LMFDB - Embedded newform 471.2.q.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(19,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 62]))

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

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

chi := DirichletCharacter("471.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.q (of order $39$, degree $24$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	471.19
Dual form			471.2.q.b.124.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.54821 - 0.628078i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(4.32800 + 2.27151i) q^{4} +(-2.61874 + 1.96786i) q^{5} +(1.81804 + 1.89278i) q^{6} +(1.20275 - 0.631251i) q^{7} +(-5.67309 - 5.02592i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(-2.54821 - 0.628078i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(4.32800 + 2.27151i) q^{4} +(-2.61874 + 1.96786i) q^{5} +(1.81804 + 1.89278i) q^{6} +(1.20275 - 0.631251i) q^{7} +(-5.67309 - 5.02592i) q^{8} +(0.428693 + 0.903450i) q^{9} +(7.90908 - 3.36974i) q^{10} +(1.33880 + 1.39384i) q^{11} +(-2.44394 - 4.23303i) q^{12} +(-3.48628 + 6.03841i) q^{13} +(-3.46134 + 0.853143i) q^{14} +(3.26509 - 0.263585i) q^{15} +(5.74631 + 8.32496i) q^{16} +(4.92226 - 3.69884i) q^{17} +(-0.524963 - 2.57144i) q^{18} +(0.795191 - 3.89510i) q^{19} +(-15.8039 + 2.56839i) q^{20} +(-1.35393 - 0.109301i) q^{21} +(-2.53611 - 4.39268i) q^{22} +(-3.07948 - 4.46139i) q^{23} +(2.10866 + 7.27992i) q^{24} +(1.59426 - 5.50402i) q^{25} +(12.6764 - 13.1975i) q^{26} +(0.120537 - 0.992709i) q^{27} +6.63939 q^{28} +(-1.05284 + 8.67095i) q^{29} +(-8.48569 - 1.37906i) q^{30} +(-3.01274 - 3.68993i) q^{31} +(-4.03887 - 10.6496i) q^{32} +(-0.386582 - 1.89361i) q^{33} +(-14.8661 + 6.33386i) q^{34} +(-1.90748 + 4.01992i) q^{35} +(-0.196815 + 4.88391i) q^{36} +(-5.26846 - 3.95899i) q^{37} +(-4.47275 + 9.42612i) q^{38} +(6.17389 - 3.24031i) q^{39} +(24.7466 + 1.99775i) q^{40} +(-2.00715 + 2.90785i) q^{41} +(3.38146 + 1.12890i) q^{42} +(0.175755 - 0.111141i) q^{43} +(2.62821 + 9.07365i) q^{44} +(-2.90050 - 1.52230i) q^{45} +(5.04506 + 13.3027i) q^{46} +(-4.67430 - 1.99153i) q^{47} +(-0.407314 - 10.1074i) q^{48} +(-2.92833 + 4.24241i) q^{49} +(-7.51947 + 13.0241i) q^{50} +(-6.13715 + 0.495442i) q^{51} +(-28.8049 + 18.2151i) q^{52} +(-7.06316 + 2.35803i) q^{53} +(-0.930652 + 2.45393i) q^{54} +(-6.24886 - 1.01554i) q^{55} +(-9.99592 - 2.46377i) q^{56} +(-2.75389 + 2.86710i) q^{57} +(8.12890 - 21.4342i) q^{58} +(-2.41115 + 2.13609i) q^{59} +(14.7300 + 6.27588i) q^{60} +(-0.836878 + 4.09930i) q^{61} +(5.35953 + 11.2950i) q^{62} +(1.08591 + 0.816011i) q^{63} +(1.16451 + 9.59062i) q^{64} +(-2.75306 - 22.6735i) q^{65} +(-0.204238 + 5.06812i) q^{66} +(-5.92064 - 5.24523i) q^{67} +(29.7055 - 4.82761i) q^{68} +(0.218282 + 5.41660i) q^{69} +(7.38548 - 9.04558i) q^{70} +(6.57848 - 2.19622i) q^{71} +(2.10866 - 7.27992i) q^{72} +(-11.5174 - 7.28318i) q^{73} +(10.9386 + 13.3974i) q^{74} +(-4.28917 + 3.79987i) q^{75} +(12.2894 - 15.0517i) q^{76} +(2.49011 + 0.831320i) q^{77} +(-17.7676 + 4.37931i) q^{78} +(-6.14709 + 1.51512i) q^{79} +(-31.4304 - 10.4930i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(6.94100 - 6.14919i) q^{82} +(-10.3471 - 12.6728i) q^{83} +(-5.61155 - 3.54853i) q^{84} +(-5.61134 + 19.3726i) q^{85} +(-0.517667 + 0.172823i) q^{86} +(5.52418 - 6.76589i) q^{87} +(-0.589814 - 14.6361i) q^{88} +(9.04624 - 1.47016i) q^{89} +(6.43496 + 5.70088i) q^{90} +(-0.381362 + 9.46341i) q^{91} +(-3.19388 - 26.3040i) q^{92} +(0.574193 + 4.72890i) q^{93} +(10.6603 + 8.01068i) q^{94} +(5.58261 + 11.7651i) q^{95} +(-2.27825 + 11.1596i) q^{96} +(7.60509 + 3.24023i) q^{97} +(10.1266 - 8.97136i) q^{98} +(-0.685332 + 1.80707i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) $ 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{31}{39}\right)$

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 $

$2$	−2.54821	−	0.628078i	−1.80186	−	0.444118i	−0.811701	−	0.584073i	$-0.801458\pi$
$2$	−2.54821	−	0.628078i	−1.80186	−	0.444118i	−0.990158	+	0.139954i	$0.955304\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	4.32800	+	2.27151i	2.16400	+	1.13575i
$5$	−2.61874	+	1.96786i	−1.17114	+	0.880052i	−0.994553	−	0.104233i	$-0.966761\pi$
$5$	−2.61874	+	1.96786i	−1.17114	+	0.880052i	−0.176584	+	0.984286i	$0.556505\pi$
$6$	1.81804	+	1.89278i	0.742211	+	0.772724i
$7$	1.20275	−	0.631251i	0.454596	−	0.238591i	−0.221852	−	0.975080i	$-0.571210\pi$
$7$	1.20275	−	0.631251i	0.454596	−	0.238591i	0.676449	+	0.736490i	$0.263518\pi$
$8$	−5.67309	−	5.02592i	−2.00574	−	1.77693i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	7.90908	−	3.36974i	2.50107	−	1.06561i
$11$	1.33880	+	1.39384i	0.403664	+	0.420259i	0.891744	−	0.452540i	$-0.149482\pi$
$11$	1.33880	+	1.39384i	0.403664	+	0.420259i	−0.488080	+	0.872799i	$0.662303\pi$
$12$	−2.44394	−	4.23303i	−0.705504	−	1.22197i
$13$	−3.48628	+	6.03841i	−0.966919	+	1.67475i	−0.262552	+	0.964918i	$0.584564\pi$
$13$	−3.48628	+	6.03841i	−0.966919	+	1.67475i	−0.704367	+	0.709836i	$0.748769\pi$
$14$	−3.46134	+	0.853143i	−0.925081	+	0.228012i
$15$	3.26509	−	0.263585i	0.843042	−	0.0680574i
$16$	5.74631	+	8.32496i	1.43658	+	2.08124i
$17$	4.92226	−	3.69884i	1.19382	−	0.897100i	0.197294	−	0.980344i	$-0.436785\pi$
$17$	4.92226	−	3.69884i	1.19382	−	0.897100i	0.996529	+	0.0832446i	$0.0265283\pi$
$18$	−0.524963	−	2.57144i	−0.123735	−	0.606094i
$19$	0.795191	−	3.89510i	0.182429	−	0.893598i	−0.780772	−	0.624816i	$-0.785174\pi$
$19$	0.795191	−	3.89510i	0.182429	−	0.893598i	0.963201	−	0.268782i	$-0.0866211\pi$
$20$	−15.8039	+	2.56839i	−3.53386	+	0.574309i
$21$	−1.35393	−	0.109301i	−0.295453	−	0.0238514i
$22$	−2.53611	−	4.39268i	−0.540701	−	0.936522i
$23$	−3.07948	−	4.46139i	−0.642116	−	0.930265i	0.357878	−	0.933768i	$-0.383500\pi$
$23$	−3.07948	−	4.46139i	−0.642116	−	0.930265i	−0.999994	+	0.00350314i	$0.998885\pi$
$24$	2.10866	+	7.27992i	0.430428	+	1.48601i
$25$	1.59426	−	5.50402i	0.318852	−	1.10080i
$26$	12.6764	−	13.1975i	2.48604	−	2.58824i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	6.63939			1.25473
$29$	−1.05284	+	8.67095i	−0.195508	+	1.61015i	0.483040	+	0.875598i	$0.339533\pi$
$29$	−1.05284	+	8.67095i	−0.195508	+	1.61015i	−0.678548	+	0.734556i	$0.737390\pi$
$30$	−8.48569	−	1.37906i	−1.54927	−	0.251781i
$31$	−3.01274	−	3.68993i	−0.541104	−	0.662732i	0.429598	−	0.903020i	$-0.358655\pi$
$31$	−3.01274	−	3.68993i	−0.541104	−	0.662732i	−0.970702	+	0.240289i	$0.922758\pi$
$32$	−4.03887	−	10.6496i	−0.713979	−	1.88261i
$33$	−0.386582	−	1.89361i	−0.0672953	−	0.329634i
$34$	−14.8661	+	6.33386i	−2.54952	+	1.08625i
$35$	−1.90748	+	4.01992i	−0.322422	+	0.679491i
$36$	−0.196815	+	4.88391i	−0.0328025	+	0.813985i
$37$	−5.26846	−	3.95899i	−0.866129	−	0.650854i	0.0718991	−	0.997412i	$-0.477094\pi$
$37$	−5.26846	−	3.95899i	−0.866129	−	0.650854i	−0.938029	+	0.346558i	$0.887350\pi$
$38$	−4.47275	+	9.42612i	−0.725576	+	1.52912i
$39$	6.17389	−	3.24031i	0.988614	−	0.518865i
$40$	24.7466	+	1.99775i	3.91279	+	0.315873i
$41$	−2.00715	+	2.90785i	−0.313463	+	0.454130i	−0.947771	−	0.318950i	$-0.896670\pi$
$41$	−2.00715	+	2.90785i	−0.313463	+	0.454130i	0.634308	+	0.773080i	$0.281285\pi$
$42$	3.38146	+	1.12890i	0.521771	+	0.174193i
$43$	0.175755	−	0.111141i	0.0268024	−	0.0169488i	−0.520997	−	0.853558i	$-0.674440\pi$
$43$	0.175755	−	0.111141i	0.0268024	−	0.0169488i	0.547800	+	0.836609i	$0.315466\pi$
$44$	2.62821	+	9.07365i	0.396218	+	1.36790i
$45$	−2.90050	−	1.52230i	−0.432380	−	0.226931i
$46$	5.04506	+	13.3027i	0.743854	+	1.96138i
$47$	−4.67430	−	1.99153i	−0.681817	−	0.290495i	0.0231532	−	0.999732i	$-0.492629\pi$
$47$	−4.67430	−	1.99153i	−0.681817	−	0.290495i	−0.704970	+	0.709237i	$0.749040\pi$
$48$	−0.407314	−	10.1074i	−0.0587907	−	1.45887i
$49$	−2.92833	+	4.24241i	−0.418332	+	0.606059i
$50$	−7.51947	+	13.0241i	−1.06341	+	1.84189i
$51$	−6.13715	+	0.495442i	−0.859372	+	0.0693757i
$52$	−28.8049	+	18.2151i	−3.99452	+	2.52598i
$53$	−7.06316	+	2.35803i	−0.970199	+	0.323900i	−0.757222	−	0.653157i	$-0.773444\pi$
$53$	−7.06316	+	2.35803i	−0.970199	+	0.323900i	−0.212977	+	0.977057i	$0.568316\pi$
$54$	−0.930652	+	2.45393i	−0.126646	+	0.333937i
$55$	−6.24886	−	1.01554i	−0.842596	−	0.136935i
$56$	−9.99592	−	2.46377i	−1.33576	−	0.329235i
$57$	−2.75389	+	2.86710i	−0.364761	+	0.379757i
$58$	8.12890	−	21.4342i	1.06738	−	2.81444i
$59$	−2.41115	+	2.13609i	−0.313904	+	0.278095i	−0.805333	−	0.592823i	$-0.798013\pi$
$59$	−2.41115	+	2.13609i	−0.313904	+	0.278095i	0.491428	+	0.870918i	$0.336475\pi$
$60$	14.7300	+	6.27588i	1.90164	+	0.810213i
$61$	−0.836878	+	4.09930i	−0.107151	+	0.524861i	0.890416	+	0.455148i	$0.150414\pi$
$61$	−0.836878	+	4.09930i	−0.107151	+	0.524861i	−0.997567	+	0.0697135i	$0.977791\pi$
$62$	5.35953	+	11.2950i	0.680661	+	1.43446i
$63$	1.08591	+	0.816011i	0.136812	+	0.102808i
$64$	1.16451	+	9.59062i	0.145564	+	1.19883i
$65$	−2.75306	−	22.6735i	−0.341476	−	2.81230i
$66$	−0.204238	+	5.06812i	−0.0251400	+	0.623842i
$67$	−5.92064	−	5.24523i	−0.723322	−	0.640807i	0.218919	−	0.975743i	$-0.429747\pi$
$67$	−5.92064	−	5.24523i	−0.723322	−	0.640807i	−0.942241	+	0.334936i	$0.891285\pi$
$68$	29.7055	−	4.82761i	3.60232	−	0.585434i
$69$	0.218282	+	5.41660i	0.0262780	+	0.652082i
$70$	7.38548	−	9.04558i	0.882734	−	1.08115i
