LMFDB - Embedded newform 572.2.bs.a.15.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(15,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 12, 5]))

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

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

chi := DirichletCharacter("572.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bs (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$80$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			15.19
Character	$\chi$	$=$	572.15
Dual form			572.2.bs.a.267.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06237 + 0.933467i) q^{2} +(0.467247 + 2.19822i) q^{3} +(0.257278 - 1.98338i) q^{4} +(0.319292 - 2.01593i) q^{5} +(-2.54836 - 1.89918i) q^{6} +(1.25573 - 0.815481i) q^{7} +(1.57810 + 2.34726i) q^{8} +(-1.87323 + 0.834017i) q^{9} +O(q^{10})$	\(q+(-1.06237 + 0.933467i) q^{2} +(0.467247 + 2.19822i) q^{3} +(0.257278 - 1.98338i) q^{4} +(0.319292 - 2.01593i) q^{5} +(-2.54836 - 1.89918i) q^{6} +(1.25573 - 0.815481i) q^{7} +(1.57810 + 2.34726i) q^{8} +(-1.87323 + 0.834017i) q^{9} +(1.54260 + 2.43972i) q^{10} +(-1.60213 - 2.90400i) q^{11} +(4.48013 - 0.361175i) q^{12} +(-2.33185 - 2.75000i) q^{13} +(-0.572831 + 2.03853i) q^{14} +(4.58065 - 0.240062i) q^{15} +(-3.86762 - 1.02056i) q^{16} +(5.27581 - 0.554510i) q^{17} +(1.21155 - 2.63464i) q^{18} +(0.221059 - 4.21805i) q^{19} +(-3.91621 - 1.15193i) q^{20} +(2.37935 + 2.37935i) q^{21} +(4.41284 + 1.58960i) q^{22} +(-0.414274 - 0.717544i) q^{23} +(-4.42243 + 4.56576i) q^{24} +(0.793261 + 0.257746i) q^{25} +(5.04433 + 0.744825i) q^{26} +(1.25423 + 1.72630i) q^{27} +(-1.29434 - 2.70040i) q^{28} +(5.52706 - 6.13843i) q^{29} +(-4.64228 + 4.53092i) q^{30} +(-1.06488 - 6.72341i) q^{31} +(5.06152 - 2.52608i) q^{32} +(5.63505 - 4.87871i) q^{33} +(-5.08727 + 5.51390i) q^{34} +(-1.24301 - 2.79184i) q^{35} +(1.17223 + 3.92991i) q^{36} +(-5.54167 + 0.290427i) q^{37} +(3.70257 + 4.68750i) q^{38} +(4.95556 - 6.41085i) q^{39} +(5.23577 - 2.43187i) q^{40} +(-2.94893 + 4.54095i) q^{41} +(-4.74880 - 0.306714i) q^{42} +(-2.04057 + 3.53437i) q^{43} +(-6.17193 + 2.43050i) q^{44} +(1.08321 + 4.04260i) q^{45} +(1.10992 + 0.375589i) q^{46} +(5.82296 + 11.4282i) q^{47} +(0.436289 - 8.97874i) q^{48} +(-1.93531 + 4.34677i) q^{49} +(-1.08334 + 0.466660i) q^{50} +(3.68405 + 11.3383i) q^{51} +(-6.05423 + 3.91743i) q^{52} +(4.57536 + 3.32419i) q^{53} +(-2.94390 - 0.663193i) q^{54} +(-6.36579 + 2.30255i) q^{55} +(3.89581 + 1.66061i) q^{56} +(9.37551 - 1.48494i) q^{57} +(-0.141790 + 11.6806i) q^{58} +(-10.2955 + 6.68596i) q^{59} +(0.702365 - 9.14695i) q^{60} +(-0.348411 - 3.31491i) q^{61} +(7.40739 + 6.14874i) q^{62} +(-1.67215 + 2.57489i) q^{63} +(-3.01921 + 7.40840i) q^{64} +(-6.28834 + 3.82279i) q^{65} +(-1.43241 + 10.4432i) q^{66} +(0.700506 - 2.61432i) q^{67} +(0.257543 - 10.6066i) q^{68} +(1.38375 - 1.24594i) q^{69} +(3.92663 + 1.80567i) q^{70} +(6.68189 - 8.25144i) q^{71} +(-4.91380 - 3.08080i) q^{72} +(6.41808 - 12.5962i) q^{73} +(5.61622 - 5.48151i) q^{74} +(-0.195935 + 1.86420i) q^{75} +(-8.30914 - 1.52366i) q^{76} +(-4.37999 - 2.34013i) q^{77} +(0.719655 + 11.4366i) q^{78} +(-5.84815 + 8.04929i) q^{79} +(-3.29228 + 7.47098i) q^{80} +(-7.32493 + 8.13516i) q^{81} +(-1.10596 - 7.57692i) q^{82} +(6.43330 + 1.01893i) q^{83} +(5.33131 - 4.10700i) q^{84} +(0.566670 - 10.8127i) q^{85} +(-1.13137 - 5.65963i) q^{86} +(16.0761 + 9.28156i) q^{87} +(4.28811 - 8.34339i) q^{88} +(-0.722802 + 2.69754i) q^{89} +(-4.92441 - 3.28361i) q^{90} +(-5.17074 - 1.55168i) q^{91} +(-1.52975 + 0.637057i) q^{92} +(14.2820 - 5.48235i) q^{93} +(-16.8540 - 6.70548i) q^{94} +(-8.43271 - 1.79243i) q^{95} +(7.91786 + 9.94605i) q^{96} +(-0.169866 + 0.442516i) q^{97} +(-2.00155 - 6.42444i) q^{98} +(5.42314 + 4.10366i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−1.06237	+	0.933467i	−0.751212	+	0.660061i
$2$	−1.06237	+	0.933467i	−0.751212	+	0.660061i
$3$	0.467247	+	2.19822i	0.269765	+	1.26915i	0.879255	+	0.476351i	$0.158041\pi$
$3$	0.467247	+	2.19822i	0.269765	+	1.26915i	−0.609490	+	0.792794i	$0.708626\pi$
$4$	0.257278	−	1.98338i	0.128639	−	0.991692i
$5$	0.319292	−	2.01593i	0.142792	−	0.901551i	−0.807427	−	0.589967i	$-0.799141\pi$
$5$	0.319292	−	2.01593i	0.142792	−	0.901551i	0.950219	−	0.311583i	$-0.100859\pi$
$6$	−2.54836	−	1.89918i	−1.04036	−	0.775336i
$7$	1.25573	−	0.815481i	0.474622	−	0.308223i	−0.285070	−	0.958507i	$-0.592017\pi$
$7$	1.25573	−	0.815481i	0.474622	−	0.308223i	0.759691	+	0.650284i	$0.225350\pi$
$8$	1.57810	+	2.34726i	0.557942	+	0.829880i
$9$	−1.87323	+	0.834017i	−0.624411	+	0.278006i
$10$	1.54260	+	2.43972i	0.487812	+	0.771507i
$11$	−1.60213	−	2.90400i	−0.483059	−	0.875588i
$11$	−1.60213	−	2.90400i	−0.483059	−	0.875588i
$12$	4.48013	−	0.361175i	1.29330	−	0.104262i
$13$	−2.33185	−	2.75000i	−0.646738	−	0.762712i
$13$	−2.33185	−	2.75000i	−0.646738	−	0.762712i
$14$	−0.572831	+	2.03853i	−0.153096	+	0.544820i
$15$	4.58065	−	0.240062i	1.18272	−	0.0619837i
$16$	−3.86762	−	1.02056i	−0.966904	−	0.255140i
$17$	5.27581	−	0.554510i	1.27957	−	0.134489i	0.559759	−	0.828656i	$-0.310894\pi$
$17$	5.27581	−	0.554510i	1.27957	−	0.134489i	0.719814	+	0.694167i	$0.244227\pi$
$18$	1.21155	−	2.63464i	0.285564	−	0.620991i
$19$	0.221059	−	4.21805i	0.0507143	−	0.967687i	−0.848231	−	0.529627i	$-0.822332\pi$
$19$	0.221059	−	4.21805i	0.0507143	−	0.967687i	0.898945	−	0.438061i	$-0.144335\pi$
$20$	−3.91621	−	1.15193i	−0.875692	−	0.257580i
$21$	2.37935	+	2.37935i	0.519216	+	0.519216i
$22$	4.41284	+	1.58960i	0.940821	+	0.338904i
$23$	−0.414274	−	0.717544i	−0.0863822	−	0.149618i	0.819597	−	0.572940i	$-0.194197\pi$
$23$	−0.414274	−	0.717544i	−0.0863822	−	0.149618i	−0.905979	+	0.423322i	$0.860864\pi$
$24$	−4.42243	+	4.56576i	−0.902725	+	0.931982i
$25$	0.793261	+	0.257746i	0.158652	+	0.0515492i
$26$	5.04433	+	0.744825i	0.989274	+	0.146072i
$27$	1.25423	+	1.72630i	0.241377	+	0.332226i
$28$	−1.29434	−	2.70040i	−0.244607	−	0.510328i
$29$	5.52706	−	6.13843i	1.02635	−	1.13988i	0.0362743	−	0.999342i	$-0.488451\pi$
$29$	5.52706	−	6.13843i	1.02635	−	1.13988i	0.990076	−	0.140535i	$-0.0448823\pi$
$30$	−4.64228	+	4.53092i	−0.847560	+	0.827230i
$31$	−1.06488	−	6.72341i	−0.191259	−	1.20756i	−0.877280	−	0.479979i	$-0.840644\pi$
$31$	−1.06488	−	6.72341i	−0.191259	−	1.20756i	0.686021	−	0.727581i	$-0.259356\pi$
$32$	5.06152	−	2.52608i	0.894758	−	0.446551i
$33$	5.63505	−	4.87871i	0.980936	−	0.849275i
$34$	−5.08727	+	5.51390i	−0.872460	+	0.945625i
$35$	−1.24301	−	2.79184i	−0.210107	−	0.471907i
$36$	1.17223	+	3.92991i	0.195372	+	0.654986i
$37$	−5.54167	+	0.290427i	−0.911045	+	0.0477458i	−0.502096	−	0.864812i	$-0.667438\pi$
$37$	−5.54167	+	0.290427i	−0.911045	+	0.0477458i	−0.408948	+	0.912558i	$0.634104\pi$
$38$	3.70257	+	4.68750i	0.600636	+	0.760413i
$39$	4.95556	−	6.41085i	0.793525	−	1.02656i
$40$	5.23577	−	2.43187i	0.827848	−	0.384513i
$41$	−2.94893	+	4.54095i	−0.460545	+	0.709178i	−0.990296	−	0.138976i	$-0.955619\pi$
$41$	−2.94893	+	4.54095i	−0.460545	+	0.709178i	0.529750	+	0.848154i	$0.322286\pi$
$42$	−4.74880	−	0.306714i	−0.732756	−	0.0473270i
$43$	−2.04057	+	3.53437i	−0.311184	+	0.538987i	−0.978619	−	0.205681i	$-0.934059\pi$
$43$	−2.04057	+	3.53437i	−0.311184	+	0.538987i	0.667435	+	0.744668i	$0.267392\pi$
$44$	−6.17193	+	2.43050i	−0.930453	+	0.366411i
$45$	1.08321	+	4.04260i	0.161476	+	0.602635i
$46$	1.10992	+	0.375589i	0.163649	+	0.0553776i
$47$	5.82296	+	11.4282i	0.849366	+	1.66697i	0.739630	+	0.673014i	$0.235000\pi$
$47$	5.82296	+	11.4282i	0.849366	+	1.66697i	0.109736	+	0.993961i	$0.465000\pi$
$48$	0.436289	−	8.97874i	0.0629729	−	1.29597i
$49$	−1.93531	+	4.34677i	−0.276472	+	0.620967i
$50$	−1.08334	+	0.466660i	−0.153207	+	0.0659957i
$51$	3.68405	+	11.3383i	0.515870	+	1.58768i
$52$	−6.05423	+	3.91743i	−0.839571	+	0.543250i
$53$	4.57536	+	3.32419i	0.628474	+	0.456613i	0.855871	−	0.517189i	$-0.173022\pi$
$53$	4.57536	+	3.32419i	0.628474	+	0.456613i	−0.227397	+	0.973802i	$0.573022\pi$
$54$	−2.94390	−	0.663193i	−0.400615	−	0.0902491i
$55$	−6.36579	+	2.30255i	−0.858364	+	0.310476i
$56$	3.89581	+	1.66061i	0.520599	+	0.221909i
$57$	9.37551	−	1.48494i	1.24182	−	0.196684i
$58$	−0.141790	+	11.6806i	−0.0186179	+	1.53374i
$59$	−10.2955	+	6.68596i	−1.34036	+	0.870437i	−0.997617	−	0.0689935i	$-0.978021\pi$
$59$	−10.2955	+	6.68596i	−1.34036	+	0.870437i	−0.342739	+	0.939431i	$0.611355\pi$
$60$	0.702365	−	9.14695i	0.0906750	−	1.18087i
$61$	−0.348411	−	3.31491i	−0.0446095	−	0.424431i	−0.993921	−	0.110094i	$-0.964885\pi$
$61$	−0.348411	−	3.31491i	−0.0446095	−	0.424431i	0.949312	−	0.314336i	$-0.101782\pi$
$62$	7.40739	+	6.14874i	0.940739	+	0.780891i
$63$	−1.67215	+	2.57489i	−0.210671	+	0.324405i
$64$	−3.01921	+	7.40840i	−0.377402	+	0.926050i
$65$	−6.28834	+	3.82279i	−0.779973	+	0.474158i
$66$	−1.43241	+	10.4432i	−0.176317	+	1.28546i
$67$	0.700506	−	2.61432i	0.0855804	−	0.319390i	−0.909843	−	0.414953i	$-0.863798\pi$
$67$	0.700506	−	2.61432i	0.0855804	−	0.319390i	0.995423	+	0.0955621i	$0.0304649\pi$
$68$	0.257543	−	10.6066i	0.0312317	−	1.28624i
$69$	1.38375	−	1.24594i	0.166584	−	0.149993i
$70$	3.92663	+	1.80567i	0.469322	+	0.215819i
$71$	6.68189	−	8.25144i	0.792994	−	0.979266i	−0.207005	−	0.978340i	$-0.566372\pi$
$71$	6.68189	−	8.25144i	0.792994	−	0.979266i	1.00000		0.000926397i	$-0.000294881\pi$
$72$	−4.91380	−	3.08080i	−0.579097	−	0.363075i
$73$	6.41808	−	12.5962i	0.751179	−	1.47427i	−0.124933	−	0.992165i	$-0.539872\pi$
