LMFDB - Embedded newform 756.2.ci.a.95.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(95,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17, 12]))

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

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

chi := DirichletCharacter("756.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ci (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.1
Character	$\chi$	$=$	756.95
Dual form			756.2.ci.a.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41419 + 0.00832720i) q^{2} +(1.09084 - 1.34539i) q^{3} +(1.99986 - 0.0235525i) q^{4} +(2.13665 + 0.376749i) q^{5} +(-1.53144 + 1.91172i) q^{6} +(2.48173 + 0.917059i) q^{7} +(-2.82799 + 0.0499609i) q^{8} +(-0.620154 - 2.93520i) q^{9} +O(q^{10})$	\(q+(-1.41419 + 0.00832720i) q^{2} +(1.09084 - 1.34539i) q^{3} +(1.99986 - 0.0235525i) q^{4} +(2.13665 + 0.376749i) q^{5} +(-1.53144 + 1.91172i) q^{6} +(2.48173 + 0.917059i) q^{7} +(-2.82799 + 0.0499609i) q^{8} +(-0.620154 - 2.93520i) q^{9} +(-3.02476 - 0.515002i) q^{10} +(0.408639 + 2.31751i) q^{11} +(2.14983 - 2.71629i) q^{12} +(-0.977014 + 5.54092i) q^{13} +(-3.51728 - 1.27623i) q^{14} +(2.83761 - 2.46366i) q^{15} +(3.99889 - 0.0942034i) q^{16} +(3.03522 - 1.75239i) q^{17} +(0.901457 + 4.14577i) q^{18} +(6.44594 + 3.72156i) q^{19} +(4.28187 + 0.703122i) q^{20} +(3.94097 - 2.33854i) q^{21} +(-0.597192 - 3.27399i) q^{22} +(0.876606 + 0.735560i) q^{23} +(-3.01765 + 3.85925i) q^{24} +(-0.275135 - 0.100141i) q^{25} +(1.33554 - 7.84404i) q^{26} +(-4.62548 - 2.36747i) q^{27} +(4.98472 + 1.77554i) q^{28} +(-9.51207 + 1.67723i) q^{29} +(-3.99240 + 3.50771i) q^{30} +(2.86446 + 0.505081i) q^{31} +(-5.65440 + 0.166521i) q^{32} +(3.56371 + 1.97824i) q^{33} +(-4.27778 + 2.50348i) q^{34} +(4.95709 + 2.89442i) q^{35} +(-1.30935 - 5.85539i) q^{36} -7.45130 q^{37} +(-9.14676 - 5.20932i) q^{38} +(6.38894 + 7.35870i) q^{39} +(-6.06124 - 0.958691i) q^{40} +(-1.55229 - 0.273710i) q^{41} +(-5.55380 + 3.33996i) q^{42} +(2.10789 + 2.51208i) q^{43} +(0.871805 + 4.62507i) q^{44} +(-0.219217 - 6.50514i) q^{45} +(-1.24581 - 1.03292i) q^{46} +(-0.810739 - 4.59793i) q^{47} +(4.23539 - 5.48283i) q^{48} +(5.31801 + 4.55179i) q^{49} +(0.389926 + 0.139327i) q^{50} +(0.953284 - 5.99512i) q^{51} +(-1.82339 + 11.1041i) q^{52} +(-7.18267 - 4.14692i) q^{53} +(6.56102 + 3.30954i) q^{54} +5.10566i q^{55} +(-7.06413 - 2.46944i) q^{56} +(12.0384 - 4.61269i) q^{57} +(13.4379 - 2.45114i) q^{58} +(1.47176 - 0.535676i) q^{59} +(5.61680 - 4.99380i) q^{60} +(-2.05678 - 11.6646i) q^{61} +(-4.05509 - 0.690427i) q^{62} +(1.15270 - 7.85311i) q^{63} +(7.99501 - 0.282577i) q^{64} +(-4.17507 + 11.4709i) q^{65} +(-5.05624 - 2.76793i) q^{66} +(2.54861 - 3.03731i) q^{67} +(6.02875 - 3.57602i) q^{68} +(1.94585 - 0.377003i) q^{69} +(-7.03437 - 4.05198i) q^{70} +(4.48169 - 7.76252i) q^{71} +(1.90043 + 8.26973i) q^{72} +9.73135 q^{73} +(10.5375 - 0.0620485i) q^{74} +(-0.434855 + 0.260926i) q^{75} +(12.9786 + 7.29079i) q^{76} +(-1.11116 + 6.12619i) q^{77} +(-9.09645 - 10.3534i) q^{78} +(-10.3755 - 12.3650i) q^{79} +(8.57972 + 1.30530i) q^{80} +(-8.23082 + 3.64055i) q^{81} +(2.19751 + 0.374152i) q^{82} +(-0.831866 - 4.71774i) q^{83} +(7.82631 - 4.76958i) q^{84} +(7.14541 - 2.60072i) q^{85} +(-3.00187 - 3.53501i) q^{86} +(-8.11957 + 14.6270i) q^{87} +(-1.27141 - 6.53347i) q^{88} +(-8.56772 - 4.94658i) q^{89} +(0.364184 + 9.19767i) q^{90} +(-7.50604 + 12.8551i) q^{91} +(1.77041 + 1.45037i) q^{92} +(3.80418 - 3.30285i) q^{93} +(1.18483 + 6.49559i) q^{94} +(12.3706 + 10.3802i) q^{95} +(-5.94399 + 7.78903i) q^{96} +(3.50909 - 2.94447i) q^{97} +(-7.55857 - 6.39281i) q^{98} +(6.54894 - 2.63665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.41419	+	0.00832720i	−0.999983	+	0.00588822i
