LMFDB - Embedded newform 644.2.be.a.187.70

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(3,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 11, 48]))

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

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

chi := DirichletCharacter("644.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.be (of order $66$, degree $20$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$1840$
Relative dimension:	$92$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			187.70
Character	$\chi$	$=$	644.187
Dual form			644.2.be.a.31.70

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00387 - 0.996119i) q^{2} +(1.62868 - 0.155520i) q^{3} +(0.0154938 - 1.99994i) q^{4} +(3.25553 - 1.12675i) q^{5} +(1.48006 - 1.77848i) q^{6} +(-2.03711 - 1.68825i) q^{7} +(-1.97662 - 2.02311i) q^{8} +(-0.317382 + 0.0611704i) q^{9} +O(q^{10})$	\(q+(1.00387 - 0.996119i) q^{2} +(1.62868 - 0.155520i) q^{3} +(0.0154938 - 1.99994i) q^{4} +(3.25553 - 1.12675i) q^{5} +(1.48006 - 1.77848i) q^{6} +(-2.03711 - 1.68825i) q^{7} +(-1.97662 - 2.02311i) q^{8} +(-0.317382 + 0.0611704i) q^{9} +(2.14574 - 4.37400i) q^{10} +(2.06518 + 5.15857i) q^{11} +(-0.285796 - 3.25967i) q^{12} +(2.16733 - 3.37243i) q^{13} +(-3.72668 + 0.334426i) q^{14} +(5.12698 - 2.34141i) q^{15} +(-3.99952 - 0.0619733i) q^{16} +(-4.66994 + 1.13291i) q^{17} +(-0.257676 + 0.377557i) q^{18} +(-1.40706 + 5.80000i) q^{19} +(-2.20299 - 6.52832i) q^{20} +(-3.58035 - 2.43280i) q^{21} +(7.21171 + 3.12135i) q^{22} +(0.145927 + 4.79361i) q^{23} +(-3.53392 - 2.98758i) q^{24} +(5.39864 - 4.24554i) q^{25} +(-1.18363 - 5.54439i) q^{26} +(-5.21684 + 1.53180i) q^{27} +(-3.40796 + 4.04794i) q^{28} +(0.241846 + 0.0710123i) q^{29} +(2.81447 - 7.45754i) q^{30} +(3.36381 - 4.72382i) q^{31} +(-4.07671 + 3.92178i) q^{32} +(4.16577 + 8.08046i) q^{33} +(-3.55947 + 5.78911i) q^{34} +(-8.53410 - 3.20084i) q^{35} +(0.117420 + 0.635693i) q^{36} +(7.36294 - 1.41909i) q^{37} +(4.36499 + 7.22403i) q^{38} +(3.00540 - 5.82967i) q^{39} +(-8.71449 - 4.35912i) q^{40} +(3.65865 + 3.17024i) q^{41} +(-6.01755 + 1.12424i) q^{42} +(0.538681 + 0.246007i) q^{43} +(10.3488 - 4.05031i) q^{44} +(-0.964323 + 0.556752i) q^{45} +(4.92150 + 4.66678i) q^{46} +(0.0686439 - 0.118895i) q^{47} +(-6.52357 + 0.521070i) q^{48} +(1.29962 + 6.87830i) q^{49} +(1.19045 - 9.63964i) q^{50} +(-7.42963 + 2.57142i) q^{51} +(-6.71108 - 4.38678i) q^{52} +(-4.83484 - 2.49253i) q^{53} +(-3.71115 + 6.73432i) q^{54} +(12.5357 + 14.4669i) q^{55} +(0.611091 + 7.45832i) q^{56} +(-1.38964 + 9.66516i) q^{57} +(0.313517 - 0.169620i) q^{58} +(0.217658 - 4.56920i) q^{59} +(-4.60325 - 10.2899i) q^{60} +(0.113789 - 1.19165i) q^{61} +(-1.32866 - 8.09284i) q^{62} +(0.749813 + 0.411210i) q^{63} +(-0.185911 + 7.99784i) q^{64} +(3.25592 - 13.4211i) q^{65} +(12.2310 + 3.96210i) q^{66} +(-3.74219 - 4.75858i) q^{67} +(2.19341 + 9.35714i) q^{68} +(0.983170 + 7.78455i) q^{69} +(-11.7555 + 5.28777i) q^{70} +(-6.44292 + 0.926352i) q^{71} +(0.751099 + 0.521186i) q^{72} +(10.9561 - 11.4904i) q^{73} +(5.97782 - 8.75895i) q^{74} +(8.13238 - 7.75421i) q^{75} +(11.5779 + 2.90391i) q^{76} +(4.50196 - 13.9951i) q^{77} +(-2.79002 - 8.84594i) q^{78} +(-1.58650 - 3.07738i) q^{79} +(-13.0904 + 4.30470i) q^{80} +(-7.35811 + 2.94574i) q^{81} +(6.83073 - 0.461957i) q^{82} +(-2.70143 - 3.11762i) q^{83} +(-4.92094 + 7.12279i) q^{84} +(-13.9266 + 8.95008i) q^{85} +(0.785816 - 0.289632i) q^{86} +(0.404932 + 0.0780443i) q^{87} +(6.35424 - 14.3746i) q^{88} +(-0.286763 + 0.204203i) q^{89} +(-0.413460 + 1.51948i) q^{90} +(-10.1086 + 3.21101i) q^{91} +(9.58920 - 0.217575i) q^{92} +(4.74392 - 8.21671i) q^{93} +(-0.0495240 - 0.187732i) q^{94} +(1.95441 + 20.4675i) q^{95} +(-6.02974 + 7.02133i) q^{96} +(-5.48928 - 4.75649i) q^{97} +(8.15625 + 5.61031i) q^{98} +(-0.971002 - 1.51091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1840 q - 7 q^{2} - 11 q^{4} - 54 q^{5} - 40 q^{8} + 66 q^{9}+O(q^{10}) $ 1840 * q - 7 * q^2 - 11 * q^4 - 54 * q^5 - 40 * q^8 + 66 * q^9	$ 1840 q - 7 q^{2} - 11 q^{4} - 54 q^{5} - 40 q^{8} + 66 q^{9} - 27 q^{10} - 27 q^{12} - 14 q^{14} - 19 q^{16} - 54 q^{17} - q^{18} - 40 q^{21} - 56 q^{22} - 78 q^{24} - 94 q^{25} - 9 q^{26} + 12 q^{28} - 120 q^{29} - 19 q^{30} + 3 q^{32} - 54 q^{33} - 114 q^{36} - 2 q^{37} - 87 q^{38} - 57 q^{40} - 114 q^{42} + 72 q^{44} - 132 q^{45} - 9 q^{46} - 20 q^{49} - 186 q^{50} + 3 q^{52} - 34 q^{53} - 51 q^{54} - 93 q^{56} - 64 q^{57} + 22 q^{58} - 11 q^{60} - 54 q^{61} - 8 q^{64} - 46 q^{65} + 150 q^{66} - 30 q^{68} - 10 q^{70} + 43 q^{72} - 54 q^{73} + 6 q^{74} - 16 q^{77} - 212 q^{78} + 216 q^{80} - 58 q^{81} - 57 q^{82} - 102 q^{84} + 152 q^{85} + 3 q^{86} + 144 q^{88} - 174 q^{89} - 250 q^{92} - 64 q^{93} + 216 q^{94} - 69 q^{96} - 44 q^{98}+O(q^{100}) $ 1840 * q - 7 * q^2 - 11 * q^4 - 54 * q^5 - 40 * q^8 + 66 * q^9 - 27 * q^10 - 27 * q^12 - 14 * q^14 - 19 * q^16 - 54 * q^17 - q^18 - 40 * q^21 - 56 * q^22 - 78 * q^24 - 94 * q^25 - 9 * q^26 + 12 * q^28 - 120 * q^29 - 19 * q^30 + 3 * q^32 - 54 * q^33 - 114 * q^36 - 2 * q^37 - 87 * q^38 - 57 * q^40 - 114 * q^42 + 72 * q^44 - 132 * q^45 - 9 * q^46 - 20 * q^49 - 186 * q^50 + 3 * q^52 - 34 * q^53 - 51 * q^54 - 93 * q^56 - 64 * q^57 + 22 * q^58 - 11 * q^60 - 54 * q^61 - 8 * q^64 - 46 * q^65 + 150 * q^66 - 30 * q^68 - 10 * q^70 + 43 * q^72 - 54 * q^73 + 6 * q^74 - 16 * q^77 - 212 * q^78 + 216 * q^80 - 58 * q^81 - 57 * q^82 - 102 * q^84 + 152 * q^85 + 3 * q^86 + 144 * q^88 - 174 * q^89 - 250 * q^92 - 64 * q^93 + 216 * q^94 - 69 * q^96 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{11}\right)$	$-1$

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 $

$2$	1.00387	−	0.996119i	0.709840	−	0.704363i
$2$	1.00387	−	0.996119i	0.709840	−	0.704363i
$3$	1.62868	−	0.155520i	0.940317	−	0.0897894i	0.386373	−	0.922343i	$-0.373728\pi$
$3$	1.62868	−	0.155520i	0.940317	−	0.0897894i	0.553945	+	0.832553i	$0.313122\pi$
$4$	0.0154938	−	1.99994i	0.00774690	−	0.999970i
$5$	3.25553	−	1.12675i	1.45592	−	0.503898i	0.519404	−	0.854529i	$-0.326154\pi$
$5$	3.25553	−	1.12675i	1.45592	−	0.503898i	0.936514	+	0.350631i	$0.114033\pi$
$6$	1.48006	−	1.77848i	0.604231	−	0.726060i
$7$	−2.03711	−	1.68825i	−0.769955	−	0.638099i
$7$	−2.03711	−	1.68825i	−0.769955	−	0.638099i
$8$	−1.97662	−	2.02311i	−0.698842	−	0.715276i
$9$	−0.317382	+	0.0611704i	−0.105794	+	0.0203901i
$10$	2.14574	−	4.37400i	0.678542	−	1.38318i
$11$	2.06518	+	5.15857i	0.622675	+	1.55537i	0.818364	+	0.574700i	$0.194881\pi$
$11$	2.06518	+	5.15857i	0.622675	+	1.55537i	−0.195689	+	0.980666i	$0.562694\pi$
$12$	−0.285796	−	3.25967i	−0.0825022	−	0.940985i
$13$	2.16733	−	3.37243i	0.601109	−	0.935344i	−0.398724	−	0.917071i	$-0.630547\pi$
$13$	2.16733	−	3.37243i	0.601109	−	0.935344i	0.999833	−	0.0182730i	$-0.00581681\pi$
$14$	−3.72668	+	0.334426i	−0.995998	+	0.0893790i
$15$	5.12698	−	2.34141i	1.32378	−	0.604550i
$16$	−3.99952	−	0.0619733i	−0.999880	−	0.0154933i
$17$	−4.66994	+	1.13291i	−1.13263	+	0.274772i	−0.757905	−	0.652365i	$-0.773777\pi$
$17$	−4.66994	+	1.13291i	−1.13263	+	0.274772i	−0.374721	+	0.927138i	$0.622262\pi$
$18$	−0.257676	+	0.377557i	−0.0607348	+	0.0889911i
$19$	−1.40706	+	5.80000i	−0.322803	+	1.33061i	0.546967	+	0.837154i	$0.315782\pi$
$19$	−1.40706	+	5.80000i	−0.322803	+	1.33061i	−0.869770	+	0.493457i	$0.835733\pi$
$20$	−2.20299	−	6.52832i	−0.492604	−	1.45978i
$21$	−3.58035	−	2.43280i	−0.781296	−	0.530881i
$22$	7.21171	+	3.12135i	1.53754	+	0.665473i
$23$	0.145927	+	4.79361i	0.0304280	+	0.999537i
$23$	0.145927	+	4.79361i	0.0304280	+	0.999537i
$24$	−3.53392	−	2.98758i	−0.721358	−	0.609838i
$25$	5.39864	−	4.24554i	1.07973	−	0.849108i
$26$	−1.18363	−	5.54439i	−0.232130	−	1.08734i
$27$	−5.21684	+	1.53180i	−1.00398	+	0.294795i
$28$	−3.40796	+	4.04794i	−0.644044	+	0.764988i
$29$	0.241846	+	0.0710123i	0.0449096	+	0.0131867i	0.304110	−	0.952637i	$-0.401641\pi$
$29$	0.241846	+	0.0710123i	0.0449096	+	0.0131867i	−0.259201	+	0.965824i	$0.583459\pi$
$30$	2.81447	−	7.45754i	0.513850	−	1.36155i
$31$	3.36381	−	4.72382i	0.604159	−	0.848422i	−0.393319	−	0.919402i	$-0.628673\pi$
$31$	3.36381	−	4.72382i	0.604159	−	0.848422i	0.997478	+	0.0709797i	$0.0226125\pi$
$32$	−4.07671	+	3.92178i	−0.720668	+	0.693280i
$33$	4.16577	+	8.08046i	0.725167	+	1.40663i
$34$	−3.55947	+	5.78911i	−0.610444	+	0.992823i
$35$	−8.53410	−	3.20084i	−1.44253	−	0.541040i
$36$	0.117420	+	0.635693i	0.0195699	+	0.105949i
$37$	7.36294	−	1.41909i	1.21046	−	0.233297i	0.456203	−	0.889876i	$-0.349209\pi$
$37$	7.36294	−	1.41909i	1.21046	−	0.233297i	0.754258	+	0.656579i	$0.227997\pi$
$38$	4.36499	+	7.22403i	0.708094	+	1.17189i
$39$	3.00540	−	5.82967i	0.481249	−	0.933494i
$40$	−8.71449	−	4.35912i	−1.37788	−	0.689237i
$41$	3.65865	+	3.17024i	0.571386	+	0.495108i	0.891960	−	0.452115i	$-0.149330\pi$
$41$	3.65865	+	3.17024i	0.571386	+	0.495108i	−0.320574	+	0.947223i	$0.603876\pi$
$42$	−6.01755	+	1.12424i	−0.928529	+	0.173475i
$43$	0.538681	+	0.246007i	0.0821481	+	0.0375158i	0.456065	−	0.889946i	$-0.349258\pi$
$43$	0.538681	+	0.246007i	0.0821481	+	0.0375158i	−0.373917	+	0.927462i	$0.621986\pi$
$44$	10.3488	−	4.05031i	1.56014	−	0.610607i
$45$	−0.964323	+	0.556752i	−0.143753	+	0.0829957i
$46$	4.92150	+	4.66678i	0.725635	+	0.688079i
$47$	0.0686439	−	0.118895i	0.0100127	−	0.0173426i	−0.860976	−	0.508646i	$-0.830146\pi$
$47$	0.0686439	−	0.118895i	0.0100127	−	0.0173426i	0.870988	+	0.491304i	$0.163479\pi$
$48$	−6.52357	+	0.521070i	−0.941596	+	0.0752100i
$49$	1.29962	+	6.87830i	0.185660	+	0.982614i
$50$	1.19045	−	9.63964i	0.168355	−	1.36325i
$51$	−7.42963	+	2.57142i	−1.04036	+	0.360071i
$52$	−6.71108	−	4.38678i	−0.930659	−	0.608337i
$53$	−4.83484	−	2.49253i	−0.664117	−	0.342376i	0.0929902	−	0.995667i	$-0.470357\pi$
$53$	−4.83484	−	2.49253i	−0.664117	−	0.342376i	−0.757107	+	0.653291i	$0.773388\pi$
$54$	−3.71115	+	6.73432i	−0.505023	+	0.916424i
$55$	12.5357	+	14.4669i	1.69031	+	1.95072i