$73$	6.41808	−	12.5962i	0.751179	−	1.47427i	0.876112	−	0.482107i	$-0.160128\pi$
$74$	5.61622	−	5.48151i	0.652873	−	0.637212i
$75$	−0.195935	+	1.86420i	−0.0226246	+	0.215259i
$76$	−8.30914	−	1.52366i	−0.953124	−	0.174775i
$77$	−4.37999	−	2.34013i	−0.499146	−	0.266683i
$78$	0.719655	+	11.4366i	0.0814849	+	1.29494i
$79$	−5.84815	+	8.04929i	−0.657969	+	0.905616i	−0.999412	−	0.0342861i	$-0.989084\pi$
$79$	−5.84815	+	8.04929i	−0.657969	+	0.905616i	0.341443	+	0.939902i	$0.389084\pi$
$80$	−3.29228	+	7.47098i	−0.368088	+	0.835281i
$81$	−7.32493	+	8.13516i	−0.813881	+	0.903907i
$82$	−1.10596	−	7.57692i	−0.122133	−	0.836731i
$83$	6.43330	+	1.01893i	0.706147	+	0.111843i	0.499171	−	0.866503i	$-0.333638\pi$
$83$	6.43330	+	1.01893i	0.706147	+	0.111843i	0.206976	+	0.978346i	$0.433638\pi$
$84$	5.33131	−	4.10700i	0.581693	−	0.448111i
$85$	0.566670	−	10.8127i	0.0614640	−	1.17280i
$86$	−1.13137	−	5.65963i	−0.121999	−	0.610294i
$87$	16.0761	+	9.28156i	1.72354	+	0.995088i
$88$	4.28811	−	8.34339i	0.457114	−	0.889408i
$89$	−0.722802	+	2.69754i	−0.0766169	+	0.285938i	−0.993595	−	0.112999i	$-0.963954\pi$
$89$	−0.722802	+	2.69754i	−0.0766169	+	0.285938i	0.916978	+	0.398937i	$0.130621\pi$
$90$	−4.92441	−	3.28361i	−0.519078	−	0.346123i
$91$	−5.17074	−	1.55168i	−0.542041	−	0.162660i
$92$	−1.52975	+	0.637057i	−0.159487	+	0.0664177i
$93$	14.2820	−	5.48235i	1.48097	−	0.568493i
$94$	−16.8540	−	6.70548i	−1.73836	−	0.691618i
$95$	−8.43271	−	1.79243i	−0.865178	−	0.183899i
$96$	7.91786	+	9.94605i	0.808113	+	1.01511i
$97$	−0.169866	+	0.442516i	−0.0172473	+	0.0449307i	−0.941934	−	0.335799i	$-0.890994\pi$
$97$	−0.169866	+	0.442516i	−0.0172473	+	0.0449307i	0.924686	+	0.380730i	$0.124327\pi$
$98$	−2.00155	−	6.42444i	−0.202187	−	0.648966i
$99$	5.42314	+	4.10366i	0.545046	+	0.412434i
$100$	0.715298	−	1.50703i	0.0715298	−	0.150703i
$101$	4.12003	+	0.433033i	0.409959	+	0.0430884i	0.307263	−	0.951624i	$-0.400587\pi$
$101$	4.12003	+	0.433033i	0.409959	+	0.0430884i	0.102695	+	0.994713i	$0.467253\pi$
$102$	−14.4978	−	8.60661i	−1.43550	−	0.852181i
$103$	−0.165352	−	0.508900i	−0.0162926	−	0.0501434i	0.942580	−	0.333981i	$-0.108392\pi$
$103$	−0.165352	−	0.508900i	−0.0162926	−	0.0501434i	−0.958872	+	0.283838i	$0.908392\pi$
$104$	2.77507	−	9.81321i	0.272118	−	0.962264i
$105$	5.55630	−	4.03689i	0.542239	−	0.393960i
$106$	−7.96377	+	0.739412i	−0.773510	+	0.0718180i
$107$	−1.70630	−	8.02751i	−0.164954	−	0.776048i	−0.980369	−	0.197171i	$-0.936824\pi$
$107$	−1.70630	−	8.02751i	−0.164954	−	0.776048i	0.815415	−	0.578877i	$-0.196509\pi$
$108$	3.74660	−	2.04348i	0.360516	−	0.196634i
$109$	11.0792	−	11.0792i	1.06119	−	1.06119i	0.0631926	−	0.998001i	$-0.479872\pi$
$109$	11.0792	−	11.0792i	1.06119	−	1.06119i	0.998001	−	0.0631926i	$-0.0201282\pi$
$110$	4.61350	−	8.38843i	0.439880	−	0.799805i
$111$	−3.22775	−	12.0461i	−0.306365	−	1.14337i
$112$	−5.68893	+	1.87242i	−0.537554	+	0.176927i
$113$	7.12017	+	7.90775i	0.669809	+	0.743898i	0.978269	−	0.207339i	$-0.0664803\pi$
$113$	7.12017	+	7.90775i	0.669809	+	0.743898i	−0.308460	+	0.951237i	$0.599814\pi$
$114$	−8.57416	+	10.3293i	−0.803044	+	0.967427i
$115$	−1.57879	+	0.606042i	−0.147223	+	0.0565137i
$116$	−10.7529	−	12.5416i	−0.998378	−	1.16446i
$117$	6.66164	+	3.20659i	0.615869	+	0.296449i
$118$	4.69652	−	16.7135i	0.432350	−	1.53860i
$119$	6.17281	−	4.99864i	0.565860	−	0.458225i
$120$	7.79220	+	10.3731i	0.711328	+	0.946932i
$121$	−5.86639	+	9.30513i	−0.533308	+	0.845921i
$122$	3.46450	+	3.19644i	0.313661	+	0.289392i
$123$	−11.3599	−	4.36066i	−1.02429	−	0.393188i
$124$	−13.6091	+	0.382288i	−1.22213	+	0.0343305i
$125$	5.40598	−	10.6098i	0.483526	−	0.948973i
$126$	−0.627123	−	4.29639i	−0.0558685	−	0.382753i
$127$	−12.0783	−	5.37761i	−1.07178	−	0.477186i	−0.206483	−	0.978450i	$-0.566202\pi$
$127$	−12.0783	−	5.37761i	−1.07178	−	0.477186i	−0.865294	+	0.501265i	$0.832868\pi$
$128$	−3.70796	−	10.6888i	−0.327740	−	0.944768i
$129$	−8.72280	−	2.83421i	−0.767999	−	0.249538i
$130$	3.11213	−	9.93119i	0.272951	−	0.871023i
$131$		−	5.41914i		−	0.473473i	−0.971574	−	0.236736i	$-0.923922\pi$
$131$		−	5.41914i		−	0.473473i	0.971574	−	0.236736i	$-0.0760777\pi$
$132$	−8.22659	−	12.4316i	−0.716033	−	1.08204i
$133$	−3.16215	−	5.47701i	−0.274193	−	0.474917i
$134$	1.69619	+	3.43129i	0.146528	+	0.296418i
$135$	3.88056	−	1.97724i	0.333985	−	0.170174i
$136$	9.62733	+	11.5086i	0.825536	+	0.986855i
$137$	−12.3183	+	15.2118i	−1.05242	+	1.29963i	−0.0999531	+	0.994992i	$0.531869\pi$
$137$	−12.3183	+	15.2118i	−1.05242	+	1.29963i	−0.952468	+	0.304639i	$0.901464\pi$
$138$	−0.307023	+	2.61534i	−0.0261355	+	0.222633i
$139$	−2.65011	+	12.4678i	−0.224779	+	1.05750i	0.710528	+	0.703669i	$0.248456\pi$
$139$	−2.65011	+	12.4678i	−0.224779	+	1.05750i	−0.935308	+	0.353835i	$0.884877\pi$
$140$	−5.85709	+	1.74708i	−0.495014	+	0.147655i
$141$	−22.4010	+	18.1400i	−1.88650	+	1.52766i
$142$	0.603788	+	15.0034i	0.0506688	+	1.25906i
$143$	−4.25007	+	11.1775i	−0.355409	+	0.934711i
$144$	8.09611	−	1.31391i	0.674676	−	0.109493i
$145$	−10.6099	−	13.1021i	−0.881103	−	1.08807i
$146$	4.93973	+	19.3729i	0.408815	+	1.60331i
$147$	−10.4594	−	2.22322i	−0.862680	−	0.183368i
$148$	−0.849721	+	11.0660i	−0.0698466	+	0.909617i
$149$	18.0482	+	14.6151i	1.47856	+	1.19732i	0.933324	+	0.359035i	$0.116894\pi$
$149$	18.0482	+	14.6151i	1.47856	+	1.19732i	0.545238	+	0.838281i	$0.316439\pi$
$150$	−1.53201	−	2.16337i	−0.125088	−	0.176639i
$151$	−3.08878	−	6.06206i	−0.251361	−	0.493324i	0.730503	−	0.682909i	$-0.239286\pi$
$151$	−3.08878	−	6.06206i	−0.251361	−	0.493324i	−0.981864	+	0.189586i	$0.939286\pi$
$152$	10.2497	−	6.13762i	0.831360	−	0.497826i
$153$	−9.42036	+	5.43885i	−0.761591	+	0.439705i
$154$	6.83763	−	1.60248i	0.550992	−	0.129132i
$155$	−13.8939			−1.11599
$156$	−11.4402	−	11.4782i	−0.915950	−	0.918988i
$157$	0.558170	−	1.71787i	0.0445468	−	0.137101i	−0.926309	−	0.376764i	$-0.877037\pi$
$157$	0.558170	−	1.71787i	0.0445468	−	0.137101i	0.970856	+	0.239663i	$0.0770369\pi$
$158$	−1.30082	−	14.0104i	−0.103488	−	1.11461i
$159$	−5.16950	+	11.6109i	−0.409968	+	0.920804i
$160$	−3.47629	−	11.0102i	−0.274825	−	0.870434i
$161$	−1.10536	−	0.563209i	−0.0871146	−	0.0443871i
$162$	0.187912	−	15.4802i	0.0147638	−	1.21624i
$163$	2.41760	−	6.29807i	0.189361	−	0.493303i	−0.805728	−	0.592286i	$-0.798226\pi$
$163$	2.41760	−	6.29807i	0.189361	−	0.493303i	0.995089	+	0.0989832i	$0.0315590\pi$
$164$	8.24775	+	7.01714i	0.644041	+	0.547947i
$165$	−8.03592	−	12.9176i	−0.625595	−	1.00563i
$166$	−7.78572	+	4.92279i	−0.604289	+	0.382082i
$167$	−1.12439	−	1.38850i	−0.0870075	−	0.107445i	0.731783	−	0.681538i	$-0.238688\pi$
$167$	−1.12439	−	1.38850i	−0.0870075	−	0.107445i	−0.818791	+	0.574092i	$0.805355\pi$
$168$	−1.83009	+	9.33978i	−0.141195	+	0.720579i
$169$	−2.12498	+	12.8251i	−0.163460	+	0.986550i
$170$	9.49130	+	12.0161i	0.727949	+	0.921594i
$171$	3.10383	+	8.08576i	0.237356	+	0.618334i
$172$	6.48502	+	4.95655i	0.494478	+	0.377933i
$173$	3.86035	−	3.47587i	0.293497	−	0.264266i	−0.509206	−	0.860644i	$-0.670061\pi$
$173$	3.86035	−	3.47587i	0.293497	−	0.264266i	0.802703	+	0.596379i	$0.203394\pi$
$174$	−25.7429	+	5.14606i	−1.95157	+	0.390122i
$175$	1.20631	−	0.323230i	0.0911884	−	0.0244339i
$176$	3.23270	+	12.8666i	0.243674	+	0.969857i
$177$	−19.5078	−	19.5078i	−1.46629	−	1.46629i
$178$	−1.75017	−	3.54050i	−0.131181	−	0.265372i
$179$	14.3714	−	3.05473i	1.07417	−	0.228321i	0.363318	−	0.931665i	$-0.381644\pi$
$179$	14.3714	−	3.05473i	1.07417	−	0.228321i	0.710850	+	0.703344i	$0.248310\pi$
$180$	8.29671	−	1.10835i	0.618400	−	0.0826117i
$181$	−3.96747	−	5.46076i	−0.294900	−	0.405895i	0.635698	−	0.771938i	$-0.280712\pi$
$181$	−3.96747	−	5.46076i	−0.294900	−	0.405895i	−0.930598	+	0.366043i	$0.880712\pi$
$182$	6.94171	−	3.17825i	0.514554	−	0.235588i
$183$	7.12412	−	2.31477i	0.526630	−	0.171113i
$184$	1.03049	−	2.10476i	0.0759690	−	0.155165i
$185$	−1.18393	+	11.2643i	−0.0870443	+	0.828171i
$186$	−10.0552	+	19.1561i	−0.737286	+	1.40459i
$187$	−10.0628	−	14.4325i	−0.735866	−	1.05541i
$188$	24.1646	−	8.60894i	1.76239	−	0.627871i
$189$	2.98274	+	1.14497i	0.216962	+	0.0832840i
$190$	10.6319	−	5.96743i	0.771317	−	0.432923i
$191$	−1.93619	+	9.10907i	−0.140098	+	0.659109i	0.850911	+	0.525310i	$0.176051\pi$
$191$	−1.93619	+	9.10907i	−0.140098	+	0.659109i	−0.991009	+	0.133798i	$0.957283\pi$
$192$	−17.6960	−	3.17536i	−1.27710	−	0.229162i
$193$	−1.05280	−	2.74263i	−0.0757819	−	0.197419i	0.890456	−	0.455068i	$-0.150385\pi$
$193$	−1.05280	−	2.74263i	−0.0757819	−	0.197419i	−0.966238	+	0.257650i	$0.917052\pi$
$194$	−0.232613	−	0.628683i	−0.0167007	−	0.0451368i
$195$	−11.3415	−	12.0370i	−0.812185	−	0.861987i
$196$	8.12340	+	4.95678i	0.580243	+	0.354056i
$197$	−12.6542	−	3.39069i	−0.901576	−	0.241576i	−0.221883	−	0.975073i	$-0.571220\pi$
$197$	−12.6542	−	3.39069i	−0.901576	−	0.241576i	−0.679693	+	0.733497i	$0.737887\pi$
$198$	−9.59204	+	0.702698i	−0.681676	+	0.0499385i
$199$	3.19797	−	5.53905i	0.226698	−	0.392653i	−0.730129	−	0.683309i	$-0.760540\pi$
$199$	3.19797	−	5.53905i	0.226698	−	0.392653i	0.956828	+	0.290656i	$0.0938736\pi$
$200$	0.646847	+	2.26873i	0.0457390	+	0.160424i
$201$	6.07418	+	0.318334i	0.428439	+	0.0224536i
$202$	−4.78124	+	3.38587i	−0.336407	+	0.238229i
$203$	1.93473	−	12.2154i	0.135792	−	0.857355i
$204$	23.4361	−	4.38977i	1.64085	−	0.307346i
$205$	8.21267	+	7.39472i	0.573598	+	0.516470i
$206$	0.650707	+	0.386292i	0.0453369	+	0.0269142i