$2$	−1.41419	+	0.00832720i	−0.999983	+	0.00588822i
$3$	1.09084	−	1.34539i	0.629794	−	0.776762i
$3$	1.09084	−	1.34539i	0.629794	−	0.776762i
$4$	1.99986	−	0.0235525i	0.999931	−	0.0117762i
$5$	2.13665	+	0.376749i	0.955538	+	0.168487i	0.629614	−	0.776908i	$-0.283213\pi$
$5$	2.13665	+	0.376749i	0.955538	+	0.168487i	0.325925	+	0.945396i	$0.394324\pi$
$6$	−1.53144	+	1.91172i	−0.625210	+	0.780457i
$7$	2.48173	+	0.917059i	0.938007	+	0.346616i
$7$	2.48173	+	0.917059i	0.938007	+	0.346616i
$8$	−2.82799	+	0.0499609i	−0.999844	+	0.0176638i
$9$	−0.620154	−	2.93520i	−0.206718	−	0.978401i
$10$	−3.02476	−	0.515002i	−0.956514	−	0.162858i
$11$	0.408639	+	2.31751i	0.123209	+	0.698755i	0.982355	+	0.187024i	$0.0598844\pi$
$11$	0.408639	+	2.31751i	0.123209	+	0.698755i	−0.859146	+	0.511731i	$0.829005\pi$
$12$	2.14983	−	2.71629i	0.620603	−	0.784125i
$13$	−0.977014	+	5.54092i	−0.270975	+	1.53677i	0.480489	+	0.877001i	$0.340459\pi$
$13$	−0.977014	+	5.54092i	−0.270975	+	1.53677i	−0.751464	+	0.659774i	$0.770652\pi$
$14$	−3.51728	−	1.27623i	−0.940032	−	0.341087i
$15$	2.83761	−	2.46366i	0.732667	−	0.636113i
$16$	3.99889	−	0.0942034i	0.999723	−	0.0235508i
$17$	3.03522	−	1.75239i	0.736149	−	0.425016i	−0.0845183	−	0.996422i	$-0.526935\pi$
$17$	3.03522	−	1.75239i	0.736149	−	0.425016i	0.820668	+	0.571406i	$0.193602\pi$
$18$	0.901457	+	4.14577i	0.212475	+	0.977166i
$19$	6.44594	+	3.72156i	1.47880	+	0.853785i	0.999712	−	0.0239820i	$-0.00763445\pi$
$19$	6.44594	+	3.72156i	1.47880	+	0.853785i	0.479087	+	0.877767i	$0.340968\pi$
$20$	4.28187	+	0.703122i	0.957456	+	0.157223i
$21$	3.94097	−	2.33854i	0.859990	−	0.510312i
$22$	−0.597192	−	3.27399i	−0.127322	−	0.698018i
$23$	0.876606	+	0.735560i	0.182785	+	0.153375i	0.729589	−	0.683886i	$-0.239711\pi$
$23$	0.876606	+	0.735560i	0.182785	+	0.153375i	−0.546804	+	0.837261i	$0.684156\pi$
$24$	−3.01765	+	3.85925i	−0.615976	+	0.787765i
$25$	−0.275135	−	0.100141i	−0.0550269	−	0.0200282i
$26$	1.33554	−	7.84404i	0.261921	−	1.53834i
$27$	−4.62548	−	2.36747i	−0.890174	−	0.455621i
$28$	4.98472	+	1.77554i	0.942024	+	0.335546i
$29$	−9.51207	+	1.67723i	−1.76635	+	0.311455i	−0.960002	−	0.279992i	$-0.909668\pi$
$29$	−9.51207	+	1.67723i	−1.76635	+	0.311455i	−0.806344	+	0.591446i	$0.798557\pi$
$30$	−3.99240	+	3.50771i	−0.728909	+	0.640417i
$31$	2.86446	+	0.505081i	0.514472	+	0.0907152i	0.424856	−	0.905261i	$-0.360325\pi$
$31$	2.86446	+	0.505081i	0.514472	+	0.0907152i	0.0896160	+	0.995976i	$0.471436\pi$
$32$	−5.65440	+	0.166521i	−0.999567	+	0.0294370i
$33$	3.56371	+	1.97824i	0.620363	+	0.344368i
$34$	−4.27778	+	2.50348i	−0.733634	+	0.429343i
$35$	4.95709	+	2.89442i	0.837902	+	0.489247i
$36$	−1.30935	−	5.85539i	−0.218226	−	0.975898i
$37$	−7.45130			−1.22499			−0.612493	−	0.790476i	$-0.709833\pi$
$37$	−7.45130			−1.22499			−0.612493	+	0.790476i	$0.709833\pi$
$38$	−9.14676	−	5.20932i	−1.48380	−	0.845063i
$39$	6.38894	+	7.35870i	1.02305	+	1.17834i
$40$	−6.06124	−	0.958691i	−0.958365	−	0.151582i
$41$	−1.55229	−	0.273710i	−0.242427	−	0.0427464i	0.0511144	−	0.998693i	$-0.483723\pi$
$41$	−1.55229	−	0.273710i	−0.242427	−	0.0427464i	−0.293541	+	0.955946i	$0.594834\pi$
$42$	−5.55380	+	3.33996i	−0.856970	+	0.515367i
$43$	2.10789	+	2.51208i	0.321450	+	0.383089i	0.902436	−	0.430825i	$-0.141777\pi$
$43$	2.10789	+	2.51208i	0.321450	+	0.383089i	−0.580986	+	0.813914i	$0.697333\pi$
$44$	0.871805	+	4.62507i	0.131430	+	0.697256i
$45$	−0.219217	−	6.50514i	−0.0326790	−	0.969729i
$46$	−1.24581	−	1.03292i	−0.183685	−	0.152296i