$56$	0.611091	+	7.45832i	0.0816604	+	0.996660i
$57$	−1.38964	+	9.66516i	−0.184062	+	1.28018i
$58$	0.313517	−	0.169620i	0.0411668	−	0.0222722i
$59$	0.217658	−	4.56920i	0.0283366	−	0.594859i	−0.939389	−	0.342853i	$-0.888607\pi$
$59$	0.217658	−	4.56920i	0.0283366	−	0.594859i	0.967726	−	0.252006i	$-0.0810902\pi$
$60$	−4.60325	−	10.2899i	−0.594277	−	1.32842i
$61$	0.113789	−	1.19165i	0.0145691	−	0.152575i	−0.985260	−	0.171064i	$-0.945280\pi$
$61$	0.113789	−	1.19165i	0.0145691	−	0.152575i	0.999829	+	0.0184890i	$0.00588558\pi$
$62$	−1.32866	−	8.09284i	−0.168741	−	1.02779i
$63$	0.749813	+	0.411210i	0.0944675	+	0.0518075i
$64$	−0.185911	+	7.99784i	−0.0232388	+	0.999730i
$65$	3.25592	−	13.4211i	0.403847	−	1.66468i
$66$	12.2310	+	3.96210i	1.50553	+	0.487701i
$67$	−3.74219	−	4.75858i	−0.457181	−	0.581353i	0.501743	−	0.865017i	$-0.332692\pi$
$67$	−3.74219	−	4.75858i	−0.457181	−	0.581353i	−0.958924	+	0.283664i	$0.908450\pi$
$68$	2.19341	+	9.35714i	0.265989	+	1.13472i
$69$	0.983170	+	7.78455i	0.118360	+	0.937150i
$70$	−11.7555	+	5.28777i	−1.40505	+	0.632009i
$71$	−6.44292	+	0.926352i	−0.764634	+	0.109938i	−0.513588	−	0.858037i	$-0.671684\pi$
$71$	−6.44292	+	0.926352i	−0.764634	+	0.109938i	−0.251047	+	0.967975i	$0.580775\pi$
$72$	0.751099	+	0.521186i	0.0885179	+	0.0614224i
$73$	10.9561	−	11.4904i	1.28231	−	1.34485i	0.373502	−	0.927629i	$-0.378157\pi$
$73$	10.9561	−	11.4904i	1.28231	−	1.34485i	0.908807	−	0.417218i	$-0.136995\pi$
$74$	5.97782	−	8.75895i	0.694908	−	1.01821i
$75$	8.13238	−	7.75421i	0.939047	−	0.895379i
$76$	11.5779	+	2.90391i	1.32807	+	0.333101i
$77$	4.50196	−	13.9951i	0.513046	−	1.59489i
$78$	−2.79002	−	8.84594i	−0.315908	−	1.00161i
$79$	−1.58650	−	3.07738i	−0.178495	−	0.346233i	0.782566	−	0.622568i	$-0.213910\pi$
$79$	−1.58650	−	3.07738i	−0.178495	−	0.346233i	−0.961061	+	0.276335i	$0.910880\pi$
$80$	−13.0904	+	4.30470i	−1.46355	+	0.481280i
$81$	−7.35811	+	2.94574i	−0.817568	+	0.327305i
$82$	6.83073	−	0.461957i	0.754328	−	0.0510146i
$83$	−2.70143	−	3.11762i	−0.296520	−	0.342203i	0.587866	−	0.808958i	$-0.299968\pi$
$83$	−2.70143	−	3.11762i	−0.296520	−	0.342203i	−0.884386	+	0.466756i	$0.845423\pi$
$84$	−4.92094	+	7.12279i	−0.536918	+	0.777160i
$85$	−13.9266	+	8.95008i	−1.51055	+	0.970773i
$86$	0.785816	−	0.289632i	0.0847368	−	0.0312318i
$87$	0.404932	+	0.0780443i	0.0434133	+	0.00836723i
$88$	6.35424	−	14.3746i	0.677364	−	1.53234i
$89$	−0.286763	+	0.204203i	−0.0303969	+	0.0216455i	−0.595154	−	0.803611i	$-0.702909\pi$
$89$	−0.286763	+	0.204203i	−0.0303969	+	0.0216455i	0.564758	+	0.825257i	$0.308970\pi$
$90$	−0.413460	+	1.51948i	−0.0435825	+	0.160168i
$91$	−10.1086	+	3.21101i	−1.05967	+	0.336606i
$92$	9.58920	−	0.217575i	0.999743	−	0.0226837i
$93$	4.74392	−	8.21671i	0.491922	−	0.852033i
$94$	−0.0495240	−	0.187732i	−0.00510801	−	0.0193631i
$95$	1.95441	+	20.4675i	0.200518	+	2.09992i
$96$	−6.02974	+	7.02133i	−0.615408	+	0.716612i
$97$	−5.48928	−	4.75649i	−0.557352	−	0.482948i	0.330038	−	0.943968i	$-0.392938\pi$
$97$	−5.48928	−	4.75649i	−0.557352	−	0.482948i	−0.887390	+	0.461019i	$0.847484\pi$
$98$	8.15625	+	5.61031i	0.823906	+	0.566727i
$99$	−0.971002	−	1.51091i	−0.0975894	−	0.151852i
$100$	−8.40718	−	10.8627i	−0.840718	−	1.08627i
$101$	−16.5470	−	5.72699i	−1.64649	−	0.569857i	−0.662656	−	0.748924i	$-0.730571\pi$
$101$	−16.5470	−	5.72699i	−1.64649	−	0.569857i	−0.983837	+	0.179068i	$0.942692\pi$
$102$	−4.89691	+	9.98215i	−0.484866	+	0.988381i
$103$	14.1584	+	11.1343i	1.39507	+	1.09709i	0.982520	+	0.186156i	$0.0596030\pi$
$103$	14.1584	+	11.1343i	1.39507	+	1.09709i	0.412546	+	0.910937i	$0.364639\pi$
$104$	−11.1068	+	2.28129i	−1.08911	+	0.223699i
$105$	−14.3971	−	3.88591i	−1.40501	−	0.379226i
$106$	−7.33639	+	2.31391i	−0.712574	+	0.224747i
$107$	0.817047	−	8.55650i	0.0789869	−	0.827189i	−0.865992	−	0.500058i	$-0.833312\pi$
$107$	0.817047	−	8.55650i	0.0789869	−	0.827189i	0.944979	−	0.327131i	$-0.106082\pi$
$108$	2.98268	+	10.4571i	0.287009	+	1.00623i
$109$	1.26241	+	5.20371i	0.120917	+	0.498425i	0.999772	+	0.0213375i	$0.00679246\pi$
$109$	1.26241	+	5.20371i	0.120917	+	0.498425i	−0.878856	+	0.477088i	$0.841692\pi$
$110$	26.9949	+	2.03584i	2.57386	+	0.194110i
$111$	11.7712	−	3.45633i	1.11727	−	0.328060i
$112$	8.04283	+	6.87844i	0.759976	+	0.649951i
$113$	0.793277	+	5.51736i	0.0746252	+	0.519030i	0.992508	+	0.122179i	$0.0389881\pi$
$113$	0.793277	+	5.51736i	0.0746252	+	0.519030i	−0.917883	+	0.396851i	$0.870103\pi$
$114$	8.23263	+	11.0868i	0.771057	+	1.03837i
$115$	5.87627	+	15.4413i	0.547965	+	1.43991i
$116$	0.145767	−	0.482577i	0.0135342	−	0.0448061i
$117$	−0.481579	+	1.20293i	−0.0445220	+	0.111210i
$118$	−4.33296	−	4.80367i	−0.398882	−	0.442214i
$119$	11.4258	+	5.57615i	1.04740	+	0.511165i
$120$	−14.8710	−	5.74432i	−1.35753	−	0.524382i
$121$	−14.3848	+	13.7158i	−1.30771	+	1.24690i
$122$	−1.07280	−	1.30960i	−0.0971263	−	0.118566i
$123$	6.45180	+	4.59431i	0.581739	+	0.414255i
$124$	−9.39523	−	6.80062i	−0.843717	−	0.610713i
$125$	3.47924	−	5.41380i	0.311193	−	0.484225i
$126$	1.16233	−	0.334103i	0.103548	−	0.0297643i
$127$	−16.4109	−	2.35953i	−1.45623	−	0.209375i	−0.631711	−	0.775204i	$-0.717647\pi$
$127$	−16.4109	−	2.35953i	−1.45623	−	0.209375i	−0.824522	+	0.565829i	$0.808556\pi$
$128$	7.78017	+	8.21395i	0.687676	+	0.726017i
$129$	0.915597	+	0.316891i	0.0806138	+	0.0279007i
$130$	−10.1005	−	16.7163i	−0.885872	−	1.46611i
$131$	0.801260	+	16.8205i	0.0700064	+	1.46962i	0.711607	+	0.702577i	$0.247967\pi$
$131$	0.801260	+	16.8205i	0.0700064	+	1.46962i	−0.641601	+	0.767039i	$0.721729\pi$
$132$	16.2250	−	8.20609i	1.41220	−	0.714249i
$133$	12.6582	−	9.43975i	1.09760	−	0.818530i
$134$	−8.49677	−	1.04931i	−0.734009	−	0.0906467i
$135$	−15.2576	+	10.8649i	−1.31317	+	0.935102i
$136$	11.5227	+	7.20843i	0.988065	+	0.618117i
$137$	5.66375	+	9.80990i	0.483887	+	0.838116i	0.999829	−	0.0185074i	$-0.00589141\pi$
$137$	5.66375	+	9.80990i	0.483887	+	0.838116i	−0.515942	+	0.856623i	$0.672558\pi$
$138$	8.74131	+	6.83529i	0.744110	+	0.581859i
$139$	−1.31706			−0.111712			−0.0558559	−	0.998439i	$-0.517789\pi$
$139$	−1.31706			−0.111712			−0.0558559	+	0.998439i	$0.517789\pi$
$140$	−6.53371	+	17.0181i	−0.552199	+	1.43829i
$141$	0.0933083	−	0.204317i	0.00785798	−	0.0172066i
$142$	−5.54507	+	7.34785i	−0.465332	+	0.616618i
$143$	21.8728	+	4.21564i	1.82910	+	0.352530i
$144$	1.27317	−	0.224983i	0.106097	−	0.0187486i
$145$	0.867349	−	0.0413169i	0.0720294	−	0.00343118i
$146$	−0.447375	−	22.4483i	−0.0370250	−	1.85784i
$147$	3.18638	+	11.0004i	0.262808	+	0.907299i
$148$	−2.72402	−	14.7474i	−0.223913	−	1.21223i
$149$	4.26370	+	3.35301i	0.349296	+	0.274689i	0.777356	−	0.629061i	$-0.216560\pi$
$149$	4.26370	+	3.35301i	0.349296	+	0.274689i	−0.428060	+	0.903750i	$0.640803\pi$
$150$	0.439705	−	15.8850i	0.0359018	−	1.29701i
$151$	−14.8191	−	0.705923i	−1.20596	−	0.0574472i	−0.565048	−	0.825058i	$-0.691142\pi$
$151$	−14.8191	−	0.705923i	−1.20596	−	0.0574472i	−0.640916	+	0.767611i	$0.721445\pi$
$152$	14.5152	−	8.61778i	1.17734	−	0.698994i
$153$	1.41285	−	0.645228i	0.114222	−	0.0521636i
$154$	−9.42142	−	18.5337i	−0.759200	−	1.49349i
$155$	5.62844	−	19.1687i	0.452087	−	1.53967i
$156$	−11.6124	−	6.10095i	−0.929737	−	0.488467i
$157$	−3.76813	+	3.95190i	−0.300730	+	0.315396i	−0.856709	−	0.515800i	$-0.827495\pi$
$157$	−3.76813	+	3.95190i	−0.300730	+	0.315396i	0.555980	+	0.831196i	$0.312343\pi$
$158$	−4.65807	−	1.50894i	−0.370576	−	0.120045i
$159$	−8.26204	−	3.30762i	−0.655222	−	0.262311i
$160$	−8.85300	+	17.3609i	−0.699891	+	1.37250i
$161$	7.79554	−	10.0115i	0.614375	−	0.789014i
$162$	−4.45225	+	10.2867i	−0.349802	+	0.808198i
$163$	3.61193	−	9.02216i	0.282908	−	0.706670i	−0.717045	−	0.697026i	$-0.754506\pi$
$163$	3.61193	−	9.02216i	0.282908	−	0.706670i	0.999953	−	0.00964370i	$-0.00306973\pi$
$164$	6.39698	−	7.26797i	0.499520	−	0.567533i
$165$	22.6664	+	21.6124i	1.76458	+	1.68252i
$166$	−5.81739	−	0.438723i	−0.451517	−	0.0340515i
$167$	11.4328	+	3.35696i	0.884694	+	0.259770i	0.692354	−	0.721558i	$-0.256574\pi$
$167$	11.4328	+	3.35696i	0.884694	+	0.259770i	0.192341	+	0.981328i	$0.438392\pi$
$168$	2.15519	+	12.0522i	0.166276	+	0.929845i
$169$	−1.27558	−	2.79312i	−0.0981213	−	0.214856i
$170$	−5.06509	+	22.8572i	−0.388475	+	1.75307i
$171$	0.0917889	−	1.92689i	0.00701927	−	0.147353i
$172$	0.500346	−	1.07352i	0.0381511	−	0.0818550i
$173$	−9.33778	+	11.8739i	−0.709938	+	0.902760i	−0.998503	−	0.0547008i	$-0.982579\pi$
$173$	−9.33778	+	11.8739i	−0.709938	+	0.902760i	0.288565	+	0.957460i	$0.406822\pi$
$174$	0.484239	−	0.325015i	0.0367101	−	0.0246393i
$175$	−18.1652	−	0.465635i	−1.37316	−	0.0351987i
$176$	−7.94003	−	20.7598i	−0.598502	−	1.56483i
$177$	−0.356107	−	7.47560i	−0.0267666	−	0.561900i
$178$	−0.0844612	+	0.490643i	−0.00633064	+	0.0367753i
$179$	−1.53495	+	7.96409i	−0.114728	+	0.595264i	0.878371	+	0.477980i	$0.158631\pi$
$179$	−1.53495	+	7.96409i	−0.114728	+	0.595264i	−0.993098	+	0.117284i	$0.962581\pi$
$180$	1.09853	+	1.93721i	0.0818796	+	0.144391i
$181$	8.65077	+	3.95068i	0.643007	+	0.293651i	0.710106	−	0.704095i	$-0.248647\pi$
$181$	8.65077	+	3.95068i	0.643007	+	0.293651i	−0.0670989	+	0.997746i	$0.521374\pi$
$182$	−6.94912	+	13.2928i	−0.515103	+	0.985327i
$183$		−	1.95851i		−	0.144777i
$184$	9.40954	−	9.77040i	0.693680	−	0.720283i
$185$	22.3713	−	12.9161i	1.64477	−	0.949610i
$186$	−3.42256	−	12.9740i	−0.250954	−	0.951299i
$187$	−15.4885	−	21.7505i	−1.13263	−	1.59055i
$188$	−0.236719	−	0.139126i	−0.0172645	−	0.0101468i
$189$	13.2133	+	5.68688i	0.961128	+	0.413660i
$190$	22.3500	+	18.5998i	1.62144	+	1.34937i
$191$	−0.873065	+	0.0415892i	−0.0631728	+	0.00300929i	−0.0791445	−	0.996863i	$-0.525219\pi$
$191$	−0.873065	+	0.0415892i	−0.0631728	+	0.00300929i	0.0159717	+	0.999872i	$0.494916\pi$
$192$	0.941034	+	13.0548i	0.0679133	+	0.942150i
$193$	7.08473	−	20.4700i	0.509970	−	1.47346i	−0.336838	−	0.941563i	$-0.609357\pi$