$71$	6.57848	−	2.19622i	0.780722	−	0.260643i	0.101753	−	0.994810i	$-0.467555\pi$
$71$	6.57848	−	2.19622i	0.780722	−	0.260643i	0.678970	+	0.734166i	$0.262427\pi$
$72$	2.10866	−	7.27992i	0.248507	−	0.857947i
$73$	−11.5174	−	7.28318i	−1.34801	−	0.852431i	−0.351525	−	0.936178i	$-0.614337\pi$
$73$	−11.5174	−	7.28318i	−1.34801	−	0.852431i	−0.996487	+	0.0837472i	$0.973311\pi$
$74$	10.9386	+	13.3974i	1.27159	+	1.55741i
$75$	−4.28917	+	3.79987i	−0.495270	+	0.438771i
$76$	12.2894	−	15.0517i	1.40969	−	1.72655i
$77$	2.49011	+	0.831320i	0.283774	+	0.0947377i
$78$	−17.7676	+	4.37931i	−2.01178	+	0.495859i
$79$	−6.14709	+	1.51512i	−0.691601	+	0.170464i	−0.569424	−	0.822044i	$-0.692834\pi$
$79$	−6.14709	+	1.51512i	−0.691601	+	0.170464i	−0.122177	+	0.992508i	$0.538988\pi$
$80$	−31.4304	−	10.4930i	−3.51403	−	1.17316i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	6.94100	−	6.14919i	0.766505	−	0.679064i
$83$	−10.3471	−	12.6728i	−1.13574	−	1.39103i	−0.908859	−	0.417103i	$-0.863046\pi$
$83$	−10.3471	−	12.6728i	−1.13574	−	1.39103i	−0.226878	−	0.973923i	$-0.572852\pi$
$84$	−5.61155	−	3.54853i	−0.612270	−	0.387176i
$85$	−5.61134	+	19.3726i	−0.608635	+	2.10125i
$86$	−0.517667	+	0.172823i	−0.0558215	+	0.0186359i
$87$	5.52418	−	6.76589i	0.592254	−	0.725379i
$88$	−0.589814	−	14.6361i	−0.0628744	−	1.56021i
$89$	9.04624	−	1.47016i	0.958899	−	0.155836i	0.339234	−	0.940702i	$-0.389832\pi$
$89$	9.04624	−	1.47016i	0.958899	−	0.155836i	0.619666	+	0.784866i	$0.287268\pi$
$90$	6.43496	+	5.70088i	0.678305	+	0.600925i
$91$	−0.381362	+	9.46341i	−0.0399776	+	0.992035i
$92$	−3.19388	−	26.3040i	−0.332985	−	2.74238i
$93$	0.574193	+	4.72890i	0.0595410	+	0.490364i
$94$	10.6603	+	8.01068i	1.09952	+	0.826239i
$95$	5.58261	+	11.7651i	0.572763	+	1.20707i
$96$	−2.27825	+	11.1596i	−0.232523	+	1.13897i
$97$	7.60509	+	3.24023i	0.772180	+	0.328995i	0.741868	−	0.670545i	$-0.233940\pi$
$97$	7.60509	+	3.24023i	0.772180	+	0.328995i	0.0303114	+	0.999541i	$0.490350\pi$
$98$	10.1266	−	8.97136i	1.02294	−	0.906244i
$99$	−0.685332	+	1.80707i	−0.0688784	+	0.181618i
$100$	19.4024	−	20.2000i	1.94024	−	2.02000i
$101$	−5.41066	−	1.33361i	−0.538380	−	0.132699i	−0.0392560	−	0.999229i	$-0.512499\pi$
$101$	−5.41066	−	1.33361i	−0.538380	−	0.132699i	−0.499124	+	0.866530i	$0.666345\pi$
$102$	15.9499	+	2.59212i	1.57928	+	0.256658i
$103$	−4.50126	+	11.8688i	−0.443522	+	1.16947i	0.507855	+	0.861443i	$0.330439\pi$
$103$	−4.50126	+	11.8688i	−0.443522	+	1.16947i	−0.951377	+	0.308029i	$0.900331\pi$
$104$	50.1265	−	16.7347i	4.91531	−	1.64097i
$105$	3.76069	−	2.37812i	0.367006	−	0.232080i
$106$	19.4795	−	1.57254i	1.89201	−	0.152739i
$107$	7.04991	−	12.2108i	0.681540	−	1.18046i	−0.292971	−	0.956121i	$-0.594644\pi$
$107$	7.04991	−	12.2108i	0.681540	−	1.18046i	0.974511	−	0.224341i	$-0.0720228\pi$
$108$	2.77663	−	4.02264i	0.267181	−	0.387079i
$109$	−0.355391	−	8.81894i	−0.0340403	−	0.844701i	−0.922558	−	0.385859i	$-0.873905\pi$
$109$	−0.355391	−	8.81894i	−0.0340403	−	0.844701i	0.888518	−	0.458843i	$-0.151736\pi$
$110$	15.2856	+	6.51258i	1.45742	+	0.620950i
$111$	2.33690	+	6.16191i	0.221809	+	0.584863i
$112$	12.1665	+	6.38548i	1.14963	+	0.603371i
$113$	−0.604530	−	2.08708i	−0.0568694	−	0.196336i	0.927054	−	0.374928i	$-0.122333\pi$
$113$	−0.604530	−	2.08708i	−0.0568694	−	0.196336i	−0.983923	+	0.178593i	$0.942846\pi$
$114$	8.81826	−	5.57633i	0.825906	−	0.522271i
$115$	16.8437	+	5.62327i	1.57069	+	0.524372i
$116$	−24.2528	+	35.1363i	−2.25182	+	3.26232i
$117$	−6.94994	−	0.561058i	−0.642523	−	0.0518698i
$118$	7.48575	−	3.92882i	0.689119	−	0.361677i
$119$	3.58535	−	7.55596i	0.328668	−	0.692653i
$120$	−19.8479	−	14.9147i	−1.81185	−	1.36152i
$121$	0.292525	−	7.25892i	0.0265931	−	0.659902i
$122$	4.70722	−	9.92027i	0.426172	−	0.898139i
$123$	3.25057	−	1.38494i	0.293094	−	0.124876i
$124$	−4.65741	−	22.8135i	−0.418248	−	2.04871i
$125$	0.848264	+	2.23669i	0.0758711	+	0.200056i
$126$	−2.25462	−	2.76141i	−0.200858	−	0.246006i
$127$	11.4690	+	1.86389i	1.01771	+	0.165393i	0.646305	−	0.763080i	$-0.276314\pi$
$127$	11.4690	+	1.86389i	1.01771	+	0.165393i	0.371401	+	0.928473i	$0.378878\pi$
$128$	0.310460	−	2.55687i	0.0274410	−	0.225997i
$129$	−0.207948			−0.0183088
$130$	−7.22535	+	59.5061i	−0.633705	+	5.21903i
$131$	−2.29550	+	2.38987i	−0.200559	+	0.208804i	−0.813885	−	0.581026i	$-0.802651\pi$
$131$	−2.29550	+	2.38987i	−0.200559	+	0.208804i	0.613327	+	0.789829i	$0.289831\pi$
$132$	2.62821	−	9.07365i	0.228757	−	0.789760i
$133$	−1.50237	−	5.18680i	−0.130272	−	0.449753i
$134$	11.7927	+	17.0846i	1.01873	+	1.47589i
$135$	1.63785	+	2.83685i	0.140964	+	0.244157i
$136$	−46.5144	−	3.75503i	−3.98858	−	0.321991i
$137$	2.28919	−	0.372029i	0.195579	−	0.0317846i	−0.0618328	−	0.998087i	$-0.519695\pi$
$137$	2.28919	−	0.372029i	0.195579	−	0.0317846i	0.257411	+	0.966302i	$0.417130\pi$
$138$	2.84582	−	13.9398i	0.242252	−	1.18663i
$139$	−0.245467	−	1.20238i	−0.0208202	−	0.101984i	0.968053	−	0.250747i	$-0.0806762\pi$
$139$	−0.245467	−	1.20238i	−0.0208202	−	0.101984i	−0.988873	+	0.148762i	$0.952471\pi$
$140$	−17.3868	+	13.0654i	−1.46946	+	1.10423i
$141$	2.88627	+	4.18148i	0.243068	+	0.352144i
$142$	−18.1428	+	1.46464i	−1.52251	+	0.122910i
$143$	−13.0840	+	3.22492i	−1.09414	+	0.269682i
$144$	−5.05779	+	8.76035i	−0.421483	+	0.730030i
$145$	−14.3061	−	24.7788i	−1.18805	−	2.05777i
$146$	24.7744	+	25.7929i	2.05035	+	2.13464i
$147$	4.74242	−	2.02056i	0.391148	−	0.166653i
$148$	−13.8090	−	29.1019i	−1.13509	−	2.39216i
$149$	−9.23467	−	8.18121i	−0.756534	−	0.670231i	0.193947	−	0.981012i	$-0.437871\pi$
$149$	−9.23467	−	8.18121i	−0.756534	−	0.670231i	−0.950481	+	0.310781i	$0.899409\pi$
$150$	13.3163	−	6.98895i	1.08727	−	0.570645i
$151$	−14.5318	−	15.1292i	−1.18258	−	1.23120i	−0.967019	−	0.254705i	$-0.918021\pi$
$151$	−14.5318	−	15.1292i	−1.18258	−	1.23120i	−0.215561	−	0.976490i	$-0.569158\pi$
$152$	−24.0877	+	18.1007i	−1.95377	+	1.46816i
$153$	5.45185	+	2.86135i	0.440756	+	0.231327i
$154$	−5.82319	−	3.68236i	−0.469246	−	0.296733i
$155$	15.1508	+	3.73435i	1.21695	+	0.299950i
$156$	34.0810			2.72866
$157$	−2.80147	+	12.2128i	−0.223581	+	0.974685i
$157$	−2.80147	+	12.2128i	−0.223581	+	0.974685i
$158$	16.6157			1.32187
$159$	7.22999	+	1.78203i	0.573376	+	0.141324i
$160$	31.5337	+	19.9407i	2.49296	+	1.57645i
$161$	−6.52010	−	3.42201i	−0.513856	−	0.269692i
$162$	2.09812	−	1.57663i	0.164844	−	0.123872i
$163$	13.2751	+	13.8208i	1.03978	+	1.08253i	0.996511	+	0.0834673i	$0.0265994\pi$
$163$	13.2751	+	13.8208i	1.03978	+	1.08253i	0.0432741	+	0.999063i	$0.486221\pi$
$164$	−15.2921	+	8.02594i	−1.19412	+	0.626720i
$165$	4.73870	+	4.19812i	0.368907	+	0.326824i
$166$	18.4070	+	38.7919i	1.42866	+	3.01083i
$167$	−14.4428	+	6.15349i	−1.11762	+	0.476171i	−0.870180	−	0.492733i	$-0.835998\pi$
$167$	−14.4428	+	6.15349i	−1.11762	+	0.476171i	−0.247435	+	0.968905i	$0.579588\pi$
$168$	7.13165	+	7.42483i	0.550218	+	0.572838i
$169$	−17.8083	−	30.8448i	−1.36987	−	2.37268i
$170$	26.4664	−	45.8412i	2.02988	−	3.51586i
$171$	3.85993	−	0.951386i	0.295176	−	0.0727543i
$172$	1.01313	−	0.0817880i	0.0772501	−	0.00623628i
$173$	−3.91313	−	5.66915i	−0.297510	−	0.431017i	0.645511	−	0.763751i	$-0.276644\pi$
$173$	−3.91313	−	5.66915i	−0.297510	−	0.431017i	−0.943021	+	0.332734i	$0.892029\pi$
$174$	−18.3263	+	13.7713i	−1.38931	+	1.04400i
$175$	−1.55693	−	7.62634i	−0.117693	−	0.576497i
$176$	−3.91051	+	19.1549i	−0.294765	+	1.44386i
$177$	3.17954	−	0.516726i	0.238989	−	0.0388395i
$178$	−23.9751	−	1.93547i	−1.79701	−	0.145070i
$179$	3.46757	+	6.00601i	0.259179	+	0.448910i	0.966022	−	0.258459i	$-0.0832148\pi$
$179$	3.46757	+	6.00601i	0.259179	+	0.448910i	−0.706844	+	0.707370i	$0.749882\pi$
$180$	−9.09543	−	13.1770i	−0.677933	−	0.982156i
$181$	1.58578	+	5.47476i	0.117870	+	0.406936i	0.997656	−	0.0684357i	$-0.0218008\pi$
$181$	1.58578	+	5.47476i	0.117870	+	0.406936i	−0.879785	+	0.475372i	$0.842314\pi$
$182$	6.91555	−	23.8753i	0.512615	−	1.76975i
$183$	2.89826	−	3.01740i	0.214245	−	0.223053i
$184$	−4.95245	+	40.7871i	−0.365099	+	3.00686i
$185$	21.5875			1.58714
$186$	1.50696	−	12.4109i	0.110495	−	0.910011i
$187$	11.7455	+	1.90883i	0.858918	+	0.139588i
$188$	−15.7066	−	19.2371i	−1.14552	−	1.40301i
$189$	−0.481673	−	1.27007i	−0.0350366	−	0.0923839i
$190$	−6.83628	−	33.4863i	−0.495956	−	2.42935i
$191$	0.274573	−	0.116985i	0.0198674	−	0.00846471i	−0.382010	−	0.924158i	$-0.624768\pi$
$191$	0.274573	−	0.116985i	0.0198674	−	0.00846471i	0.401877	+	0.915693i	$0.368358\pi$
$192$	4.14162	−	8.72829i	0.298896	−	0.629910i
$193$	0.273730	−	6.79255i	0.0197035	−	0.488938i	−0.958969	−	0.283511i	$-0.908501\pi$
$193$	0.273730	−	6.79255i	0.0197035	−	0.488938i	0.978672	−	0.205427i	$-0.0658583\pi$
$194$	−17.3443	−	13.0334i	−1.24525	−	0.935742i
$195$	−9.79136	+	20.6349i	−0.701174	+	1.47769i
$196$	−22.3105	+	11.7094i	−1.59361	+	0.836389i
$197$	−1.01584	−	0.0820067i	−0.0723753	−	0.00584274i	0.0442259	−	0.999022i	$-0.485918\pi$
$197$	−1.01584	−	0.0820067i	−0.0723753	−	0.00584274i	−0.116601	+	0.993179i	$0.537200\pi$
$198$	2.88135	−	4.17436i	0.204769	−	0.296659i
$199$	8.23037	+	2.74770i	0.583435	+	0.194779i	0.593038	−	0.805175i	$-0.297928\pi$
$199$	8.23037	+	2.74770i	0.583435	+	0.194779i	−0.00960250	+	0.999954i	$0.503057\pi$
$200$	−36.7071	+	23.2122i	−2.59559	+	1.64135i
$201$	2.20067	+	7.59760i	0.155223	+	0.535894i
$202$	12.9499	+	6.79663i	0.911152	+	0.478209i