$47$	−0.810739	−	4.59793i	−0.118258	−	0.670677i	−0.985085	−	0.172067i	$-0.944955\pi$
$47$	−0.810739	−	4.59793i	−0.118258	−	0.670677i	0.866827	−	0.498609i	$-0.166156\pi$
$48$	4.23539	−	5.48283i	0.611326	−	0.791379i
$49$	5.31801	+	4.55179i	0.759715	+	0.650256i
$50$	0.389926	+	0.139327i	0.0551439	+	0.0197038i
$51$	0.953284	−	5.99512i	0.133486	−	0.839485i
$52$	−1.82339	+	11.1041i	−0.252859	+	1.53986i
$53$	−7.18267	−	4.14692i	−0.986616	−	0.569623i	−0.0823548	−	0.996603i	$-0.526244\pi$
$53$	−7.18267	−	4.14692i	−0.986616	−	0.569623i	−0.904261	+	0.426980i	$0.859577\pi$
$54$	6.56102	+	3.30954i	0.892841	+	0.450371i
$55$			5.10566i			0.688447i
$56$	−7.06413	−	2.46944i	−0.943983	−	0.329993i
$57$	12.0384	−	4.61269i	1.59453	−	0.610966i
$58$	13.4379	−	2.45114i	1.76448	−	0.321850i
$59$	1.47176	−	0.535676i	0.191606	−	0.0697390i	−0.244435	−	0.969666i	$-0.578602\pi$
$59$	1.47176	−	0.535676i	0.191606	−	0.0697390i	0.436041	+	0.899927i	$0.356380\pi$
$60$	5.61680	−	4.99380i	0.725125	−	0.644697i
$61$	−2.05678	−	11.6646i	−0.263344	−	1.49350i	−0.773711	−	0.633539i	$-0.781602\pi$
$61$	−2.05678	−	11.6646i	−0.263344	−	1.49350i	0.510367	−	0.859957i	$-0.329509\pi$
$62$	−4.05509	−	0.690427i	−0.514997	−	0.0876843i
$63$	1.15270	−	7.85311i	0.145226	−	0.989398i
$64$	7.99501	−	0.282577i	0.999376	−	0.0353222i
$65$	−4.17507	+	11.4709i	−0.517854	+	1.42279i
$66$	−5.05624	−	2.76793i	−0.622380	−	0.340709i
$67$	2.54861	−	3.03731i	0.311362	−	0.371067i	−0.587556	−	0.809183i	$-0.699910\pi$
$67$	2.54861	−	3.03731i	0.311362	−	0.371067i	0.898918	+	0.438117i	$0.144354\pi$
$68$	6.02875	−	3.57602i	0.731093	−	0.433656i
$69$	1.94585	−	0.377003i	0.234253	−	0.0453858i
$70$	−7.03437	−	4.05198i	−0.840768	−	0.484305i
$71$	4.48169	−	7.76252i	0.531879	−	0.921241i	−0.467429	−	0.884031i	$-0.654819\pi$
$71$	4.48169	−	7.76252i	0.531879	−	0.921241i	0.999307	−	0.0372104i	$-0.0118472\pi$
$72$	1.90043	+	8.26973i	0.223968	+	0.974596i
$73$	9.73135			1.13897			0.569484	−	0.822002i	$-0.307143\pi$
$73$	9.73135			1.13897			0.569484	+	0.822002i	$0.307143\pi$
$74$	10.5375	−	0.0620485i	1.22496	−	0.00721299i
$75$	−0.434855	+	0.260926i	−0.0502127	+	0.0301292i
$76$	12.9786	+	7.29079i	1.48875	+	0.836311i
$77$	−1.11116	+	6.12619i	−0.126628	+	0.698144i
$78$	−9.09645	−	10.3534i	−1.02997	−	1.17229i
$79$	−10.3755	−	12.3650i	−1.16733	−	1.39117i	−0.904578	−	0.426308i	$-0.859814\pi$
$79$	−10.3755	−	12.3650i	−1.16733	−	1.39117i	−0.262754	−	0.964863i	$-0.584631\pi$
$80$	8.57972	+	1.30530i	0.959241	+	0.145937i
$81$	−8.23082	+	3.64055i	−0.914535	+	0.404506i
$82$	2.19751	+	0.374152i	0.242674	+	0.0413182i
$83$	−0.831866	−	4.71774i	−0.0913091	−	0.517840i	−0.995816	−	0.0913807i	$-0.970872\pi$
$83$	−0.831866	−	4.71774i	−0.0913091	−	0.517840i	0.904507	−	0.426459i	$-0.140239\pi$
$84$	7.82631	−	4.76958i	0.853920	−	0.520404i
$85$	7.14541	−	2.60072i	0.775029	−	0.282087i
$86$	−3.00187	−	3.53501i	−0.323700	−	0.381189i
$87$	−8.11957	+	14.6270i	−0.870509	+	1.56818i
$88$	−1.27141	−	6.53347i	−0.135533	−	0.696470i
$89$	−8.56772	−	4.94658i	−0.908177	−	0.524336i	−0.0283328	−	0.999599i	$-0.509020\pi$
$89$	−8.56772	−	4.94658i	−0.908177	−	0.524336i	−0.879844	+	0.475262i	$0.842353\pi$
$90$	0.364184	+	9.19767i	0.0383884	+	0.969519i
$91$	−7.50604	+	12.8551i	−0.786847	+	1.34758i
$92$	1.77041	+	1.45037i	0.184578	+	0.151212i
$93$	3.80418	−	3.30285i	0.394475	−	0.342490i
$94$	1.18483	+	6.49559i	0.122205	+	0.669969i
$95$	12.3706	+	10.3802i	1.26920	+	1.06498i
$96$	−5.94399	+	7.78903i	−0.606656	+	0.794965i
$97$	3.50909	−	2.94447i	0.356294	−	0.298966i	−0.447018	−	0.894525i	$-0.647514\pi$
$97$	3.50909	−	2.94447i	0.356294	−	0.298966i	0.803311	+	0.595559i	$0.203069\pi$