$193$	7.08473	−	20.4700i	0.509970	−	1.47346i	0.846808	−	0.531899i	$-0.178521\pi$
$194$	−10.2485	+	0.693100i	−0.735802	+	0.0497617i
$195$	3.21560	−	22.3650i	0.230274	−	1.60159i
$196$	13.7763	−	2.49260i	0.984023	−	0.178043i
$197$	−21.0232	−	13.5108i	−1.49784	−	0.962602i	−0.995175	−	0.0981200i	$-0.968717\pi$
$197$	−21.0232	−	13.5108i	−1.49784	−	0.962602i	−0.502664	−	0.864482i	$-0.667647\pi$
$198$	−2.47980	−	0.549516i	−0.176232	−	0.0390524i
$199$	4.98476	−	7.00012i	0.353361	−	0.496226i	−0.599190	−	0.800607i	$-0.704510\pi$
$199$	4.98476	−	7.00012i	0.353361	−	0.496226i	0.952550	+	0.304382i	$0.0984498\pi$
$200$	−19.2603	−	2.53019i	−1.36191	−	0.178911i
$201$	−6.83487	−	7.16821i	−0.482095	−	0.505606i
$202$	−22.3158	+	10.7337i	−1.57013	+	0.755220i
$203$	−0.372779	−	0.552956i	−0.0261640	−	0.0388099i
$204$	5.02757	+	14.8987i	0.352000	+	1.04311i
$205$	15.4829	+	6.19843i	1.08137	+	0.432917i
$206$	25.3042	−	2.92611i	1.76303	−	0.203872i
$207$	−0.339542	−	1.51248i	−0.0235998	−	0.105125i
$208$	−8.87728	+	13.3538i	−0.615529	+	0.925919i
$209$	−32.8255	+	4.71960i	−2.27059	+	0.326461i
$210$	−18.3236	+	10.4403i	−1.26445	+	0.720448i
$211$	−0.104038	−	0.354322i	−0.00716230	−	0.0243926i	0.955834	−	0.293906i	$-0.0949553\pi$
$211$	−0.104038	−	0.354322i	−0.00716230	−	0.0243926i	−0.962997	+	0.269514i	$0.913137\pi$
$212$	−5.05983	+	9.63078i	−0.347511	+	0.661444i
$213$	−10.3494	+	2.51073i	−0.709128	+	0.172032i
$214$	−7.70309	−	9.40346i	−0.526572	−	0.642807i
$215$	2.03088	+	0.193926i	0.138505	+	0.0132256i
$216$	13.4107	+	7.52642i	0.912484	+	0.512108i
$217$	−14.8274	+	3.94397i	−1.00655	+	0.267734i
$218$	6.45080	+	3.96632i	0.436904	+	0.268633i
$219$	16.0569	−	20.4180i	1.08502	−	1.37972i
$220$	29.1272	−	24.8464i	1.96376	−	1.67515i
$221$	−6.30062	+	18.2044i	−0.423825	+	1.22456i
$222$	8.37376	−	15.1952i	0.562010	−	1.01983i
$223$	6.96062	−	4.47332i	0.466118	−	0.299556i	−0.286421	−	0.958104i	$-0.592466\pi$
$223$	6.96062	−	4.47332i	0.466118	−	0.299556i	0.752538	+	0.658548i	$0.228829\pi$
$224$	14.9257	−	1.10659i	0.997263	−	0.0739370i
$225$	−1.45373	+	1.67770i	−0.0969154	+	0.111846i
$226$	6.29229	+	4.74850i	0.418557	+	0.315865i
$227$	−0.268584	+	0.0256466i	−0.0178265	+	0.00170223i	−0.103965	−	0.994581i	$-0.533153\pi$
$227$	−0.268584	+	0.0256466i	−0.0178265	+	0.00170223i	0.0861390	+	0.996283i	$0.472547\pi$
$228$	19.3082	+	2.92895i	1.27872	+	0.193974i
$229$	11.1261	+	6.42364i	0.735231	+	0.424486i	0.820333	−	0.571886i	$-0.193788\pi$
$229$	11.1261	+	6.42364i	0.735231	+	0.424486i	−0.0851016	+	0.996372i	$0.527121\pi$
$230$	21.2804	+	9.64755i	1.40319	+	0.636141i
$231$	5.15572	−	23.4936i	0.339222	−	1.54577i
$232$	−0.334373	−	0.629644i	−0.0219526	−	0.0413382i
$233$	7.20826	+	10.1226i	0.472229	+	0.663152i	0.980151	−	0.198250i	$-0.0635259\pi$
$233$	7.20826	+	10.1226i	0.472229	+	0.663152i	−0.507923	+	0.861403i	$0.669586\pi$
$234$	0.714816	+	1.68729i	0.0467290	+	0.110301i
$235$	0.0895077	−	0.464410i	0.00583884	−	0.0302948i
$236$	−9.13475	−	0.506096i	−0.594621	−	0.0329441i
$237$	−3.06249	−	4.76533i	−0.198930	−	0.309542i
$238$	17.0245	−	5.78376i	1.10353	−	0.374905i
$239$	−5.30650	+	4.59811i	−0.343249	+	0.297427i	−0.809376	−	0.587291i	$-0.800194\pi$
$239$	−5.30650	+	4.59811i	−0.343249	+	0.297427i	0.466127	+	0.884718i	$0.345649\pi$
$240$	−20.6505	+	9.04679i	−1.33299	+	0.583968i
$241$	4.15488	+	10.3784i	0.267640	+	0.668531i	0.999922	−	0.0124695i	$-0.00396926\pi$
$241$	4.15488	+	10.3784i	0.267640	+	0.668531i	−0.732283	+	0.681001i	$0.761545\pi$
$242$	−0.777761	+	28.0978i	−0.0499964	+	1.80620i
$243$	2.97213	−	1.53224i	0.190662	−	0.0982933i
$244$	−2.38146	−	0.246034i	−0.152458	−	0.0157507i
$245$	11.9811	+	20.9282i	0.765443	+	1.33705i
$246$	11.0532	−	1.81469i	0.704727	−	0.115701i
$247$	16.5105	+	17.3157i	1.05054	+	1.10177i
$248$	−16.2058	+	2.53186i	−1.02907	+	0.160773i
$249$	−4.88461	−	4.65746i	−0.309549	−	0.295155i
$250$	−1.90010	−	8.90047i	−0.120173	−	0.562915i
$251$	0.0539240	+	0.375050i	0.00340365	+	0.0236729i	0.991452	−	0.130468i	$-0.0416480\pi$
$251$	0.0539240	+	0.375050i	0.00340365	+	0.0236729i	−0.988049	+	0.154141i	$0.950739\pi$
$252$	0.834012	−	1.49321i	0.0525378	−	0.0940633i
$253$	−24.4268	+	10.6524i	−1.53570	+	0.669713i
$254$	−18.8247	+	13.9786i	−1.18117	+	0.877093i
$255$	−21.2900	+	16.7427i	−1.33323	+	1.04847i
$256$	15.9923	+	0.495727i	0.999520	+	0.0309829i
$257$	−4.14916	−	1.00658i	−0.258818	−	0.0627885i	0.104250	−	0.994551i	$-0.466756\pi$
$257$	−4.14916	−	1.00658i	−0.258818	−	0.0627885i	−0.363068	+	0.931763i	$0.618271\pi$
$258$	1.23480	−	0.593927i	0.0768752	−	0.0369763i
$259$	−17.3949	−	9.53965i	−1.08087	−	0.592765i
$260$	−26.7909	−	6.71959i	−1.66150	−	0.416731i
$261$	−0.0811013	−	0.00774424i	−0.00502005	−	0.000479356i
$262$	17.5596	+	16.0874i	1.08484	+	0.993883i
$263$	−20.6930	−	0.985731i	−1.27599	−	0.0607828i	−0.601382	−	0.798962i	$-0.705383\pi$
$263$	−20.6930	−	0.985731i	−1.27599	−	0.0607828i	−0.674605	+	0.738179i	$0.735686\pi$
$264$	8.11347	−	24.3998i	0.499350	−	1.50171i
$265$	−18.5484	−	2.66686i	−1.13942	−	0.163824i
$266$	3.30401	−	22.0853i	0.202582	−	1.35414i
$267$	−0.435287	+	0.377179i	−0.0266392	+	0.0230830i
$268$	−9.57486	+	7.41042i	−0.584877	+	0.452664i
$269$	−0.954667	+	1.85180i	−0.0582071	+	0.112906i	−0.916144	−	0.400848i	$-0.868715\pi$
$269$	−0.954667	+	1.85180i	−0.0582071	+	0.112906i	0.857937	+	0.513754i	$0.171746\pi$
$270$	−4.49387	+	26.1053i	−0.273488	+	1.58872i
$271$	−7.28170	−	21.0391i	−0.442332	−	1.27803i	−0.917358	−	0.398063i	$-0.869683\pi$
$271$	−7.28170	−	21.0391i	−0.442332	−	1.27803i	0.475026	−	0.879972i	$-0.342439\pi$
$272$	18.7477	−	4.24170i	1.13675	−	0.257191i
$273$	−15.9643	+	6.80179i	−0.966201	+	0.411663i
$274$	15.4575	+	4.20606i	0.933820	+	0.254097i
$275$	33.0501	+	19.0815i	1.99299	+	1.15066i
$276$	15.5839	−	1.84567i	0.938039	−	0.111096i
$277$	−10.9581	−	18.9799i	−0.658406	−	1.14039i	−0.981028	−	0.193865i	$-0.937898\pi$
$277$	−10.9581	−	18.9799i	−0.658406	−	1.14039i	0.322622	−	0.946528i	$-0.395436\pi$
$278$	−1.32215	+	1.31195i	−0.0792975	+	0.0786856i
$279$	−0.778657	+	1.70502i	−0.0466170	+	0.102077i
$280$	10.3931	+	23.5922i	0.621106	+	1.40991i
$281$	1.68845	−	1.94857i	0.100724	−	0.116242i	−0.703149	−	0.711042i	$-0.748223\pi$
$281$	1.68845	−	1.94857i	0.100724	−	0.116242i	0.803874	+	0.594800i	$0.202769\pi$
$282$	−0.109855	−	0.298053i	−0.00654175	−	0.0177488i
$283$	−8.78240	−	4.52764i	−0.522060	−	0.269140i	0.176991	−	0.984212i	$-0.443364\pi$
$283$	−8.78240	−	4.52764i	−0.522060	−	0.269140i	−0.699051	+	0.715072i	$0.746394\pi$
$284$	1.75282	+	12.8998i	0.104011	+	0.765463i
$285$	6.36620	+	33.0310i	0.377101	+	1.95659i
$286$	26.1567	−	17.5560i	1.54668	−	1.03811i
$287$	−2.10091	−	12.6348i	−0.124013	−	0.745811i
$288$	1.05398	−	1.49408i	0.0621063	−	0.0880394i
$289$	5.41460	−	2.79142i	0.318506	−	0.164201i
$290$	0.829546	−	0.905459i	0.0487126	−	0.0531704i
$291$	−9.68000	−	6.89309i	−0.567451	−	0.404080i
$292$	−22.8103	−	22.0895i	−1.33487	−	1.29269i
$293$	0.141859	−	0.483126i	0.00828747	−	0.0282245i	−0.955245	−	0.295814i	$-0.904409\pi$
$293$	0.141859	−	0.483126i	0.00828747	−	0.0282245i	0.963533	+	0.267590i	$0.0862272\pi$
$294$	14.1564	+	7.86893i	0.825619	+	0.458925i
$295$	−4.43975	−	15.1204i	−0.258492	−	0.880344i
$296$	−17.4247	−	12.0910i	−1.01279	−	0.702775i
$297$	−18.6756	−	23.7480i	−1.08367	−	1.37800i
$298$	7.62017	−	0.881178i	0.441425	−	0.0510453i
$299$	16.4824	+	9.89721i	0.953201	+	0.572370i
$300$	−15.3820	−	16.3844i	−0.888078	−	0.945955i
$301$	−0.682030	−	1.41057i	−0.0393115	−	0.0813040i
$302$	−15.5796	+	14.0530i	−0.896506	+	0.808658i
$303$	−27.8405	−	6.75402i	−1.59939	−	0.388008i
$304$	5.98703	−	23.1100i	0.343380	−	1.32545i
$305$	−0.972247	−	4.00766i	−0.0556707	−	0.229478i
$306$	0.775591	−	2.05509i	0.0443376	−	0.117482i
$307$	−0.693689	−	1.51897i	−0.0395909	−	0.0866920i	0.888803	−	0.458289i	$-0.151538\pi$
$307$	−0.693689	−	1.51897i	−0.0395909	−	0.0866920i	−0.928394	+	0.371597i	$0.878810\pi$
$308$	−27.9196	−	9.22048i	−1.59087	−	0.525386i
$309$	24.7910	+	15.9322i	1.41031	+	0.906353i
$310$	−13.4441	−	24.8494i	−0.763574	−	1.41135i
$311$	0.280816	−	0.112422i	0.0159236	−	0.00637486i	−0.363687	−	0.931521i	$-0.618482\pi$
$311$	0.280816	−	0.112422i	0.0159236	−	0.00637486i	0.379611	+	0.925146i	$0.376058\pi$
$312$	−17.7346	+	5.44282i	−1.00402	+	0.308139i
$313$	1.67541	+	8.69283i	0.0946995	+	0.491348i	0.998049	+	0.0624417i	$0.0198887\pi$
$313$	1.67541	+	8.69283i	0.0946995	+	0.491348i	−0.903349	+	0.428906i	$0.858899\pi$
$314$	0.153866	+	7.72069i	0.00868318	+	0.435704i
$315$	2.90437	+	0.493854i	0.163643	+	0.0278255i
$316$	−6.17916	+	3.12523i	−0.347605	+	0.175808i
$317$	−5.94759	−	17.1844i	−0.334050	−	0.965173i	−0.979513	−	0.201382i	$-0.935457\pi$
$317$	−5.94759	−	17.1844i	−0.334050	−	0.965173i	0.645463	−	0.763791i	$-0.276664\pi$
$318$	−11.5888	+	4.90956i	−0.649866	+	0.275315i
$319$	0.133133	+	1.39423i	0.00745401	+	0.0780619i
$320$	8.40633	+	26.2467i	0.469928	+	1.46723i
$321$		−	14.0629i		−	0.784912i
$322$	−2.14693	−	17.8155i	−0.119644	−	0.992817i
$323$		−	28.6797i		−	1.59578i
$324$	5.77731	+	14.7614i	0.320961	+	0.820079i
$325$	−2.61715	−	27.4080i	−0.145173	−	1.52032i
$326$	−5.36125	−	12.6549i	−0.296932	−	0.700893i
$327$	2.86533	+	8.27884i	0.158453	+	0.457821i
$328$	−0.818052	−	13.6682i	−0.0451694	−	0.754701i
$329$	−0.340559	+	0.126313i	−0.0187756	+	0.00696388i
$330$	44.2826	−	0.882512i	2.43768	−	0.0485807i
$331$	−4.47680	−	23.2278i	−0.246067	−	1.27672i	−0.869145	−	0.494558i	$-0.835330\pi$
$331$	−4.47680	−	23.2278i	−0.246067	−	1.27672i	0.623078	−	0.782160i	$-0.285882\pi$
$332$	−6.27690	+	5.35439i	−0.344490	+	0.293860i
$333$	−2.25006	+	0.900788i	−0.123303	+	0.0493629i
$334$	14.8209	−	8.01846i	0.810964	−	0.438751i
$335$	−17.5445	−	11.2752i	−0.958560	−	0.616029i
$336$	14.1689	+	9.95194i	0.772977	+	0.542923i
$337$	−9.91614	−	21.7133i	−0.540167	−	1.18280i	−0.961225	−	0.275766i	$-0.911068\pi$
$337$	−9.91614	−	21.7133i	−0.540167	−	1.18280i	0.421058	−	0.907034i	$-0.361659\pi$