$203$	4.20724	+	11.0936i	0.295290	+	0.778617i
$204$	−27.6870	−	11.7963i	−1.93848	−	0.825907i
$205$	−0.466041	−	11.5647i	−0.0325497	−	0.807713i
$206$	18.9247	−	27.4172i	1.31855	−	1.91025i
$207$	2.71050	−	4.69472i	0.188393	−	0.326306i
$208$	−70.3028	+	5.67543i	−4.87462	+	0.393520i
$209$	6.49376	−	4.10641i	0.449183	−	0.284046i
$210$	−11.0767	+	3.69794i	−0.764364	+	0.255182i
$211$	−1.04677	+	2.76010i	−0.0720624	+	0.190013i	−0.966208	−	0.257763i	$-0.917015\pi$
$211$	−1.04677	+	2.76010i	−0.0720624	+	0.190013i	0.894146	+	0.447776i	$0.147784\pi$
$212$	−35.9256	−	5.83848i	−2.46738	−	0.400989i
$213$	−6.73387	−	1.65975i	−0.461397	−	0.113724i
$214$	−25.6340	+	26.6878i	−1.75230	+	1.82434i
$215$	−0.241548	+	0.636910i	−0.0164734	+	0.0434369i
$216$	−5.67309	+	5.02592i	−0.386005	+	0.341970i
$217$	−5.95284	−	2.53627i	−0.404105	−	0.172173i
$218$	−4.63337	+	22.6958i	−0.313812	+	1.53715i
$219$	5.84180	+	12.3113i	0.394752	+	0.831923i
$220$	−24.7383	−	18.5896i	−1.66785	−	1.25331i
$221$	5.17474	+	42.6178i	0.348090	+	2.86678i
$222$	−2.08477	−	17.1696i	−0.139921	−	1.15235i
$223$	−0.849908	+	21.0902i	−0.0569140	+	1.41231i	0.678456	+	0.734641i	$0.262649\pi$
$223$	−0.849908	+	21.0902i	−0.0569140	+	1.41231i	−0.735370	+	0.677666i	$0.762992\pi$
$224$	−11.5804	−	10.2593i	−0.773745	−	0.685478i
$225$	5.65606	−	0.919199i	0.377071	−	0.0612800i
$226$	0.229622	+	5.69801i	0.0152742	+	0.379026i
$227$	−10.2156	+	12.5118i	−0.678033	+	0.830439i	−0.992932	−	0.118686i	$-0.962132\pi$
$227$	−10.2156	+	12.5118i	−0.678033	+	0.830439i	0.314899	+	0.949125i	$0.398029\pi$
$228$	−18.4315	+	6.15333i	−1.22065	+	0.407514i
$229$	4.04193	−	13.9543i	0.267098	−	0.922129i	−0.709075	−	0.705134i	$-0.750887\pi$
$229$	4.04193	−	13.9543i	0.267098	−	0.922129i	0.976173	−	0.216996i	$-0.0696258\pi$
$230$	−39.3896	−	24.9085i	−2.59727	−	1.64242i
$231$	−1.66030	−	2.03350i	−0.109240	−	0.133795i
$232$	49.5523	−	43.8995i	3.25327	−	2.88214i
$233$	−11.9308	+	14.6126i	−0.781612	+	0.957301i	−0.999827	−	0.0185998i	$-0.994079\pi$
$233$	−11.9308	+	14.6126i	−0.781612	+	0.957301i	0.218215	+	0.975901i	$0.429977\pi$
$234$	17.3576	+	5.79480i	1.13470	+	0.378818i
$235$	16.1598	−	3.98304i	1.05415	−	0.259825i
$236$	−15.2876	+	3.76805i	−0.995137	+	0.245279i
$237$	6.00524	+	2.00484i	0.390082	+	0.130229i
$238$	−13.8820	+	17.0023i	−0.899834	+	1.10210i
$239$	13.9090	−	12.3223i	0.899698	−	0.797063i	−0.0801552	−	0.996782i	$-0.525542\pi$
$239$	13.9090	−	12.3223i	0.899698	−	0.797063i	0.979853	+	0.199720i	$0.0640031\pi$
$240$	20.9565	+	25.6671i	1.35274	+	1.65680i
$241$	8.76413	+	5.54210i	0.564547	+	0.356998i	0.786051	−	0.618161i	$-0.212122\pi$
$241$	8.76413	+	5.54210i	0.564547	+	0.356998i	−0.221504	+	0.975159i	$0.571097\pi$
$242$	−5.30459	+	18.3136i	−0.340992	+	1.17724i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−12.9336	+	15.8408i	−0.827989	+	1.01410i
$245$	−0.679931	−	16.8723i	−0.0434392	−	1.07793i
$246$	−9.15299	+	1.48751i	−0.583573	+	0.0948399i
$247$	20.7480	+	18.3811i	1.32016	+	1.16956i
$248$	−1.45378	+	36.0751i	−0.0923149	+	2.29077i
$249$	1.97203	+	16.2411i	0.124972	+	1.02924i
$250$	−0.756743	−	6.23234i	−0.0478606	−	0.394168i
$251$	10.5041	+	7.89334i	0.663015	+	0.498223i	0.878165	−	0.478358i	$-0.158768\pi$
$251$	10.5041	+	7.89334i	0.663015	+	0.498223i	−0.215150	+	0.976581i	$0.569024\pi$
$252$	2.84626	+	5.99836i	0.179297	+	0.377861i
$253$	2.09566	−	10.2652i	0.131753	−	0.645370i
$254$	−28.0547	−	11.9530i	−1.76031	−	0.749997i
$255$	15.0966	−	13.3745i	0.945388	−	0.837541i
$256$	4.45469	−	11.7460i	0.278418	−	0.734128i
$257$	−4.44943	+	4.63235i	−0.277548	+	0.288958i	−0.845356	−	0.534203i	$-0.820612\pi$
$257$	−4.44943	+	4.63235i	−0.277548	+	0.288958i	0.567809	+	0.823161i	$0.307791\pi$
$258$	0.529895	+	0.130607i	0.0329898	+	0.00813126i
$259$	−8.83575	−	1.43595i	−0.549027	−	0.0892256i
$260$	39.5879	−	104.385i	2.45514	−	6.47366i
$261$	−8.28512	+	2.76598i	−0.512836	+	0.171210i
$262$	7.35044	−	4.64814i	0.454112	−	0.287163i
$263$	12.0939	−	0.976322i	0.745743	−	0.0602026i	0.298247	−	0.954489i	$-0.403598\pi$
$263$	12.0939	−	0.976322i	0.745743	−	0.0602026i	0.447496	+	0.894286i	$0.352316\pi$
$264$	−7.32399	+	12.6855i	−0.450760	+	0.780740i
$265$	13.8563	−	20.0743i	0.851187	−	1.23316i
$266$	0.570656	+	14.1607i	0.0349892	+	0.868247i
$267$	−8.43154	−	3.59234i	−0.516002	−	0.219848i
$268$	−13.7100	−	36.1502i	−0.837469	−	2.20822i
$269$	−24.2815	−	12.7439i	−1.48047	−	0.777010i	−0.485222	−	0.874391i	$-0.661261\pi$
$269$	−24.2815	−	12.7439i	−1.48047	−	0.777010i	−0.995247	+	0.0973812i	$0.968953\pi$
$270$	−2.39184	−	8.25759i	−0.145563	−	0.502541i
$271$	−16.4069	+	10.3751i	−0.996649	+	0.630243i	−0.930010	−	0.367534i	$-0.880202\pi$
$271$	−16.4069	+	10.3751i	−0.996649	+	0.630243i	−0.0666395	+	0.997777i	$0.521228\pi$
$272$	59.0775	+	19.7230i	3.58210	+	1.19588i
$273$	5.38019	−	7.79455i	0.325624	−	0.471748i
$274$	−6.06701	−	0.489779i	−0.366521	−	0.0295887i
$275$	9.80614	−	5.14666i	0.591332	−	0.310355i
$276$	−11.3591	+	23.9389i	−0.683740	+	1.44095i
$277$	14.2278	+	10.6915i	0.854865	+	0.642389i	0.935099	−	0.354387i	$-0.115310\pi$
$277$	14.2278	+	10.6915i	0.854865	+	0.642389i	−0.0802339	+	0.996776i	$0.525567\pi$
$278$	−0.129685	+	3.21809i	−0.00777796	+	0.193008i
$279$	2.04213	−	4.30371i	0.122259	−	0.257656i
$280$	31.0251	−	13.2185i	1.85410	−	0.789959i
$281$	5.26779	+	25.8033i	0.314250	+	1.53930i	0.763450	+	0.645867i	$0.223504\pi$
$281$	5.26779	+	25.8033i	0.314250	+	1.53930i	−0.449200	+	0.893431i	$0.648291\pi$
$282$	−4.72853	−	12.4681i	−0.281580	−	0.742465i
$283$	1.38695	+	1.69870i	0.0824454	+	0.100977i	0.814181	−	0.580612i	$-0.197187\pi$
$283$	1.38695	+	1.69870i	0.0824454	+	0.100977i	−0.731735	+	0.681589i	$0.761289\pi$
$284$	33.4604	+	5.43785i	1.98551	+	0.322677i
$285$	1.56968	−	12.9275i	0.0929796	−	0.765756i
$286$	35.3664			2.09126
$287$	−0.578507	+	4.76443i	−0.0341482	+	0.281235i
$288$	7.88998	−	8.21434i	0.464922	−	0.484035i
$289$	5.81753	−	20.0845i	0.342208	−	1.18144i
$290$	20.8919	+	72.1270i	1.22681	+	4.23545i
$291$	−4.69596	−	6.80327i	−0.275282	−	0.398815i
$292$	−33.3036	−	57.6835i	−1.94895	−	3.37567i
$293$	0.609222	+	0.0491815i	0.0355911	+	0.00287321i	0.0982493	−	0.995162i	$-0.468676\pi$
$293$	0.609222	+	0.0491815i	0.0355911	+	0.00287321i	−0.0626582	+	0.998035i	$0.519958\pi$
$294$	−13.3538	+	2.17020i	−0.778807	+	0.126568i
$295$	2.11065	−	10.3387i	0.122887	−	0.601940i
$296$	9.99087	+	48.9385i	0.580708	+	2.84449i
$297$	1.54505	−	1.16103i	0.0896531	−	0.0673699i
$298$	18.3935	+	26.6476i	1.06551	+	1.54365i
$299$	37.6756	−	3.04149i	2.17884	−	0.175894i
$300$	−27.1949	+	6.70295i	−1.57010	+	0.386995i
$301$	0.141232	−	0.244620i	0.00814045	−	0.0140997i
$302$	27.5278	+	47.6795i	1.58405	+	2.74365i
$303$	3.86027	+	4.01896i	0.221766	+	0.230883i
$304$	36.9960	−	15.7625i	2.12187	−	0.904043i
$305$	−5.87527	−	12.3819i	−0.336417	−	0.708983i
$306$	−12.0953	−	10.7155i	−0.691444	−	0.612566i
$307$	−16.6200	+	8.72285i	−0.948554	+	0.497839i	−0.866714	−	0.498806i	$-0.833772\pi$
$307$	−16.6200	+	8.72285i	−0.948554	+	0.497839i	−0.0818401	+	0.996645i	$0.526080\pi$
$308$	8.88884	+	9.25426i	0.506488	+	0.527310i
$309$	10.1479	−	7.62566i	0.577294	−	0.433809i
$310$	−36.2621	−	19.0318i	−2.05955	−	1.08094i
$311$	−22.2498	−	14.0699i	−1.26167	−	0.797833i	−0.275140	−	0.961404i	$-0.588724\pi$
$311$	−22.2498	−	14.0699i	−1.26167	−	0.797833i	−0.986531	+	0.163571i	$0.947699\pi$
$312$	−51.3105	−	12.6469i	−2.90489	−	0.715990i
$313$	10.2169			0.577496			0.288748	−	0.957405i	$-0.406761\pi$
$313$	10.2169			0.577496			0.288748	+	0.957405i	$0.406761\pi$
$314$	14.8093	−	29.3612i	0.835738	−	1.65695i
$315$	−4.44952			−0.250702
$316$	−30.0462	−	7.40572i	−1.69023	−	0.416605i
$317$	13.9599	+	8.82772i	0.784068	+	0.495814i	0.865527	−	0.500862i	$-0.166984\pi$
$317$	13.9599	+	8.82772i	0.784068	+	0.495814i	−0.0814593	+	0.996677i	$0.525958\pi$
$318$	−17.3043	−	9.08201i	−0.970378	−	0.509294i
$319$	−13.4955	+	10.1412i	−0.755601	+	0.567798i
$320$	−21.9225	−	22.8238i	−1.22551	−	1.27589i
$321$	−12.4848	+	6.55251i	−0.696831	+	0.365725i
$322$	14.4653	+	12.8152i	0.806121	+	0.714161i
$323$	−10.4932	−	22.1140i	−0.583858	−	1.23046i
$324$	−4.49675	+	1.91588i	−0.249819	+	0.106438i
$325$	27.6775	+	28.8154i	1.53527	+	1.59839i
$326$	−25.1472	−	43.5562i	−1.39277	−	2.41236i
$327$	−4.41305	+	7.64362i	−0.244042	+	0.422693i
$328$	26.0013	−	6.40875i	1.43568	−	0.353864i
$329$	−6.87917	+	0.555344i	−0.379261	+	0.0306171i
$330$	−9.43848	−	13.6740i	−0.519571	−	0.752729i
$331$	−15.1952	+	11.4184i	−0.835201	+	0.627613i	−0.929867	−	0.367896i	$-0.880078\pi$
$331$	−15.1952	+	11.4184i	−0.835201	+	0.627613i	0.0946656	+	0.995509i	$0.469822\pi$
$332$	−15.9956	−	78.3515i	−0.877871	−	4.30010i
$333$	1.31820	−	6.45698i	0.0722370	−	0.353840i
$334$	40.6681	−	6.60922i	2.22526	−	0.361640i
$335$	25.8265	+	2.08493i	1.41105	+	0.113912i
$336$	−6.87020	−	11.8995i	−0.374800	−	0.649172i
$337$	−3.86329	−	5.59695i	−0.210447	−	0.304885i	0.703519	−	0.710677i	$-0.251611\pi$
$337$	−3.86329	−	5.59695i	−0.210447	−	0.304885i	−0.913966	+	0.405792i	$0.866996\pi$
$338$	26.0063	+	89.7842i	1.41456	+	4.88361i
$339$	−0.604530	+	2.08708i	−0.0328335	+	0.113355i
$340$	−68.2909	+	71.0984i	−3.70360	+	3.85585i
$341$	1.10972	−	9.13937i	0.0600948	−	0.494925i
$342$	−10.4335			−0.564177
$343$	−1.99012	+	16.3901i	−0.107456	+	0.884983i