$98$	−7.55857	−	6.39281i	−0.763531	−	0.645772i
$99$	6.54894	−	2.63665i	0.658193	−	0.264993i
$100$	−0.552589	−	0.193788i	−0.0552589	−	0.0193788i
$101$	4.94080	+	5.88822i	0.491628	+	0.585900i	0.953631	−	0.300979i	$-0.0973133\pi$
$101$	4.94080	+	5.88822i	0.491628	+	0.585900i	−0.462002	+	0.886879i	$0.652869\pi$
$102$	−1.29820	+	8.48618i	−0.128541	+	0.840257i
$103$	−0.320030	−	0.0564300i	−0.0315335	−	0.00556021i	0.157859	−	0.987462i	$-0.449541\pi$
$103$	−0.320030	−	0.0564300i	−0.0315335	−	0.00556021i	−0.189393	+	0.981901i	$0.560652\pi$
$104$	2.48615	−	15.7185i	0.243787	−	1.54132i
$105$	9.30151	−	3.51189i	0.907734	−	0.342725i
$106$	10.1922	+	5.80471i	0.989953	+	0.563804i
$107$	0.0801945	+	0.138901i	0.00775270	+	0.0134281i	0.869876	−	0.493271i	$-0.164199\pi$
$107$	0.0801945	+	0.138901i	0.00775270	+	0.0134281i	−0.862123	+	0.506699i	$0.830866\pi$
$108$	−9.30608	−	4.62568i	−0.895478	−	0.445106i
$109$	6.56013	−	11.3625i	0.628347	−	1.08833i	−0.359537	−	0.933131i	$-0.617065\pi$
$109$	6.56013	−	11.3625i	0.628347	−	1.08833i	0.987884	−	0.155197i	$-0.0496013\pi$
$110$	−0.0425158	−	7.22037i	−0.00405373	−	0.688435i
$111$	−8.12814	+	10.0249i	−0.771489	+	0.951522i
$112$	10.0106	+	3.43343i	0.945910	+	0.324429i
$113$	8.54679	−	10.1857i	0.804014	−	0.958187i	−0.195733	−	0.980657i	$-0.562709\pi$
$113$	8.54679	−	10.1857i	0.804014	−	0.958187i	0.999748	+	0.0224705i	$0.00715319\pi$
$114$	−16.9862	+	6.62346i	−1.59090	+	0.620344i
$115$	1.59588	+	1.90189i	0.148816	+	0.177352i
$116$	−18.9833	+	3.57827i	−1.76256	+	0.332234i
$117$	16.8696	−	0.568491i	1.55960	−	0.0525570i
$118$	−2.07688	+	0.769802i	−0.191192	+	0.0708660i
$119$	9.13965	−	1.56548i	0.837831	−	0.143507i
$120$	−7.90163	+	7.10896i	−0.721317	+	0.648956i
$121$	5.13276	−	1.86817i	0.466614	−	0.169834i
$122$	3.00581	+	16.4788i	0.272133	+	1.49192i
$123$	−2.06154	+	1.78986i	−0.185883	+	0.161386i
$124$	5.74041	+	0.942627i	0.515504	+	0.0846504i
$125$	−9.94483	−	5.74165i	−0.889492	−	0.513549i
$126$	−1.56474	+	11.1154i	−0.139398	+	0.990236i
$127$	−14.4253	+	8.32842i	−1.28003	+	0.739028i	−0.976854	−	0.213905i	$-0.931382\pi$
$127$	−14.4253	+	8.32842i	−1.28003	+	0.739028i	−0.303180	+	0.952933i	$0.598048\pi$
$128$	−11.3041	+	0.466194i	−0.999151	+	0.0412061i
$129$	5.67909	−	0.0956630i	0.500016	−	0.00842266i
$130$	5.80882	−	16.2568i	0.509467	−	1.42582i
$131$	4.61230	+	3.87018i	0.402978	+	0.338139i	0.821644	−	0.570002i	$-0.193057\pi$
$131$	4.61230	+	3.87018i	0.402978	+	0.338139i	−0.418665	+	0.908141i	$0.637502\pi$
$132$	7.17353	+	3.87228i	0.624375	+	0.337038i
$133$	12.5842	+	15.1472i	1.09119	+	1.31343i
$134$	−3.57892	+	4.31656i	−0.309172	+	0.372894i
$135$	−8.99108	−	6.80110i	−0.773829	−	0.585346i
$136$	−8.49601	+	5.10736i	−0.728527	+	0.437953i
$137$	0.664246	−	1.82500i	0.0567504	−	0.155920i	−0.908078	−	0.418801i	$-0.862450\pi$
$137$	0.664246	−	1.82500i	0.0567504	−	0.155920i	0.964828	+	0.262881i	$0.0846726\pi$
$138$	−2.74866	+	0.549357i	−0.233981	+	0.0467643i
$139$	0.862854	+	2.37067i	0.0731863	+	0.201078i	0.970892	−	0.239518i	$-0.0769894\pi$
$139$	0.862854	+	2.37067i	0.0731863	+	0.201078i	−0.897706	+	0.440596i	$0.854767\pi$
$140$	9.98167	+	5.67169i	0.843605	+	0.479346i
$141$	−7.07039	−	3.92482i	−0.595435	−	0.330530i
$142$	−6.27332	+	11.0150i	−0.526445	+	0.924357i
$143$	−13.2404			−1.10722
$144$	−2.75643	−	11.6791i	−0.229703	−	0.973261i
$145$	−20.9558			−1.74029
$146$	−13.7620	+	0.0810349i	−1.13895	+	0.00670649i
$147$	11.9250	−	2.18954i	0.983558	−	0.180590i
$148$	−14.9016	+	0.175497i	−1.22490	+	0.0144257i
$149$	3.88785	+	10.6818i	0.318505	+	0.875086i	0.990865	+	0.134861i	$0.0430588\pi$