$338$	−4.06279	−	1.53330i	−0.220987	−	0.0834003i
$339$	2.15005	+	8.86264i	0.116775	+	0.481352i
$340$	17.6839	+	27.9910i	0.959042	+	1.51803i
$341$	31.3150	+	7.59694i	1.69580	+	0.411397i
$342$	−1.82726	−	2.02577i	−0.0988071	−	0.109541i
$343$	8.96482	−	16.2059i	0.484055	−	0.875038i
$344$	−0.567071	−	1.57607i	−0.0305744	−	0.0849762i
$345$	11.9720	+	24.2351i	0.644550	+	1.30477i
$346$	2.45399	+	21.2214i	0.131927	+	1.14087i
$347$	−0.392667	−	0.499317i	−0.0210795	−	0.0268047i	0.775399	−	0.631471i	$-0.217549\pi$
$347$	−0.392667	−	0.499317i	−0.0210795	−	0.0268047i	−0.796479	+	0.604667i	$0.793306\pi$
$348$	0.162358	−	0.808631i	0.00870330	−	0.0433472i
$349$	−6.82040	−	23.2281i	−0.365087	−	1.24337i	−0.913387	−	0.407092i	$-0.866543\pi$
$349$	−6.82040	−	23.2281i	−0.365087	−	1.24337i	0.548300	−	0.836282i	$-0.315275\pi$
$350$	−18.6992	+	17.6272i	−0.999515	+	0.942215i
$351$	−6.14071	+	20.9133i	−0.327767	+	1.11627i
$352$	−28.6499	−	12.9308i	−1.52705	−	0.689215i
$353$	12.3958	+	8.82699i	0.659760	+	0.469813i	0.860243	−	0.509884i	$-0.170312\pi$
$353$	12.3958	+	8.82699i	0.659760	+	0.469813i	−0.200483	+	0.979697i	$0.564251\pi$
$354$	−7.80407	−	7.14977i	−0.414782	−	0.380006i
$355$	−19.9314	+	10.2753i	−1.05785	+	0.545358i
$356$	0.403951	+	0.576673i	0.0214094	+	0.0305636i
$357$	19.4762	+	7.30481i	1.03079	+	0.386612i
$358$	6.39230	+	9.52388i	0.337843	+	0.503353i
$359$	−6.69587	−	34.7415i	−0.353394	−	1.83358i	−0.528373	−	0.849012i	$-0.677198\pi$
$359$	−6.69587	−	34.7415i	−0.353394	−	1.83358i	0.174979	−	0.984572i	$-0.444014\pi$
$360$	3.03247	+	0.850437i	0.159825	+	0.0448220i
$361$	−14.7723	−	7.61564i	−0.777489	−	0.400823i
$362$	12.6196	−	4.65125i	0.663269	−	0.244464i
$363$	−21.2951	+	24.5758i	−1.11770	+	1.28990i
$364$	6.26521	+	20.2663i	0.328386	+	1.06224i
$365$	22.7210	−	49.7520i	1.18927	−	2.60414i
$366$	−1.95091	−	1.96608i	−0.101976	−	0.102769i
$367$	0.102592	+	0.177694i	0.00535525	+	0.00927557i	0.868691	−	0.495355i	$-0.164962\pi$
$367$	0.102592	+	0.177694i	0.00535525	+	0.00927557i	−0.863335	+	0.504631i	$0.831629\pi$
$368$	−0.286564	−	19.1812i	−0.0149382	−	0.999888i
$369$	−1.35512	−	0.782376i	−0.0705445	−	0.0407289i
$370$	9.59185	−	35.2505i	0.498656	−	1.83259i
$371$	5.64108	+	13.2400i	0.292870	+	0.687386i
$372$	−16.3594	−	9.61487i	−0.848197	−	0.498508i
$373$	7.83726	+	22.6443i	0.405798	+	1.17248i	0.944081	+	0.329713i	$0.106952\pi$
$373$	7.83726	+	22.6443i	0.405798	+	1.17248i	−0.538283	+	0.842764i	$0.680927\pi$
$374$	−37.2144	−	6.40624i	−1.92431	−	0.331259i
$375$	4.82460	−	9.35843i	0.249141	−	0.483267i
$376$	−0.376220	+	0.0961364i	−0.0194021	+	0.00495786i
$377$	0.763643	−	0.661701i	0.0393296	−	0.0340793i
$378$	18.9292	−	7.45318i	0.973614	−	0.383350i
$379$	−28.5849	−	4.10989i	−1.46831	−	0.211111i	−0.638699	−	0.769456i	$-0.720527\pi$
$379$	−28.5849	−	4.10989i	−1.46831	−	0.211111i	−0.829609	+	0.558345i	$0.811436\pi$
$380$	40.9640	−	3.59158i	2.10141	−	0.184244i
$381$	−27.0950	−	1.29070i	−1.38812	−	0.0661243i
$382$	−0.835013	+	0.911427i	−0.0427230	+	0.0466327i
$383$	24.4829	+	2.33783i	1.25102	+	0.119458i	0.699455	−	0.714677i	$-0.253426\pi$
$383$	24.4829	+	2.33783i	1.25102	+	0.119458i	0.551562	+	0.834134i	$0.314032\pi$
$384$	13.9488	+	12.1679i	0.711823	+	0.620941i
$385$	−1.11271	−	50.6340i	−0.0567092	−	2.58055i
$386$	−13.2784	−	27.6064i	−0.675854	−	1.40513i
$387$	−0.186016	−	0.0451270i	−0.00945573	−	0.00229394i
$388$	−9.59774	+	10.9045i	−0.487251	+	0.553594i
$389$	6.38681	−	5.02265i	0.323824	−	0.254658i	−0.442991	−	0.896526i	$-0.646083\pi$
$389$	6.38681	−	5.02265i	0.323824	−	0.254658i	0.766815	+	0.641868i	$0.221840\pi$
$390$	−19.0502	−	25.6546i	−0.964642	−	1.29907i
$391$	−6.11222	−	22.2205i	−0.309108	−	1.12374i
$392$	11.3467	−	16.2251i	0.573093	−	0.819491i
$393$	3.92092	+	27.2706i	0.197784	+	1.37562i
$394$	−34.5628	+	7.37857i	−1.74125	+	0.371727i
$395$	−8.63234	−	8.23092i	−0.434340	−	0.414143i
$396$	−3.03677	+	1.91854i	−0.152603	+	0.0964101i
$397$	24.3933	+	25.5830i	1.22427	+	1.28397i	0.946264	+	0.323394i	$0.104824\pi$
$397$	24.3933	+	25.5830i	1.22427	+	1.28397i	0.278002	+	0.960580i	$0.410328\pi$
$398$	−1.96892	−	11.9926i	−0.0986930	−	0.601135i
$399$	19.1480	−	17.3429i	0.958601	−	0.868232i
$400$	−21.8551	+	16.6455i	−1.09275	+	0.832277i
$401$	21.7968	−	11.2370i	1.08848	−	0.561150i	0.181956	−	0.983307i	$-0.441757\pi$
$401$	21.7968	−	11.2370i	1.08848	−	0.561150i	0.906523	+	0.422157i	$0.138727\pi$
$402$	−14.0017	−	0.387574i	−0.698341	−	0.0193304i
$403$	−8.64025	−	21.5823i	−0.430401	−	1.07509i
$404$	−11.7100	+	33.0044i	−0.582595	+	1.64203i
$405$	−20.6354	+	17.8807i	−1.02538	+	0.888499i
$406$	−0.925030	−	0.183761i	−0.0459085	−	0.00911990i
$407$	22.5263	+	35.0516i	1.11659	+	1.73744i
$408$	19.8878	+	9.94819i	0.984595	+	0.492509i
$409$	−7.32143	+	37.9872i	−0.362021	+	1.87835i	0.105588	+	0.994410i	$0.466328\pi$
$409$	−7.32143	+	37.9872i	−0.362021	+	1.87835i	−0.467609	+	0.883935i	$0.654884\pi$
$410$	21.7171	−	9.20044i	1.07253	−	0.454377i
$411$	10.7501	+	15.0963i	0.530261	+	0.744647i
$412$	22.4872	−	28.1434i	1.10787	−	1.38653i
$413$	−8.15734	+	8.94049i	−0.401396	+	0.439933i
$414$	−1.84746	−	1.18010i	−0.0907979	−	0.0579989i
$415$	−12.3074	−	7.10566i	−0.604144	−	0.348803i
$416$	4.39036	+	22.2482i	0.215255	+	1.09081i
$417$	−2.14507	+	0.204829i	−0.105045	+	0.0100305i
$418$	−28.2511	+	37.4360i	−1.38181	+	1.83105i
$419$	−11.4745	+	13.2423i	−0.560568	+	0.646930i	−0.963312	−	0.268383i	$-0.913511\pi$
$419$	−11.4745	+	13.2423i	−0.560568	+	0.646930i	0.402744	+	0.915312i	$0.368056\pi$
$420$	−7.99465	+	28.7331i	−0.390099	+	1.40203i
$421$	25.5233	−	16.4028i	1.24393	−	0.799426i	0.257929	−	0.966164i	$-0.416960\pi$
$421$	25.5233	−	16.4028i	1.24393	−	0.799426i	0.986001	+	0.166738i	$0.0533235\pi$
$422$	−0.457388	−	0.252058i	−0.0222653	−	0.0122700i
$423$	−0.0145135	+	0.0419340i	−0.000705671	+	0.00203890i
$424$	4.51401	+	14.7082i	0.219220	+	0.714293i
$425$	−20.4015	+	25.9426i	−0.989617	+	1.25840i
$426$	−7.88840	+	12.8296i	−0.382194	+	0.621598i
$427$	−2.24360	+	2.23541i	−0.108575	+	0.108179i
$428$	−17.0998	−	1.76662i	−0.826552	−	0.0853927i
$429$	36.2794	+	3.46426i	1.75159	+	0.167256i
$430$	2.23191	−	1.82832i	0.107632	−	0.0881696i
$431$	1.93689	−	0.469886i	0.0932969	−	0.0226336i	−0.188839	−	0.982008i	$-0.560472\pi$
$431$	1.93689	−	0.469886i	0.0932969	−	0.0226336i	0.282136	+	0.959375i	$0.408957\pi$
$432$	20.9598	−	5.80317i	1.00843	−	0.279205i
$433$	−5.68102	−	19.3478i	−0.273012	−	0.929795i	−0.975849	−	0.218444i	$-0.929902\pi$
$433$	−5.68102	−	19.3478i	−0.273012	−	0.929795i	0.702837	−	0.711351i	$-0.251916\pi$
$434$	−10.9561	+	18.7291i	−0.525910	+	0.899026i
$435$	1.40621	−	0.202182i	0.0674224	−	0.00969388i
$436$	10.4267	−	2.44411i	0.499347	−	0.117052i
$437$	−28.0083	−	5.89854i	−1.33982	−	0.282166i
$438$	−4.21979	−	36.4915i	−0.201629	−	1.74363i
$439$	6.54514	+	2.62028i	0.312382	+	0.125059i	0.522556	−	0.852605i	$-0.324979\pi$
$439$	6.54514	+	2.62028i	0.312382	+	0.125059i	−0.210174	+	0.977664i	$0.567403\pi$
$440$	4.48982	−	53.9566i	0.214044	−	2.57228i
$441$	−0.833225	−	2.10355i	−0.0396774	−	0.100169i
$442$	11.8088	+	24.5510i	0.561688	+	1.16777i
$443$	15.2423	+	15.9857i	0.724184	+	0.759502i	0.978193	−	0.207700i	$-0.0665977\pi$
$443$	15.2423	+	15.9857i	0.724184	+	0.759502i	−0.254009	+	0.967202i	$0.581749\pi$
$444$	−6.73006	−	23.5952i	−0.319395	−	1.11978i
$445$	−0.703481	+	0.987900i	−0.0333482	+	0.0468310i
$446$	2.53157	−	11.4242i	0.119873	−	0.540952i
$447$	7.46564	+	4.79788i	0.353113	+	0.226932i
$448$	13.8811	−	15.9786i	0.655819	−	0.754918i
$449$	4.31877	−	30.0377i	0.203815	−	1.41757i	−0.589014	−	0.808123i	$-0.700484\pi$
$449$	4.31877	−	30.0377i	0.203815	−	1.41757i	0.792829	−	0.609444i	$-0.208607\pi$
$450$	0.211833	+	3.13227i	0.00998590	+	0.147657i
$451$	−8.79812	+	25.4205i	−0.414288	+	1.19701i
$452$	11.0467	−	1.50102i	0.519592	−	0.0706021i
$453$	−24.2454	+	1.15495i	−1.13915	+	0.0542643i
$454$	−0.244075	+	0.293287i	−0.0114550	+	0.0137647i
$455$	−29.2908	+	21.8434i	−1.37317	+	1.02403i
$456$	22.3004	−	16.2930i	1.04431	−	0.762989i
$457$	−3.04020	−	4.26937i	−0.142215	−	0.199713i	0.737325	−	0.675538i	$-0.236089\pi$
$457$	−3.04020	−	4.26937i	−0.142215	−	0.199713i	−0.879540	+	0.475826i	$0.842149\pi$
$458$	17.5678	−	4.63442i	0.820889	−	0.216552i
$459$	22.6269	−	13.0636i	1.05613	−	0.609759i
$460$	30.9728	−	11.5129i	1.44411	−	0.536794i
$461$			23.7160i			1.10456i	0.833658	+	0.552282i	$0.186243\pi$
$461$			23.7160i			1.10456i	−0.833658	+	0.552282i	$0.813757\pi$
$462$	−18.2268	−	28.7202i	−0.847988	−	1.33618i
$463$	−2.45008	−	1.11891i	−0.113865	−	0.0520004i	0.357668	−	0.933849i	$-0.383572\pi$
$463$	−2.45008	−	1.11891i	−0.113865	−	0.0520004i	−0.471533	+	0.881848i	$0.656299\pi$
$464$	−0.962866	−	0.299003i	−0.0446999	−	0.0138809i
$465$	6.18580	−	32.0950i	0.286860	−	1.48837i
$466$	17.3194	+	2.98143i	0.802307	+	0.138112i
$467$	0.855889	+	17.9673i	0.0396058	+	0.831428i	0.928053	+	0.372449i	$0.121482\pi$
$467$	0.855889	+	17.9673i	0.0396058	+	0.831428i	−0.888447	+	0.458979i	$0.848215\pi$
$468$	2.39832	+	0.981766i	0.110862	+	0.0453822i
$469$	−0.410429	+	16.0115i	−0.0189519	+	0.739342i
$470$	−0.372754	−	0.555366i	−0.0171939	−	0.0256171i
$471$	−5.52247	+	7.02239i	−0.254462	+	0.323575i
$472$	−9.67419	+	8.59124i	−0.445291	+	0.395444i
$473$	−0.156573	+	3.28687i	−0.00719923	+	0.151131i
$474$	−7.82117	−	1.73315i	−0.359238	−	0.0796061i
$475$	17.0279	+	37.2859i	0.781293	+	1.71079i
$476$	11.3290	−	22.7645i	0.519264	−	1.04341i
$477$	1.68696	+	0.495337i	0.0772407	+	0.0226799i
$478$	−0.746752	+	9.90179i	−0.0341556	+	0.452897i
$479$	27.2101	+	25.9448i	1.24326	+	1.18545i	0.975025	+	0.222095i	$0.0712897\pi$
$479$	27.2101	+	25.9448i	1.24326	+	1.18545i	0.268237	+	0.963353i	$0.413559\pi$
$480$	−11.7187	+	29.6522i	−0.534883	+	1.35343i
$481$	11.1721	−	27.9067i	0.509406	−	1.27243i
$482$	14.5091	+	6.27976i	0.660870	+	0.286035i
$483$	11.1394	−	17.5178i	0.506862	−	0.797088i
$484$	27.2080	+	28.9812i	1.23673	+	1.31733i
$485$	−23.2299	−	9.29984i	−1.05481	−	0.422284i