$344$	−1.55566	−	0.252819i	−0.0838755	−	0.0136311i
$345$	−11.2307	−	13.7551i	−0.604642	−	0.740552i
$346$	6.41082	+	16.9040i	0.344648	+	0.908762i
$347$	−0.343285	−	1.68152i	−0.0184285	−	0.0902688i	0.969536	−	0.244948i	$-0.0787708\pi$
$347$	−0.343285	−	1.68152i	−0.0184285	−	0.0902688i	−0.987965	+	0.154679i	$0.950566\pi$
$348$	39.2774	−	16.7345i	2.10549	−	0.897066i
$349$	−4.01095	+	8.45290i	−0.214701	+	0.452474i	−0.982016	−	0.188797i	$-0.939541\pi$
$349$	−4.01095	+	8.45290i	−0.214701	+	0.452474i	0.767315	+	0.641271i	$0.221592\pi$
$350$	−0.822552	+	20.4114i	−0.0439673	+	1.09104i
$351$	5.57416	+	4.18871i	0.297527	+	0.223577i
$352$	9.43665	−	19.8873i	0.502975	−	1.06000i
$353$	−24.9212	+	13.0797i	−1.32642	+	0.696160i	−0.971120	−	0.238591i	$-0.923314\pi$
$353$	−24.9212	+	13.0797i	−1.32642	+	0.696160i	−0.355302	+	0.934751i	$0.615622\pi$
$354$	−8.42670	−	0.680274i	−0.447874	−	0.0361561i
$355$	−12.9055	+	18.6968i	−0.684953	+	0.992326i
$356$	42.4916	+	14.1858i	2.25205	+	0.751845i
$357$	−7.06870	+	4.46997i	−0.374115	+	0.236576i
$358$	−5.06387	−	17.4825i	−0.267634	−	0.923980i
$359$	−6.60580	−	3.46699i	−0.348641	−	0.182981i	0.281308	−	0.959618i	$-0.409232\pi$
$359$	−6.60580	−	3.46699i	−0.348641	−	0.182981i	−0.629949	+	0.776637i	$0.716924\pi$
$360$	8.80382	+	23.2138i	0.464002	+	1.22347i
$361$	2.94010	+	1.25266i	0.154742	+	0.0659294i
$362$	−0.602338	−	14.9469i	−0.0316582	−	0.785590i
$363$	−4.12688	+	5.97882i	−0.216605	+	0.313807i
$364$	−23.1468	+	40.0914i	−1.21322	+	2.10136i
$365$	44.4934	−	3.59188i	2.32889	−	0.188007i
$366$	−9.28054	+	5.86866i	−0.485102	+	0.306760i
$367$	4.25242	−	1.41967i	0.221974	−	0.0741059i	−0.203506	−	0.979074i	$-0.565234\pi$
$367$	4.25242	−	1.41967i	0.221974	−	0.0741059i	0.425480	+	0.904968i	$0.360105\pi$
$368$	19.4453	−	51.2731i	1.01366	−	2.67279i
$369$	−3.48755	−	0.566782i	−0.181555	−	0.0295055i
$370$	−55.0095	−	13.5586i	−2.85981	−	0.704879i
$371$	−7.00670	+	7.29474i	−0.363769	+	0.378724i
$372$	−8.25664	+	21.7710i	−0.428087	+	1.12877i
$373$	23.1101	−	20.4738i	1.19660	−	1.06009i	0.199822	−	0.979832i	$-0.435964\pi$
$373$	23.1101	−	20.4738i	1.19660	−	1.06009i	0.996774	−	0.0802594i	$-0.0255749\pi$
$374$	−28.7312	−	12.2412i	−1.48566	−	0.632979i
$375$	0.478489	−	2.34380i	0.0247091	−	0.121033i
$376$	16.5084	+	34.7908i	0.851358	+	1.79420i
$377$	−48.6882	−	36.5868i	−2.50757	−	1.88432i
$378$	0.429705	+	3.53894i	0.0221016	+	0.182023i
$379$	0.561375	+	4.62334i	0.0288359	+	0.237485i	1.00000		0.000928721i	$-0.000295621\pi$
$379$	0.561375	+	4.62334i	0.0288359	+	0.237485i	−0.971164	+	0.238414i	$0.923373\pi$
$380$	−2.56300	+	63.6003i	−0.131479	+	3.26263i
$381$	−8.69726	−	7.70510i	−0.445574	−	0.394744i
$382$	−0.773146	+	0.125649i	−0.0395576	+	0.00642874i
$383$	−0.268610	−	6.66550i	−0.0137254	−	0.340591i	−0.991433	−	0.130619i	$-0.958304\pi$
$383$	−0.268610	−	6.66550i	−0.0137254	−	0.340591i	0.977707	−	0.209972i	$-0.0673374\pi$
$384$	−1.62895	+	1.99511i	−0.0831272	+	0.101812i
$385$	−8.15687	+	2.72316i	−0.415713	+	0.138785i
$386$	−4.96377	+	17.1369i	−0.252649	+	0.872247i
$387$	0.175755	+	0.111141i	0.00893414	+	0.00564961i
$388$	25.5546	+	31.2987i	1.29734	+	1.58895i
$389$	1.14024	−	1.01016i	0.0578123	−	0.0512172i	−0.633722	−	0.773561i	$-0.718474\pi$
$389$	1.14024	−	1.01016i	0.0578123	−	0.0512172i	0.691534	+	0.722344i	$0.256935\pi$
$390$	37.9108	−	46.4323i	1.91969	−	2.35119i
$391$	−31.6600	−	10.5696i	−1.60111	−	0.534530i
$392$	37.9347	−	9.35005i	1.91599	−	0.472249i
$393$	3.21743	−	0.793026i	0.162298	−	0.0400029i
$394$	2.53706	+	0.846995i	0.127815	+	0.0426710i
$395$	13.1161	−	16.0643i	0.659942	−	0.808282i
$396$	−7.07090	+	6.26427i	−0.355326	+	0.314791i
$397$	−15.7547	−	19.2960i	−0.790706	−	0.968439i	0.209250	−	0.977862i	$-0.432898\pi$
$397$	−15.7547	−	19.2960i	−0.790706	−	0.968439i	−0.999956	+	0.00942318i	$0.997000\pi$
$398$	−19.2470	−	12.1710i	−0.964763	−	0.610079i
$399$	−1.50237	+	5.18680i	−0.0752128	+	0.259665i
$400$	54.9819	−	18.3557i	2.74910	−	0.917783i
$401$	−13.9728	+	17.1136i	−0.697771	+	0.854614i	−0.994967	−	0.100203i	$-0.968051\pi$
$401$	−13.9728	+	17.1136i	−0.697771	+	0.854614i	0.297196	+	0.954816i	$0.403948\pi$
$402$	−0.835895	−	20.7425i	−0.0416906	−	1.03454i
$403$	32.7846	−	5.32801i	1.63312	−	0.265407i
$404$	−20.3880	−	18.0622i	−1.01434	−	0.898628i
$405$	0.131899	−	3.27305i	0.00655414	−	0.162639i
$406$	−3.75331	−	30.9113i	−0.186274	−	1.53410i
$407$	−1.53522	−	12.6437i	−0.0760982	−	0.626725i
$408$	37.3066	+	28.0341i	1.84695	+	1.38789i
$409$	−6.21592	−	13.0998i	−0.307357	−	0.647742i	0.689725	−	0.724071i	$-0.257731\pi$
$409$	−6.21592	−	13.0998i	−0.307357	−	0.647742i	−0.997083	+	0.0763294i	$0.975680\pi$
$410$	−6.07596	+	29.7620i	−0.300070	+	1.46984i
$411$	−2.13364	−	0.909058i	−0.105245	−	0.0448405i
$412$	−46.4416	+	41.1437i	−2.28802	+	2.02700i
$413$	−1.55159	+	4.09122i	−0.0763490	+	0.201316i
$414$	−9.85559	+	10.2608i	−0.484376	+	0.504288i
$415$	52.0346	+	12.8254i	2.55428	+	0.629573i
$416$	78.3875	+	12.7392i	3.84326	+	0.624591i
$417$	−0.435163	+	1.14743i	−0.0213100	+	0.0561900i
$418$	−19.1266	+	6.38541i	−0.935515	+	0.312321i
$419$	8.39877	−	5.31106i	0.410307	−	0.259462i	−0.313329	−	0.949645i	$-0.601444\pi$
$419$	8.39877	−	5.31106i	0.410307	−	0.259462i	0.723635	+	0.690182i	$0.242470\pi$
$420$	21.6782	−	1.75004i	1.05779	−	0.0853934i
$421$	17.3008	−	29.9659i	0.843191	−	1.46045i	−0.0439912	−	0.999032i	$-0.514007\pi$
$421$	17.3008	−	29.9659i	0.843191	−	1.46045i	0.887183	−	0.461418i	$-0.152659\pi$
$422$	4.40094	−	6.37587i	0.214235	−	0.310372i
$423$	−0.204586	−	5.07676i	−0.00994733	−	0.246840i
$424$	51.9211	+	22.1215i	2.52151	+	1.07432i
$425$	−12.5111	−	32.9891i	−0.606879	−	1.60021i
$426$	16.1169	+	8.45880i	0.780866	+	0.409830i
$427$	1.58113	+	5.45871i	0.0765164	+	0.264165i
$428$	58.2489	−	36.8344i	2.81557	−	1.78046i
$429$	12.7821	+	4.26729i	0.617125	+	0.206027i
$430$	1.01555	−	1.47127i	0.0489740	−	0.0709511i
$431$	−6.75059	−	0.544964i	−0.325164	−	0.0262500i	−0.0831933	−	0.996533i	$-0.526512\pi$
$431$	−6.75059	−	0.544964i	−0.325164	−	0.0262500i	−0.241971	+	0.970283i	$0.577794\pi$
$432$	8.95691	−	4.70095i	0.430939	−	0.226174i
$433$	−12.5128	+	26.3701i	−0.601325	+	1.26727i	0.343335	+	0.939213i	$0.388443\pi$
$433$	−12.5128	+	26.3701i	−0.601325	+	1.26727i	−0.944660	+	0.328052i	$0.893608\pi$
$434$	13.5761	+	10.2018i	0.651676	+	0.489703i
$435$	−1.15209	+	28.5889i	−0.0552386	+	1.37073i
$436$	18.4942	−	38.9756i	0.885710	−	1.86659i
$437$	−19.8264	+	8.44723i	−0.948424	+	0.404086i
$438$	−7.15368	−	35.0410i	−0.341816	−	1.67432i
$439$	−1.57454	−	4.15172i	−0.0751487	−	0.198151i	0.892178	−	0.451684i	$-0.149177\pi$
$439$	−1.57454	−	4.15172i	−0.0751487	−	0.198151i	−0.967327	+	0.253533i	$0.918407\pi$
$440$	30.3463	+	37.1675i	1.44670	+	1.77189i
$441$	−5.08816	−	0.826907i	−0.242293	−	0.0393765i
$442$	13.5810	−	111.849i	0.645981	−	5.32013i
$443$	24.4934			1.16372			0.581858	−	0.813290i	$-0.302326\pi$
$443$	24.4934			1.16372			0.581858	+	0.813290i	$0.302326\pi$
$444$	−3.88272	+	31.9771i	−0.184266	+	1.51756i
$445$	−20.7967	+	21.6517i	−0.985858	+	1.02639i
$446$	15.4121	−	53.2086i	0.729783	−	2.51950i
$447$	3.43248	+	11.8503i	0.162351	+	0.560500i
$448$	7.45471	+	10.8000i	0.352202	+	0.510252i
$449$	3.43500	+	5.94960i	0.162108	+	0.280779i	0.935624	−	0.352997i	$-0.114837\pi$
$449$	3.43500	+	5.94960i	0.162108	+	0.280779i	−0.773517	+	0.633776i	$0.781504\pi$
$450$	−14.9902	−	1.21013i	−0.706644	−	0.0570462i
$451$	−6.74026	+	1.09540i	−0.317386	+	0.0515803i
$452$	2.12441	−	10.4061i	0.0999240	−	0.489460i
$453$	4.19608	+	20.5538i	0.197149	+	0.965701i
$454$	33.8899	−	25.4666i	1.59053	−	1.19521i
$455$	−17.6239	−	25.5327i	−0.826223	−	1.19699i
$456$	30.0329	−	2.42450i	1.40642	−	0.113538i
$457$	−4.64554	+	1.14502i	−0.217309	+	0.0535619i	−0.346467	−	0.938062i	$-0.612619\pi$
$457$	−4.64554	+	1.14502i	−0.217309	+	0.0535619i	0.129158	+	0.991624i	$0.458773\pi$
$458$	−19.0641	+	33.0200i	−0.890808	+	1.54292i
$459$	−3.07856	−	5.33222i	−0.143695	−	0.248886i
$460$	60.1264	+	62.5982i	2.80341	+	2.91866i
$461$	−5.11318	+	2.17852i	−0.238145	+	0.101464i	−0.507742	−	0.861509i	$-0.669520\pi$
$461$	−5.11318	+	2.17852i	−0.238145	+	0.101464i	0.269597	+	0.962973i	$0.413109\pi$
$462$	2.95361	+	6.22460i	0.137414	+	0.289594i
$463$	10.0179	+	8.87507i	0.465571	+	0.412460i	0.863024	−	0.505163i	$-0.168568\pi$
$463$	10.0179	+	8.87507i	0.465571	+	0.412460i	−0.397453	+	0.917622i	$0.630106\pi$
$464$	−78.2353	+	41.0610i	−3.63198	+	1.90621i
$465$	−10.8095	−	11.2538i	−0.501277	−	0.521884i
$466$	39.5800	−	29.7425i	1.83351	−	1.37779i
$467$	4.37377	+	2.29553i	0.202394	+	0.106224i	0.562875	−	0.826542i	$-0.309695\pi$
$467$	4.37377	+	2.29553i	0.202394	+	0.106224i	−0.360481	+	0.932766i	$0.617388\pi$
$468$	−28.8049	−	18.2151i	−1.33151	−	0.841994i
$469$	−10.4321	−	2.57128i	−0.481710	−	0.118731i
$470$	−43.6804			−2.01483
$471$	8.89508	−	8.82482i	0.409864	−	0.406626i
$472$	24.4144			1.12377
$473$	0.390214	+	0.0961792i	0.0179421	+	0.00442232i
$474$	−14.0434	−	8.88053i	−0.645036	−	0.407896i
$475$	−20.1710	−	10.5866i	−0.925509	−	0.485745i
$476$	32.6808	−	24.5580i	1.49792	−	1.12562i
$477$	−5.15828	−	5.37034i	−0.236182	−	0.245891i
$478$	−43.1825	+	22.6639i	−1.97512	+	1.03662i
$479$	−11.6751	−	10.3433i	−0.533450	−	0.472596i	0.352867	−	0.935673i	$-0.385207\pi$
$479$	−11.6751	−	10.3433i	−0.533450	−	0.472596i	−0.886318	+	0.463077i	$0.846745\pi$