$207$	1.37448	+	0.998616i	0.0955328	+	0.0694086i
$208$	6.21215	+	13.0157i	0.430735	+	0.902478i
$209$	−12.6034	+	6.11590i	−0.871793	+	0.423045i
$210$	−2.13457	+	9.47531i	−0.147299	+	0.653858i
$211$	−15.8806	−	1.66912i	−1.09326	−	0.114907i	−0.459309	−	0.888276i	$-0.651903\pi$
$211$	−15.8806	−	1.66912i	−1.09326	−	0.114907i	−0.633955	+	0.773370i	$0.718570\pi$
$212$	7.77029	−	8.21945i	0.533666	−	0.564514i
$213$	21.2606	+	10.8328i	1.45675	+	0.742253i
$214$	9.30614	+	6.93544i	0.636155	+	0.474097i
$215$	6.47351	+	5.24214i	0.441490	+	0.357511i
$216$	−2.07277	+	5.66826i	−0.141034	+	0.385677i
$217$	−6.82002	−	7.57440i	−0.462973	−	0.514184i
$218$	−1.42818	+	22.1123i	−0.0967288	+	1.49763i
$219$	30.6881	+	8.22284i	2.07371	+	0.555648i
$220$	2.92906	+	13.2182i	0.197477	+	0.891171i
$221$	−13.8273	−	13.2154i	−0.930124	−	0.888967i
$222$	14.6737	+	9.78450i	0.984837	+	0.656692i
$223$	8.85044	+	5.74754i	0.592669	+	0.384884i	0.805842	−	0.592131i	$-0.201713\pi$
$223$	8.85044	+	5.74754i	0.592669	+	0.384884i	−0.213173	+	0.977015i	$0.568380\pi$
$224$	4.29593	−	7.29964i	0.287034	−	0.487728i
$225$	−1.70093	+	0.178775i	−0.113395	+	0.0119183i
$226$	−14.9459	−	1.75454i	−0.994187	−	0.116710i
$227$	−9.79207	−	15.0785i	−0.649922	−	1.00079i	−0.997993	−	0.0633244i	$-0.979830\pi$
$227$	−9.79207	−	15.0785i	−0.649922	−	1.00079i	0.348071	−	0.937468i	$-0.386837\pi$
$228$	−0.533084	−	18.9773i	−0.0353044	−	1.25680i
$229$	2.72092	+	17.1792i	0.179804	+	1.13524i	0.898195	+	0.439597i	$0.144879\pi$
$229$	2.72092	+	17.1792i	0.179804	+	1.13524i	−0.718391	+	0.695639i	$0.755121\pi$
$230$	1.11155	−	2.11759i	0.0732933	−	0.139630i
$231$	3.09760	−	10.7216i	0.203807	−	0.705431i
$232$	23.1307	+	3.28639i	1.51860	+	0.215762i
$233$	−5.74329	+	7.90496i	−0.376256	+	0.517871i	−0.954588	−	0.297930i	$-0.903704\pi$
$233$	−5.74329	+	7.90496i	−0.376256	+	0.517871i	0.578332	+	0.815801i	$0.303704\pi$
$234$	−10.0704	+	2.81183i	−0.658323	+	0.183815i
$235$	24.8977	−	8.08974i	1.62414	−	0.527717i
$236$	10.6120	+	22.1400i	0.690783	+	1.44119i
$237$	−20.4267	−	9.09455i	−1.32686	−	0.590754i
$238$	−1.89176	+	11.0725i	−0.122625	+	0.717726i
$239$	13.9525	−	7.10915i	0.902512	−	0.459853i	0.0597954	−	0.998211i	$-0.480955\pi$
$239$	13.9525	−	7.10915i	0.902512	−	0.459853i	0.842716	+	0.538358i	$0.180955\pi$
$240$	−17.9612	−	3.74637i	−1.15939	−	0.241827i
$241$	−7.47162	+	2.00202i	−0.481290	+	0.128961i	−0.491303	−	0.870989i	$-0.663479\pi$
$241$	−7.47162	+	2.00202i	−0.481290	+	0.128961i	0.0100135	+	0.999950i	$0.496813\pi$
$242$	−2.45374	−	15.3616i	−0.157732	−	0.987482i
$243$	−15.7616	−	9.09998i	−1.01111	−	0.583764i
$244$	−6.66437	−	0.161820i	−0.426643	−	0.0103595i
$245$	8.14485	+	5.28933i	0.520355	+	0.337923i
$246$	16.1390	−	5.97145i	1.02899	−	0.380726i
$247$	−12.1151	+	9.22794i	−0.770866	+	0.587160i
$248$	14.1011	−	13.1098i	0.895419	−	0.832470i
$249$	0.766093	+	14.6179i	0.0485492	+	0.926374i
$250$	4.16076	+	16.3179i	0.263150	+	1.03204i
$251$	−5.01375	+	2.23227i	−0.316465	+	0.140899i	−0.558822	−	0.829288i	$-0.688746\pi$
$251$	−5.01375	+	2.23227i	−0.316465	+	0.140899i	0.242356	+	0.970187i	$0.422080\pi$
$252$	4.67678	+	3.97898i	0.294610	+	0.250652i
$253$	−1.42003	+	2.35265i	−0.0892763	+	0.147910i
$254$	17.8515	−	5.56167i	1.12010	−	0.348970i
$255$	24.0335	−	3.80654i	1.50504	−	0.238375i
$256$	13.9169	+	7.89427i	0.869807	+	0.493392i
$257$	7.06052	+	6.35732i	0.440423	+	0.396559i	0.859290	−	0.511489i	$-0.170906\pi$
$257$	7.06052	+	6.35732i	0.440423	+	0.396559i	−0.418867	+	0.908048i	$0.637573\pi$
$258$	11.9125	−	5.13145i	0.741641	−	0.319470i
$259$	−6.72201	+	4.88382i	−0.417685	+	0.303466i
$260$	5.96420	+	13.4557i	0.369884	+	0.834487i
$261$	−5.23393	+	16.1084i	−0.323972	+	0.997083i
$262$	5.05859	+	5.75716i	0.312521	+	0.355678i
$263$	−4.34401	+	2.50802i	−0.267863	+	0.154651i	−0.627916	−	0.778281i	$-0.716092\pi$
$263$	−4.34401	+	2.50802i	−0.267863	+	0.154651i	0.360053	+	0.932932i	$0.382759\pi$
$264$	20.3442	+	5.52780i	1.25210	+	0.340213i
$265$	8.16222	−	8.16222i	0.501401	−	0.501401i
$266$	8.47199	+	2.86687i	0.519451	+	0.175779i
$267$	−6.26752	−	0.328467i	−0.383566	−	0.0201018i
$268$	−5.00498	−	2.06198i	−0.305728	−	0.125955i
$269$	0.646387	+	6.14997i	0.0394109	+	0.374970i	0.996395	+	0.0848308i	$0.0270350\pi$
$269$	0.646387	+	6.14997i	0.0394109	+	0.374970i	−0.956984	+	0.290139i	$0.906298\pi$
$270$	−2.27691	+	5.72295i	−0.138569	+	0.348288i
$271$	0.597183	+	11.3949i	0.0362763	+	0.692193i	0.954876	+	0.297004i	$0.0959875\pi$
$271$	0.597183	+	11.3949i	0.0362763	+	0.692193i	−0.918600	+	0.395189i	$0.870679\pi$
$272$	−20.9707	−	3.23966i	−1.27154	−	0.196433i
$273$	0.994927	−	12.0915i	0.0602157	−	0.731809i
$274$	−1.11310	−	27.6593i	−0.0672450	−	1.67096i
$275$	−0.522410	−	2.71657i	−0.0315025	−	0.163815i
$276$	−2.11516	−	3.06507i	−0.127318	−	0.184495i
$277$	3.35382	+	7.53280i	0.201511	+	0.452602i	0.985828	−	0.167759i	$-0.0536529\pi$
$277$	3.35382	+	7.53280i	0.201511	+	0.452602i	−0.784317	+	0.620361i	$0.786986\pi$
$278$	−8.82286	−	15.7192i	−0.529160	−	0.942778i
$279$	7.60222	+	11.7064i	0.455133	+	0.700843i
$280$	4.59157	−	7.32345i	0.274399	−	0.437660i
$281$	1.98070	+	0.313712i	0.118159	+	0.0187145i	0.215234	−	0.976563i	$-0.430949\pi$
$281$	1.98070	+	0.313712i	0.118159	+	0.0187145i	−0.0970750	+	0.995277i	$0.530949\pi$
$282$	6.86517	−	40.1820i	0.408815	−	2.39280i
$283$	5.35424	−	1.13808i	0.318277	−	0.0676518i	−0.0460033	−	0.998941i	$-0.514648\pi$
$283$	5.35424	−	1.13808i	0.318277	−	0.0676518i	0.364280	+	0.931289i	$0.381315\pi$
$284$	−14.6467	−	15.3757i	−0.869120	−	0.912377i
$285$		−	19.3745i		−	1.14765i
$286$	−5.91868	−	15.8420i	−0.349979	−	0.936758i
$287$			8.10701i			0.478542i
$288$	−7.37461	+	8.95332i	−0.434553	+	0.527580i
$289$	10.8982	−	2.31649i	0.641072	−	0.136264i
$290$	23.5021	+	4.01537i	1.38009	+	0.235791i
$291$	−1.05212	−	0.166639i	−0.0616764	−	0.00976858i
$292$	−23.3318	−	15.9702i	−1.36539	−	0.934587i
$293$	3.38530	+	5.21290i	0.197771	+	0.304541i	0.923617	−	0.383316i	$-0.125218\pi$
$293$	3.38530	+	5.21290i	0.197771	+	0.304541i	−0.725846	+	0.687857i	$0.758551\pi$
$294$	13.1871	−	7.40165i	0.769090	−	0.431673i
$295$	10.1912	+	22.8897i	0.593352	+	1.33269i
$296$	−9.42700	−	12.5494i	−0.547933	−	0.729418i
$297$	3.00373	−	6.40802i	0.174294	−	0.371831i
$298$	−32.8166	+	1.32065i	−1.90102	+	0.0765031i
$299$	−1.00722	+	2.81246i	−0.0582491	+	0.162649i
$300$	3.64701	+	0.868230i	0.210560	+	0.0501273i
$301$	0.319806	+	6.10227i	0.0184333	+	0.351729i
$302$	8.94017	+	3.55691i	0.514449	+	0.204677i
$303$	0.973170	+	9.25909i	0.0559071	+	0.531921i
$304$	−5.15975	+	16.0882i	−0.295932	+	0.922722i
$305$	−6.79387	−	0.356052i	−0.389016	−	0.0203875i
$306$	4.93096	−	14.5717i	0.281884	−	0.833008i
$307$	−3.96060	+	3.96060i	−0.226043	+	0.226043i	−0.811037	−	0.584994i	$-0.801097\pi$
$307$	−3.96060	+	3.96060i	−0.226043	+	0.226043i	0.584994	+	0.811037i	$0.301097\pi$
$308$	−5.76826	+	8.08514i	−0.328677	+	0.460693i
$309$	1.04142	−	0.601262i	0.0592441	−	0.0342046i
$310$	14.7605	−	12.9695i	0.838343	−	0.736620i
$311$	4.56023	−	14.0349i	0.258587	−	0.795849i	−0.734515	−	0.678593i	$-0.762590\pi$
$311$	4.56023	−	14.0349i	0.258587	−	0.795849i	0.993102	−	0.117256i	$-0.0374098\pi$
$312$	22.8683	+	1.51503i	1.29466	+	0.0857714i
$313$	−12.0331	+	8.74260i	−0.680154	+	0.494161i	−0.873409	−	0.486988i	$-0.838096\pi$
$313$	−12.0331	+	8.74260i	−0.680154	+	0.494161i	0.193255	+	0.981149i	$0.438096\pi$
$314$	1.01059	+	2.34605i	0.0570309	+	0.132396i
$315$	4.65689	+	4.19308i	0.262386	+	0.236253i
$316$	14.4602	+	13.6700i	0.813452	+	0.769000i
$317$	−32.8568	+	5.20400i	−1.84542	+	0.292286i	−0.978513	−	0.206184i	$-0.933895\pi$
$317$	−32.8568	+	5.20400i	−1.84542	+	0.292286i	−0.866907	+	0.498470i	$0.833895\pi$
$318$	−5.34644	−	17.1607i	−0.299814	−	0.962323i
$319$	−26.6810	−	6.21604i	−1.49385	−	0.348031i
$320$	13.9708	+	8.45196i	0.780991	+	0.472479i
$321$	16.8490	−	7.50166i	0.940419	−	0.418702i
$322$	1.70004	−	0.433479i	0.0947398	−	0.0241568i
$323$	−1.17269	−	22.3762i	−0.0652501	−	1.24505i
$324$	14.2506	+	16.6211i	0.791700	+	0.923397i
$325$	−1.14096	−	2.78249i	−0.0632892	−	0.154345i
$326$	3.31064	+	8.94765i	0.183359	+	0.495565i
$327$	29.5313	+	19.1778i	1.63308	+	1.06054i
$328$	−15.3125	+	0.244178i	−0.845490	+	0.0134825i
$329$	16.6315	+	9.60223i	0.916927	+	0.529388i
$330$	20.5953	+	6.22204i	1.13373	+	0.342512i
$331$	−13.6802	+	3.66559i	−0.751929	+	0.201479i	−0.614374	−	0.789015i	$-0.710591\pi$
$331$	−13.6802	+	3.66559i	−0.751929	+	0.201479i	−0.137556	+	0.990494i	$0.543925\pi$
$332$	3.67608	−	12.4976i	0.201751	−	0.685892i
$333$	10.1386	−	5.16588i	0.555593	−	0.283089i
$334$	2.49064	+	0.425530i	0.136282	+	0.0232840i
$335$	−5.04662	−	2.24690i	−0.275726	−	0.122761i
$336$	−6.77413	−	11.6307i	−0.369559	−	0.634505i
$337$	13.5227	−	4.39378i	0.736627	−	0.239345i	0.0834101	−	0.996515i	$-0.473419\pi$
$337$	13.5227	−	4.39378i	0.736627	−	0.239345i	0.653217	+	0.757171i	$0.273419\pi$
$338$	−9.71433	−	15.6087i	−0.528390	−	0.849002i
$339$	−14.0561	+	19.3466i	−0.763424	+	1.05076i
$340$	−21.3000	−	3.90580i	−1.15515	−	0.211822i
$341$	−17.8187	+	13.8642i	−0.964936	+	0.750787i
$342$	−10.8452	−	5.69278i	−0.586443	−	0.307830i
$343$	2.75408	+	17.3885i	0.148706	+	0.938893i
$344$	−11.5163	+	0.787845i	−0.620917	+	0.0424777i
$345$	−2.06990	−	3.18737i	−0.111440	−	0.171602i
$346$	−0.856520	+	7.29618i	−0.0460468	+	0.392245i
$347$	34.4760	−	3.62358i	1.85077	−	0.194524i	0.887093	−	0.461591i	$-0.152721\pi$
$347$	34.4760	−	3.62358i	1.85077	−	0.194524i	0.963678	+	0.267068i	$0.0860547\pi$