$149$	3.88785	+	10.6818i	0.318505	+	0.875086i	−0.672359	+	0.740225i	$0.734719\pi$
$150$	0.612795	−	0.372620i	0.0500345	−	0.0304243i
$151$	8.15310	−	1.43761i	0.663490	−	0.116991i	0.168246	−	0.985745i	$-0.446190\pi$
$151$	8.15310	−	1.43761i	0.663490	−	0.116991i	0.495244	+	0.868754i	$0.335079\pi$
$152$	−18.4150	−	10.2025i	−1.49365	−	0.827531i
$153$	−7.02591	−	7.82224i	−0.568011	−	0.632390i
$154$	1.52037	−	8.67284i	0.122515	−	0.698877i
$155$	5.93005	+	2.15836i	0.476313	+	0.173364i
$156$	12.9503	+	14.5659i	1.03685	+	1.16621i
$157$	−20.1390	+	7.32999i	−1.60727	+	0.584997i	−0.980897	−	0.194529i	$-0.937682\pi$
$157$	−20.1390	+	7.32999i	−1.60727	+	0.584997i	−0.626369	+	0.779526i	$0.715460\pi$
$158$	14.7758	+	17.4001i	1.17550	+	1.38427i
$159$	−13.4143	+	5.13990i	−1.06383	+	0.407620i
$160$	−12.1442	−	1.77449i	−0.960084	−	0.140286i
$161$	1.50095	+	2.62936i	0.118292	+	0.207223i
$162$	11.6096	−	5.21697i	0.912138	−	0.409884i
$163$	−12.5782	+	7.26205i	−0.985204	+	0.568808i	−0.903837	−	0.427876i	$-0.859262\pi$
$163$	−12.5782	+	7.26205i	−0.985204	+	0.568808i	−0.0813669	+	0.996684i	$0.525929\pi$
$164$	−3.11081	−	0.510823i	−0.242913	−	0.0398886i
$165$	6.86911	+	5.56943i	0.534759	+	0.433580i
$166$	1.21570	+	6.66485i	0.0943567	+	0.517293i
$167$	−8.03119	−	6.73897i	−0.621472	−	0.521477i	0.276794	−	0.960929i	$-0.410728\pi$
$167$	−8.03119	−	6.73897i	−0.621472	−	0.521477i	−0.898266	+	0.439452i	$0.855173\pi$
$168$	−11.0282	+	6.81026i	−0.850841	+	0.525423i
$169$	−17.5312	−	6.38085i	−1.34856	−	0.490834i
$170$	−10.0833	+	3.73741i	−0.773354	+	0.286646i
$171$	6.92607	−	21.2281i	0.529650	−	1.62335i
$172$	4.27465	+	4.97417i	0.325939	+	0.379277i
$173$	2.12799	−	5.84661i	0.161788	−	0.444510i	−0.832136	−	0.554571i	$-0.812882\pi$
$173$	2.12799	−	5.84661i	0.161788	−	0.444510i	0.993925	+	0.110061i	$0.0351046\pi$
$174$	11.3608	−	20.7530i	0.861260	−	1.57328i
$175$	−0.590976	−	0.500837i	−0.0446736	−	0.0378597i
$176$	1.85242	+	9.22897i	0.139632	+	0.695660i
$177$	0.884752	−	2.56442i	0.0665020	−	0.192754i
$178$	12.1576	+	6.92405i	0.911249	+	0.518980i
$179$	0.290070	+	0.502417i	0.0216809	+	0.0375524i	0.876662	−	0.481106i	$-0.159765\pi$
$179$	0.290070	+	0.502417i	0.0216809	+	0.0375524i	−0.854981	+	0.518659i	$0.826432\pi$
$180$	−0.591616	−	13.0042i	−0.0440965	−	0.969277i
$181$	−2.57474	−	4.45959i	−0.191379	−	0.331478i	0.754328	−	0.656497i	$-0.227963\pi$
$181$	−2.57474	−	4.45959i	−0.191379	−	0.331478i	−0.945708	+	0.325019i	$0.894629\pi$
$182$	10.5079	−	18.2421i	0.778898	−	1.35219i
$183$	−17.9370	−	9.95696i	−1.32594	−	0.736040i
$184$	−2.51578	−	2.03636i	−0.185466	−	0.150122i
$185$	−15.9208	−	2.80727i	−1.17052	−	0.206394i
$186$	−5.35233	+	4.70254i	−0.392452	+	0.344807i
$187$	5.30148	+	6.31806i	0.387683	+	0.462022i
$188$	−1.72966	−	9.17612i	−0.126148	−	0.669238i
$189$	−9.30810	−	10.1173i	−0.677064	−	0.735924i
$190$	−17.5808	−	14.5765i	−1.27545	−	1.05749i
$191$	5.15549	−	4.32597i	0.373039	−	0.313016i	−0.436924	−	0.899499i	$-0.643932\pi$
$191$	5.15549	−	4.32597i	0.373039	−	0.313016i	0.809962	+	0.586482i	$0.199488\pi$
$192$	8.34106	−	11.0647i	0.601964	−	0.798523i
$193$	2.25647	−	12.7971i	0.162425	−	0.921155i	−0.789256	−	0.614065i	$-0.789533\pi$
$193$	2.25647	−	12.7971i	0.162425	−	0.921155i	0.951680	−	0.307091i	$-0.0993555\pi$
$194$	−4.93799	+	4.19326i	−0.354527	+	0.301059i
$195$	10.8785	+	18.1300i	0.779029	+	1.29832i
$196$	10.7425	+	8.97770i	0.767320	+	0.641264i
$197$	−4.17509	+	2.41049i	−0.297463	+	0.171740i	−0.641303	−	0.767288i	$-0.721606\pi$
$197$	−4.17509	+	2.41049i	−0.297463	+	0.171740i	0.343840	+	0.939028i	$0.388272\pi$
$198$	−9.23948	+	3.78326i	−0.656621	+	0.268864i
$199$	−5.97465	+	3.44947i	−0.423532	+	0.244526i	−0.696587	−	0.717472i	$-0.745299\pi$