$480$	−15.9944	−	33.7074i	−0.730039	−	1.53853i
$481$	42.2733	−	18.0110i	1.92750	−	0.821230i
$482$	−18.8520	−	19.6270i	−0.858685	−	0.893986i
$483$	3.68178	+	6.37702i	0.167527	+	0.290165i
$484$	17.7548	−	30.7521i	0.807034	−	1.39782i
$485$	−26.2921	+	6.48041i	−1.19386	+	0.294260i
$486$	−2.61597	+	0.211183i	−0.118663	+	0.00957944i
$487$	9.40758	+	13.6292i	0.426298	+	0.617599i	0.976002	−	0.217760i	$-0.0698750\pi$
$487$	9.40758	+	13.6292i	0.426298	+	0.617599i	−0.549704	+	0.835359i	$0.685260\pi$
$488$	25.3504	−	19.0496i	1.14756	−	0.862335i
$489$	−3.83321	−	18.7763i	−0.173344	−	0.849094i
$490$	−8.86452	+	43.4213i	−0.400458	+	1.96157i
$491$	−29.9484	+	4.86709i	−1.35155	+	0.219649i	−0.792697	−	0.609616i	$-0.791324\pi$
$491$	−29.9484	+	4.86709i	−1.35155	+	0.219649i	−0.558856	+	0.829265i	$0.688759\pi$
$492$	17.2144	+	1.38969i	0.776083	+	0.0626519i
$493$	26.8901	+	46.5749i	1.21107	+	2.09763i
$494$	−41.3255	−	59.8703i	−1.85932	−	2.69369i
$495$	−1.76135	−	6.08089i	−0.0791668	−	0.273316i
$496$	13.4065	−	46.2844i	0.601967	−	2.07823i
$497$	6.52590	−	6.79418i	0.292727	−	0.304761i
$498$	5.17554	−	42.6244i	0.231922	−	1.91005i
$499$	24.7409			1.10756			0.553778	−	0.832665i	$-0.313186\pi$
$499$	24.7409			1.10756			0.553778	+	0.832665i	$0.313186\pi$
$500$	−1.40937	+	11.6072i	−0.0630291	+	0.519091i
$501$	15.4957	+	2.51830i	0.692297	+	0.112509i
$502$	−21.8091	−	26.7113i	−0.973389	−	1.19219i
$503$	12.4533	+	32.8367i	0.555267	+	1.46412i	0.859308	+	0.511459i	$0.170895\pi$
$503$	12.4533	+	32.8367i	0.555267	+	1.46412i	−0.304041	+	0.952659i	$0.598336\pi$
$504$	−2.05928	−	10.0870i	−0.0917276	−	0.449311i
$505$	16.7935	−	7.15502i	0.747299	−	0.318394i
$506$	−11.7876	+	24.8418i	−0.524021	+	1.10435i
$507$	−1.43413	+	35.5876i	−0.0636921	+	1.58050i
$508$	45.4038	+	34.1187i	2.01447	+	1.51377i
$509$	−6.03211	+	12.7124i	−0.267369	+	0.563468i	−0.992083	−	0.125582i	$-0.959920\pi$
$509$	−6.03211	+	12.7124i	−0.267369	+	0.563468i	0.724715	+	0.689049i	$0.241972\pi$
$510$	−46.8697	+	24.5991i	−2.07542	+	1.08927i
$511$	−18.4501	−	1.48944i	−0.816184	−	0.0658891i
$512$	−21.6552	+	31.3730i	−0.957034	+	1.38650i
$513$	−3.77086	−	1.25890i	−0.166487	−	0.0555816i
$514$	14.2476	−	9.00963i	0.628434	−	0.397398i
$515$	−11.5685	−	39.9393i	−0.509771	−	1.75993i
$516$	−0.899997	−	0.472355i	−0.0396202	−	0.0207943i
$517$	−3.48209	−	9.18151i	−0.153142	−	0.403802i
$518$	21.6135	+	9.20865i	0.949643	+	0.404605i
$519$	0.277373	+	6.88294i	0.0121753	+	0.302128i
$520$	−98.3369	+	142.466i	−4.31236	+	6.24753i
$521$	−9.56007	+	16.5585i	−0.418834	+	0.725442i	−0.995823	−	0.0913101i	$-0.970895\pi$
$521$	−9.56007	+	16.5585i	−0.418834	+	0.725442i	0.576988	+	0.816753i	$0.304228\pi$
$522$	22.8495	−	1.84460i	1.00010	−	0.0807361i
$523$	−9.94759	+	6.29048i	−0.434978	+	0.275063i	−0.733956	−	0.679196i	$-0.762328\pi$
$523$	−9.94759	+	6.29048i	−0.434978	+	0.275063i	0.298979	+	0.954260i	$0.403354\pi$
$524$	−15.3635	+	5.12910i	−0.671158	+	0.224066i
$525$	−2.76012	+	7.27783i	−0.120461	+	0.317631i
$526$	−31.4311	−	5.10805i	−1.37046	−	0.222721i
$527$	−28.4779	−	7.01918i	−1.24052	−	0.305760i
$528$	13.5428	−	14.0995i	0.589374	−	0.613603i
$529$	−2.26494	+	5.97217i	−0.0984758	+	0.259659i
$530$	−47.9171	+	42.4509i	−2.08139	+	1.84395i
$531$	−2.96349	−	1.26263i	−0.128605	−	0.0547933i
$532$	5.27959	−	25.8611i	0.228899	−	1.12122i
$533$	−10.5613	−	22.2575i	−0.457462	−	0.964081i
$534$	19.2291	+	14.4497i	0.832124	+	0.625301i
$535$	5.56721	+	45.8501i	0.240692	+	1.98227i
$536$	7.22623	+	59.5133i	0.312125	+	2.57058i
$537$	0.279250	−	6.92952i	0.0120505	−	0.299031i
$538$	53.8703	+	47.7249i	2.32251	+	2.05757i
$539$	−9.83370	+	1.59813i	−0.423568	+	0.0688364i
$540$	0.644708	+	15.9983i	0.0277438	+	0.688456i
$541$	2.79372	−	3.42169i	0.120111	−	0.147110i	−0.711049	−	0.703142i	$-0.751780\pi$
$541$	2.79372	−	3.42169i	0.120111	−	0.147110i	0.831160	+	0.556033i	$0.187677\pi$
$542$	48.3247	−	16.1332i	2.07572	−	0.692979i
$543$	1.58578	−	5.47476i	0.0680525	−	0.234945i
$544$	−59.2717	−	37.4811i	−2.54125	−	1.60699i
$545$	18.2851	+	22.3952i	0.783247	+	0.959303i
$546$	−18.6055	+	16.4830i	−0.796241	+	0.705408i
$547$	−2.62194	+	3.21130i	−0.112106	+	0.137305i	−0.827610	−	0.561304i	$-0.810300\pi$
$547$	−2.62194	+	3.21130i	−0.112106	+	0.137305i	0.715504	+	0.698609i	$0.246197\pi$
$548$	10.7527	+	3.58977i	0.459332	+	0.153347i
$549$	−4.06228	+	1.00126i	−0.173374	+	0.0427328i
$550$	−28.2206	+	6.95576i	−1.20333	+	0.296595i
$551$	32.9370	+	10.9960i	1.40316	+	0.468445i
$552$	25.9851	−	31.8259i	1.10600	−	1.35460i
$553$	−6.43698	+	5.70267i	−0.273728	+	0.242502i
$554$	−29.5404	−	36.1804i	−1.25505	−	1.53716i
$555$	−18.2455	−	11.5378i	−0.774479	−	0.489751i
$556$	1.66883	−	5.76147i	0.0707742	−	0.244341i
$557$	30.3734	−	10.1401i	1.28696	−	0.429652i	0.410827	−	0.911714i	$-0.365240\pi$
$557$	30.3734	−	10.1401i	1.28696	−	0.429652i	0.876137	+	0.482062i	$0.160112\pi$
$558$	−7.90686	+	9.68415i	−0.334724	+	0.409963i
$559$	0.0583826	+	1.44875i	0.00246932	+	0.0612756i
$560$	−44.4267	+	7.22003i	−1.87737	+	0.305102i
$561$	−8.90700	−	7.89091i	−0.376054	−	0.333154i
$562$	2.78306	−	69.0610i	0.117396	−	2.91316i
$563$	3.05886	+	25.1920i	0.128916	+	1.06172i	0.903303	+	0.429003i	$0.141135\pi$
$563$	3.05886	+	25.1920i	0.128916	+	1.06172i	−0.774387	+	0.632712i	$0.781942\pi$
$564$	2.99349	+	24.6536i	0.126049	+	1.03811i
$565$	5.69018	+	4.27589i	0.239388	+	0.179888i
$566$	−2.46732	−	5.19977i	−0.103709	−	0.218562i
$567$	−0.271703	+	1.33089i	−0.0114104	+	0.0558920i
$568$	−48.3583	−	20.6036i	−2.02907	−	0.864506i
$569$	33.9372	−	30.0658i	1.42272	−	1.26042i	0.505049	−	0.863091i	$-0.331475\pi$
$569$	33.9372	−	30.0658i	1.42272	−	1.26042i	0.917675	−	0.397332i	$-0.130064\pi$
$570$	−12.1193	+	31.9560i	−0.507623	+	1.33849i
$571$	16.6336	−	17.3174i	0.696096	−	0.724712i	−0.275515	−	0.961297i	$-0.588848\pi$
$571$	16.6336	−	17.3174i	0.696096	−	0.724712i	0.971611	+	0.236584i	$0.0760280\pi$
$572$	−63.9531	−	15.7630i	−2.67401	−	0.659085i
$573$	−0.294591	−	0.0478757i	−0.0123067	−	0.00200003i
$574$	4.46659	−	11.7774i	0.186432	−	0.491581i
$575$	−29.4651	+	9.83690i	−1.22878	+	0.410227i
$576$	−8.16543	+	5.16351i	−0.340226	+	0.215146i
$577$	4.21276	−	0.340089i	0.175380	−	0.0141581i	0.00753525	−	0.999972i	$-0.497601\pi$
$577$	4.21276	−	0.340089i	0.175380	−	0.0141581i	0.167844	+	0.985813i	$0.446319\pi$
$578$	−27.4389	+	47.5256i	−1.14131	+	1.97681i
$579$	−3.86174	+	5.59469i	−0.160488	+	0.232507i
$580$	−5.63129	−	139.739i	−0.233827	−	5.80235i
$581$	−20.4447	−	8.71066i	−0.848188	−	0.361379i
$582$	7.69332	+	20.2856i	0.318898	+	0.840866i
$583$	−12.7429	−	6.68798i	−0.527757	−	0.276988i
$584$	28.7347	+	99.2037i	1.18905	+	4.10508i
$585$	19.3042	−	12.2072i	0.798130	−	0.504707i
$586$	−1.52154	−	0.507964i	−0.0628542	−	0.0209838i
$587$	0.936068	−	1.35613i	0.0386357	−	0.0559734i	−0.803190	−	0.595723i	$-0.796866\pi$
$587$	0.936068	−	1.35613i	0.0386357	−	0.0559734i	0.841826	+	0.539749i	$0.181481\pi$
$588$	25.1149	+	2.02748i	1.03572	+	0.0836120i
$589$	−16.7684	+	8.80073i	−0.690929	+	0.362628i
$590$	−11.8719	+	25.0194i	−0.488757	+	1.03003i
$591$	0.814745	+	0.612241i	0.0335141	+	0.0251842i
$592$	2.68426	−	66.6093i	0.110323	−	2.73763i
$593$	9.55214	−	20.1307i	0.392259	−	0.826669i	−0.607224	−	0.794531i	$-0.707717\pi$
$593$	9.55214	−	20.1307i	0.392259	−	0.826669i	0.999483	−	0.0321383i	$-0.0102317\pi$
$594$	−4.66635	+	1.98814i	−0.191463	+	0.0815746i
$595$	5.47994	+	26.8425i	0.224656	+	1.10044i
$596$	−21.3840	−	56.3849i	−0.875922	−	2.30962i
$597$	−5.48767	−	6.72118i	−0.224596	−	0.275080i
$598$	−97.9159	−	15.9129i	−4.00408	−	0.650726i
$599$	1.41938	−	11.6897i	0.0579944	−	0.477627i	−0.934558	−	0.355810i	$-0.884205\pi$
$599$	1.41938	−	11.6897i	0.0579944	−	0.477627i	0.992553	−	0.121817i	$-0.0388720\pi$
$600$	43.4306			1.77305
$601$	−4.10498	+	33.8075i	−0.167446	+	1.37904i	0.630444	+	0.776235i	$0.282873\pi$
$601$	−4.10498	+	33.8075i	−0.167446	+	1.37904i	−0.797890	+	0.602804i	$0.794050\pi$
$602$	−0.513529	+	0.534640i	−0.0209299	+	0.0217903i
$603$	2.20067	−	7.59760i	0.0896183	−	0.309398i
$604$	−28.5275	−	98.4882i	−1.16077	−	4.00743i
$605$	13.5185	+	19.5849i	0.549604	+	0.796239i
$606$	−7.31256	−	12.6657i	−0.297052	−	0.514510i
$607$	−37.4993	−	3.02726i	−1.52205	−	0.122873i	−0.709060	−	0.705148i	$-0.750880\pi$
$607$	−37.4993	−	3.02726i	−1.52205	−	0.122873i	−0.812991	+	0.582276i	$0.802162\pi$
$608$	−44.6931	+	7.26334i	−1.81255	+	0.294567i
$609$	2.37322	−	11.6248i	0.0961678	−	0.471061i
$610$	7.19466	+	35.2418i	0.291303	+	1.42690i
$611$	28.3216	−	21.2823i	1.14577	−	0.860990i
$612$	17.0960	+	24.7679i	0.691066	+	1.00118i
$613$	−20.7309	+	1.67357i	−0.837311	+	0.0675948i	−0.491680	−	0.870776i	$-0.663617\pi$
$613$	−20.7309	+	1.67357i	−0.837311	+	0.0675948i	−0.345631	+	0.938371i	$0.612335\pi$
$614$	47.8300	−	11.7890i	1.93026	−	0.475766i
$615$	−5.78704	+	10.0234i	−0.233356	+	0.404184i
$616$	−9.94845	−	17.2312i	−0.400835	−	0.694266i
$617$	30.7177	+	31.9805i	1.23665	+	1.28749i	0.943481	+	0.331426i	$0.107530\pi$
$617$	30.7177	+	31.9805i	1.23665	+	1.28749i	0.293167	+	0.956061i	$0.405291\pi$
$618$	−30.6486	+	13.0581i	−1.23287	+	0.525275i
$619$	16.7686	+	35.3390i	0.673985	+	1.42039i	0.895422	+	0.445219i	$0.146874\pi$
$619$	16.7686	+	35.3390i	0.673985	+	1.42039i	−0.221436	+	0.975175i	$0.571074\pi$
$620$	57.0902	+	50.5775i	2.29280	+	2.03124i