$348$	22.5449	−	29.4972i	1.20854	−	1.58122i
$349$	−3.34932	−	2.17507i	−0.179285	−	0.116429i	0.451877	−	0.892080i	$-0.350755\pi$
$349$	−3.34932	−	2.17507i	−0.179285	−	0.116429i	−0.631161	+	0.775652i	$0.717421\pi$
$350$	−0.979827	+	1.46944i	−0.0523740	+	0.0785449i
$351$	1.82265	−	7.47459i	0.0972857	−	0.398964i
$352$	−15.4449	−	10.6515i	−0.823216	−	0.567728i
$353$	20.8289	+	5.58110i	1.10861	+	0.297052i	0.766267	−	0.642522i	$-0.222112\pi$
$353$	20.8289	+	5.58110i	1.10861	+	0.297052i	0.342345	+	0.939574i	$0.388779\pi$
$354$	38.9344	+	2.51468i	2.06934	+	0.133654i
$355$	−14.5009	−	16.1048i	−0.769625	−	0.854755i
$356$	5.16429	+	2.12761i	0.273707	+	0.112763i
$357$	13.8724	+	11.2336i	0.734203	+	0.594546i
$358$	−12.4163	+	16.6605i	−0.656222	+	0.880534i
$359$	27.6775	+	14.1024i	1.46076	+	0.744295i	0.990407	−	0.138183i	$-0.0441261\pi$
$359$	27.6775	+	14.1024i	1.46076	+	0.744295i	0.470354	+	0.882478i	$0.344126\pi$
$360$	−7.77960	+	8.92219i	−0.410021	+	0.470241i
$361$	1.15282	+	0.121167i	0.0606750	+	0.00637719i
$362$	9.31238	+	2.09786i	0.489448	+	0.110261i
$363$	−23.1958	−	8.54784i	−1.21746	−	0.448645i
$364$	−4.40789	+	9.85635i	−0.231036	+	0.516613i
$365$	−23.3438	−	16.9602i	−1.22187	−	0.887740i
$366$	−5.40772	+	9.10928i	−0.282666	+	0.476150i
$367$	26.6891	+	24.0310i	1.39316	+	1.25441i	0.929715	+	0.368279i	$0.120053\pi$
$367$	26.6891	+	24.0310i	1.39316	+	1.25441i	0.463443	+	0.886127i	$0.346614\pi$
$368$	0.869957	+	3.19798i	0.0453496	+	0.166706i
$369$	1.73680	−	10.9657i	0.0904142	−	0.570853i
$370$	−9.25712	−	13.0721i	−0.481255	−	0.679586i
$371$	8.45624	+	0.443173i	0.439026	+	0.0230084i
$372$	−7.19915	−	29.7372i	−0.373259	−	1.54180i
$373$	−9.02614	+	15.6337i	−0.467356	+	0.809484i	−0.999304	−	0.0372925i	$-0.988127\pi$
$373$	−9.02614	+	15.6337i	−0.467356	+	0.809484i	0.531948	+	0.846777i	$0.321460\pi$
$374$	24.1628	+	5.93946i	1.24943	+	0.307122i
$375$	25.8487	+	6.92615i	1.33482	+	0.357665i
$376$	−17.6357	+	31.7028i	−0.909492	+	1.63495i
$377$	−29.7689	−	0.885546i	−1.53318	−	0.0456080i
$378$	−4.23757	+	1.56791i	−0.217957	+	0.0806444i
$379$	2.77051	+	7.21742i	0.142311	+	0.370734i	0.986148	−	0.165866i	$-0.0530419\pi$
$379$	2.77051	+	7.21742i	0.142311	+	0.370734i	−0.843837	+	0.536600i	$0.819709\pi$
$380$	−5.72462	+	16.2641i	−0.293667	+	0.834333i
$381$	6.17764	−	29.0635i	0.316490	−	1.48897i
$382$	−6.44606	−	11.4846i	−0.329809	−	0.587604i
$383$	−18.3218	−	7.03308i	−0.936201	−	0.359374i	−0.158036	−	0.987433i	$-0.550516\pi$
$383$	−18.3218	−	7.03308i	−0.936201	−	0.359374i	−0.778165	+	0.628060i	$0.783849\pi$
$384$	21.7639	−	13.1453i	1.11063	−	0.670816i
$385$	−6.11604	+	8.08257i	−0.311702	+	0.411926i
$386$	3.67861	+	1.93094i	0.187237	+	0.0982825i
$387$	0.874738	−	8.32258i	0.0444654	−	0.423060i
$388$	0.833977	+	0.450759i	0.0423388	+	0.0228838i
$389$	−6.44191	+	2.09310i	−0.326618	+	0.106125i	−0.467736	−	0.883868i	$-0.654930\pi$
$389$	−6.44191	+	2.09310i	−0.326618	+	0.106125i	0.141118	+	0.989993i	$0.454930\pi$
$390$	23.2851	+	2.20083i	1.17909	+	0.111443i
$391$	−2.58352	−	3.55591i	−0.130654	−	0.179830i
$392$	−13.2571	+	2.31697i	−0.669584	+	0.117025i
$393$	11.9125	−	2.53208i	0.600906	−	0.127726i
$394$	16.6086	−	8.21012i	0.836730	−	0.413620i
$395$	14.3595	+	14.3595i	0.722507	+	0.722507i
$396$	9.53439	−	9.70038i	0.479121	−	0.487462i
$397$	11.6530	−	3.12242i	0.584850	−	0.156710i	0.0457514	−	0.998953i	$-0.485432\pi$
$397$	11.6530	−	3.12242i	0.584850	−	0.156710i	0.539098	+	0.842243i	$0.318765\pi$
$398$	1.77308	+	8.86974i	0.0888763	+	0.444600i
$399$	10.5622	−	9.51023i	0.528770	−	0.476107i
$400$	−2.80498	−	1.80643i	−0.140249	−	0.0903217i
$401$	8.38748	+	21.8501i	0.418851	+	1.09114i	0.967003	+	0.254765i	$0.0819980\pi$
$401$	8.38748	+	21.8501i	0.418851	+	1.09114i	−0.548152	+	0.836378i	$0.684669\pi$
$402$	−6.75020	+	5.33186i	−0.336670	+	0.265929i
$403$	−16.0062	+	18.6064i	−0.797327	+	0.926851i
$404$	1.91886	−	8.06019i	0.0954670	−	0.401010i
$405$	14.0611	+	17.3640i	0.698702	+	0.862826i
$406$	9.34729	+	14.7834i	0.463898	+	0.733686i
$407$	9.72185	+	15.6277i	0.481894	+	0.774636i
$408$	−20.8002	+	26.5404i	−1.02976	+	1.31394i
$409$	−8.23714	+	21.4585i	−0.407301	+	1.06105i	0.564538	+	0.825407i	$0.309054\pi$
$409$	−8.23714	+	21.4585i	−0.407301	+	1.06105i	−0.971839	+	0.235647i	$0.924279\pi$
$410$	−15.6277	−	0.189702i	−0.771795	−	0.00936874i
$411$	−39.1946	−	19.9707i	−1.93333	−	0.985080i
$412$	−1.05189	+	0.197027i	−0.0518227	+	0.00970682i
$413$	−7.47607	+	16.7915i	−0.367873	+	0.826257i
$414$	−2.39238	+	0.222125i	−0.117579	+	0.0109169i
$415$	4.10820	−	12.6437i	0.201664	−	0.620657i
$416$	−18.7494	−	8.02874i	−0.919264	−	0.393641i
$417$	−28.6453			−1.40276
$418$	7.68051	−	18.2622i	0.375666	−	0.893233i
$419$	0.933668	−	0.539054i	0.0456127	−	0.0263345i	−0.477020	−	0.878892i	$-0.658283\pi$
$419$	0.933668	−	0.539054i	0.0456127	−	0.0263345i	0.522633	+	0.852558i	$0.324950\pi$
$420$	−6.57718	−	12.0589i	−0.320934	−	0.588413i
$421$	−4.31418	−	8.46706i	−0.210260	−	0.412659i	0.761657	−	0.647980i	$-0.224386\pi$
$421$	−4.31418	−	8.46706i	−0.210260	−	0.412659i	−0.971918	+	0.235321i	$0.924386\pi$
$422$	18.4292	−	13.0508i	0.897119	−	0.635302i
$423$	−20.4391	−	16.5512i	−0.993782	−	0.804749i
$424$	−0.582366	+	15.9854i	−0.0282822	+	0.776322i
$425$	4.32802	+	0.919949i	0.209940	+	0.0446241i
$426$	−32.6988	+	8.33757i	−1.58426	+	0.403957i
$427$	−3.14076	−	3.87851i	−0.151992	−	0.187694i
$428$	−16.3606	+	1.31895i	−0.790820	+	0.0637537i
$429$	−26.5565	−	4.11995i	−1.28216	−	0.198913i
$430$	−11.7707	+	0.473690i	−0.567631	+	0.0228434i
$431$	13.6234	−	11.0320i	0.656217	−	0.531394i	−0.242373	−	0.970183i	$-0.577926\pi$
$431$	13.6234	−	11.0320i	0.656217	−	0.531394i	0.898590	+	0.438789i	$0.144592\pi$
$432$	−3.08909	−	7.95668i	−0.148624	−	0.382816i
$433$	0.290367	−	1.36607i	0.0139541	−	0.0656490i	−0.970620	−	0.240619i	$-0.922650\pi$
$433$	0.290367	−	1.36607i	0.0139541	−	0.0656490i	0.984574	+	0.174970i	$0.0559829\pi$
$434$	14.3159	+	1.68058i	0.687184	+	0.0806705i
$435$	23.8440	−	29.4448i	1.14323	−	1.41177i
$436$	−19.1238	−	24.8247i	−0.915866	−	1.18889i
$437$	−3.11822	+	1.58881i	−0.149165	+	0.0760031i
$438$	−40.2780	+	19.9106i	−1.92456	+	0.951364i
$439$	−5.19444	−	8.99703i	−0.247917	−	0.429405i	0.715031	−	0.699093i	$-0.246413\pi$
$439$	−5.19444	−	8.99703i	−0.247917	−	0.429405i	−0.962948	+	0.269688i	$0.913079\pi$
$440$	−15.4505	−	11.3085i	−0.736575	−	0.539111i
$441$		−	9.75659i		−	0.464600i
$442$	27.0259	+	1.13242i	1.28549	+	0.0538639i
$443$	−12.7474	−	4.14188i	−0.605647	−	0.196787i	−0.00988961	−	0.999951i	$-0.503148\pi$
$443$	−12.7474	−	4.14188i	−0.605647	−	0.196787i	−0.595757	+	0.803164i	$0.703148\pi$
$444$	−24.7225	+	3.30266i	−1.17328	+	0.156738i
$445$	5.20725	+	2.31842i	0.246848	+	0.109904i
$446$	−14.7676	+	2.15555i	−0.699267	+	0.102068i
$447$	−23.6943	+	46.5028i	−1.12070	+	2.19950i
$448$	2.25009	+	11.7651i	0.106307	+	0.555847i
$449$	−38.8636	−	14.9183i	−1.83408	−	0.704039i	−0.984197	−	0.177075i	$-0.943336\pi$
$449$	−38.8636	−	14.9183i	−1.83408	−	0.704039i	−0.849887	−	0.526964i	$-0.823330\pi$
$450$	1.64014	−	1.77769i	0.0773170	−	0.0838009i
$451$	17.9115	+	1.28850i	0.843418	+	0.0606732i
$452$	17.5159	−	12.0875i	0.823881	−	0.568550i
$453$	11.8826	−	9.62230i	0.558291	−	0.452095i
$454$	24.4781	+	6.87839i	1.14881	+	0.322819i
$455$	−4.77905	+	9.92841i	−0.224045	+	0.465451i
$456$	18.2810	+	19.6633i	0.856086	+	0.920821i
$457$	38.1463	−	14.6430i	1.78441	−	0.684970i	0.786697	−	0.617339i	$-0.211789\pi$
$457$	38.1463	−	14.6430i	1.78441	−	0.684970i	0.997710	−	0.0676308i	$-0.0215440\pi$
$458$	−18.9269	−	15.7109i	−0.884396	−	0.734121i
$459$	7.57433	+	8.41215i	0.353539	+	0.392645i
$460$	0.795824	+	3.28727i	0.0371055	+	0.153270i
$461$	2.96292	+	11.0578i	0.137997	+	0.515012i	0.999968	+	0.00805357i	$0.00256356\pi$
$461$	2.96292	+	11.0578i	0.137997	+	0.515012i	−0.861971	+	0.506958i	$0.830770\pi$
$462$	6.71748	+	14.2819i	0.312525	+	0.664454i
$463$	−9.99881	+	9.99881i	−0.464684	+	0.464684i	−0.900187	−	0.435503i	$-0.856571\pi$
$463$	−9.99881	+	9.99881i	−0.464684	+	0.464684i	0.435503	+	0.900187i	$0.356571\pi$
$464$	−27.6412	+	18.1004i	−1.28321	+	0.840289i
$465$	−6.49190	−	30.5420i	−0.301054	−	1.41635i
$466$	−1.27750	−	13.7592i	−0.0591790	−	0.637383i
$467$	−22.0528	+	16.0223i	−1.02048	+	0.741424i	−0.966382	−	0.257111i	$-0.917229\pi$
$467$	−22.0528	+	16.0223i	−1.02048	+	0.741424i	−0.0541012	+	0.998535i	$0.517229\pi$
$468$	8.07378	−	12.3876i	0.373211	−	0.572617i
$469$	−1.25228	−	3.85413i	−0.0578251	−	0.177967i
$470$	−18.8991	+	31.8355i	−0.871752	+	1.46846i
$471$	4.03707	+	0.424313i	0.186018	+	0.0195513i
$472$	−31.9409	−	13.6150i	−1.47020	−	0.626681i
$473$	13.5331	+	0.263301i	0.622251	+	0.0121066i
$474$	30.1902	−	9.40583i	1.38668	−	0.432024i
$475$	1.26254	−	3.28904i	0.0579295	−	0.150911i
$476$	−8.32609	−	13.5291i	−0.381626	−	0.620104i
$477$	−11.3432	−	2.41106i	−0.519367	−	0.110395i
$478$	−8.18661	+	20.5768i	−0.374447	+	0.941160i
$479$	−32.6054	+	12.5160i	−1.48978	+	0.571873i	−0.960918	−	0.276835i	$-0.910715\pi$
$479$	−32.6054	+	12.5160i	−1.48978	+	0.571873i	−0.528862	+	0.848708i	$0.677381\pi$
$480$	22.5786	−	12.7861i	1.03057	−	0.583605i
$481$	13.7210	+	14.5623i	0.625624	+	0.663986i
$482$	6.06884	−	9.10140i	0.276428	−	0.414558i
$483$	0.721584	−	2.69299i	0.0328332	−	0.122535i
$484$	16.9464	+	14.0293i	0.770289	+	0.637695i
$485$	0.837845	+	0.483730i	0.0380446	+	0.0219650i
$486$	25.2393	−	5.04538i	1.14488	−	0.228863i