$199$	−5.97465	+	3.44947i	−0.423532	+	0.244526i	0.273055	+	0.961998i	$0.411966\pi$
$200$	0.783080	+	0.269451i	0.0553721	+	0.0190530i
$201$	−1.30626	−	6.74208i	−0.0921365	−	0.475550i
$202$	−7.03626	−	8.28592i	−0.495070	−	0.582995i
$203$	−25.1445	−	4.56068i	−1.76480	−	0.320097i
$204$	1.76524	−	12.0119i	0.123591	−	0.840999i
$205$	−3.21358	−	1.16965i	−0.224446	−	0.0816916i
$206$	0.453053	+	0.0771377i	0.0315657	+	0.00537444i
$207$	1.61539	−	3.02918i	0.112277	−	0.210542i
$208$	−3.38500	+	22.2496i	−0.234707	+	1.54273i
$209$	−5.99069	+	16.4593i	−0.414385	+	1.13851i
$210$	−13.1248	+	5.04393i	−0.905700	+	0.348064i
$211$	13.8093	−	16.4573i	0.950674	−	1.13297i	−0.0403367	−	0.999186i	$-0.512843\pi$
$211$	13.8093	−	16.4573i	0.950674	−	1.13297i	0.991011	−	0.133783i	$-0.0427125\pi$
$212$	−14.4620	−	8.12409i	−0.993255	−	0.557965i
$213$	−5.55483	−	14.4973i	−0.380611	−	0.993336i
$214$	−0.114567	−	0.195764i	−0.00783163	−	0.0133822i
$215$	3.55739	+	6.16158i	0.242612	+	0.420216i
$216$	13.1991	+	6.46409i	0.898083	+	0.439826i
$217$	6.64563	+	3.88035i	0.451135	+	0.263415i
$218$	−9.18265	+	16.1233i	−0.621927	+	1.09201i
$219$	10.6153	−	13.0925i	0.717316	−	0.884707i
$220$	0.120251	+	10.2106i	0.00810731	+	0.688399i
$221$	6.74438	+	18.5300i	0.453676	+	1.24646i
$222$	11.4113	−	14.2448i	0.765873	−	0.956049i
$223$	−1.62321	+	4.45974i	−0.108698	+	0.298646i	−0.982102	−	0.188351i	$-0.939686\pi$
$223$	−1.62321	+	4.45974i	−0.108698	+	0.298646i	0.873403	+	0.486997i	$0.161908\pi$
$224$	−14.1854	−	4.77216i	−0.947804	−	0.318853i
$225$	−0.123308	+	0.869678i	−0.00822051	+	0.0579785i
$226$	−12.0020	+	14.4756i	−0.798358	+	0.962904i
$227$	3.32860	+	18.8774i	0.220927	+	1.25294i	0.870320	+	0.492486i	$0.163912\pi$
$227$	3.32860	+	18.8774i	0.220927	+	1.25294i	−0.649393	+	0.760453i	$0.724977\pi$
$228$	23.9665	−	9.50828i	1.58722	−	0.629701i
$229$	10.1504	−	3.69443i	0.670755	−	0.244135i	0.0158819	−	0.999874i	$-0.494944\pi$
$229$	10.1504	−	3.69443i	0.670755	−	0.244135i	0.654873	+	0.755739i	$0.272722\pi$
$230$	−2.27271	−	2.67635i	−0.149858	−	0.176473i
$231$	7.03003	+	8.17761i	0.462542	+	0.538047i
$232$	26.8162	−	5.21843i	1.76057	−	0.342606i
$233$			19.6072i			1.28451i	0.766491	+	0.642256i	$0.222001\pi$
$233$			19.6072i			1.28451i	−0.766491	+	0.642256i	$0.777999\pi$
$234$	−23.8521	+	0.944431i	−1.55926	+	0.0617394i
$235$		−	10.1296i		−	0.660782i
$236$	2.93069	−	1.10594i	0.190772	−	0.0719906i
$237$	−27.9537	+	0.470874i	−1.81579	+	0.0305865i
$238$	−12.9122	+	2.28999i	−0.836971	+	0.148438i
$239$	12.0017	−	4.36828i	0.776329	−	0.282560i	0.0766877	−	0.997055i	$-0.475566\pi$
$239$	12.0017	−	4.36828i	0.776329	−	0.282560i	0.699641	+	0.714495i	$0.253343\pi$
$240$	11.1152	−	10.1192i	0.717483	−	0.653192i
$241$	−7.21153	−	2.62478i	−0.464536	−	0.169077i	0.0991398	−	0.995074i	$-0.468391\pi$
$241$	−7.21153	−	2.62478i	−0.464536	−	0.169077i	−0.563675	+	0.825996i	$0.690613\pi$
$242$	−7.24313	+	2.68469i	−0.465606	+	0.172578i
$243$	−4.08050	+	15.0449i	−0.261764	+	0.965132i
$244$	−4.38800	−	23.2791i	−0.280913	−	1.49029i
$245$	9.64783	+	11.7291i	0.616377	+	0.749347i
$246$	2.90050	−	2.54837i	0.184929	−	0.162478i
$247$	−26.9187	+	32.0804i	−1.71279	+	2.04123i
$248$	−8.12588	−	1.28525i	−0.515994	−	0.0816135i
$249$	−7.25464	−	4.02710i	−0.459744	−	0.255207i
$250$	14.1117	+	8.03696i	0.892501	+	0.508302i
$251$	−5.10632	−	8.84441i	−0.322308	−	0.558254i	0.658656	−	0.752444i	$-0.271125\pi$
$251$	−5.10632	−	8.84441i	−0.322308	−	0.558254i	−0.980964	+	0.194190i	$0.937792\pi$
$252$	2.12027	−	15.7323i	0.133565	−	0.991040i
$253$	−1.34645	+	2.33212i	−0.0846506	+	0.146619i