$621$	−4.80006	+	2.51926i	−0.192620	+	0.101095i
$622$	47.8603	+	49.8278i	1.91902	+	1.99791i
$623$	9.95231	−	7.47868i	0.398731	−	0.299627i
$624$	62.4525	+	32.7776i	2.50010	+	1.31215i
$625$	17.5930	+	11.1251i	0.703718	+	0.445004i
$626$	−26.0350	−	6.41704i	−1.04057	−	0.256477i
$627$	−7.68320			−0.306837
$628$	−39.8662	+	46.4933i	−1.59083	+	1.85529i
$629$	−40.5764			−1.61789
$630$	11.3383	+	2.79465i	0.451730	+	0.111341i
$631$	−5.94151	−	3.75718i	−0.236528	−	0.149571i	0.410944	−	0.911661i	$-0.365199\pi$
$631$	−5.94151	−	3.75718i	−0.236528	−	0.149571i	−0.647472	+	0.762090i	$0.724174\pi$
$632$	42.4878	+	22.2993i	1.69007	+	0.887020i
$633$	2.35990	−	1.77335i	0.0937974	−	0.0704842i
$634$	−30.0284	−	31.2629i	−1.19258	−	1.24161i
$635$	−33.7021	+	17.6882i	−1.33743	+	0.701936i
$636$	27.2435	+	24.1356i	1.08028	+	0.957040i
$637$	−15.4085	−	32.4727i	−0.610506	−	1.28661i
$638$	40.7588	−	17.3657i	1.61366	−	0.687515i
$639$	4.80432	+	5.00183i	0.190056	+	0.197869i
$640$	4.21853	+	7.30671i	0.166752	+	0.288823i
$641$	−19.9368	+	34.5315i	−0.787456	+	1.36391i	0.140065	+	0.990142i	$0.455269\pi$
$641$	−19.9368	+	34.5315i	−0.787456	+	1.36391i	−0.927521	+	0.373771i	$0.878065\pi$
$642$	35.9293	−	8.85579i	1.41802	−	0.349510i
$643$	−6.62209	+	0.534590i	−0.261150	+	0.0210822i	−0.210348	−	0.977627i	$-0.567460\pi$
$643$	−6.62209	+	0.534590i	−0.261150	+	0.0210822i	−0.0508017	+	0.998709i	$0.516178\pi$
$644$	−20.4459	−	29.6209i	−0.805680	−	1.16723i
$645$	0.544561	−	0.409211i	0.0214421	−	0.0161127i
$646$	12.8497	+	62.9418i	0.505563	+	2.47641i
$647$	7.82042	−	38.3069i	0.307452	−	1.50600i	−0.473155	−	0.880979i	$-0.656885\pi$
$647$	7.82042	−	38.3069i	0.307452	−	1.50600i	0.780607	−	0.625022i	$-0.214910\pi$
$648$	7.48102	−	1.21578i	0.293882	−	0.0477605i
$649$	−6.20542	−	0.500953i	−0.243584	−	0.0196641i
$650$	−52.4299	−	90.8113i	−2.05647	−	3.56191i
$651$	3.67574	+	5.32522i	0.144063	+	0.208712i
$652$	26.0604	+	89.9710i	1.02060	+	3.52354i
$653$	0.258709	−	0.893168i	0.0101241	−	0.0349523i	−0.955297	−	0.295648i	$-0.904465\pi$
$653$	0.258709	−	0.893168i	0.0101241	−	0.0349523i	0.965421	+	0.260695i	$0.0839518\pi$
$654$	16.0462	−	16.7059i	0.627456	−	0.653250i
$655$	1.30840	−	10.7757i	0.0511234	−	0.421039i
$656$	−35.7414			−1.39547
$657$	1.64256	−	13.5277i	0.0640822	−	0.527764i
$658$	17.8784	+	2.90552i	0.696973	+	0.113269i
$659$	−15.9798	−	19.5717i	−0.622484	−	0.762404i	0.363071	−	0.931761i	$-0.381728\pi$
$659$	−15.9798	−	19.5717i	−0.622484	−	0.762404i	−0.985555	+	0.169357i	$0.945831\pi$
$660$	10.9730	+	28.9335i	0.427124	+	1.12623i
$661$	0.625685	+	3.06481i	0.0243363	+	0.119207i	0.990144	−	0.140052i	$-0.0447269\pi$
$661$	0.625685	+	3.06481i	0.0243363	+	0.119207i	−0.965808	+	0.259259i	$0.916522\pi$
$662$	45.8922	−	19.5528i	1.78365	−	0.759942i
$663$	18.4041	−	38.7858i	0.714757	−	1.50632i
$664$	−4.99290	+	123.898i	−0.193762	+	4.80816i
$665$	14.1412	+	10.6264i	0.548372	+	0.412075i
$666$	−7.41455	+	15.6258i	−0.287308	+	0.605489i
$667$	41.9267	−	22.0048i	1.62341	−	0.852031i
$668$	−76.4860	−	6.17459i	−2.95933	−	0.238902i
$669$	11.9903	−	17.3710i	0.463574	−	0.671602i
$670$	−64.5020	−	21.5339i	−2.49193	−	0.831928i
$671$	−6.83419	+	4.32168i	−0.263831	+	0.166837i
$672$	4.30435	+	14.8604i	0.166044	+	0.573251i
$673$	−17.8096	−	9.34721i	−0.686511	−	0.360309i	0.0851277	−	0.996370i	$-0.472870\pi$
$673$	−17.8096	−	9.34721i	−0.686511	−	0.360309i	−0.771638	+	0.636061i	$0.780562\pi$
$674$	6.32918	+	16.6887i	0.243791	+	0.642824i
$675$	−5.27173	−	2.24607i	−0.202909	−	0.0864514i
$676$	−7.00986	−	173.948i	−0.269610	−	6.69031i
$677$	−19.8308	+	28.7299i	−0.762159	+	1.10418i	0.229248	+	0.973368i	$0.426373\pi$
$677$	−19.8308	+	28.7299i	−0.762159	+	1.10418i	−0.991407	+	0.130810i	$0.958242\pi$
$678$	2.85132	−	4.93863i	0.109504	−	0.189667i
$679$	11.1924	−	0.903545i	0.429525	−	0.0346749i
$680$	129.199	−	81.7003i	4.95454	−	3.13306i
$681$	15.3213	−	5.11499i	0.587112	−	0.196007i
$682$	−8.56805	+	22.5921i	−0.328088	+	0.865096i
$683$	−44.5075	−	7.23317i	−1.70303	−	0.276770i	−0.770390	−	0.637573i	$-0.779938\pi$
$683$	−44.5075	−	7.23317i	−1.70303	−	0.276770i	−0.932642	+	0.360803i	$0.882503\pi$
$684$	18.8668	+	4.65026i	0.721392	+	0.177807i
$685$	−5.26269	+	5.47904i	−0.201077	+	0.209344i
$686$	15.3655	−	40.5156i	0.586658	−	1.54689i
$687$	−10.8743	+	9.63381i	−0.414881	+	0.367553i
$688$	1.93519	+	0.824506i	0.0737783	+	0.0314340i
$689$	10.3854	−	50.8710i	0.395652	−	1.93803i
$690$	19.9790	+	42.1048i	0.760587	+	1.60290i
$691$	10.6357	+	7.99217i	0.404599	+	0.304037i	0.783490	−	0.621405i	$-0.213438\pi$
$691$	10.6357	+	7.99217i	0.404599	+	0.304037i	−0.378890	+	0.925442i	$0.623694\pi$
$692$	−4.05850	−	33.4248i	−0.154281	−	1.27062i
$693$	0.316434	+	2.60607i	0.0120203	+	0.0989964i
$694$	−0.181363	+	4.50049i	−0.00688446	+	0.170836i
$695$	3.00892	+	2.66567i	0.114135	+	0.101115i
$696$	−65.3439	+	10.6194i	−2.47686	+	0.402528i
$697$	0.875984	+	21.7373i	0.0331802	+	0.823359i
$698$	15.5299	−	19.0206i	0.587814	−	0.719941i
$699$	17.8937	−	5.97380i	0.676802	−	0.225950i
$700$	10.5849	−	36.5434i	0.400072	−	1.38121i
$701$	11.8692	+	7.50564i	0.448295	+	0.283484i	0.739475	−	0.673184i	$-0.235074\pi$
$701$	11.8692	+	7.50564i	0.448295	+	0.283484i	−0.291181	+	0.956668i	$0.594048\pi$
$702$	−11.5733	−	14.1747i	−0.436806	−	0.534991i
$703$	−19.6101	+	17.3730i	−0.739610	+	0.655237i
$704$	−11.8087	+	14.4631i	−0.445059	+	0.545098i
$705$	−15.7869	−	5.27046i	−0.594571	−	0.198497i
$706$	71.7196	−	17.6773i	2.69920	−	0.665294i
$707$	−7.34950	+	1.81149i	−0.276406	+	0.0681281i
$708$	14.9348	+	4.98597i	0.561285	+	0.187384i
$709$	−32.0049	+	39.1988i	−1.20197	+	1.47214i	−0.359713	+	0.933063i	$0.617125\pi$
$709$	−32.0049	+	39.1988i	−1.20197	+	1.47214i	−0.842255	+	0.539080i	$0.818772\pi$
$710$	44.6291	−	39.5379i	1.67490	−	1.48383i
$711$	−4.00405	−	4.90407i	−0.150163	−	0.183917i
$712$	−58.7090	−	37.1253i	−2.20021	−	1.39133i
$713$	−7.18459	+	24.8041i	−0.269065	+	0.928920i
$714$	20.8200	−	6.95075i	0.779171	−	0.260125i
$715$	27.9175	−	34.1927i	1.04405	−	1.27874i
$716$	1.36494	+	33.8706i	0.0510102	+	1.26581i
$717$	−18.3416	+	2.98080i	−0.684979	+	0.111320i
$718$	14.6555	+	12.9836i	0.546937	+	0.484544i
$719$	−1.84414	+	45.7618i	−0.0687747	+	1.70663i	0.485454	+	0.874262i	$0.338654\pi$
$719$	−1.84414	+	45.7618i	−0.0687747	+	1.70663i	−0.554229	+	0.832364i	$0.686987\pi$
$720$	−3.99407	−	32.8941i	−0.148850	−	1.22589i
$721$	2.07834	+	17.1167i	0.0774014	+	0.637458i
$722$	−6.70523	−	5.03866i	−0.249543	−	0.187519i
$723$	−4.44529	−	9.36826i	−0.165322	−	0.348409i
$724$	−5.57270	+	27.2969i	−0.207108	+	1.01448i
$725$	46.0466	+	19.6186i	1.71013	+	0.728617i
$726$	14.2714	−	12.6433i	0.529660	−	0.469237i
$727$	12.6054	−	33.2377i	0.467508	−	1.23272i	−0.469351	−	0.883012i	$-0.655512\pi$
$727$	12.6054	−	33.2377i	0.467508	−	1.23272i	0.936859	−	0.349707i	$-0.113719\pi$
$728$	49.7258	−	51.7700i	1.84296	−	1.91873i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−115.635	−	18.7925i	−4.27983	−	0.695540i
$731$	0.454021	−	1.19715i	0.0167926	−	0.0442783i
$732$	19.3977	−	6.47591i	0.716960	−	0.239356i
$733$	−17.4625	+	11.0426i	−0.644993	+	0.407869i	−0.816525	−	0.577310i	$-0.804103\pi$
$733$	−17.4625	+	11.0426i	−0.644993	+	0.407869i	0.171532	+	0.985178i	$0.445128\pi$
$734$	−11.7277	+	0.946760i	−0.432878	+	0.0349456i
$735$	−8.44300	+	14.6237i	−0.311425	+	0.539404i
$736$	−35.0746	+	50.8143i	−1.29287	+	1.87304i
$737$	−0.615552	−	15.2748i	−0.0226742	−	0.562654i
$738$	8.53104	+	3.63474i	0.314032	+	0.133796i
$739$	2.36474	+	6.23530i	0.0869883	+	0.229369i	0.971450	−	0.237243i	$-0.0762437\pi$
$739$	2.36474	+	6.23530i	0.0869883	+	0.229369i	−0.884462	+	0.466612i	$0.845474\pi$
$740$	93.4305	+	49.0361i	3.43457	+	1.80260i
$741$	−7.71191	−	26.6246i	−0.283304	−	0.978080i
$742$	22.4362	−	14.1878i	0.823660	−	0.520851i
$743$	13.5675	+	4.52951i	0.497745	+	0.166172i	0.554446	−	0.832220i	$-0.312930\pi$
$743$	13.5675	+	4.52951i	0.497745	+	0.166172i	−0.0567015	+	0.998391i	$0.518058\pi$
$744$	20.5096	−	29.7133i	0.751919	−	1.08934i
$745$	40.2827	+	3.25195i	1.47584	+	0.119142i
$746$	−71.7486	+	37.6566i	−2.62690	+	1.37871i
$747$	7.01358	−	14.7808i	0.256614	−	0.540802i
$748$	46.4987	+	34.9415i	1.70016	+	1.27759i
$749$	0.771186	−	19.1368i	0.0281785	−	0.699243i
$750$	−2.69138	+	5.67196i	−0.0982753	+	0.207111i
$751$	36.8954	−	15.7197i	1.34633	−	0.573618i	0.405999	−	0.913874i	$-0.366924\pi$
$751$	36.8954	−	15.7197i	1.34633	−	0.573618i	0.940333	+	0.340255i	$0.110513\pi$
$752$	−10.2805	−	50.3574i	−0.374892	−	1.83634i
$753$	−4.65926	−	12.2855i	−0.169793	−	0.447707i
$754$	101.089	+	123.811i	3.68143	+	4.50893i
$755$	67.8271	+	11.0230i	2.46848	+	0.401167i
$756$	0.800290	−	6.59098i	0.0291063	−	0.239712i
$757$	16.9794			0.617128			0.308564	−	0.951204i	$-0.400152\pi$
$757$	16.9794			0.617128			0.308564	+	0.951204i	$0.400152\pi$
$758$	1.47332	−	12.1339i	0.0535133	−	0.440721i
$759$	−7.25765	+	7.55601i	−0.263436	+	0.274266i
$760$	27.4598	−	94.8021i	0.996070	−	3.43883i
$761$	0.115681	+	0.399376i	0.00419342	+	0.0144774i	0.962588	−	0.270971i	$-0.0873447\pi$
$761$	0.115681	+	0.399376i	0.00419342	+	0.0144774i	−0.958394	+	0.285448i	$0.907858\pi$
$762$	17.3231	+	25.0968i	0.627549	+	0.909162i
$763$	−5.99441	−	10.3826i	−0.217012	−	0.375876i
$764$	1.45408	+	0.117386i	0.0526069	+	0.00424687i
$765$	−19.9077	+	3.23532i	−0.719765	+	0.116973i