$486$	1.45733	−	4.49876i	0.0661058	−	0.204068i
$487$	6.29224	−	6.59911i	0.285129	−	0.299034i	−0.565557	−	0.824709i	$-0.691339\pi$
$487$	6.29224	−	6.59911i	0.285129	−	0.299034i	0.850685	+	0.525675i	$0.176187\pi$
$488$	−2.63575	+	2.12524i	−0.119315	+	0.0962049i
$489$	4.47954	−	15.2559i	0.202572	−	0.689896i
$490$	32.8743	+	9.07448i	1.48511	+	0.409943i
$491$	−33.3189	+	15.2162i	−1.50366	+	0.686699i	−0.985670	−	0.168687i	$-0.946047\pi$
$491$	−33.3189	+	15.2162i	−1.50366	+	0.686699i	−0.517992	+	0.855386i	$0.673320\pi$
$492$	9.28830	−	12.8320i	0.418749	−	0.578513i
$493$	−1.20985	−	0.0576325i	−0.0544891	−	0.00259564i
$494$	33.8229	+	0.936234i	1.52176	+	0.0421232i
$495$	−4.86354	−	3.82473i	−0.218600	−	0.171909i
$496$	−13.7464	+	18.6845i	−0.617231	+	0.838960i
$497$	14.6888	+	8.99018i	0.658885	+	0.403265i
$498$	−9.54288	+	0.190181i	−0.427627	+	0.00852221i
$499$	−10.9922	+	0.523624i	−0.492079	+	0.0234406i	−0.292155	−	0.956371i	$-0.594372\pi$
$499$	−10.9922	+	0.523624i	−0.492079	+	0.0234406i	−0.199924	+	0.979811i	$0.564069\pi$
$500$	−10.7734	−	7.04215i	−0.481800	−	0.314934i
$501$	19.1424	+	3.68939i	0.855218	+	0.164830i
$502$	0.427726	+	0.322785i	0.0190904	+	0.0144066i
$503$	16.2105	−	35.4960i	0.722790	−	1.58269i	−0.0871620	−	0.996194i	$-0.527780\pi$
$503$	16.2105	−	35.4960i	0.722790	−	1.58269i	0.809952	−	0.586496i	$-0.199493\pi$
$504$	−0.650178	−	2.32976i	−0.0289612	−	0.103776i
$505$	−60.3223			−2.68431
$506$	−13.9101	+	35.0256i	−0.618381	+	1.55708i
$507$	−2.51189	−	4.35072i	−0.111557	−	0.193222i
$508$	−4.97319	+	32.7843i	−0.220650	+	1.45457i
$509$	27.7596	−	19.7675i	1.23042	−	0.876180i	0.235023	−	0.971990i	$-0.424484\pi$
$509$	27.7596	−	19.7675i	1.23042	−	0.876180i	0.995400	+	0.0958101i	$0.0305442\pi$
$510$	−4.69465	+	38.0148i	−0.207883	+	1.68332i
$511$	−41.7173	+	4.91059i	−1.84546	+	0.217232i
$512$	16.5479	−	15.4326i	0.731323	−	0.682031i
$513$	−1.54402	−	32.4130i	−0.0681702	−	1.43107i
$514$	−5.16787	+	3.12259i	−0.227945	+	0.137732i
$515$	58.6386	+	20.2950i	2.58392	+	0.894305i
$516$	0.647949	−	1.82623i	0.0285244	−	0.0803953i
$517$	0.755088	+	0.108565i	0.0332087	+	0.00477470i
$518$	−26.9648	+	7.75086i	−1.18476	+	0.340553i
$519$	−13.3616	+	20.7910i	−0.586509	+	0.912625i
$520$	−33.5880	+	19.9414i	−1.47293	+	0.874487i
$521$	15.9249	+	11.3400i	0.697681	+	0.496816i	0.873015	−	0.487693i	$-0.162161\pi$
$521$	15.9249	+	11.3400i	0.697681	+	0.496816i	−0.175335	+	0.984509i	$0.556101\pi$
$522$	−0.0891291	+	0.0730124i	−0.00390107	+	0.00319567i
$523$	23.6692	−	22.5686i	1.03498	−	0.986855i	0.0350619	−	0.999385i	$-0.488837\pi$
$523$	23.6692	−	22.5686i	1.03498	−	0.986855i	0.999921	+	0.0125304i	$0.00398867\pi$
$524$	33.6524	−	1.34186i	1.47011	−	0.0586194i
$525$	−29.6576	+	2.06667i	−1.29436	+	0.0901970i
$526$	−21.7549	+	19.6232i	−0.948560	+	0.855611i
$527$	−10.3571	+	25.8708i	−0.451163	+	1.12695i
$528$	−16.1603	−	32.5761i	−0.703287	−	1.41769i
$529$	−22.9574	+	1.39904i	−0.998148	+	0.0608278i
$530$	−21.2767	+	15.7993i	−0.924199	+	0.686277i
$531$	0.210419	+	1.46350i	0.00913140	+	0.0635103i
$532$	−18.6828	−	25.4619i	−0.810003	−	1.10391i
$533$	18.6209	−	5.46760i	0.806562	−	0.236828i
$534$	−0.0612553	+	0.812235i	−0.00265078	+	0.0351488i
$535$	−6.98112	−	28.7766i	−0.301820	−	1.24412i
$536$	−2.23021	+	16.9768i	−0.0963303	+	0.733285i
$537$	−1.26137	+	13.2097i	−0.0544321	+	0.570039i
$538$	0.886251	+	2.80992i	0.0382090	+	0.121144i
$539$	−32.7982	+	20.9091i	−1.41272	+	0.900619i
$540$	21.4927	+	30.6827i	0.924901	+	1.32037i
$541$	22.3934	+	17.6103i	0.962765	+	0.757127i	0.970065	−	0.242846i	$-0.0780811\pi$
$541$	22.3934	+	17.6103i	0.962765	+	0.757127i	−0.00729939	+	0.999973i	$0.502323\pi$
$542$	−28.2673	−	13.8670i	−1.21418	−	0.595638i
$543$	14.7037	+	5.08901i	0.630997	+	0.218390i
$544$	14.5949	−	22.9331i	0.625753	−	0.983246i
$545$	9.97309	+	15.5184i	0.427200	+	0.664736i
$546$	−9.25059	+	22.7304i	−0.395889	+	0.972771i
$547$	2.93772	+	2.54554i	0.125608	+	0.108840i	0.715399	−	0.698716i	$-0.246245\pi$
$547$	2.93772	+	2.54554i	0.125608	+	0.108840i	−0.589792	+	0.807555i	$0.700790\pi$
$548$	19.7070	−	11.1752i	0.841839	−	0.477379i
$549$	0.0367791	+	0.385168i	0.00156969	+	0.0164386i
$550$	52.1852	−	13.7666i	2.22519	−	0.587008i
$551$	−0.752164	+	1.30279i	−0.0320433	+	0.0555006i
$552$	13.8056	−	17.3762i	0.587606	−	0.739580i
$553$	−1.96352	+	8.94737i	−0.0834973	+	0.380481i
$554$	−29.9067	−	8.13776i	−1.27061	−	0.345740i
$555$	34.4270	−	24.5153i	1.46134	−	1.04062i
$556$	−0.0204063	+	2.63405i	−0.000865419	+	0.111708i
$557$	38.1647	+	7.35565i	1.61709	+	0.311669i	0.915932	−	0.401334i	$-0.131453\pi$
$557$	38.1647	+	7.35565i	1.61709	+	0.311669i	0.701161	+	0.713003i	$0.252666\pi$
$558$	0.916736	+	2.48725i	0.0388085	+	0.105294i
$559$	1.99714	−	1.28349i	0.0844701	−	0.0542857i
$560$	33.9339	+	13.3307i	1.43397	+	0.563325i
$561$	−28.6083	−	33.0158i	−1.20785	−	1.39393i
$562$	−0.246035	−	3.63800i	−0.0103784	−	0.153460i
$563$	5.83181	−	2.33470i	0.245781	−	0.0983960i	−0.245501	−	0.969396i	$-0.578953\pi$
$563$	5.83181	−	2.33470i	0.245781	−	0.0983960i	0.491282	+	0.871000i	$0.336528\pi$
$564$	−0.407175	−	0.189777i	−0.0171452	−	0.00799104i
$565$	8.79923	+	17.0681i	0.370186	+	0.718061i
$566$	−13.3264	+	4.20317i	−0.560151	+	0.176672i
$567$	19.9624	+	6.42153i	0.838343	+	0.269679i
$568$	14.6093	+	11.2037i	0.612995	+	0.470095i
$569$	−5.77414	+	5.50563i	−0.242064	+	0.230808i	−0.801393	−	0.598138i	$-0.795907\pi$
$569$	−5.77414	+	5.50563i	−0.242064	+	0.230808i	0.559329	+	0.828946i	$0.311059\pi$
$570$	39.2936	+	26.8172i	1.64583	+	1.12325i
$571$	5.85852	−	6.14423i	0.245171	−	0.257128i	−0.589638	−	0.807668i	$-0.700730\pi$
$571$	5.85852	−	6.14423i	0.245171	−	0.257128i	0.834809	+	0.550540i	$0.185578\pi$
$572$	8.76992	−	43.6790i	0.366689	−	1.82631i
$573$	−1.41547	+	0.203514i	−0.0591323	+	0.00850194i
$574$	−14.6948	−	10.5909i	−0.613351	−	0.442057i
$575$	21.1393	+	25.2595i	0.881569	+	1.05339i
$576$	−0.430226	−	2.54974i	−0.0179261	−	0.106239i
$577$	−16.9607	−	21.5673i	−0.706083	−	0.897857i	0.292205	−	0.956356i	$-0.405611\pi$
$577$	−16.9607	−	21.5673i	−0.706083	−	0.897857i	−0.998287	+	0.0584987i	$0.981369\pi$
$578$	2.65495	−	8.19580i	0.110431	−	0.340900i
$579$	8.35525	−	34.4408i	0.347232	−	1.43131i
$580$	−0.0691928	−	1.73529i	−0.00287308	−	0.0720538i
$581$	0.239789	+	10.9116i	0.00994814	+	0.452690i
$582$	−16.5838	+	2.72269i	−0.687419	+	0.112859i
$583$	2.87309	−	30.0884i	0.118991	−	1.24613i
$584$	−44.9022	+	0.546913i	−1.85807	+	0.0226314i
$585$	−0.212398	+	4.45878i	−0.00878157	+	0.184348i
$586$	−0.338844	−	0.626302i	−0.0139975	−	0.0258723i
$587$	1.05018	−	7.30416i	0.0433456	−	0.301475i	−0.956604	−	0.291392i	$-0.905881\pi$
$587$	1.05018	−	7.30416i	0.0433456	−	0.301475i	0.999949	−	0.0100826i	$-0.00320944\pi$
$588$	22.0495	−	6.20213i	0.909307	−	0.255771i
$589$	22.6650	+	26.1568i	0.933896	+	1.07777i
$590$	−19.5186	−	10.7563i	−0.803569	−	0.442831i
$591$	−36.3411	−	18.7352i	−1.49487	−	0.770661i
$592$	−29.5362	+	5.21938i	−1.21393	+	0.214515i
$593$	−17.9628	+	6.21697i	−0.737642	+	0.255300i	−0.669950	−	0.742406i	$-0.733685\pi$
$593$	−17.9628	+	6.21697i	−0.737642	+	0.255300i	−0.0676915	+	0.997706i	$0.521563\pi$
$594$	−42.4036	−	5.23665i	−1.73984	−	0.214862i
$595$	43.4800	+	5.27930i	1.78251	+	0.216430i
$596$	6.77187	−	8.47518i	0.277387	−	0.347157i
$597$	7.02992	−	12.1762i	0.287715	−	0.498338i
$598$	26.4049	−	6.48296i	1.07978	−	0.265108i
$599$	28.5282	−	16.4708i	1.16563	−	0.672978i	0.212985	−	0.977055i	$-0.431681\pi$
$599$	28.5282	−	16.4708i	1.16563	−	0.672978i	0.952647	+	0.304077i	$0.0983481\pi$
$600$	−31.7623	−	1.12550i	−1.29669	−	0.0459485i
$601$	−2.61443	−	1.19397i	−0.106645	−	0.0487031i	0.361378	−	0.932419i	$-0.382306\pi$
$601$	−2.61443	−	1.19397i	−0.106645	−	0.0487031i	−0.468023	+	0.883716i	$0.655034\pi$
$602$	−2.08976	−	0.736643i	−0.0851724	−	0.0300233i
$603$	1.47879	+	1.28138i	0.0602209	+	0.0521817i
$604$	−1.64141	+	29.6265i	−0.0667879	+	1.20548i
$605$	−31.3757	+	60.8604i	−1.27560	+	2.47433i
$606$	−34.6759	+	20.9523i	−1.40861	+	0.851128i
$607$	−6.87167	+	1.32441i	−0.278912	+	0.0537560i	−0.326789	−	0.945097i	$-0.605967\pi$
$607$	−6.87167	+	1.32441i	−0.278912	+	0.0537560i	0.0478766	+	0.998853i	$0.484755\pi$
$608$	−17.0101	−	29.1631i	−0.689853	−	1.18272i
$609$	−0.693133	−	0.842612i	−0.0280872	−	0.0341444i
$610$	−4.96811	−	3.05468i	−0.201153	−	0.123680i
$611$	−0.252190	−	0.489181i	−0.0102025	−	0.0197901i
$612$	−1.26853	−	2.83562i	−0.0512772	−	0.114623i
$613$	−21.8810	+	30.7276i	−0.883767	+	1.24108i	0.0858155	+	0.996311i	$0.472650\pi$
$613$	−21.8810	+	30.7276i	−0.883767	+	1.24108i	−0.969582	+	0.244766i	$0.921289\pi$
$614$	−2.20944	−	0.833843i	−0.0891659	−	0.0336511i
$615$	26.1807	+	7.68734i	1.05571	+	0.309983i
$616$	−37.2122	+	18.5551i	−1.49932	+	0.747607i
$617$	−31.7199	+	9.31380i	−1.27700	+	0.374960i	−0.848794	−	0.528724i	$-0.822671\pi$
$617$	−31.7199	+	9.31380i	−1.27700	+	0.374960i	−0.428201	+	0.903683i	$0.640853\pi$
$618$	40.7573	−	8.70100i	1.63950	−	0.350005i
$619$	−2.10190	+	1.65295i	−0.0844823	+	0.0664376i	−0.659507	−	0.751698i	$-0.729235\pi$
$619$	−2.10190	+	1.65295i	−0.0844823	+	0.0664376i	0.575025	+	0.818136i	$0.304992\pi$
$620$	−38.2490	−	11.5535i	−1.53612	−	0.464001i
$621$	−8.10414	−	24.7840i	−0.325208	−	0.994546i
$622$	0.169916	−	0.392583i	0.00681302	−	0.0157411i
$623$	0.928914	+	0.0681441i	0.0372162	+	0.00273014i
$624$	−12.3814	+	23.1296i	−0.495655	+	0.925925i
$625$	−2.86924	+	11.8272i	−0.114770	+	0.473087i
$626$	10.3410	+	7.05753i	0.413308	+	0.282076i
$627$	−52.7282	+	12.7917i	−2.10576	+	0.510852i
$628$	7.84518	+	7.59727i	0.313057	+	0.303164i
$629$	−32.7768	+	14.9686i	−1.30690	+	0.596839i
$630$	3.40753	−	2.39733i	0.135759	−	0.0955120i
$631$	22.2483	−	34.6190i	0.885689	−	1.37816i	−0.0397284	−	0.999211i	$-0.512649\pi$
$631$	22.2483	−	34.6190i	0.885689	−	1.37816i	0.925418	−	0.378949i	$-0.123714\pi$
$632$	−3.08995	+	9.29249i	−0.122912	+	0.369635i
$633$	−0.224549	−	0.560897i	−0.00892503	−	0.0222936i