$254$	20.3307	−	11.8981i	1.27566	−	0.746552i
$255$	4.29549	−	12.4503i	0.268994	−	0.779670i
$256$	15.9823	−	0.753418i	0.998891	−	0.0470886i
$257$	−2.91922	−	8.02050i	−0.182096	−	0.500305i	0.814737	−	0.579831i	$-0.196881\pi$
$257$	−2.91922	−	8.02050i	−0.182096	−	0.500305i	−0.996833	+	0.0795262i	$0.974659\pi$
$258$	−8.03051	+	0.182577i	−0.499958	+	0.0113667i
$259$	−18.4921	−	6.83328i	−1.14905	−	0.424599i
$260$	−8.07939	+	23.0386i	−0.501063	+	1.42879i
$261$	10.8220	+	26.8797i	0.669863	+	1.66381i
$262$	−6.55489	−	5.43476i	−0.404963	−	0.335760i
$263$	1.64100	−	1.37696i	0.101188	−	0.0849071i	−0.590790	−	0.806825i	$-0.701184\pi$
$263$	1.64100	−	1.37696i	0.101188	−	0.0849071i	0.691978	+	0.721918i	$0.256739\pi$
$264$	−10.1770	−	5.41640i	−0.626349	−	0.333356i
$265$	−13.7845	−	11.5666i	−0.846775	−	0.710529i
$266$	−17.9226	−	21.3163i	−1.09890	−	1.30698i
$267$	−16.0011	+	6.13103i	−0.979249	+	0.375213i
$268$	5.02533	−	6.13423i	0.306971	−	0.374708i
$269$	25.7736	+	14.8804i	1.57145	+	0.907274i	0.995992	+	0.0894398i	$0.0285077\pi$
$269$	25.7736	+	14.8804i	1.57145	+	0.907274i	0.575453	+	0.817835i	$0.304826\pi$
$270$	12.7717	+	9.54318i	0.777263	+	0.580779i
$271$	−22.7517	+	13.1357i	−1.38207	+	0.797936i	−0.992404	−	0.123022i	$-0.960741\pi$
$271$	−22.7517	+	13.1357i	−1.38207	+	0.797936i	−0.389662	+	0.920958i	$0.627408\pi$
$272$	11.9724	−	7.29353i	0.725936	−	0.442235i
$273$	9.10729	+	24.1214i	0.551198	+	1.45989i
$274$	−0.924172	+	2.58643i	−0.0558313	+	0.156252i
$275$	0.119646	−	0.678548i	0.00721495	−	0.0409180i
$276$	3.88255	−	0.799783i	0.233702	−	0.0481413i
$277$	−11.9325	+	10.0125i	−0.716953	+	0.601595i	−0.926541	−	0.376195i	$-0.877232\pi$
$277$	−11.9325	+	10.0125i	−0.716953	+	0.601595i	0.209588	+	0.977790i	$0.432788\pi$
$278$	−1.23998	−	3.34539i	−0.0743690	−	0.200643i
$279$	−0.293890	−	8.72099i	−0.0175947	−	0.522112i
$280$	−14.1632	−	7.93773i	−0.846413	−	0.474370i
$281$	12.3218	+	14.6846i	0.735059	+	0.876009i	0.996001	−	0.0893452i	$-0.0284774\pi$
$281$	12.3218	+	14.6846i	0.735059	+	0.876009i	−0.260942	+	0.965355i	$0.584033\pi$
$282$	10.0316	+	5.49157i	0.597371	+	0.327018i
$283$	16.6651	−	19.8607i	0.990636	−	1.18059i	0.00708336	−	0.999975i	$-0.497745\pi$
$283$	16.6651	−	19.8607i	0.990636	−	1.18059i	0.983553	−	0.180620i	$-0.0578103\pi$
$284$	8.77993	−	15.6295i	0.520993	−	0.927441i
$285$	27.4597	−	5.32024i	1.62657	−	0.315144i
$286$	18.7244	−	0.110255i	1.10720	−	0.00651953i
$287$	−3.60136	−	2.10282i	−0.212582	−	0.124125i
$288$	3.99537	+	16.4935i	0.235430	+	0.971891i
$289$	−2.35829	+	4.08468i	−0.138723	+	0.240275i
$290$	29.6355	−	0.174504i	1.74026	−	0.0102472i
$291$	−0.133630	−	7.93303i	−0.00783353	−	0.465042i
$292$	19.4613	−	0.229197i	1.13889	−	0.0134128i
$293$	7.19419	+	19.7659i	0.420289	+	1.15474i	0.951541	+	0.307521i	$0.0994996\pi$
$293$	7.19419	+	19.7659i	0.420289	+	1.15474i	−0.531252	+	0.847214i	$0.678278\pi$
$294$	−16.8460	+	3.19572i	−0.982478	+	0.186378i
$295$	3.34644	−	0.590068i	0.194837	−	0.0343551i
$296$	21.0722	−	0.372274i	1.22479	−	0.0216380i
$297$	3.59649	−	11.6870i	0.208689	−	0.678151i
$298$	−5.58711	−	15.0737i	−0.323652	−	0.873195i
$299$	−4.93213	+	4.13855i	−0.285233	+	0.239339i
$300$	−0.863504	+	0.532058i	−0.0498545	+	0.0307184i
$301$	2.92749	+	8.16737i	0.168738	+	0.470760i
$302$	−11.5181	+	2.10095i	−0.662789	+	0.120896i
$303$	13.3116	−	0.224230i	0.764730	−	0.0128817i
$304$	26.1272	+	14.2749i	1.49850	+	0.818722i
$305$		−	25.6980i		−	1.47146i
$306$	10.0011	+	11.0036i	0.571725	+	0.629035i
$307$	−22.7015	−	13.1067i	−1.29564	−	0.748040i	−0.315995	−	0.948761i	$-0.602338\pi$
$307$	−22.7015	−	13.1067i	−1.29564	−	0.748040i	−0.979648	+	0.200721i	$0.935671\pi$