$766$	−3.50198	+	17.1538i	−0.126532	+	0.619793i
$767$	−4.49266	−	22.0065i	−0.162220	−	0.794608i
$768$	−10.0429	+	7.54676i	−0.362393	+	0.272320i
$769$	−16.3835	−	23.7356i	−0.590803	−	0.855926i	0.407556	−	0.913180i	$-0.366381\pi$
$769$	−16.3835	−	23.7356i	−0.590803	−	0.855926i	−0.998360	+	0.0572538i	$0.981766\pi$
$770$	22.4958	−	1.81605i	0.810693	−	0.0654459i
$771$	6.23645	−	1.53715i	0.224600	−	0.0553590i
$772$	16.6140	−	28.7764i	0.597952	−	1.03568i
$773$	15.7631	+	27.3024i	0.566958	+	0.982000i	0.996865	+	0.0791266i	$0.0252131\pi$
$773$	15.7631	+	27.3024i	0.566958	+	0.982000i	−0.429907	+	0.902873i	$0.641454\pi$
$774$	−0.378057	−	0.393599i	−0.0135890	−	0.0141476i
$775$	−25.1126	+	10.6995i	−0.902070	+	0.384336i
$776$	−26.8592	−	56.6046i	−0.964190	−	2.03199i
$777$	6.70043	+	5.93606i	0.240376	+	0.212955i
$778$	−3.54003	+	1.85795i	−0.126916	+	0.0666107i
$779$	9.73032	+	10.1303i	0.348625	+	0.362957i
$780$	−89.2493	+	67.0665i	−3.19564	+	2.40137i
$781$	11.8685	+	6.22906i	0.424687	+	0.222893i
$782$	74.0378	+	46.8187i	2.64759	+	1.67423i
$783$	8.48082	+	2.09033i	0.303080	+	0.0747024i
$784$	−52.1450			−1.86232
$785$	−16.6967	−	37.4950i	−0.595929	−	1.33825i
$786$	−8.69679			−0.310204
$787$	−38.3908	−	9.46247i	−1.36848	−	0.337301i	−0.514450	−	0.857520i	$-0.672004\pi$
$787$	−38.3908	−	9.46247i	−1.36848	−	0.337301i	−0.854033	+	0.520219i	$0.825850\pi$
$788$	−4.21026	−	2.66241i	−0.149984	−	0.0948443i
$789$	−10.7435	−	5.63861i	−0.382478	−	0.200740i
$790$	−43.5122	+	32.6973i	−1.54810	+	1.16332i
$791$	−2.04457	−	2.12862i	−0.0726965	−	0.0756851i
$792$	12.9701	−	6.80725i	0.460874	−	0.241885i
$793$	−21.8357	−	19.3447i	−0.775407	−	0.686951i
$794$	28.0270	+	59.0656i	0.994639	+	2.09616i
$795$	−22.4403	+	9.56091i	−0.795874	+	0.339090i
$796$	29.3796	+	30.5874i	1.04133	+	1.08414i
$797$	12.6870	+	21.9745i	0.449397	+	0.778378i	0.998347	−	0.0574770i	$-0.0183056\pi$
$797$	12.6870	+	21.9745i	0.449397	+	0.778378i	−0.548950	+	0.835855i	$0.684972\pi$
$798$	7.08609	−	12.2735i	0.250845	−	0.434476i
$799$	−30.3745	+	7.48664i	−1.07457	+	0.264858i
$800$	−65.0549	+	5.25177i	−2.30004	+	0.185678i
$801$	5.20627	+	7.54258i	0.183954	+	0.266504i
$802$	46.3545	−	34.8331i	1.63683	−	1.23000i
$803$	−5.26796	−	25.8042i	−0.185902	−	0.910610i
$804$	−7.73352	+	37.8813i	−0.272740	+	1.33597i
$805$	23.8085	−	3.86926i	0.839139	−	0.136373i
$806$	−86.8885	−	7.01437i	−3.06052	−	0.247071i
$807$	13.7113	+	23.7487i	0.482660	+	0.835992i
$808$	23.9925	+	34.7592i	0.844054	+	1.22282i
$809$	−1.19018	−	4.10898i	−0.0418445	−	0.144464i	0.936876	−	0.349662i	$-0.113703\pi$
$809$	−1.19018	−	4.10898i	−0.0418445	−	0.144464i	−0.978721	+	0.205198i	$0.934216\pi$
$810$	−2.39184	+	8.25759i	−0.0840407	+	0.290142i
$811$	24.8967	−	25.9202i	0.874241	−	0.910181i	−0.122366	−	0.992485i	$-0.539048\pi$
$811$	24.8967	−	25.9202i	0.874241	−	0.910181i	0.996607	+	0.0823039i	$0.0262278\pi$
$812$	−6.99024	+	57.5698i	−0.245309	+	2.02030i
$813$	19.4121			0.680812
$814$	−4.02916	+	33.1831i	−0.141222	+	1.16307i
$815$	−61.9614	−	10.0697i	−2.17041	−	0.352727i
$816$	−39.3905	−	48.2446i	−1.37894	−	1.68890i
$817$	−0.293146	−	0.772963i	−0.0102559	−	0.0270426i
$818$	7.61180	+	37.2851i	0.266141	+	1.30364i
$819$	−8.71321	+	3.71235i	−0.304464	+	0.129720i
$820$	24.2523	−	51.1106i	0.846926	−	1.78486i
$821$	2.07270	−	51.4335i	0.0723377	−	1.79504i	−0.402962	−	0.915217i	$-0.632019\pi$
$821$	2.07270	−	51.4335i	0.0723377	−	1.79504i	0.475299	−	0.879824i	$-0.342340\pi$
$822$	4.86600	+	3.65656i	0.169721	+	0.127537i
$823$	10.3323	−	21.7749i	0.360162	−	0.759025i	−0.639793	−	0.768548i	$-0.720980\pi$
$823$	10.3323	−	21.7749i	0.360162	−	0.759025i	0.999955	+	0.00952229i	$0.00303108\pi$
$824$	85.1878	−	44.7100i	2.96766	−	1.55755i
$825$	−11.0388	−	0.891141i	−0.384320	−	0.0310255i
$826$	6.52340	−	9.45078i	0.226978	−	0.328835i
$827$	−20.8877	−	6.97334i	−0.726337	−	0.242487i	−0.0706300	−	0.997503i	$-0.522501\pi$
$827$	−20.8877	−	6.97334i	−0.726337	−	0.242487i	−0.655707	+	0.755016i	$0.727629\pi$
$828$	22.3952	−	14.1618i	0.778285	−	0.492158i
$829$	4.86469	+	16.7949i	0.168958	+	0.583310i	0.999647	+	0.0265733i	$0.00845954\pi$
$829$	4.86469	+	16.7949i	0.168958	+	0.583310i	−0.830689	+	0.556737i	$0.812053\pi$
$830$	−124.540	−	65.3636i	−4.32285	−	2.26880i
$831$	−6.31095	−	16.6406i	−0.218924	−	0.577256i
$832$	−61.9719	−	26.4038i	−2.14849	−	0.915386i
$833$	1.27802	+	31.7137i	0.0442807	+	1.09881i
$834$	1.82957	−	2.65058i	0.0633527	−	0.0917822i
$835$	25.7127	−	44.5357i	0.889824	−	1.54122i
$836$	37.4327	−	3.02188i	1.29464	−	0.104514i
$837$	−4.02618	+	2.54600i	−0.139165	+	0.0880026i
$838$	−24.7376	+	8.25863i	−0.854547	+	0.285290i
$839$	10.4302	−	27.5021i	0.360090	−	0.949479i	−0.625484	−	0.780237i	$-0.715099\pi$
$839$	10.4302	−	27.5021i	0.360090	−	0.949479i	0.985574	−	0.169243i	$-0.0541322\pi$
$840$	−33.2869	−	5.40965i	−1.14851	−	0.186651i
$841$	−45.9195	−	11.3181i	−1.58343	−	0.390281i
$842$	−62.9072	+	65.4933i	−2.16793	+	2.25705i
$843$	9.33872	−	24.6242i	0.321643	−	0.848102i
$844$	−10.8000	+	9.56796i	−0.371751	+	0.329343i
$845$	107.333	+	45.7305i	3.69238	+	1.57318i
$846$	−2.66727	+	13.0652i	−0.0917027	+	0.449189i
$847$	−4.23037	−	8.91532i	−0.145357	−	0.306334i
$848$	−60.2176	−	45.2506i	−2.06788	−	1.55391i
$849$	−0.264336	−	2.17700i	−0.00907198	−	0.0747145i
$850$	11.1613	+	91.9214i	0.382829	+	3.15288i
$851$	−1.43851	+	35.6963i	−0.0493116	+	1.22365i
$852$	−25.3741	−	22.4795i	−0.869301	−	0.770134i
$853$	−33.4942	+	5.44334i	−1.14682	+	0.186376i	−0.703977	−	0.710223i	$-0.748594\pi$
$853$	−33.4942	+	5.44334i	−1.14682	+	0.186376i	−0.442843	+	0.896599i	$0.646030\pi$
$854$	−0.600572	−	14.9030i	−0.0205511	−	0.509971i
$855$	−8.23596	+	10.0872i	−0.281664	+	0.344976i
$856$	−101.365	+	33.8407i	−3.46459	+	1.15665i
$857$	0.785072	−	2.71038i	0.0268175	−	0.0925849i	−0.945993	−	0.324187i	$-0.894909\pi$
$857$	0.785072	−	2.71038i	0.0268175	−	0.0925849i	0.972811	+	0.231602i	$0.0743966\pi$
$858$	−29.8913	−	18.9021i	−1.02047	−	0.645308i
$859$	−34.3375	−	42.0558i	−1.17158	−	1.43493i	−0.877784	−	0.479057i	$-0.840979\pi$
$859$	−34.3375	−	42.0558i	−1.17158	−	1.43493i	−0.293797	−	0.955868i	$-0.594919\pi$
$860$	−2.49217	+	2.20787i	−0.0849822	+	0.0752877i
$861$	3.03537	−	3.71766i	0.103445	−	0.126697i
$862$	16.8597	+	5.62858i	0.574242	+	0.191710i
$863$	−16.8408	+	4.15089i	−0.573269	+	0.141298i	−0.515284	−	0.857019i	$-0.672314\pi$
$863$	−16.8408	+	4.15089i	−0.573269	+	0.141298i	−0.0579845	+	0.998317i	$0.518467\pi$
$864$	−11.0588	+	2.72575i	−0.376229	+	0.0927321i
$865$	21.4035	+	7.14555i	0.727742	+	0.242956i
$866$	48.4477	−	59.3376i	1.64632	−	2.01637i
$867$	−15.6514	+	13.8659i	−0.531549	+	0.470911i
$868$	−20.0027	−	24.4989i	−0.678938	−	0.831548i
$869$	−10.3416	−	6.53962i	−0.350814	−	0.221841i
$870$	20.8919	−	72.1270i	0.708300	−	2.44534i
$871$	52.3139	−	17.4649i	1.77259	−	0.591777i
$872$	−42.3071	+	51.8168i	−1.43270	+	1.75474i
$873$	0.332862	+	8.25988i	0.0112657	+	0.279555i
$874$	55.8274	−	9.07283i	1.88839	−	0.306893i
$875$	2.43216	+	2.15471i	0.0822221	+	0.0728424i
$876$	−2.68200	+	66.5532i	−0.0906164	+	2.24862i
$877$	4.77483	+	39.3243i	0.161235	+	1.32789i	0.818622	+	0.574333i	$0.194739\pi$
$877$	4.77483	+	39.3243i	0.161235	+	1.32789i	−0.657387	+	0.753553i	$0.728338\pi$
$878$	1.40466	+	11.5684i	0.0474050	+	0.390415i
$879$	−0.488623	−	0.367176i	−0.0164808	−	0.0123845i
$880$	−27.4535	−	57.8571i	−0.925459	−	1.95036i
$881$	−3.30739	+	16.2007i	−0.111429	+	0.545814i	0.885302	+	0.465017i	$0.153952\pi$
$881$	−3.30739	+	16.2007i	−0.111429	+	0.545814i	−0.996731	+	0.0807973i	$0.974253\pi$
$882$	12.4464	+	5.30290i	0.419091	+	0.178558i
$883$	10.4220	−	9.23308i	0.350728	−	0.310718i	−0.469303	−	0.883037i	$-0.655495\pi$
$883$	10.4220	−	9.23308i	0.350728	−	0.310718i	0.820031	+	0.572319i	$0.193956\pi$
$884$	−74.4104	+	196.204i	−2.50269	+	6.59906i
$885$	−7.30956	+	7.61006i	−0.245708	+	0.255809i
$886$	−62.4144	−	15.3838i	−2.09685	−	0.516828i
$887$	−0.715560	−	0.116290i	−0.0240262	−	0.00390463i	0.148386	−	0.988929i	$-0.452592\pi$
$887$	−0.715560	−	0.116290i	−0.0240262	−	0.00390463i	−0.172412	+	0.985025i	$0.555156\pi$
$888$	17.7118	−	46.7021i	0.594369	−	1.56722i
$889$	14.9709	−	4.99801i	0.502106	−	0.167628i
$890$	66.5934	−	42.1111i	2.23221	−	1.41157i
$891$	−1.92640	+	0.155515i	−0.0645367	+	0.00520994i
$892$	−51.5851	+	89.3480i	−1.72720	+	2.99159i
$893$	−11.4742	+	16.6232i	−0.383969	+	0.556276i
$894$	−1.30378	−	32.3529i	−0.0436049	−	1.08204i
$895$	−20.8996	−	8.90451i	−0.698598	−	0.297645i
$896$	−1.24062	−	3.27125i	−0.0414462	−	0.109285i
$897$	−33.4687	−	17.5657i	−1.11749	−	0.586502i
$898$	−5.01631	−	17.3183i	−0.167396	−	0.577919i
$899$	35.1672	−	22.2384i	1.17289	−	0.741691i
$900$	26.5674	+	8.86950i	0.885580	+	0.295650i
$901$	−26.0447	+	37.7323i	−0.867675	+	1.25704i
$902$	17.8636	+	1.44210i	0.594793	+	0.0480167i
$903$	−0.250109	+	0.131267i	−0.00832310	+	0.00436830i
$904$	−7.05993	+	14.8785i	−0.234810	+	0.494851i
$905$	−14.9263	−	11.2164i	−0.496167	−	0.372845i
$906$	2.21686	−	55.0109i	0.0736504	−	1.82761i
$907$	10.2714	−	21.6466i	0.341058	−	0.718764i	−0.658366	−	0.752698i	$-0.728752\pi$
$907$	10.2714	−	21.6466i	0.341058	−	0.718764i	0.999424	+	0.0339335i	$0.0108034\pi$
$908$	−72.6338	+	30.9464i	−2.41044	+	1.02699i
$909$	−1.11466	−	5.45997i	−0.0369709	−	0.181096i
$910$	28.8730	+	76.1320i	0.957132	+	2.52375i