$634$	−23.0883	−	11.3264i	−0.916954	−	0.449827i
$635$	−56.0848	+	10.8095i	−2.22566	+	0.428960i
$636$	−6.74305	+	16.4723i	−0.267379	+	0.653170i
$637$	26.0133	+	10.5247i	1.03068	+	0.417002i
$638$	1.52247	+	1.26700i	0.0602750	+	0.0501612i
$639$	1.98820	−	0.688124i	0.0786521	−	0.0272217i
$640$	34.5836	+	17.9744i	1.36704	+	0.710502i
$641$	−12.8714	+	1.22907i	−0.508390	+	0.0485454i	−0.346100	−	0.938198i	$-0.612494\pi$
$641$	−12.8714	+	1.22907i	−0.508390	+	0.0485454i	−0.162290	+	0.986743i	$0.551888\pi$
$642$	−14.0083	−	14.1172i	−0.552863	−	0.557162i
$643$	−6.09757			−0.240465			−0.120232	−	0.992746i	$-0.538364\pi$
$643$	−6.09757			−0.240465			−0.120232	+	0.992746i	$0.538364\pi$
$644$	−19.9016	−	15.7457i	−0.784231	−	0.620469i
$645$	3.33781			0.131426
$646$	−28.5684	−	28.7906i	−1.12401	−	1.13275i
$647$	−4.51794	+	0.431411i	−0.177619	+	0.0169605i	−0.183486	−	0.983022i	$-0.558738\pi$
$647$	−4.51794	+	0.431411i	−0.177619	+	0.0169605i	0.00586768	+	0.999983i	$0.498132\pi$
$648$	20.5038	+	9.06361i	0.805464	+	0.356052i
$649$	24.0200	−	8.31340i	0.942868	−	0.326330i
$650$	−29.9289	−	24.9070i	−1.17391	−	0.976933i
$651$	−23.5358	+	8.72941i	−0.922439	+	0.342133i
$652$	−17.9878	−	7.36343i	−0.704457	−	0.288374i
$653$	41.3696	−	7.97334i	1.61892	−	0.312021i	0.702330	−	0.711852i	$-0.252143\pi$
$653$	41.3696	−	7.97334i	1.61892	−	0.312021i	0.916589	+	0.399831i	$0.130931\pi$
$654$	11.1231	+	5.45663i	0.434949	+	0.213371i
$655$	21.5610	+	53.8569i	0.842460	+	2.10436i
$656$	−14.4364	−	12.9062i	−0.563646	−	0.503902i
$657$	−2.77438	+	4.31703i	−0.108239	+	0.168423i
$658$	−0.216053	+	0.466039i	−0.00842261	+	0.0181681i
$659$	2.82797	−	1.29149i	0.110162	−	0.0503093i	−0.359572	−	0.933117i	$-0.617077\pi$
$659$	2.82797	−	1.29149i	0.110162	−	0.0503093i	0.469734	+	0.882808i	$0.344350\pi$
$660$	43.5747	−	44.9967i	1.69614	−	1.75149i
$661$	4.05837	−	0.984551i	0.157852	−	0.0382946i	−0.156054	−	0.987749i	$-0.549877\pi$
$661$	4.05837	−	0.984551i	0.157852	−	0.0382946i	0.313906	+	0.949454i	$0.398362\pi$
$662$	−27.6318	−	18.8582i	−1.07394	−	0.732945i
$663$	−7.43052	+	30.6290i	−0.288578	+	1.18953i
$664$	−0.967553	+	11.6276i	−0.0375484	+	0.451240i
$665$	30.5729	−	44.9940i	1.18557	−	1.74479i
$666$	−1.36147	+	3.14560i	−0.0527557	+	0.121889i
$667$	−0.305113	+	1.16968i	−0.0118140	+	0.0452901i
$668$	6.89087	−	22.8128i	0.266616	−	0.882656i
$669$	10.6409	−	8.36811i	0.411402	−	0.323530i
$670$	−28.8438	+	6.15767i	−1.11433	+	0.237891i
$671$	6.38219	−	1.87398i	0.246382	−	0.0723442i
$672$	24.1370	−	4.12351i	0.931105	−	0.159068i
$673$	46.2215	+	13.5719i	1.78171	+	0.523157i	0.995496	−	0.0948000i	$-0.0302212\pi$
$673$	46.2215	+	13.5719i	1.78171	+	0.523157i	0.786212	+	0.617957i	$0.212039\pi$
$674$	−31.5835	−	11.9196i	−1.21655	−	0.459126i
$675$	−21.6605	+	30.4179i	−0.833714	+	1.17079i
$676$	−5.60584	+	2.50780i	−0.215609	+	0.0964539i
$677$	−20.2185	−	39.2183i	−0.777059	−	1.50728i	−0.859754	−	0.510708i	$-0.829383\pi$
$677$	−20.2185	−	39.2183i	−0.777059	−	1.50728i	0.0826955	−	0.996575i	$-0.473647\pi$
$678$	10.9866	+	6.75519i	0.421938	+	0.259432i
$679$	3.15212	+	18.9568i	0.120967	+	0.727494i
$680$	45.6346	+	10.4840i	1.75001	+	0.402044i
$681$	−0.433448	+	0.0835402i	−0.0166098	+	0.00320127i
$682$	39.0035	−	23.5672i	1.49352	−	0.902433i
$683$	8.32381	−	16.1459i	0.318502	−	0.617808i	−0.674180	−	0.738567i	$-0.735503\pi$
$683$	8.32381	−	16.1459i	0.318502	−	0.617808i	0.992682	+	0.120760i	$0.0385330\pi$
$684$	−3.85223	−	0.213427i	−0.147294	−	0.00816059i
$685$	29.4918	+	25.5548i	1.12682	+	0.976398i
$686$	−7.14356	−	25.1986i	−0.272742	−	0.962087i
$687$	19.1198	+	8.73171i	0.729465	+	0.333136i
$688$	−2.13922	−	1.01730i	−0.0815570	−	0.0387840i
$689$	−18.8846	+	10.9030i	−0.719446	+	0.415372i
$690$	36.1593	+	12.4032i	1.37656	+	0.472183i
$691$	11.7704	−	20.3870i	0.447769	−	0.775559i	−0.550472	−	0.834854i	$-0.685552\pi$
$691$	11.7704	−	20.3870i	0.447769	−	0.775559i	0.998240	+	0.0592954i	$0.0188854\pi$
$692$	23.6025	+	18.8590i	0.897233	+	0.716910i
$693$	−0.572755	+	4.71718i	−0.0217572	+	0.179191i
$694$	−0.891564	−	0.110104i	−0.0338433	−	0.00417949i
$695$	−4.28773	+	1.48400i	−0.162643	+	0.0562913i
$696$	−0.642508	−	0.973485i	−0.0243542	−	0.0368999i
$697$	−20.6773	−	10.6599i	−0.783208	−	0.403772i
$698$	−29.9848	−	16.5240i	−1.13494	−	0.625443i
$699$	13.3142	+	15.3654i	0.503589	+	0.581173i
$700$	−1.21269	+	36.3220i	−0.0458353	+	1.37284i
$701$	−3.89715	+	27.1053i	−0.147193	+	1.02375i	0.773592	+	0.633684i	$0.218458\pi$
$701$	−3.89715	+	27.1053i	−0.147193	+	1.02375i	−0.920786	+	0.390069i	$0.872451\pi$
$702$	14.6677	+	27.1111i	0.553598	+	1.02324i
$703$	−2.12941	+	44.7018i	−0.0803122	+	1.68596i
$704$	−41.6413	+	15.5579i	−1.56942	+	0.586362i
$705$	0.0735542	−	0.770294i	0.00277021	−	0.0290110i
$706$	21.2364	−	3.48655i	0.799243	−	0.131218i
$707$	24.0395	+	39.6020i	0.904100	+	1.48939i
$708$	−14.9563	+	0.596366i	−0.562091	+	0.0224128i
$709$	−7.54327	+	31.0938i	−0.283294	+	1.16775i	0.635210	+	0.772339i	$0.280914\pi$
$709$	−7.54327	+	31.0938i	−0.283294	+	1.16775i	−0.918504	+	0.395413i	$0.870602\pi$
$710$	−9.77296	+	30.1691i	−0.366773	+	1.13222i
$711$	0.691772	+	0.879659i	0.0259435	+	0.0329898i
$712$	0.979948	+	0.176519i	0.0367251	+	0.00661534i
$713$	23.1350	+	15.4355i	0.866413	+	0.578063i
$714$	26.8279	−	12.0675i	1.00401	−	0.451616i
$715$	75.9576	−	10.9211i	2.84065	−	0.408424i
$716$	15.9039	+	3.19321i	0.594358	+	0.119336i
$717$	−7.92748	+	8.31410i	−0.296057	+	0.310496i
$718$	−41.3284	−	28.2059i	−1.54236	−	1.05263i
$719$	−5.50438	+	5.24841i	−0.205279	+	0.195733i	−0.785743	−	0.618553i	$-0.787719\pi$
$719$	−5.50438	+	5.24841i	−0.205279	+	0.195733i	0.580465	+	0.814285i	$0.302871\pi$
$720$	3.89133	−	2.16698i	0.145021	−	0.0807585i
$721$	−10.0447	−	46.5846i	−0.374085	−	1.73490i
$722$	−22.4155	+	7.06987i	−0.834218	+	0.263113i
$723$	8.38101	+	16.2569i	0.311693	+	0.604600i
$724$	8.03515	−	17.2398i	0.298624	−	0.640713i
$725$	1.60712	−	0.643395i	0.0596871	−	0.0238951i
$726$	3.10304	+	45.8832i	0.115165	+	1.70289i
$727$	−1.25672	−	1.45034i	−0.0466093	−	0.0537900i	0.731966	−	0.681341i	$-0.238603\pi$
$727$	−1.25672	−	1.45034i	−0.0466093	−	0.0537900i	−0.778576	+	0.627551i	$0.784057\pi$
$728$	26.4771	+	14.1038i	0.981307	+	0.522721i
$729$	24.6053	−	15.8129i	0.911308	−	0.585662i
$730$	−26.7501	−	72.5771i	−0.990065	−	2.68620i
$731$	−2.79431	−	0.538559i	−0.103351	−	0.0199193i
$732$	−3.91690	−	0.0303447i	−0.144773	−	0.00112157i
$733$	1.98278	−	1.41193i	0.0732358	−	0.0521510i	−0.542853	−	0.839828i	$-0.682656\pi$
$733$	1.98278	−	1.41193i	0.0732358	−	0.0521510i	0.616088	+	0.787677i	$0.288716\pi$
$734$	0.279993	+	0.0761876i	0.0103347	+	0.00281214i
$735$	22.7681	+	32.2219i	0.839812	+	1.18852i
$736$	−19.3944	−	18.9699i	−0.714888	−	0.699239i
$737$	16.8192	−	29.1316i	0.619542	−	1.07308i
$738$	−2.13969	+	0.564455i	−0.0787632	+	0.0207779i
$739$	−0.0376149	−	0.393922i	−0.00138369	−	0.0144906i	0.994754	−	0.102299i	$-0.0326198\pi$
$739$	−0.0376149	−	0.393922i	−0.00138369	−	0.0144906i	−0.996137	+	0.0878082i	$0.972014\pi$
$740$	−25.4848	−	44.9414i	−0.936839	−	1.65208i
$741$	29.5833	+	25.6340i	1.08677	+	0.941690i
$742$	18.8515	+	7.67199i	0.692060	+	0.281648i
$743$	9.70825	+	15.1063i	0.356161	+	0.554197i	0.972388	−	0.233371i	$-0.0749758\pi$
$743$	9.70825	+	15.1063i	0.356161	+	0.554197i	−0.616227	+	0.787569i	$0.711339\pi$
$744$	−26.0002	+	6.64390i	−0.953215	+	0.243577i
$745$	17.6586	+	6.11170i	0.646961	+	0.223915i
$746$	30.4240	+	14.9250i	1.11390	+	0.546442i
$747$	1.04809	+	0.824228i	0.0383476	+	0.0301569i
$748$	−43.7397	+	30.6390i	−1.59928	+	1.12027i
$749$	−16.1099	+	16.0511i	−0.588644	+	0.586496i
$750$	−4.47885	−	14.2005i	−0.163544	−	0.518528i
$751$	0.00657300	−	0.0688356i	0.000239852	−	0.00251185i	−0.995351	−	0.0963119i	$-0.969295\pi$
$751$	0.00657300	−	0.0688356i	0.000239852	−	0.00251185i	0.995591	+	0.0938000i	$0.0299014\pi$
$752$	−0.281911	+	0.471268i	−0.0102802	+	0.0171854i
$753$	0.146152	+	0.602449i	0.00532609	+	0.0219544i
$754$	0.107463	−	1.42494i	0.00391357	−	0.0518932i
$755$	−49.0395	+	14.3993i	−1.78473	+	0.524045i
$756$	11.5781	−	26.3378i	0.421093	−	0.957895i
$757$	6.38478	+	44.4071i	0.232059	+	1.61401i	0.689173	+	0.724597i	$0.257974\pi$
$757$	6.38478	+	44.4071i	0.232059	+	1.61401i	−0.457114	+	0.889408i	$0.651117\pi$
$758$	−32.7894	+	24.3482i	−1.19096	+	0.884366i
$759$	−38.1267	+	21.1482i	−1.38391	+	0.767632i
$760$	37.5447	−	44.4105i	1.36189	−	1.61094i
$761$	−15.0927	+	37.6997i	−0.547109	+	1.36661i	0.354904	+	0.934903i	$0.384514\pi$
$761$	−15.0927	+	37.6997i	−0.547109	+	1.36661i	−0.902013	+	0.431709i	$0.857911\pi$
$762$	−28.4855	+	25.6942i	−1.03192	+	0.930803i
$763$	6.21351	−	12.7318i	0.224944	−	0.460922i
$764$	0.0696489	+	1.74672i	0.00251981	+	0.0631942i
$765$	3.87257	−	3.69249i	0.140013	−	0.133502i
$766$	26.9063	−	22.0410i	0.972164	−	0.796373i
$767$	−14.9376	−	10.6370i	−0.539364	−	0.384079i
$768$	26.1234	−	1.67974i	0.942648	−	0.0606125i
$769$	−11.5957	+	18.0432i	−0.418150	+	0.650655i	−0.984878	−	0.173251i	$-0.944573\pi$
$769$	−11.5957	+	18.0432i	−0.418150	+	0.650655i	0.566727	+	0.823905i	$0.308209\pi$
$770$	−51.5545	−	49.7214i	−1.85790	−	1.79183i
$771$	−6.91419	−	0.994111i	−0.249009	−	0.0358020i
$772$	−40.8290	−	14.4862i	−1.46947	−	0.521369i
$773$	−0.0774400	−	0.0268022i	−0.00278532	−	0.000964009i	0.325675	−	0.945482i	$-0.394408\pi$
$773$	−0.0774400	−	0.0268022i	−0.00278532	−	0.000964009i	−0.328460	+	0.944518i	$0.606530\pi$
$774$	−0.231687	+	0.139993i	−0.00832782	+	0.00503193i
$775$	−1.89512	−	39.7834i	−0.0680746	−	1.42906i
$776$	1.22737	+	20.5072i	0.0440600	+	0.736165i
$777$	−29.8143	−	12.8318i	−1.06958	−	0.460337i
$778$	1.40835	−	11.4041i	0.0504919	−	0.408856i
$779$	−23.5354	+	16.7594i	−0.843242	+	0.600470i
$780$	−44.6788	−	6.77752i	−1.59976	−	0.242674i
$781$	−18.0844	−	31.3232i	−0.647112	−	1.12083i
$782$	−28.2701	−	16.2179i	−1.01094	−	0.579952i
$783$	−1.37045			−0.0489758
$784$	−4.77159	−	27.5904i	−0.170414	−	0.985373i