$487$	1.08878	−	20.7752i	0.0493373	−	0.941412i	−0.856068	−	0.516864i	$-0.827099\pi$
$487$	1.08878	−	20.7752i	0.0493373	−	0.941412i	0.905405	−	0.424549i	$-0.139567\pi$
$488$	7.23111	−	6.04906i	0.327337	−	0.273828i
$489$	14.9742	+	2.37168i	0.677156	+	0.107251i
$490$	−13.5903	+	1.98371i	−0.613947	+	0.0896147i
$491$	−21.0326	+	23.3591i	−0.949188	+	1.05418i	0.0492769	+	0.998785i	$0.484308\pi$
$491$	−21.0326	+	23.3591i	−0.949188	+	1.05418i	−0.998465	+	0.0553945i	$0.982358\pi$
$492$	−11.5715	+	21.4092i	−0.521684	+	0.965199i
$493$	25.7559	−	35.4500i	1.15999	−	1.59659i
$494$	4.25680	−	21.1126i	0.191523	−	0.949900i
$495$	10.0043	−	9.62240i	0.449658	−	0.432495i
$496$	−2.74309	+	27.0904i	−0.123168	+	1.21639i
$497$	1.66176	−	15.8105i	0.0745399	−	0.709200i
$498$	−14.4592	−	14.8146i	−0.647934	−	0.663858i
$499$	14.3591	−	28.1813i	0.642800	−	1.26157i	−0.307890	−	0.951422i	$-0.599623\pi$
$499$	14.3591	−	28.1813i	0.642800	−	1.26157i	0.950690	−	0.310144i	$-0.100377\pi$
$500$	−19.6525	−	13.4518i	−0.878888	−	0.601583i
$501$	2.52687	−	3.12042i	0.112892	−	0.139410i
$502$	3.24273	−	7.05168i	0.144730	−	0.314732i
$503$	−0.213255	+	0.192015i	−0.00950856	+	0.00856155i	−0.673871	−	0.738849i	$-0.735370\pi$
$503$	−0.213255	+	0.192015i	−0.00950856	+	0.00856155i	0.664363	+	0.747410i	$0.268703\pi$
$504$	−8.68274	+	0.138458i	−0.386760	+	0.00616741i
$505$	2.18846	−	8.16743i	0.0973850	−	0.363446i
$506$	−0.687520	−	3.82494i	−0.0305640	−	0.170039i
$507$	−29.1854	+	1.32133i	−1.29617	+	0.0586822i
$508$	−13.7733	+	22.5724i	−0.611093	+	1.00149i
$509$	−13.9716	+	21.5144i	−0.619281	+	0.953609i	0.380306	+	0.924861i	$0.375819\pi$
$509$	−13.9716	+	21.5144i	−0.619281	+	0.953609i	−0.999587	+	0.0287480i	$0.990848\pi$
$510$	−21.9793	+	26.4785i	−0.973261	+	1.17249i
$511$	−2.21257	−	21.0512i	−0.0978785	−	0.931252i
$512$	−22.1540	+	4.60431i	−0.979078	+	0.203484i
$513$	7.55887	−	4.90879i	0.333732	−	0.216728i
$514$	−13.4353	−	0.163089i	−0.592604	−	0.00719356i
$515$	−1.07870	+	0.170850i	−0.0475333	+	0.00752853i
$516$	−7.86550	+	16.5715i	−0.346259	+	0.729518i
$517$	23.8583	−	35.2193i	1.04929	−	1.54894i
$518$	2.58240	−	11.4632i	0.113464	−	0.503665i
$519$	9.44448	+	6.86181i	0.414567	+	0.301200i
$520$	−18.8967	−	8.72761i	−0.828674	−	0.382731i
$521$	−9.12773	−	28.0923i	−0.399893	−	1.23074i	−0.925085	−	0.379761i	$-0.876006\pi$
$521$	−9.12773	−	28.0923i	−0.399893	−	1.23074i	0.525192	−	0.850984i	$-0.323994\pi$
$522$	−9.47625	−	21.9988i	−0.414764	−	0.962862i
$523$	−14.2868	+	32.0886i	−0.624717	+	1.40314i	0.272763	+	0.962081i	$0.412063\pi$
$523$	−14.2868	+	32.0886i	−0.624717	+	1.40314i	−0.897480	+	0.441056i	$0.854604\pi$
$524$	−10.7482	−	1.39422i	−0.469539	−	0.0609070i
$525$	1.27418	+	2.50071i	0.0556096	+	0.109140i
$526$	2.27382	−	6.71945i	0.0991431	−	0.292982i
$527$	−9.34633	−	34.8810i	−0.407133	−	1.51944i
$528$	−26.7732	+	13.1181i	−1.16515	+	0.570892i
$529$	11.1568	−	19.3241i	0.485076	−	0.840177i
$530$	−1.05217	+	16.2905i	−0.0457032	+	0.707614i
$531$	13.7096	−	21.1110i	0.594947	−	0.916137i
$532$	−11.6766	+	4.86264i	−0.506243	+	0.210822i
$533$	19.3641	−	2.47926i	0.838751	−	0.107389i
$534$	6.96506	−	5.50157i	0.301408	−	0.238076i
$535$	−16.7277	+	0.876661i	−0.723201	+	0.0379014i
$536$	7.24195	−	2.48139i	0.312805	−	0.107180i
$537$	13.4300	+	30.1642i	0.579546	+	1.30168i
$538$	−6.42750	−	5.93018i	−0.277109	−	0.255668i
$539$	15.7236	−	1.34395i	0.677264	−	0.0578880i
$540$	−2.92325	−	8.20534i	−0.125797	−	0.353102i
$541$	6.10731	+	38.5600i	0.262574	+	1.65783i	0.668345	+	0.743851i	$0.267003\pi$
$541$	6.10731	+	38.5600i	0.262574	+	1.65783i	−0.405771	+	0.913975i	$0.632997\pi$
$542$	−11.2712	−	11.5482i	−0.484141	−	0.496039i
$543$	10.1502	−	11.2729i	0.435586	−	0.483767i
$544$	25.3029	−	16.1338i	1.08485	−	0.691730i
$545$	−18.7974	−	25.8724i	−0.805191	−	1.10825i
$546$	10.2300	+	13.7744i	0.437804	+	0.589490i
$547$	13.7165	+	4.45677i	0.586476	+	0.190558i	0.587200	−	0.809442i	$-0.300230\pi$
$547$	13.7165	+	4.45677i	0.586476	+	0.190558i	−0.000723600		1.00000i	$0.500230\pi$
$548$	27.0016	+	28.3455i	1.15345	+	1.21086i
$549$	3.41735	+	5.91902i	0.145849	+	0.252618i
$550$	3.09082	+	2.39836i	0.131793	+	0.102266i
$551$	−24.6704	−	24.6704i	−1.05099	−	1.05099i
$552$	5.10824	+	1.28181i	0.217421	+	0.0545576i
$553$	−0.779660	+	14.8768i	−0.0331545	+	0.632626i
$554$	−10.5946	−	4.87197i	−0.450123	−	0.206990i
$555$	−25.3147	+	2.66069i	−1.07455	+	0.112940i
$556$	24.0466	+	8.46387i	1.01980	+	0.358948i
$557$	−5.15760	+	0.270299i	−0.218535	+	0.0114529i	−0.161289	−	0.986907i	$-0.551565\pi$
$557$	−5.15760	+	0.270299i	−0.218535	+	0.0114529i	−0.0572456	+	0.998360i	$0.518232\pi$
$558$	−19.0039	−	5.34014i	−0.804501	−	0.226066i
$559$	14.4778	−	2.63005i	0.612347	−	0.111239i
$560$	1.95823	+	12.0663i	0.0827504	+	0.509896i
$561$	27.0242	−	28.8639i	1.14096	−	1.21863i
$562$	−2.39709	+	1.51564i	−0.101115	+	0.0639334i
$563$	11.2009	−	4.98696i	0.472062	−	0.210175i	−0.156896	−	0.987615i	$-0.550149\pi$
$563$	11.2009	−	4.98696i	0.472062	−	0.210175i	0.628957	+	0.777440i	$0.283482\pi$
$564$	30.2152	+	49.0967i	1.27229	+	2.06735i
$565$	18.2149	−	11.8289i	0.766305	−	0.497644i
$566$	−4.62585	+	6.20708i	−0.194439	+	0.260903i
$567$	−2.56407	+	16.1889i	−0.107681	+	0.679871i
$568$	29.9129	+	2.66251i	1.25512	+	0.111716i
$569$	−3.07703	−	14.4763i	−0.128996	−	0.606877i	−0.994389	−	0.105784i	$-0.966265\pi$
$569$	−3.07703	−	14.4763i	−0.128996	−	0.606877i	0.865393	−	0.501093i	$-0.167069\pi$
$570$	18.0855	+	20.5830i	0.757516	+	0.862125i
$571$	21.2852			0.890758			0.445379	−	0.895342i	$-0.353069\pi$
$571$	21.2852			0.890758			0.445379	+	0.895342i	$0.353069\pi$
$572$	21.0758	+	11.3052i	0.881225	+	0.472696i
$573$	−20.9285			−0.874299
$574$	−7.56763	−	8.61268i	−0.315867	−	0.359486i
$575$	−0.143683	−	0.675977i	−0.00599201	−	0.0281902i
$576$	−0.523037	−	16.3957i	−0.0217932	−	0.683156i
$577$	5.35318	−	33.7986i	0.222856	−	1.40706i	−0.581808	−	0.813326i	$-0.697655\pi$
$577$	5.35318	−	33.7986i	0.222856	−	1.40706i	0.804664	−	0.593730i	$-0.202345\pi$
$578$	−9.41562	+	12.6341i	−0.391638	+	0.525510i
$579$	5.53699	−	3.59576i	0.230109	−	0.149435i
$580$	−28.7162	+	17.6726i	−1.19238	+	0.733814i
$581$	8.90942	−	3.96673i	0.369625	−	0.164568i
$582$	1.27330	−	0.805086i	0.0527799	−	0.0333719i
$583$	2.32314	−	18.6126i	0.0962148	−	0.770856i
$584$	39.6948	−	4.81315i	1.64258	−	0.199169i
$585$	8.59126	−	12.4056i	0.355205	−	0.512907i
$586$	−8.46252	−	2.37799i	−0.349584	−	0.0982337i
$587$	−3.12875	+	0.163971i	−0.129138	+	0.00676781i	−0.116795	−	0.993156i	$-0.537262\pi$
$587$	−3.12875	+	0.163971i	−0.129138	+	0.00676781i	−0.0123423	+	0.999924i	$0.503929\pi$
$588$	−7.10048	+	20.1731i	−0.292819	+	0.831924i
$589$	−28.5951	+	3.00547i	−1.17824	+	0.123838i
$590$	−32.1936	−	14.8043i	−1.32539	−	0.609484i
$591$	1.54085	−	29.4011i	0.0633819	−	1.20940i
$592$	21.7294	+	4.53235i	0.893075	+	0.186278i
$593$	22.5406	+	22.5406i	0.925630	+	0.925630i	0.997420	−	0.0717898i	$-0.0228711\pi$
$593$	22.5406	+	22.5406i	0.925630	+	0.925630i	−0.0717898	+	0.997420i	$0.522871\pi$
$594$	2.79059	+	9.61160i	0.114499	+	0.394369i
$595$	−8.10598	−	14.0400i	−0.332313	−	0.575583i
$596$	33.6307	−	32.0363i	1.37757	−	1.31226i
$597$	13.6703	+	4.44175i	0.559488	+	0.181789i
$598$	−1.55529	−	3.92809i	−0.0636006	−	0.160632i
$599$	11.1287	+	15.3173i	0.454705	+	0.625848i	0.973400	−	0.229111i	$-0.0735820\pi$
$599$	11.1287	+	15.3173i	0.454705	+	0.625848i	−0.518695	+	0.854959i	$0.673582\pi$
$600$	−4.68495	+	2.48198i	−0.191262	+	0.101326i
$601$	−18.4221	+	20.4598i	−0.751453	+	0.834573i	−0.990654	−	0.136397i	$-0.956448\pi$
$601$	−18.4221	+	20.4598i	−0.751453	+	0.834573i	0.239201	+	0.970970i	$0.423115\pi$
$602$	−6.03602	−	6.18436i	−0.246010	−	0.252056i
$603$	0.868180	+	5.48147i	0.0353550	+	0.223223i
$604$	−12.8181	+	4.56659i	−0.521560	+	0.185812i
$605$	16.8854	+	14.7973i	0.686489	+	0.601595i
$606$	−9.67693	−	8.92820i	−0.393098	−	0.362683i
$607$	−13.3050	−	29.8835i	−0.540033	−	1.21293i	−0.953217	−	0.302286i	$-0.902250\pi$
$607$	−13.3050	−	29.8835i	−0.540033	−	1.21293i	0.413184	−	0.910647i	$-0.364417\pi$
$608$	−9.53623	−	21.9081i	−0.386745	−	0.888493i
$609$	27.7562	−	1.45464i	1.12474	−	0.0589451i
$610$	7.54999	−	5.96359i	0.305690	−	0.241459i
$611$	17.8493	−	42.6619i	0.722105	−	1.72592i
$612$	8.36367	+	20.0835i	0.338081	+	0.811826i
$613$	6.51420	−	10.0310i	0.263106	−	0.405148i	−0.682285	−	0.731087i	$-0.739014\pi$
$613$	6.51420	−	10.0310i	0.263106	−	0.405148i	0.945391	+	0.325938i	$0.105680\pi$
$614$	0.510548	−	7.90473i	0.0206041	−	0.319009i
$615$	−12.4179	+	21.5084i	−0.500738	+	0.867304i
$616$	−1.41916	−	13.9739i	−0.0571798	−	0.563025i
$617$	11.6709	+	43.5565i	0.469853	+	1.75352i	0.640275	+	0.768146i	$0.278820\pi$
$617$	11.6709	+	43.5565i	0.469853	+	1.75352i	−0.170422	+	0.985371i	$0.554513\pi$
$618$	−0.545115	+	1.61089i	−0.0219278	+	0.0647996i
$619$	−5.04505	−	9.90147i	−0.202778	−	0.397974i	0.767114	−	0.641511i	$-0.221692\pi$
$619$	−5.04505	−	9.90147i	−0.202778	−	0.397974i	−0.969892	+	0.243537i	$0.921692\pi$
$620$	−3.57460	+	27.5570i	−0.143559	+	1.10671i
$621$	0.719101	−	1.61513i	0.0288565	−	0.0648128i
$622$	8.25649	+	19.1672i	0.331055	+	0.768534i
$623$	1.29214	+	3.97681i	0.0517687	+	0.159328i
$624$	−25.7089	+	19.7373i	−1.02918	+	0.790123i
$625$	−16.2887	−	11.8344i	−0.651546	−	0.473376i
$626$	4.62278	−	20.5205i	0.184764	−	0.820162i
$627$	−19.3330	−	24.8474i	−0.772085	−	0.992309i
$628$	−3.26359	−	1.54903i	−0.130231	−	0.0618132i
$629$	−29.0758	+	4.60515i	−1.15933	+	0.183619i