$911$	21.8369	+	26.7453i	0.723488	+	0.886112i	0.997129	−	0.0757199i	$-0.0241255\pi$
$911$	21.8369	+	26.7453i	0.723488	+	0.886112i	−0.273641	+	0.961832i	$0.588228\pi$
$912$	−39.6932	−	6.45077i	−1.31437	−	0.213606i
$913$	3.81127	−	31.3886i	0.126135	−	1.03881i
$914$	12.5570			0.415349
$915$	−1.65196	+	13.6052i	−0.0546123	+	0.449772i
$916$	49.1909	−	51.2131i	1.62531	−	1.69213i
$917$	−1.25230	+	4.32344i	−0.0413546	+	0.142773i
$918$	4.49577	+	15.5212i	0.148383	+	0.512276i
$919$	13.9601	+	20.2247i	0.460502	+	0.667152i	0.982600	−	0.185733i	$-0.0594659\pi$
$919$	13.9601	+	20.2247i	0.460502	+	0.667152i	−0.522098	+	0.852885i	$0.674851\pi$
$920$	−67.2939	−	116.557i	−2.21862	−	3.84275i
$921$	18.7091	+	1.51036i	0.616487	+	0.0497680i
$922$	14.3978	−	2.33986i	0.474165	−	0.0770593i
$923$	−9.67274	+	47.3802i	−0.318382	+	1.55954i
$924$	−2.56667	−	12.5724i	−0.0844373	−	0.413601i
$925$	−30.1897	+	22.6861i	−0.992630	+	0.745913i
$926$	−19.9535	−	28.9076i	−0.655712	−	0.949963i
$927$	−12.6526	+	1.02142i	−0.415565	+	0.0335479i
$928$	96.5947	−	23.8085i	3.17088	−	0.781551i
$929$	8.57678	−	14.8554i	0.281395	−	0.487390i	−0.690334	−	0.723491i	$-0.742536\pi$
$929$	8.57678	−	14.8554i	0.281395	−	0.487390i	0.971729	+	0.236101i	$0.0758696\pi$
$930$	20.4765	+	35.4664i	0.671452	+	1.16299i
$931$	14.1961	+	14.7797i	0.465257	+	0.484384i
$932$	−84.8290	+	36.1423i	−2.77867	+	1.18388i
$933$	11.2854	+	23.7835i	0.369468	+	0.778638i
$934$	−9.70352	−	8.59657i	−0.317509	−	0.281288i
$935$	−34.5148	+	18.1148i	−1.12875	+	0.592416i
$936$	36.6078	+	38.1128i	1.19656	+	1.24575i
$937$	−18.5923	+	13.9712i	−0.607384	+	0.456419i	−0.859400	−	0.511304i	$-0.829163\pi$
$937$	−18.5923	+	13.9712i	−0.607384	+	0.456419i	0.252016	+	0.967723i	$0.418906\pi$
$938$	24.9683	+	13.1044i	0.815243	+	0.427873i
$939$	−8.63526	−	5.46061i	−0.281801	−	0.178200i
$940$	78.9873	+	19.4686i	2.57628	+	0.634997i
$941$	1.41869			0.0462480			0.0231240	−	0.999733i	$-0.492639\pi$
$941$	1.41869			0.0462480			0.0231240	+	0.999733i	$0.492639\pi$
$942$	−28.2093	+	16.9007i	−0.919107	+	0.550656i
$943$	19.1540			0.623741
$944$	−31.6381	−	7.79808i	−1.02973	−	0.253806i
$945$	3.76069	+	2.37812i	0.122335	+	0.0773602i
$946$	−0.933941	−	0.490170i	−0.0303651	−	0.0159368i
$947$	20.5681	−	15.4559i	0.668373	−	0.502250i	−0.211549	−	0.977367i	$-0.567851\pi$
$947$	20.5681	−	15.4559i	0.668373	−	0.502250i	0.879922	+	0.475118i	$0.157594\pi$
$948$	21.4366	+	22.3179i	0.696230	+	0.724852i
$949$	84.1317	−	44.1557i	2.73103	−	1.43336i
$950$	44.7509	+	39.6458i	1.45191	+	1.28628i
$951$	−7.08068	−	14.9222i	−0.229607	−	0.483886i
$952$	−58.3156	+	24.8459i	−1.89002	+	0.805262i
$953$	5.63912	+	5.87094i	0.182669	+	0.190178i	0.806241	−	0.591588i	$-0.201499\pi$
$953$	5.63912	+	5.87094i	0.182669	+	0.190178i	−0.623572	+	0.781766i	$0.714319\pi$
$954$	9.77141	+	16.9246i	0.316361	+	0.547954i
$955$	−0.488827	+	0.846673i	−0.0158181	+	0.0273977i
$956$	88.1883	−	21.7365i	2.85221	−	0.703008i
$957$	16.8264	−	1.35836i	0.543919	−	0.0439097i
$958$	23.2544	+	33.6898i	0.751314	+	1.08847i
$959$	2.51848	−	1.89251i	0.0813258	−	0.0611124i
$960$	6.33018	+	31.0072i	0.204306	+	1.00075i
$961$	1.66177	−	8.13990i	0.0536055	−	0.262577i
$962$	−119.034	+	19.3449i	−3.83780	+	0.623704i
$963$	14.0541	+	1.13456i	0.452887	+	0.0365608i
$964$	25.3422	+	43.8940i	0.816218	+	1.41373i
$965$	12.6499	+	18.3266i	0.407216	+	0.589954i
$966$	−5.37668	−	18.5625i	−0.172992	−	0.597237i
$967$	8.56481	−	29.5691i	0.275426	−	0.950879i	−0.696884	−	0.717184i	$-0.745431\pi$
$967$	8.56481	−	29.5691i	0.275426	−	0.950879i	0.972310	−	0.233696i	$-0.0750820\pi$
$968$	−38.1422	+	39.7103i	−1.22594	+	1.27634i
$969$	−2.95041	+	24.2988i	−0.0947808	+	0.780590i
$970$	71.0680			2.28186
$971$	5.69572	−	46.9085i	0.182784	−	1.50536i	−0.555864	−	0.831273i	$-0.687612\pi$
$971$	5.69572	−	46.9085i	0.182784	−	1.50536i	0.738648	−	0.674091i	$-0.235465\pi$
$972$	4.82458	+	0.784071i	0.154748	+	0.0251491i
$973$	−1.05424	−	1.29121i	−0.0337973	−	0.0413942i
$974$	−15.4123	−	40.6389i	−0.493842	−	1.30215i
$975$	−7.99195	−	39.1471i	−0.255947	−	1.25371i
$976$	−38.9355	+	16.5889i	−1.24629	+	0.530996i
$977$	−22.0005	+	46.3651i	−0.703860	+	1.48335i	0.163957	+	0.986468i	$0.447574\pi$
$977$	−22.0005	+	46.3651i	−0.703860	+	1.48335i	−0.867816	+	0.496885i	$0.834477\pi$
$978$	−2.02515	+	50.2536i	−0.0647572	+	1.60693i
$979$	14.1603	+	10.6408i	0.452565	+	0.340080i
$980$	35.3829	−	74.5678i	1.13026	−	2.38198i
$981$	7.81512	−	4.10169i	0.249518	−	0.130957i
$982$	79.3718	+	6.40756i	2.53286	+	0.204473i
$983$	5.93657	−	8.60061i	0.189347	−	0.274317i	−0.716800	−	0.697278i	$-0.754394\pi$
$983$	5.93657	−	8.60061i	0.189347	−	0.274317i	0.906148	+	0.422962i	$0.139010\pi$
$984$	−25.4013	−	8.48021i	−0.809765	−	0.270339i
$985$	2.82159	−	1.78426i	0.0899033	−	0.0568514i
$986$	−39.2689	−	135.572i	−1.25058	−	4.31749i
$987$	6.11102	+	3.20731i	0.194516	+	0.102090i
$988$	48.0444	+	126.683i	1.52850	+	4.03031i
$989$	−1.03708	−	0.441857i	−0.0329772	−	0.0140503i
$990$	0.669024	+	16.6017i	0.0212630	+	0.527636i
$991$	−32.5032	+	47.0890i	−1.03250	+	1.49583i	−0.172847	+	0.984949i	$0.555297\pi$
$991$	−32.5032	+	47.0890i	−1.03250	+	1.49583i	−0.859651	+	0.510882i	$0.829319\pi$
$992$	−27.1284	+	46.9877i	−0.861327	+	1.49186i
$993$	18.9455	−	1.52944i	0.601219	−	0.0485354i
$994$	−20.8967	+	13.2142i	−0.662802	+	0.419131i
$995$	−26.9603	+	9.00067i	−0.854699	+	0.285340i
$996$	−28.3569	+	74.7710i	−0.898523	+	2.36921i
$997$	−17.7243	−	2.88047i	−0.561333	−	0.0912255i	−0.126877	−	0.991918i	$-0.540495\pi$
$997$	−17.7243	−	2.88047i	−0.561333	−	0.0912255i	−0.434456	+	0.900693i	$0.643059\pi$
$998$	−63.0451	−	15.5392i	−1.99566	−	0.491886i
$999$	−4.56517	+	4.75284i	−0.144436	+	0.150373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.q.b.19.2	✓	336
157.124	even	39	inner	471.2.q.b.124.2	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.q.b.19.2	✓	336	1.1	even	1	trivial
471.2.q.b.124.2	yes	336	157.124	even	39	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.54821 - 0.628078i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(4.32800 + 2.27151i) q^{4} +(-2.61874 + 1.96786i) q^{5} +(1.81804 + 1.89278i) q^{6} +(1.20275 - 0.631251i) q^{7} +(-5.67309 - 5.02592i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(-2.54821 - 0.628078i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(4.32800 + 2.27151i) q^{4} +(-2.61874 + 1.96786i) q^{5} +(1.81804 + 1.89278i) q^{6} +(1.20275 - 0.631251i) q^{7} +(-5.67309 - 5.02592i) q^{8} +(0.428693 + 0.903450i) q^{9} +(7.90908 - 3.36974i) q^{10} +(1.33880 + 1.39384i) q^{11} +(-2.44394 - 4.23303i) q^{12} +(-3.48628 + 6.03841i) q^{13} +(-3.46134 + 0.853143i) q^{14} +(3.26509 - 0.263585i) q^{15} +(5.74631 + 8.32496i) q^{16} +(4.92226 - 3.69884i) q^{17} +(-0.524963 - 2.57144i) q^{18} +(0.795191 - 3.89510i) q^{19} +(-15.8039 + 2.56839i) q^{20} +(-1.35393 - 0.109301i) q^{21} +(-2.53611 - 4.39268i) q^{22} +(-3.07948 - 4.46139i) q^{23} +(2.10866 + 7.27992i) q^{24} +(1.59426 - 5.50402i) q^{25} +(12.6764 - 13.1975i) q^{26} +(0.120537 - 0.992709i) q^{27} +6.63939 q^{28} +(-1.05284 + 8.67095i) q^{29} +(-8.48569 - 1.37906i) q^{30} +(-3.01274 - 3.68993i) q^{31} +(-4.03887 - 10.6496i) q^{32} +(-0.386582 - 1.89361i) q^{33} +(-14.8661 + 6.33386i) q^{34} +(-1.90748 + 4.01992i) q^{35} +(-0.196815 + 4.88391i) q^{36} +(-5.26846 - 3.95899i) q^{37} +(-4.47275 + 9.42612i) q^{38} +(6.17389 - 3.24031i) q^{39} +(24.7466 + 1.99775i) q^{40} +(-2.00715 + 2.90785i) q^{41} +(3.38146 + 1.12890i) q^{42} +(0.175755 - 0.111141i) q^{43} +(2.62821 + 9.07365i) q^{44} +(-2.90050 - 1.52230i) q^{45} +(5.04506 + 13.3027i) q^{46} +(-4.67430 - 1.99153i) q^{47} +(-0.407314 - 10.1074i) q^{48} +(-2.92833 + 4.24241i) q^{49} +(-7.51947 + 13.0241i) q^{50} +(-6.13715 + 0.495442i) q^{51} +(-28.8049 + 18.2151i) q^{52} +(-7.06316 + 2.35803i) q^{53} +(-0.930652 + 2.45393i) q^{54} +(-6.24886 - 1.01554i) q^{55} +(-9.99592 - 2.46377i) q^{56} +(-2.75389 + 2.86710i) q^{57} +(8.12890 - 21.4342i) q^{58} +(-2.41115 + 2.13609i) q^{59} +(14.7300 + 6.27588i) q^{60} +(-0.836878 + 4.09930i) q^{61} +(5.35953 + 11.2950i) q^{62} +(1.08591 + 0.816011i) q^{63} +(1.16451 + 9.59062i) q^{64} +(-2.75306 - 22.6735i) q^{65} +(-0.204238 + 5.06812i) q^{66} +(-5.92064 - 5.24523i) q^{67} +(29.7055 - 4.82761i) q^{68} +(0.218282 + 5.41660i) q^{69} +(7.38548 - 9.04558i) q^{70} +(6.57848 - 2.19622i) q^{71} +(2.10866 - 7.27992i) q^{72} +(-11.5174 - 7.28318i) q^{73} +(10.9386 + 13.3974i) q^{74} +(-4.28917 + 3.79987i) q^{75} +(12.2894 - 15.0517i) q^{76} +(2.49011 + 0.831320i) q^{77} +(-17.7676 + 4.37931i) q^{78} +(-6.14709 + 1.51512i) q^{79} +(-31.4304 - 10.4930i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(6.94100 - 6.14919i) q^{82} +(-10.3471 - 12.6728i) q^{83} +(-5.61155 - 3.54853i) q^{84} +(-5.61134 + 19.3726i) q^{85} +(-0.517667 + 0.172823i) q^{86} +(5.52418 - 6.76589i) q^{87} +(-0.589814 - 14.6361i) q^{88} +(9.04624 - 1.47016i) q^{89} +(6.43496 + 5.70088i) q^{90} +(-0.381362 + 9.46341i) q^{91} +(-3.19388 - 26.3040i) q^{92} +(0.574193 + 4.72890i) q^{93} +(10.6603 + 8.01068i) q^{94} +(5.58261 + 11.7651i) q^{95} +(-2.27825 + 11.1596i) q^{96} +(7.60509 + 3.24023i) q^{97} +(10.1266 - 8.97136i) q^{98} +(-0.685332 + 1.80707i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Introduction

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