.0170501	−	0.0434430i
$993$	4.32139	+	18.9332i	0.137135	+	0.600828i
$994$	−0.289600	−	3.86445i	−0.00918557	−	0.122573i
$995$	19.9117	+	34.4881i	0.631243	+	1.09335i
$996$	−27.2264	+	47.1575i	−0.862701	+	1.49424i
$997$	1.52025	+	0.732116i	0.0481469	+	0.0231863i	0.457802	−	0.889054i	$-0.348637\pi$
$997$	1.52025	+	0.732116i	0.0481469	+	0.0231863i	−0.409655	+	0.912240i	$0.634351\pi$
$998$	−0.399600	−	0.370775i	−0.0126491	−	0.0117367i
$999$	−2.41452	−	1.64619i	−0.0763920	−	0.0520832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	473.2.r.a.144.9	yes	216
43.23	even	21	inner	473.2.r.a.23.9	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
473.2.r.a.23.9	✓	216	43.23	even	21	inner
473.2.r.a.144.9	yes	216	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 473 = 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	473.r (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.182040 - 0.228271i) q^{2} +(0.878059 - 2.23726i) q^{3} +(0.426073 + 1.86675i) q^{4} +(0.135358 + 1.80623i) q^{5} +(-0.350859 - 0.607706i) q^{6} +(-1.86992 + 3.23880i) q^{7} +(1.02980 + 0.495924i) q^{8} +(-2.03518 - 1.88837i) q^{9} +O(q^{10})\)	\(q+(0.182040 - 0.228271i) q^{2} +(0.878059 - 2.23726i) q^{3} +(0.426073 + 1.86675i) q^{4} +(0.135358 + 1.80623i) q^{5} +(-0.350859 - 0.607706i) q^{6} +(-1.86992 + 3.23880i) q^{7} +(1.02980 + 0.495924i) q^{8} +(-2.03518 - 1.88837i) q^{9} +(0.436949 + 0.297907i) q^{10} +(-0.222521 + 0.974928i) q^{11} +(4.55051 + 0.685879i) q^{12} +(5.89166 - 4.01686i) q^{13} +(0.398923 + 1.01644i) q^{14} +(4.15984 + 1.28314i) q^{15} +(-3.14960 + 1.51677i) q^{16} +(-0.313558 + 4.18415i) q^{17} +(-0.801543 + 0.120813i) q^{18} +(-4.45026 + 4.12924i) q^{19} +(-3.31409 + 1.02226i) q^{20} +(5.60412 + 7.02735i) q^{21} +(0.182040 + 0.228271i) q^{22} +(4.81489 - 1.48520i) q^{23} +(2.01373 - 1.86847i) q^{24} +(1.70003 - 0.256238i) q^{25} +(0.155584 - 2.07612i) q^{26} +(0.484381 - 0.233265i) q^{27} +(-6.84274 - 2.11070i) q^{28} +(-1.15749 - 2.94922i) q^{29} +(1.05016 - 0.715988i) q^{30} +(-0.439561 - 0.0662532i) q^{31} +(-0.735797 + 3.22374i) q^{32} +(1.98578 + 1.35388i) q^{33} +(0.898039 + 0.833258i) q^{34} +(-6.10310 - 2.93910i) q^{35} +(2.65797 - 4.60374i) q^{36} +(-2.71780 - 4.70737i) q^{37} +(0.132460 + 1.76755i) q^{38} +(-3.81354 - 16.7082i) q^{39} +(-0.756360 + 1.92717i) q^{40} +(4.46857 - 5.60341i) q^{41} +2.62431 q^{42} +(-2.56713 - 6.03406i) q^{43} -1.91475 q^{44} +(3.13534 - 3.93159i) q^{45} +(0.537476 - 1.36947i) q^{46} +(0.978553 + 4.28732i) q^{47} +(0.627865 + 8.37827i) q^{48} +(-3.49320 - 6.05040i) q^{49} +(0.250981 - 0.434712i) q^{50} +(9.08569 + 4.37544i) q^{51} +(10.0087 + 9.28676i) q^{52} +(-4.29003 - 2.92489i) q^{53} +(0.0349289 - 0.153034i) q^{54} +(-1.79106 - 0.269959i) q^{55} +(-3.53184 + 2.40796i) q^{56} +(5.33058 + 13.5821i) q^{57} +(-0.883931 - 0.272656i) q^{58} +(12.8429 - 6.18480i) q^{59} +(-0.622905 + 8.31208i) q^{60} +(-13.4614 + 2.02898i) q^{61} +(-0.0951414 + 0.0882783i) q^{62} +(9.92166 - 3.06043i) q^{63} +(-3.75724 - 4.71143i) q^{64} +(8.05284 + 10.0979i) q^{65} +(0.670543 - 0.206835i) q^{66} +(-2.56145 + 2.37668i) q^{67} +(-7.94434 + 1.19742i) q^{68} +(0.904989 - 12.0762i) q^{69} +(-1.78192 + 0.858127i) q^{70} +(-3.39138 - 1.04610i) q^{71} +(-1.15933 - 2.95393i) q^{72} +(4.18989 - 2.85662i) q^{73} +(-1.56930 - 0.236535i) q^{74} +(0.919453 - 4.02839i) q^{75} +(-9.60438 - 6.54816i) q^{76} +(-2.74150 - 2.54374i) q^{77} +(-4.50821 - 2.17104i) q^{78} +(-4.91076 + 8.50568i) q^{79} +(-3.16594 - 5.48358i) q^{80} +(-0.718981 - 9.59414i) q^{81} +(-0.465637 - 2.04009i) q^{82} +(-4.32295 + 11.0147i) q^{83} +(-10.7305 + 13.4556i) q^{84} -7.59995 q^{85} +(-1.84472 - 0.512437i) q^{86} -7.61451 q^{87} +(-0.712642 + 0.893624i) q^{88} +(1.45769 - 3.71412i) q^{89} +(-0.326711 - 1.43141i) q^{90} +(1.99288 + 26.5931i) q^{91} +(4.82398 + 8.35538i) q^{92} +(-0.534186 + 0.925237i) q^{93} +(1.15681 + 0.557088i) q^{94} +(-8.06071 - 7.47925i) q^{95} +(6.56626 + 4.47680i) q^{96} +(2.73216 - 11.9704i) q^{97} +(-2.01703 - 0.304019i) q^{98} +(2.29389 - 1.56395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 2 q^{2} + 3 q^{3} - 44 q^{4} + 6 q^{5} - 2 q^{6} - 23 q^{7} - 6 q^{8} + q^{9}+O(q^{10}) \) 216 * q - 2 * q^2 + 3 * q^3 - 44 * q^4 + 6 * q^5 - 2 * q^6 - 23 * q^7 - 6 * q^8 + q^9	\( 216 q - 2 q^{2} + 3 q^{3} - 44 q^{4} + 6 q^{5} - 2 q^{6} - 23 q^{7} - 6 q^{8} + q^{9} - 40 q^{10} - 36 q^{11} - 32 q^{12} - 9 q^{13} + 6 q^{14} - 32 q^{16} - 21 q^{18} - 4 q^{19} + 168 q^{20} + 76 q^{21} - 2 q^{22} - 13 q^{23} - 6 q^{24} + 2 q^{25} - 13 q^{26} - 12 q^{27} + 18 q^{28} - 23 q^{29} - 150 q^{30} - 51 q^{31} - 54 q^{32} + 3 q^{33} + 30 q^{34} - 28 q^{35} - 74 q^{36} - 115 q^{37} + 28 q^{38} + 21 q^{39} - q^{40} + 36 q^{41} + 80 q^{42} + 44 q^{43} + 208 q^{44} - 22 q^{45} + 84 q^{46} + 14 q^{47} + 29 q^{48} - 99 q^{49} + 23 q^{50} - 72 q^{51} - 9 q^{52} - 47 q^{53} + 58 q^{54} + 6 q^{55} - 156 q^{56} - 52 q^{57} - 45 q^{58} + 14 q^{59} - 78 q^{60} + 25 q^{61} + 19 q^{62} + 203 q^{63} + 82 q^{64} + 46 q^{65} - 2 q^{66} - 31 q^{67} - 12 q^{68} + 2 q^{69} - 36 q^{70} + 51 q^{71} + 56 q^{72} - 51 q^{73} - 25 q^{74} + 4 q^{75} + 69 q^{76} + 5 q^{77} - 182 q^{78} + 43 q^{79} - 149 q^{80} - 152 q^{81} + 16 q^{82} + 127 q^{83} + 331 q^{84} + 298 q^{85} + 73 q^{86} - 210 q^{87} - 6 q^{88} + 52 q^{89} - 26 q^{90} + 19 q^{91} + 28 q^{92} - 75 q^{93} + 47 q^{94} + 13 q^{95} - 345 q^{96} - 51 q^{97} - 115 q^{98} + 15 q^{99}+O(q^{100}) \) 216 * q - 2 * q^2 + 3 * q^3 - 44 * q^4 + 6 * q^5 - 2 * q^6 - 23 * q^7 - 6 * q^8 + q^9 - 40 * q^10 - 36 * q^11 - 32 * q^12 - 9 * q^13 + 6 * q^14 - 32 * q^16 - 21 * q^18 - 4 * q^19 + 168 * q^20 + 76 * q^21 - 2 * q^22 - 13 * q^23 - 6 * q^24 + 2 * q^25 - 13 * q^26 - 12 * q^27 + 18 * q^28 - 23 * q^29 - 150 * q^30 - 51 * q^31 - 54 * q^32 + 3 * q^33 + 30 * q^34 - 28 * q^35 - 74 * q^36 - 115 * q^37 + 28 * q^38 + 21 * q^39 - q^40 + 36 * q^41 + 80 * q^42 + 44 * q^43 + 208 * q^44 - 22 * q^45 + 84 * q^46 + 14 * q^47 + 29 * q^48 - 99 * q^49 + 23 * q^50 - 72 * q^51 - 9 * q^52 - 47 * q^53 + 58 * q^54 + 6 * q^55 - 156 * q^56 - 52 * q^57 - 45 * q^58 + 14 * q^59 - 78 * q^60 + 25 * q^61 + 19 * q^62 + 203 * q^63 + 82 * q^64 + 46 * q^65 - 2 * q^66 - 31 * q^67 - 12 * q^68 + 2 * q^69 - 36 * q^70 + 51 * q^71 + 56 * q^72 - 51 * q^73 - 25 * q^74 + 4 * q^75 + 69 * q^76 + 5 * q^77 - 182 * q^78 + 43 * q^79 - 149 * q^80 - 152 * q^81 + 16 * q^82 + 127 * q^83 + 331 * q^84 + 298 * q^85 + 73 * q^86 - 210 * q^87 - 6 * q^88 + 52 * q^89 - 26 * q^90 + 19 * q^91 + 28 * q^92 - 75 * q^93 + 47 * q^94 + 13 * q^95 - 345 * q^96 - 51 * q^97 - 115 * q^98 + 15 * q^99

Introduction

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