$630$	−8.86146	−	0.107568i	−0.353049	−	0.00428562i
$631$	−37.0748	+	24.0767i	−1.47593	+	0.958477i	−0.479192	+	0.877710i	$0.659070\pi$
$631$	−37.0748	+	24.0767i	−1.47593	+	0.958477i	−0.996733	+	0.0807671i	$0.974263\pi$
$632$	−28.1227	−	1.02454i	−1.11866	−	0.0407539i
$633$	−3.75106	−	35.6890i	−0.149091	−	1.41851i
$634$	30.0484	−	36.1993i	1.19338	−	1.43766i
$635$	−14.6974	+	22.6320i	−0.583248	+	0.898123i
$636$	21.6988	+	13.2403i	0.860415	+	0.525013i
$637$	16.4664	−	4.81391i	0.652424	−	0.190734i
$638$	34.1477	−	18.3021i	1.35192	−	0.724587i
$639$	−5.63489	+	21.0297i	−0.222913	+	0.831922i
$640$	−22.7318	+	4.06213i	−0.898555	+	0.160570i
$641$	8.30543	−	7.47824i	0.328045	−	0.295373i	−0.488606	−	0.872504i	$-0.662495\pi$
$641$	8.30543	−	7.47824i	0.328045	−	0.295373i	0.816651	+	0.577131i	$0.195828\pi$
$642$	−10.8974	+	23.6976i	−0.430086	+	0.935268i
$643$	−15.6468	+	19.3221i	−0.617048	+	0.761991i	−0.985871	−	0.167509i	$-0.946428\pi$
$643$	−15.6468	+	19.3221i	−0.617048	+	0.761991i	0.368823	+	0.929500i	$0.379761\pi$
$644$	−1.40144	+	2.04745i	−0.0552247	+	0.0806809i
$645$	−8.49868	+	16.6796i	−0.334635	+	0.656758i
$646$	22.1333	+	22.6773i	0.870824	+	0.892225i
$647$	−4.54117	+	43.2063i	−0.178532	+	1.69862i	0.428180	+	0.903694i	$0.359155\pi$
$647$	−4.54117	+	43.2063i	−0.178532	+	1.69862i	−0.606711	+	0.794922i	$0.707512\pi$
$648$	−30.6548	−	4.35541i	−1.20423	−	0.171096i
$649$	35.9106	+	19.1863i	1.40962	+	0.753127i
$650$	3.80949	+	1.89100i	0.149421	+	0.0741710i
$651$	13.4636	−	18.5311i	0.527680	−	0.726289i
$652$	−11.8695	−	6.41538i	−0.464845	−	0.251246i
$653$	21.9388	−	24.3655i	0.858532	−	0.953497i	−0.140800	−	0.990038i	$-0.544967\pi$
$653$	21.9388	−	24.3655i	0.858532	−	0.953497i	0.999332	+	0.0365413i	$0.0116340\pi$
$654$	−49.2751	+	7.19244i	−1.92681	+	0.281247i
$655$	−10.9246	−	1.73029i	−0.426860	−	0.0676079i
$656$	16.0396	−	14.5531i	0.626243	−	0.568203i
$657$	−1.51712	+	28.9484i	−0.0591885	+	1.12938i
$658$	−26.6323	+	5.32385i	−1.03824	+	0.207545i
$659$	9.51840	+	5.49545i	0.370784	+	0.214072i	0.673801	−	0.738913i	$-0.264661\pi$
$659$	9.51840	+	5.49545i	0.370784	+	0.214072i	−0.303017	+	0.952985i	$0.597994\pi$
$660$	−27.6880	+	12.6149i	−1.07775	+	0.491034i
$661$	−5.57150	+	20.7931i	−0.216706	+	0.808759i	0.768852	+	0.639426i	$0.220828\pi$
$661$	−5.57150	+	20.7931i	−0.216706	+	0.808759i	−0.985559	+	0.169333i	$0.945839\pi$
$662$	11.1117	−	16.6642i	0.431870	−	0.647673i
$663$	22.5898	−	36.5704i	0.877313	−	1.42028i
$664$	7.76068	+	16.7086i	0.301173	+	0.648419i
$665$	−12.0509	+	4.62591i	−0.467314	+	0.179385i
$666$	−5.94882	+	14.9522i	−0.230512	+	0.579385i
$667$	−6.69431	−	1.42292i	−0.259205	−	0.0550957i
$668$	−3.04321	+	1.87286i	−0.117745	+	0.0724630i
$669$	−8.49904	+	22.1408i	−0.328592	+	0.856012i
$670$	7.45881	−	2.32381i	0.288159	−	0.0897765i
$671$	−9.06829	+	6.32269i	−0.350077	+	0.244085i
$672$	18.0535	+	6.03269i	0.696429	+	0.232716i
$673$	13.7674	+	1.44701i	0.530694	+	0.0557782i	0.366086	−	0.930581i	$-0.380698\pi$
$673$	13.7674	+	1.44701i	0.530694	+	0.0557782i	0.164608	+	0.986359i	$0.447364\pi$
$674$	−10.2647	+	17.2908i	−0.395381	+	0.666018i
$675$	0.549984	+	1.69268i	0.0211689	+	0.0651512i
$676$	24.8905	+	7.51428i	0.957326	+	0.289011i
$677$	−21.5052	+	15.6245i	−0.826513	+	0.600497i	−0.918571	−	0.395257i	$-0.870656\pi$
$677$	−21.5052	+	15.6245i	−0.826513	+	0.600497i	0.0920578	+	0.995754i	$0.470656\pi$
$678$	−3.12655	−	33.6743i	−0.120074	−	1.29325i
$679$	0.147558	+	0.694204i	0.00566274	+	0.0266411i
$680$	26.2745	−	15.7334i	1.00758	−	0.603348i
$681$	28.5705	−	28.5705i	1.09483	−	1.09483i
$682$	5.98836	−	31.3621i	0.229306	−	1.20092i
$683$	−3.72891	−	13.9165i	−0.142683	−	0.532499i	−0.999848	−	0.0174571i	$-0.994443\pi$
$683$	−3.72891	−	13.9165i	−0.142683	−	0.532499i	0.857165	−	0.515042i	$-0.172224\pi$
$684$	16.8357	−	4.07580i	0.643730	−	0.155842i
$685$	26.7328	+	29.6898i	1.02141	+	1.13439i
$686$	−19.1575	−	15.9023i	−0.731437	−	0.607153i
$687$	−36.4925	+	14.0081i	−1.39227	+	0.534444i
$688$	11.4992	−	11.5871i	0.438403	−	0.441753i
$689$	−1.52751	−	20.3338i	−0.0581936	−	0.774654i
$690$	5.17431	+	1.45399i	0.196983	+	0.0553526i
$691$	−3.91743	+	3.17227i	−0.149026	+	0.120679i	−0.700934	−	0.713226i	$-0.747233\pi$
$691$	−3.91743	+	3.17227i	−0.149026	+	0.120679i	0.551908	+	0.833905i	$0.313900\pi$
$692$	−5.90080	−	8.55081i	−0.224315	−	0.325053i
$693$	10.1565	+	0.730628i	0.385812	+	0.0277543i
$694$	−33.2440	+	36.0318i	−1.26192	+	1.36775i
$695$	24.2880	+	9.32330i	0.921297	+	0.353653i
$696$	3.58352	+	52.3820i	0.135833	+	1.98554i
$697$	−13.0400	+	25.5924i	−0.493925	+	0.969383i
$698$	5.58859	−	0.815737i	0.211531	−	0.0308761i
$699$	−20.0604	−	8.93147i	−0.758755	−	0.337819i
$700$	−0.330731	−	2.47573i	−0.0125005	−	0.0935739i
$701$	−35.9148	−	11.6694i	−1.35648	−	0.440748i	−0.461615	−	0.887080i	$-0.652730\pi$
$701$	−35.9148	−	11.6694i	−1.35648	−	0.440748i	−0.894867	+	0.446332i	$0.852730\pi$
$702$	5.04095	+	9.64220i	0.190259	+	0.363921i
$703$			23.4392i			0.884028i
$704$	26.3511	−	3.10140i	0.993145	−	0.116888i
$705$	29.4164	+	50.9507i	1.10789	+	1.91892i
$706$	−27.3379	+	13.5139i	−1.02888	+	0.508603i
$707$	5.52678	−	2.81604i	0.207856	−	0.105908i
$708$	−43.7103	+	33.6724i	−1.64273	+	1.26549i
$709$	8.55131	−	10.5600i	0.321151	−	0.396589i	−0.590846	−	0.806784i	$-0.701206\pi$
$709$	8.55131	−	10.5600i	0.321151	−	0.396589i	0.911998	+	0.410195i	$0.134539\pi$
$710$	30.4387	+	3.57328i	1.14234	+	0.134103i
$711$	4.24171	−	19.9557i	0.159076	−	0.748396i
$712$	−7.47246	+	2.56037i	−0.280042	+	0.0959540i
$713$	−4.38319	+	3.54944i	−0.164152	+	0.132928i
$714$	−25.2239	+	1.01509i	−0.943979	+	0.0379888i
$715$	21.1761	+	12.1367i	0.791940	+	0.453888i
$716$	−2.36127	−	29.2899i	−0.0882447	−	1.09461i
$717$	22.1468	+	27.3490i	0.827086	+	1.02137i
$718$	−42.5679	+	10.8540i	−1.58862	+	0.405068i
$719$	27.9345	+	5.93765i	1.04178	+	0.221437i	0.696869	−	0.717199i	$-0.254576\pi$
$719$	27.9345	+	5.93765i	1.04178	+	0.221437i	0.344910	+	0.938636i	$0.387909\pi$
$720$	−0.0637271	−	16.7407i	−0.00237497	−	0.623889i
$721$	−0.622636	−	0.504200i	−0.0231882	−	0.0187774i
$722$	−1.33784	+	0.947399i	−0.0497891	+	0.0352585i
$723$	−7.89197	−	15.4889i	−0.293506	−	0.576037i
$724$	−11.8515	+	6.46409i	−0.440458	+	0.240236i
$725$	5.96656	−	3.44479i	0.221592	−	0.127936i
$726$	32.6218	−	12.5715i	1.21071	−	0.466574i
$727$	29.7162			1.10211			0.551057	−	0.834468i	$-0.314225\pi$
$727$	29.7162			1.10211			0.551057	+	0.834468i	$0.314225\pi$
$728$	−4.51775	−	14.5858i	−0.167439	−	0.540584i
$729$	2.49085	−	7.66606i	0.0922538	−	0.283928i
$730$	40.6317	−	3.77252i	1.50384	−	0.139627i
$731$	−8.80583	+	19.7782i	−0.325695	+	0.731524i
$732$	−2.75819	−	14.7254i	−0.101946	−	0.544266i
$733$	4.53667	+	2.31155i	0.167566	+	0.0853790i	0.535762	−	0.844369i	$-0.320024\pi$
$733$	4.53667	+	2.31155i	0.167566	+	0.0853790i	−0.368196	+	0.929748i	$0.620024\pi$
$734$	−50.7859	−	0.616484i	−1.87454	−	0.0227549i
$735$	−7.82147	+	20.3756i	−0.288499	+	0.751566i
$736$	−3.90943	−	2.58537i	−0.144103	−	0.0952981i
$737$	−8.71428	+	2.15421i	−0.320995	+	0.0793513i
$738$	8.39101	+	13.2709i	0.308877	+	0.488510i
$739$	10.0993	+	12.4715i	0.371507	+	0.458773i	0.928275	−	0.371895i	$-0.121292\pi$
$739$	10.0993	+	12.4715i	0.371507	+	0.458773i	−0.556768	+	0.830668i	$0.687959\pi$
$740$	22.0369	+	5.24625i	0.810093	+	0.192856i
$741$	−25.9458	−	22.3200i	−0.953144	−	0.819946i
$742$	−9.39738	+	7.42281i	−0.344989	+	0.272500i
$743$	−7.18930	−	18.7288i	−0.263750	−	0.687092i	−0.999947	−	0.0103245i	$-0.996714\pi$
$743$	−7.18930	−	18.7288i	−0.263750	−	0.687092i	0.736197	−	0.676768i	$-0.236620\pi$
$744$	35.4069	+	24.8718i	1.29808	+	0.911845i
$745$	35.2256	−	31.7173i	1.29057	−	1.16203i
$746$	−5.00444	−	25.0345i	−0.183226	−	0.916578i
$747$	−12.9009	+	3.45678i	−0.472019	+	0.126477i
$748$	−31.2142	+	16.2452i	−1.14130	+	0.593985i
$749$	−8.68893	−	8.68893i	−0.317487	−	0.317487i
$750$	−33.9264	+	16.7708i	−1.23882	+	0.612383i
$751$	13.5842	−	2.88741i	0.495695	−	0.105363i	0.0467207	−	0.998908i	$-0.485123\pi$
$751$	13.5842	−	2.88741i	0.495695	−	0.105363i	0.448974	+	0.893545i	$0.351790\pi$
$752$	−10.8578	−	50.1426i	−0.395943	−	1.82851i
$753$	−7.24968	−	9.97834i	−0.264193	−	0.363631i
$754$	32.4524	−	26.8475i	1.18185	−	0.977730i
$755$	−13.2069	+	4.29118i	−0.480649	+	0.156172i
$756$	3.03830	−	5.62134i	0.110502	−	0.204446i
$757$	4.37650	−	41.6396i	0.159066	−	1.51342i	−0.565809	−	0.824536i	$-0.691436\pi$
$757$	4.37650	−	41.6396i	0.159066	−	1.51342i	0.724876	−	0.688880i	$-0.241897\pi$
$758$	−9.68054	−	5.08142i	−0.351613	−	0.184566i
$759$	−5.83515	−	2.02227i	−0.211802	−	0.0734037i
$760$	−9.10035	−	22.6223i	−0.330105	−	0.820599i
$761$	−42.6148	−	16.3583i	−1.54479	−	0.592988i	−0.571100	−	0.820881i	$-0.693483\pi$
$761$	−42.6148	−	16.3583i	−1.54479	−	0.592988i	−0.973686	+	0.227893i	$0.926816\pi$
$762$	20.5669	+	36.6429i	0.745059	+	1.32743i
$763$	4.87761	−	22.9473i	0.176581	−	0.830750i
$764$	17.5686	+	6.18377i	0.635611	+	0.223721i
$765$	7.95649	+	20.7274i	0.287667	+	0.749399i
$766$	26.0298	−	9.63104i	0.940494	−	0.347984i
$767$	42.3938	+	12.7219i	1.53075	+	0.459361i
$768$	−10.8508	+	34.2811i	−0.391543	+	1.23701i
$769$	−7.69134	−	2.06089i	−0.277357	−	0.0743175i	0.117459	−	0.993078i	$-0.462525\pi$
$769$	−7.69134	−	2.06089i	−0.277357	−	0.0743175i	−0.394816	+	0.918760i	$0.629192\pi$
$770$	−1.04729	−	14.2958i	−0.0377417	−	0.515186i
$771$	−10.6758	+	18.4910i	−0.384480	+	0.665939i
$772$	−5.71054	+	1.38248i	−0.205527	+	0.0497565i