$785$	−7.81446	+	17.1113i	−0.278910	+	0.610728i
$786$	31.1008	+	23.4703i	1.10933	+	0.837159i
$787$	−18.9835	−	3.65876i	−0.676687	−	0.130421i	−0.160682	−	0.987006i	$-0.551369\pi$
$787$	−18.9835	−	3.65876i	−0.676687	−	0.130421i	−0.516005	+	0.856586i	$0.672581\pi$
$788$	−27.3464	+	41.8357i	−0.974177	+	1.49034i
$789$	−33.8556	+	1.61274i	−1.20529	+	0.0574151i
$790$	−16.8647	+	0.336098i	−0.600019	+	0.0119578i
$791$	7.69870	−	12.5787i	0.273734	−	0.447248i
$792$	−1.13742	+	4.95094i	−0.0404165	+	0.175924i
$793$	−3.77213	−	2.96644i	−0.133952	−	0.105341i
$794$	49.9714	+	1.38323i	1.77342	+	0.0490891i
$795$	−30.6242	−	1.45881i	−1.08613	−	0.0517386i
$796$	−13.9226	−	10.0777i	−0.493473	−	0.357194i
$797$	−3.95200	+	1.80482i	−0.139987	+	0.0639300i	−0.484177	−	0.874970i	$-0.660881\pi$
$797$	−3.95200	+	1.80482i	−0.139987	+	0.0639300i	0.344190	+	0.938900i	$0.388154\pi$
$798$	1.94647	−	36.4837i	0.0689043	−	1.29151i
$799$	−0.185865	+	0.632998i	−0.00657543	+	0.0223939i
$800$	−5.35863	+	38.4802i	−0.189456	+	1.36048i
$801$	0.0785223	−	0.0823519i	0.00277445	−	0.00290976i
$802$	10.6876	−	32.9926i	0.377393	−	1.16501i
$803$	81.9001	+	32.7878i	2.89019	+	1.15706i
$804$	−14.4419	+	13.5583i	−0.509326	+	0.478163i
$805$	14.0982	−	41.3763i	0.496897	−	1.45832i
$806$	−30.1722	−	13.0590i	−1.06277	−	0.459984i
$807$	−1.26685	+	3.16445i	−0.0445954	+	0.111394i
$808$	21.1210	+	44.7965i	0.743034	+	1.57594i
$809$	24.7402	+	23.5898i	0.869821	+	0.829372i	0.986494	−	0.163798i	$-0.0523745\pi$
$809$	24.7402	+	23.5898i	0.869821	+	0.829372i	−0.116673	+	0.993170i	$0.537223\pi$
$810$	−2.90390	+	38.5052i	−0.102033	+	1.35293i
$811$	−29.4003	−	8.63270i	−1.03238	−	0.303135i	−0.278704	−	0.960377i	$-0.589905\pi$
$811$	−29.4003	−	8.63270i	−1.03238	−	0.303135i	−0.753680	+	0.657242i	$0.771723\pi$
$812$	−1.11165	+	0.736969i	−0.0390114	+	0.0258625i
$813$	−15.1315	−	33.1335i	−0.530686	−	1.16204i
$814$	57.5289	+	12.7482i	2.01639	+	0.446825i
$815$	1.59302	−	33.4416i	0.0558011	−	1.17141i
$816$	29.8743	−	9.82400i	1.04581	−	0.343909i
$817$	−2.18480	+	2.77820i	−0.0764366	+	0.0971970i
$818$	30.4900	+	45.4271i	1.06606	+	1.58832i
$819$	3.01187	−	1.63746i	0.105243	−	0.0572176i
$820$	12.6364	−	30.8689i	0.441281	−	1.07799i
$821$	−0.999994	−	20.9924i	−0.0349000	−	0.732642i	−0.946721	−	0.322054i	$-0.895627\pi$
$821$	−0.999994	−	20.9924i	−0.0349000	−	0.732642i	0.911821	−	0.410587i	$-0.134676\pi$
$822$	25.8294	+	4.44637i	0.900902	+	0.155085i
$823$	−5.44607	+	28.2569i	−0.189838	+	0.984973i	0.754575	+	0.656213i	$0.227843\pi$
$823$	−5.44607	+	28.2569i	−0.189838	+	0.984973i	−0.944413	+	0.328760i	$0.893369\pi$
$824$	−5.45999	−	50.6522i	−0.190208	−	1.76455i
$825$	56.7954	+	25.9376i	1.97736	+	0.903031i
$826$	0.716915	+	17.1007i	0.0249447	+	0.595011i
$827$		−	31.8983i		−	1.10921i	−0.832113	−	0.554606i	$-0.812869\pi$
$827$		−	31.8983i		−	1.10921i	0.832113	−	0.554606i	$-0.187131\pi$
$828$	−3.03013	+	0.655629i	−0.105304	+	0.0227847i
$829$	9.93953	−	5.73859i	0.345214	−	0.199310i	−0.317361	−	0.948305i	$-0.602797\pi$
$829$	9.93953	−	5.73859i	0.345214	−	0.199310i	0.662575	+	0.748995i	$0.269463\pi$
$830$	−19.4330	+	5.12647i	−0.674530	+	0.177942i
$831$	−20.7989	−	29.2080i	−0.721506	−	1.01321i
$832$	26.5692	+	17.9609i	0.921122	+	0.622683i
$833$	−13.8617	−	30.6488i	−0.480279	−	1.06192i
$834$	−1.94933	+	2.34237i	−0.0674997	+	0.0811095i
$835$	41.0022	−	1.95317i	1.41894	−	0.0675924i
$836$	8.93032	+	65.7222i	0.308862	+	2.27305i
$837$	−10.3125	+	29.7961i	−0.356453	+	1.02990i
$838$	1.67203	+	24.7235i	0.0577594	+	0.854060i
$839$	0.703039	−	4.88974i	0.0242716	−	0.168813i	−0.974080	−	0.226203i	$-0.927369\pi$
$839$	0.703039	−	4.88974i	0.0242716	−	0.168813i	0.998352	+	0.0573901i	$0.0182779\pi$
$840$	20.5960	+	36.8078i	0.710631	+	1.26999i
$841$	−24.3429	−	15.6442i	−0.839411	−	0.539456i
$842$	9.28281	−	41.8905i	0.319907	−	1.44364i
$843$	2.44690	−	3.43618i	0.0842756	−	0.118348i
$844$	−0.710235	+	0.202581i	−0.0244473	+	0.00697312i
$845$	−7.29983	−	7.65584i	−0.251122	−	0.263369i
$846$	0.0272017	+	0.0565533i	0.000935213	+	0.00194434i
$847$	52.4591	−	3.65558i	1.80252	−	0.125607i
$848$	19.1826	+	10.2686i	0.658732	+	0.352624i
$849$	−15.0078	−	6.00823i	−0.515068	−	0.206202i
$850$	5.36156	+	46.3652i	0.183900	+	1.59031i
$851$	7.87703	+	35.0880i	0.270021	+	1.20280i
$852$	4.86096	+	20.7370i	0.166534	+	0.710439i
$853$	25.6330	−	3.68547i	0.877658	−	0.126188i	0.311265	−	0.950323i	$-0.399247\pi$
$853$	25.6330	−	3.68547i	0.877658	−	0.126188i	0.566393	+	0.824135i	$0.308338\pi$
$854$	−0.0255363	+	4.47895i	−0.000873834	+	0.153266i
$855$	−1.87230	−	6.37646i	−0.0640312	−	0.218070i
$856$	−18.9257	+	15.2600i	−0.646867	+	0.521577i
$857$	15.1149	−	3.66683i	0.516314	−	0.125256i	0.0308685	−	0.999523i	$-0.490173\pi$
$857$	15.1149	−	3.66683i	0.516314	−	0.125256i	0.485445	+	0.874267i	$0.338658\pi$
$858$	39.8705	−	32.6609i	1.36116	−	1.11503i
$859$	39.4779	+	3.76968i	1.34697	+	0.128620i	0.743483	−	0.668754i	$-0.233172\pi$
$859$	39.4779	+	3.76968i	1.34697	+	0.128620i	0.603485	+	0.797374i	$0.293778\pi$
$860$	0.419306	−	4.05864i	0.0142982	−	0.138398i
$861$	−5.38668	−	20.2514i	−0.183578	−	0.690164i
$862$	1.47632	−	2.40108i	0.0502837	−	0.0817811i
$863$	−3.89493	+	4.95281i	−0.132585	+	0.168596i	−0.847812	−	0.530296i	$-0.822081\pi$
$863$	−3.89493	+	4.95281i	−0.132585	+	0.168596i	0.715227	+	0.698892i	$0.246323\pi$
$864$	15.2602	−	26.7040i	0.519161	−	0.908490i
$865$	−17.0204	+	49.1773i	−0.578712	+	1.67208i
$866$	−24.9757	−	13.7636i	−0.848708	−	0.467706i
$867$	8.38452	−	5.38840i	0.284753	−	0.183000i
$868$	7.65796	+	29.7151i	0.259928	+	1.00860i
$869$	12.5985	−	14.5394i	0.427374	−	0.493216i
$870$	1.21025	−	1.60371i	0.0410312	−	0.0543709i
$871$	−24.1585	+	2.30686i	−0.818581	+	0.0781650i
$872$	8.03235	−	12.8398i	0.272010	−	0.434809i
$873$	2.03316	+	1.17384i	0.0688119	+	0.0397286i
$874$	−33.9922	+	21.9782i	−1.14980	+	0.743425i
$875$	−16.2274	+	5.15467i	−0.548587	+	0.174260i
$876$	−40.5860	−	32.4292i	−1.37127	−	1.09568i
$877$	−30.9390	−	43.4477i	−1.04473	−	1.46712i	−0.876515	−	0.481375i	$-0.840138\pi$
$877$	−30.9390	−	43.4477i	−1.04473	−	1.46712i	−0.168220	−	0.985749i	$-0.553802\pi$
$878$	9.18055	−	3.88933i	0.309828	−	0.131258i
$879$	0.155906	−	0.808918i	0.00525859	−	0.0272841i
$880$	−49.2401	−	58.6376i	−1.65988	−	1.97667i
$881$	−14.5597	−	22.6553i	−0.490528	−	0.763276i	0.504443	−	0.863445i	$-0.331698\pi$
$881$	−14.5597	−	22.6553i	−0.490528	−	0.763276i	−0.994970	+	0.100169i	$0.968062\pi$
$882$	−2.93183	−	1.28169i	−0.0987199	−	0.0431568i
$883$	−31.5248	+	27.3164i	−1.06090	+	0.919271i	−0.996900	−	0.0786792i	$-0.974930\pi$
$883$	−31.5248	+	27.3164i	−1.06090	+	0.919271i	−0.0639953	+	0.997950i	$0.520384\pi$
$884$	36.3102	+	12.8829i	1.22124	+	0.433299i
$885$	−9.58244	−	23.9358i	−0.322110	−	0.804593i
$886$	31.2249	+	0.864320i	1.04902	+	0.0290374i
$887$	−5.94158	+	3.06310i	−0.199499	+	0.102849i	−0.555081	−	0.831796i	$-0.687313\pi$
$887$	−5.94158	+	3.06310i	−0.199499	+	0.102849i	0.355582	+	0.934645i	$0.384283\pi$
$888$	−30.2597	−	16.9824i	−1.01545	−	0.569894i
$889$	29.4473	+	32.5124i	0.987632	+	1.09043i
$890$	0.277866	+	1.69247i	0.00931409	+	0.0567317i
$891$	−30.3916	−	31.8738i	−1.01816	−	1.06781i
$892$	−8.83852	−	13.9901i	−0.295936	−	0.468424i
$893$	0.593003	+	0.565427i	0.0198441	+	0.0189213i
$894$	12.2738	−	2.62024i	0.410496	−	0.0876341i
$895$	3.97646	+	27.6569i	0.132918	+	0.924467i
$896$	−1.98185	−	29.8676i	−0.0662090	−	0.997806i
$897$	28.3837	+	13.5560i	0.947705	+	0.452622i
$898$	−25.5857	−	34.4558i	−0.853804	−	1.14981i
$899$	1.14897	−	0.903562i	0.0383204	−	0.0301355i
$900$	3.33277	+	2.93337i	0.111092	+	0.0977790i
$901$	25.4022	+	6.16251i	0.846271	+	0.205303i
$902$	16.4897	+	34.2828i	0.549048	+	1.14149i
$903$	−1.33018	−	2.19130i	−0.0442656	−	0.0729218i
$904$	9.59420	−	12.5106i	0.319098	−	0.416098i
$905$	32.6143	+	3.11429i	1.08414	+	0.103522i
$906$	−23.1887	+	25.3107i	−0.770391	+	0.840892i
$907$	52.6494	+	2.50800i	1.74819	+	0.0832767i	0.897125	−	0.441777i	$-0.145652\pi$
$907$	52.6494	+	2.50800i	1.74819	+	0.0832767i	0.851069	+	0.525054i	$0.175955\pi$
$908$	0.0471304	+	0.537549i	0.00156408	+	0.0178392i
$909$	5.60206	+	0.805454i	0.185808	+	0.0267152i
$910$	−7.64543	+	51.1050i	−0.253443	+	1.69411i
$911$	15.3242	−	13.2785i	0.507715	−	0.439938i	−0.362954	−	0.931807i	$-0.618232\pi$
$911$	15.3242	−	13.2785i	0.507715	−	0.439938i	0.870669	+	0.491870i	$0.163686\pi$
$912$	6.15687	−	38.5699i	0.203874	−	1.27718i
$913$	10.5035	−	20.3739i	0.347615	−	0.674279i
$914$	−7.30476	−	1.25747i	−0.241620	−	0.0415934i
$915$	−2.20675	−	6.37598i	−0.0729528	−	0.210783i
$916$	13.0193	−	22.1519i	0.430169	−	0.731921i
$917$	26.7650	−	35.6180i	0.883858	−	1.17621i
$918$	9.70143	−	35.6532i	0.320195	−	1.17673i
$919$	−50.9385	−	29.4094i	−1.68031	−	0.970126i	−0.961455	−	0.274963i	$-0.911334\pi$
$919$	−50.9385	−	29.4094i	−1.68031	−	0.970126i	−0.718853	−	0.695162i	$-0.755332\pi$
$920$	19.6242	−	42.4100i	0.646992	−	1.39822i
$921$	−1.36603	−	2.36603i	−0.0450121	−	0.0779632i
$922$	23.6239	+	23.8077i	0.778013	+	0.784064i
$923$	−10.8399	+	23.7360i	−0.356799	+	0.781281i
$924$	−46.9060	−	10.6751i	−1.54309	−	0.351186i
$925$	33.7251	−	38.9208i	1.10887	−	1.27971i
$926$	−3.57412	+	1.31733i	−0.117453	+	0.0432902i
$927$	−5.17470	−	2.66774i	−0.169960	−	0.0876202i
$928$	−1.26443	+	0.658970i	−0.0415070	+	0.0216317i
$929$	8.68097	+	45.0412i	0.284814	+	1.47775i	0.789126	+	0.614232i	$0.210534\pi$
$929$	8.68097	+	45.0412i	0.284814	+	1.47775i	−0.504312	+	0.863521i	$0.668254\pi$
$930$	−25.7607	−	38.3808i	−0.844726	−	1.25856i
$931$	−41.7228	−	2.14040i	−1.36741	−	0.0701488i
$932$	20.3562	−	14.2592i	0.666791	−	0.467077i
$933$	0.439875	−	0.226771i	0.0144009	−	0.00742416i
$934$	18.7568	+	17.1842i	0.613741	+	0.562284i
$935$	−74.9305	−	53.3578i	−2.45049	−	1.74499i
$936$	3.38555	−	1.40345i	0.110660	−	0.0458731i
$937$	−8.21190	+	27.9671i	−0.268271	+	0.913647i	0.709629	+	0.704575i	$0.248862\pi$