$773$	4.31055	+	0.225906i	0.155040	+	0.00812528i	0.129698	−	0.991554i	$-0.458599\pi$
$773$	4.31055	+	0.225906i	0.155040	+	0.00812528i	0.0253417	+	0.999679i	$0.491933\pi$
$774$	6.83956	+	9.65823i	0.245843	+	0.347158i
$775$	0.888202	−	5.60789i	0.0319052	−	0.201441i
$776$	−1.30676	+	0.299615i	−0.0469101	+	0.0107556i
$777$	−13.8766	−	12.4945i	−0.497819	−	0.448239i
$778$	4.88988	−	8.23697i	0.175311	−	0.295310i
$779$	18.5021	+	13.4426i	0.662906	+	0.481629i
$780$	−26.7919	+	19.3978i	−0.959304	+	0.694552i
$781$	−34.6674	−	6.18432i	−1.24050	−	0.221293i
$782$	6.06399	+	1.36608i	0.216848	+	0.0488508i
$783$	17.5290	+	1.84237i	0.626434	+	0.0658409i
$784$	11.9212	−	14.8365i	0.425756	−	0.529876i
$785$	−3.28489	−	1.67373i	−0.117243	−	0.0597381i
$786$	−10.2919	+	13.8099i	−0.367100	+	0.492584i
$787$	42.0243	+	34.0306i	1.49800	+	1.21306i	0.916828	+	0.399283i	$0.130741\pi$
$787$	42.0243	+	34.0306i	1.49800	+	1.21306i	0.581177	+	0.813777i	$0.302592\pi$
$788$	−9.98068	+	24.2258i	−0.355547	+	0.863009i
$789$	−7.54291	−	8.37725i	−0.268535	−	0.298238i
$790$	−28.6594	−	1.85104i	−1.01965	−	0.0658572i
$791$	15.3896	+	4.12364i	0.547192	+	0.146620i
$792$	−1.07410	+	19.2055i	−0.0381665	+	0.682437i
$793$	−8.30356	+	8.68799i	−0.294868	+	0.308520i
$794$	−9.46522	+	14.1949i	−0.335908	+	0.503759i
$795$	21.7562	+	14.1286i	0.771611	+	0.501090i
$796$	−10.1633	−	7.76787i	−0.360228	−	0.275325i
$797$	−6.73884	+	0.708280i	−0.238702	+	0.0250886i	−0.223124	−	0.974790i	$-0.571625\pi$
$797$	−6.73884	+	0.708280i	−0.238702	+	0.0250886i	−0.0155779	+	0.999879i	$0.504959\pi$
$798$	−2.34350	+	19.9629i	−0.0829590	+	0.706678i
$799$	37.0579	+	57.0642i	1.31101	+	2.01879i
$800$	4.66619	−	0.699251i	0.164975	−	0.0247223i
$801$	−0.895813	−	5.65594i	−0.0316520	−	0.199843i
$802$	−29.3070	−	15.3836i	−1.03487	−	0.543213i
$803$	−46.8618	+	1.54260i	−1.65372	+	0.0544373i
$804$	2.19413	−	11.9655i	0.0773810	−	0.421991i
$805$	−1.48832	+	2.04850i	−0.0524565	+	0.0722002i
$806$	−0.363860	−	34.7082i	−0.0128164	−	1.22255i
$807$	−13.2170	+	4.29446i	−0.465260	+	0.151172i
$808$	5.48538	+	10.3541i	0.192975	+	0.364257i
$809$	44.4823	+	19.8048i	1.56391	+	0.696299i	0.992258	−	0.124195i	$-0.0396348\pi$
$809$	44.4823	+	19.8048i	1.56391	+	0.696299i	0.571655	+	0.820494i	$0.306301\pi$
$810$	−31.1469	−	5.32151i	−1.09439	−	0.186979i
$811$	11.7320	−	5.97776i	0.411967	−	0.209908i	−0.235709	−	0.971824i	$-0.575741\pi$
$811$	11.7320	−	5.97776i	0.411967	−	0.209908i	0.647676	+	0.761916i	$0.275741\pi$
$812$	−23.7301	−	6.98008i	−0.832763	−	0.244953i
$813$	−24.7696	+	6.63699i	−0.868707	+	0.232769i
$814$	−24.9162	−	7.52742i	−0.873311	−	0.263836i
$815$	−11.9245	−	6.88463i	−0.417698	−	0.241158i
$816$	−2.67702	−	47.6121i	−0.0937146	−	1.66676i
$817$	14.4571	+	9.38854i	0.505789	+	0.328463i
$818$	−11.2799	−	30.4861i	−0.394391	−	1.06592i
$819$	10.9801	−	1.40583i	0.383677	−	0.0491237i
$820$	16.7795	−	14.3864i	0.585966	−	0.502394i
$821$	−0.137503	−	2.62372i	−0.00479889	−	0.0915683i	0.995180	−	0.0980651i	$-0.0312653\pi$
$821$	−0.137503	−	2.62372i	−0.00479889	−	0.0915683i	−0.999979	+	0.00649675i	$0.997932\pi$
$822$	60.2813	−	15.3706i	2.10255	−	0.536111i
$823$	43.0084	−	19.1486i	1.49918	−	0.667478i	0.517096	−	0.855927i	$-0.327013\pi$
$823$	43.0084	−	19.1486i	1.49918	−	0.667478i	0.982083	+	0.188450i	$0.0603462\pi$
$824$	0.933577	−	1.19122i	0.0325227	−	0.0414980i
$825$	5.72753	−	2.41768i	0.199407	−	0.0841729i
$826$	−7.73195	−	24.8175i	−0.269029	−	0.863513i
$827$	−19.5292	+	3.09312i	−0.679096	+	0.107558i	−0.486448	−	0.873710i	$-0.661708\pi$
$827$	−19.5292	+	3.09312i	−0.679096	+	0.107558i	−0.192648	+	0.981268i	$0.561708\pi$
$828$	2.33426	−	2.46919i	0.0811212	−	0.0858104i
$829$	4.23801	+	3.81592i	0.147192	+	0.132533i	0.739437	−	0.673225i	$-0.235092\pi$
$829$	4.23801	+	3.81592i	0.147192	+	0.132533i	−0.592245	+	0.805758i	$0.701758\pi$
$830$	7.43807	+	17.2673i	0.258179	+	0.599355i
$831$	−14.9917	+	10.8921i	−0.520057	+	0.377843i
$832$	27.4134	−	8.97241i	0.950389	−	0.311062i
$833$	−7.79999	+	24.0059i	−0.270254	+	0.831755i
$834$	30.4320	−	26.7394i	1.05377	−	0.925910i
$835$	−3.15812	+	1.82334i	−0.109291	+	0.0630994i
$836$	8.88760	+	26.5708i	0.307384	+	0.918970i
$837$	10.2710	−	10.2710i	0.355018	−	0.355018i
$838$	−0.488716	+	1.44423i	−0.0168824	+	0.0498899i
$839$	42.7602	+	2.24097i	1.47625	+	0.0773668i	0.773374	−	0.633950i	$-0.218567\pi$
$839$	42.7602	+	2.24097i	1.47625	+	0.0773668i	0.702872	+	0.711316i	$0.251901\pi$
$840$	18.2440	+	6.67145i	0.629477	+	0.230187i
$841$	−4.10052	−	39.0138i	−0.141397	−	1.34530i
$842$	12.4870	+	4.96804i	0.430330	+	0.171210i
$843$	0.235867	+	4.50061i	0.00812369	+	0.155009i
$844$	−7.39622	+	31.0679i	−0.254588	+	1.06940i
$845$	25.1761	+	8.37877i	0.866084	+	0.288239i
$846$	37.1640	−	1.49560i	1.27772	−	0.0514198i
$847$	0.221559	+	16.4687i	0.00761286	+	0.565870i
$848$	−14.3032	−	17.5261i	−0.491174	−	0.601850i
$849$	5.00351	+	11.2381i	0.171720	+	0.385689i
$850$	−5.45672	+	3.06273i	−0.187164	+	0.105051i
$851$	2.50417	+	3.85608i	0.0858417	+	0.132185i
$852$	26.9555	−	39.3809i	0.923481	−	1.34917i
$853$	−54.7105	−	8.66529i	−1.87325	−	0.296694i	−0.886977	−	0.461813i	$-0.847199\pi$
$853$	−54.7105	−	8.66529i	−1.87325	−	0.296694i	−0.986274	+	0.165120i	$0.947199\pi$
$854$	6.95712	+	1.18864i	0.238068	+	0.0406743i
$855$	17.2913	−	3.67539i	0.591352	−	0.125696i
$856$	16.1499	−	16.6733i	0.551992	−	0.569882i
$857$			0.134341i			0.00458900i	0.999997	+	0.00229450i	$0.000730362\pi$
$857$			0.134341i			0.00458900i	−0.999997	+	0.00229450i	$0.999270\pi$
$858$	32.0588	−	20.4127i	1.09447	−	0.696879i
$859$		−	36.3597i		−	1.24058i	−0.784374	−	0.620288i	$-0.787016\pi$
$859$		−	36.3597i		−	1.24058i	0.784374	−	0.620288i	$-0.212984\pi$
$860$	12.0627	−	11.4908i	0.411334	−	0.391832i
$861$	−17.8210	+	3.78798i	−0.607339	+	0.129094i
$862$	−4.17513	+	24.4372i	−0.142206	+	0.832333i
$863$	41.9588	+	6.64562i	1.42829	+	0.226220i	0.822212	−	0.569182i	$-0.192740\pi$
$863$	41.9588	+	6.64562i	1.42829	+	0.226220i	0.606083	+	0.795401i	$0.292740\pi$
$864$	10.7091	+	5.56941i	0.364330	+	0.189475i
$865$	−5.77453	−	8.89200i	−0.196340	−	0.302337i
$866$	0.966702	+	1.72232i	0.0328499	+	0.0585269i
$867$	10.1843	+	22.8744i	0.345878	+	0.776854i
$868$	−16.7776	+	11.5780i	−0.569468	+	0.392983i
$869$	32.7446	+	4.08704i	1.11078	+	0.138643i
$870$	2.15458	+	53.5390i	0.0730472	+	1.81514i
$871$	−8.82286	+	4.16981i	−0.298951	+	0.141289i
$872$	43.4897	+	8.52164i	1.47275	+	0.288579i
$873$	−0.0508674	−	0.970608i	−0.00172160	−	0.0328501i
$874$	1.82961	−	4.59867i	0.0618875	−	0.155552i
$875$	−1.86366	−	17.7316i	−0.0630033	−	0.599437i
$876$	24.2044	−	58.7506i	0.817791	−	1.98500i
$877$	−15.0449	−	0.788469i	−0.508030	−	0.0266247i	−0.203400	−	0.979096i	$-0.565199\pi$
$877$	−15.0449	−	0.788469i	−0.508030	−	0.0266247i	−0.304630	+	0.952471i	$0.598533\pi$
$878$	13.9169	+	4.70937i	0.469671	+	0.158934i
$879$	−9.87735	+	9.87735i	−0.333155	+	0.333155i
$880$	26.9703	−	2.40870i	0.909170	−	0.0811972i
$881$	−39.9639	+	23.0732i	−1.34642	+	0.777355i	−0.987740	−	0.156106i	$-0.950106\pi$
$881$	−39.9639	+	23.0732i	−1.34642	+	0.777355i	−0.358678	+	0.933461i	$0.616772\pi$
$882$	9.10746	+	10.3652i	0.306664	+	0.349013i
$883$	5.62174	−	17.3019i	0.189187	−	0.582257i	−0.810809	−	0.585311i	$-0.800972\pi$
$883$	5.62174	−	17.3019i	0.189187	−	0.582257i	0.999995	+	0.00305445i	$0.000972264\pi$
$884$	−29.7687	+	24.0248i	−1.00123	+	0.808041i
$885$	−45.5549	+	33.0976i	−1.53131	+	1.11256i
$886$	17.4088	−	7.49905i	0.584860	−	0.251935i
$887$	1.51473	+	1.36387i	0.0508596	+	0.0457942i	0.694169	−	0.719813i	$-0.255772\pi$
$887$	1.51473	+	1.36387i	0.0508596	+	0.0457942i	−0.643309	+	0.765607i	$0.722439\pi$
$888$	23.1816	−	26.5863i	0.777925	−	0.892179i
$889$	−19.5524	+	3.09680i	−0.655768	+	0.103863i
$890$	−7.69622	+	2.39777i	−0.257978	+	0.0803735i
$891$	35.3599	+	8.23802i	1.18460	+	0.275984i
$892$	13.6766	−	16.0751i	0.457926	−	0.538234i
$893$	49.4920	−	22.0352i	1.65619	−	0.737381i
$894$	−18.2365	−	71.5212i	−0.609921	−	2.39203i
$895$	−1.56946	−	29.9470i	−0.0524612	−	1.00102i
$896$	−13.3727	−	10.3985i	−0.446752	−	0.347390i
$897$	−6.65303	−	0.899986i	−0.222138	−	0.0300496i
$898$	55.2134	−	20.4290i	1.84250	−	0.681725i
$899$	−47.1568	−	30.6240i	−1.57277	−	1.02137i
$900$	−0.0830322	+	3.41959i	−0.00276774	+	0.113986i
$901$	25.9821	+	15.0007i	0.865588	+	0.499747i
$902$	−20.2315	+	15.3509i	−0.673634	+	0.511129i
$903$	−13.2647	+	3.55427i	−0.441422	+	0.118279i
$904$	−7.32518	+	29.1920i	−0.243632	+	0.970913i
$905$	−12.2753	+	6.25457i	−0.408044	+	0.207909i
$906$	−3.64161	+	21.3145i	−0.120985	+	0.708125i
$907$	32.6591	+	14.5408i	1.08443	+	0.482819i	0.869562	−	0.493824i	$-0.164401\pi$
$907$	32.6591	+	14.5408i	1.08443	+	0.482819i	0.214867	+	0.976643i	$0.431068\pi$
$908$	−32.4256	+	15.5421i	−1.07608	+	0.515782i
$909$	−8.07894	+	2.62501i	−0.267962	+	0.0870660i
$910$	−4.19070	−	15.0088i	−0.138920	−	0.497536i
$911$	−3.47385	+	4.78134i	−0.115094	+	0.158413i	−0.862677	−	0.505755i	$-0.831214\pi$
$911$	−3.47385	+	4.78134i	−0.115094	+	0.158413i	0.747583	+	0.664168i	$0.231214\pi$
$912$	−37.7763	−	3.82512i	−1.25090	−	0.126662i
$913$	−7.34798	−	20.3147i	−0.243183	−	0.672320i
$914$	−26.8569	+	51.1646i	−0.888346	+	1.69238i
$915$	−2.39173	−	15.1008i	−0.0790683	−	0.499217i
$916$	34.7730	−	0.976798i	1.14893	−	0.0322743i
$917$	−4.41921	−	6.80498i	−0.145935	−	0.224720i
$918$	−15.8992	−	1.86646i	−0.524753	−	0.0616023i
$919$	25.2052	−	2.64918i	0.831444	−	0.0873883i	0.320764	−	0.947159i	$-0.396060\pi$
$919$	25.2052	−	2.64918i	0.831444	−	0.0873883i	0.510680	+	0.859771i	$0.329394\pi$
$920$	−3.91402	−	2.74944i	−0.129042	−	0.0906462i
$921$	−10.5569	−	6.85570i	−0.347860	−	0.225903i
$922$	−13.4698	−	8.98170i	−0.443604	−	0.295797i
$923$	−38.2726	+	0.865924i	−1.25976	+	0.0285022i
$924$	−20.4681	−	8.90216i	−0.673353	−	0.292860i
$925$	−4.47085	−	1.19796i	−0.147000	−	0.0393887i
$926$	1.28892	−	19.9560i	0.0423564	−	0.655796i
$927$	0.734174	+	0.815383i	0.0241134	+	0.0267807i
$928$	12.4692	−	45.0315i	0.409321	−	1.47823i
$929$	−30.3497	−	24.5767i	−0.995741	−	0.806335i	−0.0146520	−	0.999893i	$-0.504664\pi$
$929$	−30.3497	−	24.5767i	−0.995741	−	0.806335i	−0.981089	+	0.193558i	$0.937997\pi$
$930$	35.4067	+	26.3870i	1.16103	+	0.865265i
$931$	17.9071	+	9.12411i	0.586881	+	0.299031i
$932$	14.2010	+	13.4249i	0.465168	+	0.439748i
$933$	32.9827	+	3.46662i	1.07981	+	0.113492i
$934$	8.47205	−	37.6073i	0.277214	−	1.23055i
$935$	−32.3080	+	15.6777i	−1.05658	+	0.512716i
$936$	2.98604	+	20.6969i	0.0976017	+	0.676499i
$937$	−14.4775	−	10.5185i	−0.472960	−	0.343626i	0.325634	−	0.945496i	$-0.394422\pi$
$937$	−14.4775	−	10.5185i	−0.472960	−	0.343626i	−0.798594	+	0.601870i	$0.794422\pi$
$938$	4.92810	+	2.92557i	0.160908	+	0.0955231i
$939$	−24.8406	−	22.3666i	−0.810644	−	0.729907i
$940$	−9.63944	−	51.4629i	−0.314404	−	1.67854i
$941$	6.92883	−	43.7469i	0.225873	−	1.42611i	−0.570497	−	0.821299i	$-0.693250\pi$
$941$	6.92883	−	43.7469i	0.225873	−	1.42611i	0.796371	−	0.604809i	$-0.206750\pi$
$942$	−4.68496	+	3.31769i	−0.152644	+	0.108096i
$943$	4.48000	+	0.234787i	0.145889	+	0.00764571i
$944$	46.6423	−	15.3516i	1.51808	−	0.499651i
$945$	3.26053	−	5.64741i	0.106065	−	0.183710i
$946$	−14.6230	+	12.3529i	−0.475433	+	0.401629i
$947$	−12.3367	−	3.30561i	−0.400889	−	0.107418i	0.0527406	−	0.998608i	$-0.483204\pi$
$947$	−12.3367	−	3.30561i	−0.400889	−	0.107418i	−0.453629	+	0.891190i	$0.649871\pi$
$948$	−23.2933	+	38.1741i	−0.756531	+	1.23984i
$949$	−49.6055	+	11.7227i	−1.61026	+	0.380534i
$950$	1.72892	+	4.67273i	0.0560934	+	0.151603i
$951$	−26.7918	−	69.7950i	−0.868783	−	2.26326i
$952$	21.4744	+	6.60081i	0.695989	+	0.213934i
$953$	−10.0054	+	47.0719i	−0.324108	+	1.52481i	0.450737	+	0.892657i	$0.351161\pi$
$953$	−10.0054	+	47.0719i	−0.324108	+	1.52481i	−0.774845	+	0.632151i	$0.782172\pi$
$954$	14.3013	−	8.02702i	0.463023	−	0.259884i
$955$	17.7450	+	6.81168i	0.574215	+	0.220421i
$956$	−10.5105	−	29.5022i	−0.339934	−	0.954168i
$957$	1.19763	−	61.5553i	0.0387138	−	1.98980i
$958$	22.9558	−	43.7328i	0.741669	−	1.41294i
$959$	−3.06350	+	29.1472i	−0.0989255	+	0.941213i
$960$	−12.0515	+	34.6601i	−0.388960	+	1.11865i
$961$	−14.5875	+	4.73978i	−0.470566	+	0.152896i
$962$	−28.1703	−	2.66256i	−0.908247	−	0.0858445i
$963$	9.89138	+	13.6143i	0.318745	+	0.438715i
$964$	2.04848	+	15.3342i	0.0659771	+	0.493880i
$965$	−5.86509	+	1.24666i	−0.188804	+	0.0401315i
$966$	1.74722	+	3.53454i	0.0562160	+	0.113722i
$967$	−16.3362	−	16.3362i	−0.525336	−	0.525336i	0.393842	−	0.919178i	$-0.371146\pi$
$967$	−16.3362	−	16.3362i	−0.525336	−	0.525336i	−0.919178	+	0.393842i	$0.871146\pi$
$968$	−31.0993	+	0.914505i	−0.999568	+	0.0293933i
$969$	48.6400	−	13.0331i	1.56254	−	0.418682i
$970$	−1.34165	+	0.268199i	−0.0430778	+	0.00861134i
$971$	−8.39184	+	7.55604i	−0.269307	+	0.242485i	−0.792708	−	0.609601i	$-0.791330\pi$
$971$	−8.39184	+	7.55604i	−0.269307	+	0.242485i	0.523401	+	0.852086i	$0.324663\pi$
$972$	−22.1039	+	28.9201i	−0.708982	+	0.927613i
$973$	6.83942	+	17.8173i	0.219262	+	0.571196i
$974$	18.2362	+	23.0873i	0.584327	+	0.739766i
$975$	5.58343	−	3.80820i	0.178813	−	0.121960i
$976$	−2.03555	+	13.1764i	−0.0651563	+	0.421765i
$977$	−13.4043	−	16.5529i	−0.428841	−	0.529575i	0.516225	−	0.856453i	$-0.327337\pi$
$977$	−13.4043	−	16.5529i	−0.428841	−	0.529575i	−0.945067	+	0.326878i	$0.894003\pi$
$978$	−18.1221	+	11.4583i	−0.579480	+	0.366396i
$979$	8.99165	−	2.22278i	0.287374	−	0.0710402i
$980$	12.5863	−	14.7935i	0.402053	−	0.472562i
$981$	−11.5137	+	29.9941i	−0.367603	+	0.957639i
$982$	0.539565	−	44.4493i	0.0172182	−	1.41843i
$983$	4.43448	+	2.25948i	0.141438	+	0.0720662i	0.523277	−	0.852163i	$-0.324709\pi$
$983$	4.43448	+	2.25948i	0.141438	+	0.0720662i	−0.381839	+	0.924229i	$0.624709\pi$
$984$	−7.69147	−	33.5462i	−0.245195	−	1.06941i
$985$	−10.8758	+	24.4274i	−0.346531	+	0.778321i
$986$	5.72898	+	61.7035i	0.182448	+	1.96504i
$987$	−13.3368	+	41.0465i	−0.424515	+	1.30652i
$988$	15.1856	+	26.4030i	0.483118	+	0.839993i
$989$	3.38143			0.107523
$990$	−1.64607	+	19.5612i	−0.0523155	+	0.621697i
$991$	26.3593	−	15.2185i	0.837330	−	0.483433i	−0.0190259	−	0.999819i	$-0.506056\pi$
$991$	26.3593	−	15.2185i	0.837330	−	0.483433i	0.856356	+	0.516386i	$0.172723\pi$
$992$	−22.3738	−	31.3407i	−0.710368	−	0.995067i
$993$	−14.4498	−	28.3593i	−0.458550	−	0.899956i
$994$	12.9932	+	18.3479i	0.412120	+	0.581960i
$995$	−10.1452	−	8.21545i	−0.321626	−	0.260447i
$996$	29.1901	+	2.24141i	0.924922	+	0.0710219i
$997$	−40.5774	−	8.62498i	−1.28510	−	0.273156i	−0.485789	−	0.874076i	$-0.661468\pi$
$997$	−40.5774	−	8.62498i	−1.28510	−	0.273156i	−0.799309	+	0.600920i	$0.794801\pi$
$998$	11.0516	+	43.3427i	0.349832	+	1.37199i
$999$	−7.45189	−	9.20231i	−0.235767	−	0.291148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bs.a.15.19	✓	1280
4.3	odd	2	inner	572.2.bs.a.15.64	yes	1280
11.3	even	5	inner	572.2.bs.a.223.51	yes	1280
13.7	odd	12	inner	572.2.bs.a.59.32	yes	1280
44.3	odd	10	inner	572.2.bs.a.223.32	yes	1280
52.7	even	12	inner	572.2.bs.a.59.51	yes	1280
143.124	odd	60	inner	572.2.bs.a.267.64	yes	1280
572.267	even	60	inner	572.2.bs.a.267.19	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bs.a.15.19	✓	1280	1.1	even	1	trivial
572.2.bs.a.15.64	yes	1280	4.3	odd	2	inner
572.2.bs.a.59.32	yes	1280	13.7	odd	12	inner
572.2.bs.a.59.51	yes	1280	52.7	even	12	inner
572.2.bs.a.223.32	yes	1280	44.3	odd	10	inner
572.2.bs.a.223.51	yes	1280	11.3	even	5	inner
572.2.bs.a.267.19	yes	1280	572.267	even	60	inner
572.2.bs.a.267.64	yes	1280	143.124	odd	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06237 + 0.933467i) q^{2} +(0.467247 + 2.19822i) q^{3} +(0.257278 - 1.98338i) q^{4} +(0.319292 - 2.01593i) q^{5} +(-2.54836 - 1.89918i) q^{6} +(1.25573 - 0.815481i) q^{7} +(1.57810 + 2.34726i) q^{8} +(-1.87323 + 0.834017i) q^{9} +O(q^{10})\)	\(q+(-1.06237 + 0.933467i) q^{2} +(0.467247 + 2.19822i) q^{3} +(0.257278 - 1.98338i) q^{4} +(0.319292 - 2.01593i) q^{5} +(-2.54836 - 1.89918i) q^{6} +(1.25573 - 0.815481i) q^{7} +(1.57810 + 2.34726i) q^{8} +(-1.87323 + 0.834017i) q^{9} +(1.54260 + 2.43972i) q^{10} +(-1.60213 - 2.90400i) q^{11} +(4.48013 - 0.361175i) q^{12} +(-2.33185 - 2.75000i) q^{13} +(-0.572831 + 2.03853i) q^{14} +(4.58065 - 0.240062i) q^{15} +(-3.86762 - 1.02056i) q^{16} +(5.27581 - 0.554510i) q^{17} +(1.21155 - 2.63464i) q^{18} +(0.221059 - 4.21805i) q^{19} +(-3.91621 - 1.15193i) q^{20} +(2.37935 + 2.37935i) q^{21} +(4.41284 + 1.58960i) q^{22} +(-0.414274 - 0.717544i) q^{23} +(-4.42243 + 4.56576i) q^{24} +(0.793261 + 0.257746i) q^{25} +(5.04433 + 0.744825i) q^{26} +(1.25423 + 1.72630i) q^{27} +(-1.29434 - 2.70040i) q^{28} +(5.52706 - 6.13843i) q^{29} +(-4.64228 + 4.53092i) q^{30} +(-1.06488 - 6.72341i) q^{31} +(5.06152 - 2.52608i) q^{32} +(5.63505 - 4.87871i) q^{33} +(-5.08727 + 5.51390i) q^{34} +(-1.24301 - 2.79184i) q^{35} +(1.17223 + 3.92991i) q^{36} +(-5.54167 + 0.290427i) q^{37} +(3.70257 + 4.68750i) q^{38} +(4.95556 - 6.41085i) q^{39} +(5.23577 - 2.43187i) q^{40} +(-2.94893 + 4.54095i) q^{41} +(-4.74880 - 0.306714i) q^{42} +(-2.04057 + 3.53437i) q^{43} +(-6.17193 + 2.43050i) q^{44} +(1.08321 + 4.04260i) q^{45} +(1.10992 + 0.375589i) q^{46} +(5.82296 + 11.4282i) q^{47} +(0.436289 - 8.97874i) q^{48} +(-1.93531 + 4.34677i) q^{49} +(-1.08334 + 0.466660i) q^{50} +(3.68405 + 11.3383i) q^{51} +(-6.05423 + 3.91743i) q^{52} +(4.57536 + 3.32419i) q^{53} +(-2.94390 - 0.663193i) q^{54} +(-6.36579 + 2.30255i) q^{55} +(3.89581 + 1.66061i) q^{56} +(9.37551 - 1.48494i) q^{57} +(-0.141790 + 11.6806i) q^{58} +(-10.2955 + 6.68596i) q^{59} +(0.702365 - 9.14695i) q^{60} +(-0.348411 - 3.31491i) q^{61} +(7.40739 + 6.14874i) q^{62} +(-1.67215 + 2.57489i) q^{63} +(-3.01921 + 7.40840i) q^{64} +(-6.28834 + 3.82279i) q^{65} +(-1.43241 + 10.4432i) q^{66} +(0.700506 - 2.61432i) q^{67} +(0.257543 - 10.6066i) q^{68} +(1.38375 - 1.24594i) q^{69} +(3.92663 + 1.80567i) q^{70} +(6.68189 - 8.25144i) q^{71} +(-4.91380 - 3.08080i) q^{72} +(6.41808 - 12.5962i) q^{73} +(5.61622 - 5.48151i) q^{74} +(-0.195935 + 1.86420i) q^{75} +(-8.30914 - 1.52366i) q^{76} +(-4.37999 - 2.34013i) q^{77} +(0.719655 + 11.4366i) q^{78} +(-5.84815 + 8.04929i) q^{79} +(-3.29228 + 7.47098i) q^{80} +(-7.32493 + 8.13516i) q^{81} +(-1.10596 - 7.57692i) q^{82} +(6.43330 + 1.01893i) q^{83} +(5.33131 - 4.10700i) q^{84} +(0.566670 - 10.8127i) q^{85} +(-1.13137 - 5.65963i) q^{86} +(16.0761 + 9.28156i) q^{87} +(4.28811 - 8.34339i) q^{88} +(-0.722802 + 2.69754i) q^{89} +(-4.92441 - 3.28361i) q^{90} +(-5.17074 - 1.55168i) q^{91} +(-1.52975 + 0.637057i) q^{92} +(14.2820 - 5.48235i) q^{93} +(-16.8540 - 6.70548i) q^{94} +(-8.43271 - 1.79243i) q^{95} +(7.91786 + 9.94605i) q^{96} +(-0.169866 + 0.442516i) q^{97} +(-2.00155 - 6.42444i) q^{98} +(5.42314 + 4.10366i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Introduction

L-functions

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