$937$	−8.21190	+	27.9671i	−0.268271	+	0.913647i	−0.977900	+	0.209072i	$0.932956\pi$
$938$	15.5373	+	16.4822i	0.507312	+	0.538164i
$939$	4.08060	+	13.8973i	0.133165	+	0.453520i
$940$	−0.927405	−	0.186205i	−0.0302486	−	0.00607335i
$941$	19.9805	+	25.4072i	0.651345	+	0.828252i	0.993788	−	0.111286i	$-0.0354970\pi$
$941$	19.9805	+	25.4072i	0.651345	+	0.828252i	−0.342444	+	0.939538i	$0.611255\pi$
$942$	1.45132	+	12.5506i	0.0472865	+	0.408920i
$943$	−14.6630	+	18.0008i	−0.477493	+	0.586186i
$944$	−1.15369	+	18.2611i	−0.0375496	+	0.594348i
$945$	49.4241	+	3.62569i	1.60777	+	0.117944i
$946$	3.11694	+	3.45554i	0.101340	+	0.112349i
$947$	10.4896	+	2.54475i	0.340866	+	0.0826933i	0.402538	−	0.915403i	$-0.368128\pi$
$947$	10.4896	+	2.54475i	0.340866	+	0.0826933i	−0.0616719	+	0.998096i	$0.519643\pi$
$948$	−9.57783	+	6.05097i	−0.311073	+	0.196526i
$949$	−15.0051	−	61.8520i	−0.487087	−	2.00780i
$950$	54.2349	+	20.4682i	1.75961	+	0.664077i
$951$	−12.3592	−	27.0629i	−0.400775	−	0.877575i
$952$	−11.3034	−	34.1376i	−0.366345	−	1.10641i
$953$	−17.1537	−	11.0240i	−0.555662	−	0.357102i	0.232475	−	0.972602i	$-0.425318\pi$
$953$	−17.1537	−	11.0240i	−0.555662	−	0.357102i	−0.788137	+	0.615500i	$0.788954\pi$
$954$	2.18690	−	1.18316i	0.0708034	−	0.0383063i
$955$	−2.79543	+	1.11912i	−0.0904580	+	0.0362139i
$956$	9.11372	+	10.6839i	0.294759	+	0.345543i
$957$	0.433661	+	2.25005i	0.0140183	+	0.0727337i
$958$	53.1594	−	1.05942i	1.71750	−	0.0342283i
$959$	5.02389	−	29.5456i	0.162230	−	0.954079i
$960$	17.7731	+	41.4400i	0.573624	+	1.33747i
$961$	−0.860087	−	2.48506i	−0.0277447	−	0.0801632i
$962$	−16.5830	−	39.1433i	−0.534658	−	1.26203i
$963$	0.264089	+	2.76566i	0.00851013	+	0.0891221i
$964$	20.8205	−	8.14872i	0.670585	−	0.262452i
$965$		−	74.6234i		−	2.40221i
$966$	−6.26732	−	28.6818i	−0.201648	−	0.922820i
$967$			50.4333i			1.62183i	0.585167	+	0.810913i	$0.301029\pi$
$967$			50.4333i			1.62183i	−0.585167	+	0.810913i	$0.698971\pi$
$968$	56.1819	+	1.99082i	1.80575	+	0.0639873i
$969$	−4.46026	−	46.7100i	−0.143284	−	1.50054i
$970$	−32.5834	+	13.8039i	−1.04619	+	0.443218i
$971$	8.01994	+	23.1721i	0.257372	+	0.743628i	0.997467	+	0.0711260i	$0.0226592\pi$
$971$	8.01994	+	23.1721i	0.257372	+	0.743628i	−0.740095	+	0.672502i	$0.765220\pi$
$972$	−3.01834	−	5.96783i	−0.0968133	−	0.191418i
$973$	2.68300	+	2.22353i	0.0860130	+	0.0712831i
$974$	−0.256935	−	12.8924i	−0.00823272	−	0.413100i
$975$	−8.52499	−	44.2318i	−0.273018	−	1.41655i
$976$	−0.528950	+	4.75897i	−0.0169313	+	0.152331i
$977$	19.9417	−	7.98346i	0.637992	−	0.255413i	−0.0300370	−	0.999549i	$-0.509563\pi$
$977$	19.9417	−	7.98346i	0.637992	−	0.255413i	0.668029	+	0.744135i	$0.267138\pi$
$978$	−10.6998	−	19.7771i	−0.342143	−	0.632400i
$979$	−1.64561	−	1.05757i	−0.0525940	−	0.0338001i
$980$	42.0407	−	23.6372i	1.34294	−	0.755062i
$981$	−0.718978	−	1.57434i	−0.0229552	−	0.0502649i
$982$	−18.2905	+	48.4647i	−0.583674	+	1.54657i
$983$	−8.43222	−	34.7581i	−0.268946	−	1.10861i	−0.932698	−	0.360658i	$-0.882552\pi$
$983$	−8.43222	−	34.7581i	−0.268946	−	1.10861i	0.663752	−	0.747953i	$-0.268963\pi$
$984$	−3.45802	−	22.1339i	−0.110238	−	0.705603i
$985$	−83.6648	−	20.2969i	−2.66578	−	0.646712i
$986$	−1.27194	+	1.14730i	−0.0405068	+	0.0365376i
$987$	−0.535017	+	0.258687i	−0.0170298	+	0.00823411i
$988$	34.8863	−	32.7518i	1.10988	−	1.04197i
$989$	−1.10066	+	2.61813i	−0.0349988	+	0.0832516i
$990$	−8.69223	+	1.00515i	−0.276257	+	0.0319457i
$991$	−30.6431	−	38.9659i	−0.973411	−	1.23779i	−0.971315	−	0.237795i	$-0.923576\pi$
$991$	−30.6431	−	38.9659i	−0.973411	−	1.23779i	−0.00209519	−	0.999998i	$-0.500667\pi$
$992$	4.81248	+	32.4498i	0.152796	+	1.03028i
$993$	−10.9037	−	37.1344i	−0.346017	−	1.17843i
$994$	23.7009	−	5.60690i	0.751748	−	0.177840i
$995$	8.34066	−	28.4057i	0.264417	−	0.900521i
$996$	−9.39033	+	9.69676i	−0.297544	+	0.307254i
$997$	−0.363966	−	0.259179i	−0.0115269	−	0.00820827i	0.574279	−	0.818660i	$-0.305282\pi$
$997$	−0.363966	−	0.259179i	−0.0115269	−	0.00820827i	−0.585806	+	0.810451i	$0.699222\pi$
$998$	−10.5131	+	11.4752i	−0.332787	+	0.363241i
$999$	−36.2375	+	18.6817i	−1.14650	+	0.591064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.be.a.187.70	yes	1840
4.3	odd	2	inner	644.2.be.a.187.47	yes	1840
7.3	odd	6	inner	644.2.be.a.3.54	yes	1840
23.8	even	11	inner	644.2.be.a.215.15	yes	1840
28.3	even	6	inner	644.2.be.a.3.15	✓	1840
92.31	odd	22	inner	644.2.be.a.215.54	yes	1840
161.31	odd	66	inner	644.2.be.a.31.47	yes	1840
644.31	even	66	inner	644.2.be.a.31.70	yes	1840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.be.a.3.15	✓	1840	28.3	even	6	inner
644.2.be.a.3.54	yes	1840	7.3	odd	6	inner
644.2.be.a.31.47	yes	1840	161.31	odd	66	inner
644.2.be.a.31.70	yes	1840	644.31	even	66	inner
644.2.be.a.187.47	yes	1840	4.3	odd	2	inner
644.2.be.a.187.70	yes	1840	1.1	even	1	trivial
644.2.be.a.215.15	yes	1840	23.8	even	11	inner
644.2.be.a.215.54	yes	1840	92.31	odd	22	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00387 - 0.996119i) q^{2} +(1.62868 - 0.155520i) q^{3} +(0.0154938 - 1.99994i) q^{4} +(3.25553 - 1.12675i) q^{5} +(1.48006 - 1.77848i) q^{6} +(-2.03711 - 1.68825i) q^{7} +(-1.97662 - 2.02311i) q^{8} +(-0.317382 + 0.0611704i) q^{9} +O(q^{10})\)	\(q+(1.00387 - 0.996119i) q^{2} +(1.62868 - 0.155520i) q^{3} +(0.0154938 - 1.99994i) q^{4} +(3.25553 - 1.12675i) q^{5} +(1.48006 - 1.77848i) q^{6} +(-2.03711 - 1.68825i) q^{7} +(-1.97662 - 2.02311i) q^{8} +(-0.317382 + 0.0611704i) q^{9} +(2.14574 - 4.37400i) q^{10} +(2.06518 + 5.15857i) q^{11} +(-0.285796 - 3.25967i) q^{12} +(2.16733 - 3.37243i) q^{13} +(-3.72668 + 0.334426i) q^{14} +(5.12698 - 2.34141i) q^{15} +(-3.99952 - 0.0619733i) q^{16} +(-4.66994 + 1.13291i) q^{17} +(-0.257676 + 0.377557i) q^{18} +(-1.40706 + 5.80000i) q^{19} +(-2.20299 - 6.52832i) q^{20} +(-3.58035 - 2.43280i) q^{21} +(7.21171 + 3.12135i) q^{22} +(0.145927 + 4.79361i) q^{23} +(-3.53392 - 2.98758i) q^{24} +(5.39864 - 4.24554i) q^{25} +(-1.18363 - 5.54439i) q^{26} +(-5.21684 + 1.53180i) q^{27} +(-3.40796 + 4.04794i) q^{28} +(0.241846 + 0.0710123i) q^{29} +(2.81447 - 7.45754i) q^{30} +(3.36381 - 4.72382i) q^{31} +(-4.07671 + 3.92178i) q^{32} +(4.16577 + 8.08046i) q^{33} +(-3.55947 + 5.78911i) q^{34} +(-8.53410 - 3.20084i) q^{35} +(0.117420 + 0.635693i) q^{36} +(7.36294 - 1.41909i) q^{37} +(4.36499 + 7.22403i) q^{38} +(3.00540 - 5.82967i) q^{39} +(-8.71449 - 4.35912i) q^{40} +(3.65865 + 3.17024i) q^{41} +(-6.01755 + 1.12424i) q^{42} +(0.538681 + 0.246007i) q^{43} +(10.3488 - 4.05031i) q^{44} +(-0.964323 + 0.556752i) q^{45} +(4.92150 + 4.66678i) q^{46} +(0.0686439 - 0.118895i) q^{47} +(-6.52357 + 0.521070i) q^{48} +(1.29962 + 6.87830i) q^{49} +(1.19045 - 9.63964i) q^{50} +(-7.42963 + 2.57142i) q^{51} +(-6.71108 - 4.38678i) q^{52} +(-4.83484 - 2.49253i) q^{53} +(-3.71115 + 6.73432i) q^{54} +(12.5357 + 14.4669i) q^{55} +(0.611091 + 7.45832i) q^{56} +(-1.38964 + 9.66516i) q^{57} +(0.313517 - 0.169620i) q^{58} +(0.217658 - 4.56920i) q^{59} +(-4.60325 - 10.2899i) q^{60} +(0.113789 - 1.19165i) q^{61} +(-1.32866 - 8.09284i) q^{62} +(0.749813 + 0.411210i) q^{63} +(-0.185911 + 7.99784i) q^{64} +(3.25592 - 13.4211i) q^{65} +(12.2310 + 3.96210i) q^{66} +(-3.74219 - 4.75858i) q^{67} +(2.19341 + 9.35714i) q^{68} +(0.983170 + 7.78455i) q^{69} +(-11.7555 + 5.28777i) q^{70} +(-6.44292 + 0.926352i) q^{71} +(0.751099 + 0.521186i) q^{72} +(10.9561 - 11.4904i) q^{73} +(5.97782 - 8.75895i) q^{74} +(8.13238 - 7.75421i) q^{75} +(11.5779 + 2.90391i) q^{76} +(4.50196 - 13.9951i) q^{77} +(-2.79002 - 8.84594i) q^{78} +(-1.58650 - 3.07738i) q^{79} +(-13.0904 + 4.30470i) q^{80} +(-7.35811 + 2.94574i) q^{81} +(6.83073 - 0.461957i) q^{82} +(-2.70143 - 3.11762i) q^{83} +(-4.92094 + 7.12279i) q^{84} +(-13.9266 + 8.95008i) q^{85} +(0.785816 - 0.289632i) q^{86} +(0.404932 + 0.0780443i) q^{87} +(6.35424 - 14.3746i) q^{88} +(-0.286763 + 0.204203i) q^{89} +(-0.413460 + 1.51948i) q^{90} +(-10.1086 + 3.21101i) q^{91} +(9.58920 - 0.217575i) q^{92} +(4.74392 - 8.21671i) q^{93} +(-0.0495240 - 0.187732i) q^{94} +(1.95441 + 20.4675i) q^{95} +(-6.02974 + 7.02133i) q^{96} +(-5.48928 - 4.75649i) q^{97} +(8.15625 + 5.61031i) q^{98} +(-0.971002 - 1.51091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1840 q - 7 q^{2} - 11 q^{4} - 54 q^{5} - 40 q^{8} + 66 q^{9}+O(q^{10}) \) 1840 * q - 7 * q^2 - 11 * q^4 - 54 * q^5 - 40 * q^8 + 66 * q^9	\( 1840 q - 7 q^{2} - 11 q^{4} - 54 q^{5} - 40 q^{8} + 66 q^{9} - 27 q^{10} - 27 q^{12} - 14 q^{14} - 19 q^{16} - 54 q^{17} - q^{18} - 40 q^{21} - 56 q^{22} - 78 q^{24} - 94 q^{25} - 9 q^{26} + 12 q^{28} - 120 q^{29} - 19 q^{30} + 3 q^{32} - 54 q^{33} - 114 q^{36} - 2 q^{37} - 87 q^{38} - 57 q^{40} - 114 q^{42} + 72 q^{44} - 132 q^{45} - 9 q^{46} - 20 q^{49} - 186 q^{50} + 3 q^{52} - 34 q^{53} - 51 q^{54} - 93 q^{56} - 64 q^{57} + 22 q^{58} - 11 q^{60} - 54 q^{61} - 8 q^{64} - 46 q^{65} + 150 q^{66} - 30 q^{68} - 10 q^{70} + 43 q^{72} - 54 q^{73} + 6 q^{74} - 16 q^{77} - 212 q^{78} + 216 q^{80} - 58 q^{81} - 57 q^{82} - 102 q^{84} + 152 q^{85} + 3 q^{86} + 144 q^{88} - 174 q^{89} - 250 q^{92} - 64 q^{93} + 216 q^{94} - 69 q^{96} - 44 q^{98}+O(q^{100}) \) 1840 * q - 7 * q^2 - 11 * q^4 - 54 * q^5 - 40 * q^8 + 66 * q^9 - 27 * q^10 - 27 * q^12 - 14 * q^14 - 19 * q^16 - 54 * q^17 - q^18 - 40 * q^21 - 56 * q^22 - 78 * q^24 - 94 * q^25 - 9 * q^26 + 12 * q^28 - 120 * q^29 - 19 * q^30 + 3 * q^32 - 54 * q^33 - 114 * q^36 - 2 * q^37 - 87 * q^38 - 57 * q^40 - 114 * q^42 + 72 * q^44 - 132 * q^45 - 9 * q^46 - 20 * q^49 - 186 * q^50 + 3 * q^52 - 34 * q^53 - 51 * q^54 - 93 * q^56 - 64 * q^57 + 22 * q^58 - 11 * q^60 - 54 * q^61 - 8 * q^64 - 46 * q^65 + 150 * q^66 - 30 * q^68 - 10 * q^70 + 43 * q^72 - 54 * q^73 + 6 * q^74 - 16 * q^77 - 212 * q^78 + 216 * q^80 - 58 * q^81 - 57 * q^82 - 102 * q^84 + 152 * q^85 + 3 * q^86 + 144 * q^88 - 174 * q^89 - 250 * q^92 - 64 * q^93 + 216 * q^94 - 69 * q^96 - 44 * q^98

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