$308$	−2.07788	+	12.2777i	−0.118398	+	0.699587i
$309$	−0.425021	+	0.369010i	−0.0241786	+	0.0209923i
$310$	−8.40418	−	3.00295i	−0.477326	−	0.170556i
$311$	26.1148	+	21.9130i	1.48084	+	1.24257i	0.905285	+	0.424804i	$0.139657\pi$
$311$	26.1148	+	21.9130i	1.48084	+	1.24257i	0.575551	+	0.817766i	$0.304788\pi$
$312$	−18.4355	−	20.4911i	−1.04370	−	1.16008i
$313$	−23.5700	−	8.57878i	−1.33226	−	0.484902i	−0.424891	−	0.905245i	$-0.639688\pi$
$313$	−23.5700	−	8.57878i	−1.33226	−	0.484902i	−0.907365	+	0.420343i	$0.861910\pi$
$314$	28.4193	−	10.5337i	1.60379	−	0.594451i
$315$	5.42156	−	16.3451i	0.305470	−	0.920940i
$316$	−21.0407	−	24.4839i	−1.18363	−	1.37733i
$317$	−19.5266	+	3.44306i	−1.09672	+	0.193382i	−0.692599	−	0.721323i	$-0.743534\pi$
$317$	−19.5266	+	3.44306i	−1.09672	+	0.193382i	−0.404123	+	0.914705i	$0.632423\pi$
$318$	18.9276	−	7.38049i	1.06141	−	0.413877i
$319$	−7.77401	−	21.3589i	−0.435261	−	1.19587i
$320$	17.1890	+	2.40834i	0.960893	+	0.134630i
$321$	0.274355	+	0.0436252i	0.0153130	+	0.00243492i
$322$	−2.14452	−	3.70592i	−0.119510	−	0.206523i
$323$	26.0865			1.45149
$324$	−16.3748	+	7.47446i	−0.909708	+	0.415248i
$325$	0.823682	−	1.42666i	0.0456897	−	0.0791368i
$326$	17.7275	−	10.3747i	0.981838	−	0.574599i
$327$	−8.13095	−	21.2205i	−0.449643	−	1.17350i
$328$	4.40353	+	0.696496i	0.243144	+	0.0384575i
$329$	2.20453	−	12.1543i	0.121540	−	0.670090i
$330$	−9.76059	−	7.81903i	−0.537303	−	0.430424i
$331$	19.5344	−	3.44444i	1.07371	−	0.189324i	0.391276	−	0.920273i	$-0.372034\pi$
$331$	19.5344	−	3.44444i	1.07371	−	0.189324i	0.682431	+	0.730950i	$0.260923\pi$
$332$	−1.77473	−	9.41524i	−0.0974010	−	0.516728i
$333$	4.62095	+	21.8711i	0.253227	+	1.19853i
$334$	11.4137	+	9.46330i	0.624532	+	0.517809i
$335$	6.58978	−	5.52949i	0.360038	−	0.302108i
$336$	15.5392	−	9.72282i	0.847733	−	0.530424i
$337$	−2.83574	+	16.0823i	−0.154473	+	0.876059i	0.804793	+	0.593555i	$0.202276\pi$
$337$	−2.83574	+	16.0823i	−0.154473	+	0.876059i	−0.959266	+	0.282504i	$0.908835\pi$
$338$	24.8456	+	8.87774i	1.35142	+	0.482885i
$339$	−4.38056	−	22.6097i	−0.237919	−	1.22799i
$340$	14.2286	−	5.36937i	0.771653	−	0.291195i
$341$			6.84480i			0.370667i
$342$	−9.61800	+	30.0782i	−0.520082	+	1.62644i
$343$	9.02361	+	16.1733i	0.487229	+	0.873274i
$344$	−6.08658	−	6.99882i	−0.328166	−	0.377351i
$345$	4.29963	−	0.0724263i	0.231484	−	0.00389930i
$346$	−2.96070	+	8.28594i	−0.159168	+	0.445455i
$347$	−5.63041	+	31.9316i	−0.302256	+	1.71418i	0.333890	+	0.942612i	$0.391639\pi$
$347$	−5.63041	+	31.9316i	−0.302256	+	1.71418i	−0.636146	+	0.771568i	$0.719473\pi$
$348$	−15.8935	+	29.4433i	−0.851982	+	1.57833i
$349$	0.0587192	+	0.333013i	0.00314316	+	0.0178258i	0.986339	−	0.164728i	$-0.0526747\pi$
$349$	0.0587192	+	0.333013i	0.00314316	+	0.0178258i	−0.983196	+	0.182554i	$0.941564\pi$
$350$	0.839922	+	0.703358i	0.0448957	+	0.0375960i
$351$	17.6371	−	23.3164i	0.941401	−	1.24454i
$352$	−2.69653	−	13.0361i	−0.143725	−	0.694826i
$353$	0.360116	−	0.989410i	0.0191670	−	0.0526610i	−0.929740	−	0.368216i	$-0.879969\pi$
$353$	0.360116	−	0.989410i	0.0191670	−	0.0526610i	0.948907	+	0.315555i	$0.102191\pi$
$354$	−1.22985	+	3.63395i	−0.0653659	+	0.193142i
$355$	12.5003	−	14.8973i	0.663448	−	0.790667i
$356$	−17.2508	−	9.69068i	−0.914289	−	0.513605i
$357$	7.86368	−	14.0041i	0.416190	−	0.741175i
$358$	−0.414398	−	0.708097i	−0.0219016	−	0.0374241i
$359$	−6.51975	+	11.2925i	−0.344099	+	0.595997i	−0.985190	−	0.171468i	$-0.945149\pi$
$359$	−6.51975	+	11.2925i	−0.344099	+	0.595997i	0.641091	+	0.767465i	$0.278482\pi$
$360$	0.944946	+	18.3855i	0.0498030	+	0.969000i
$361$	18.2001	+	31.5235i	0.957899	+	1.65913i
$362$	3.67831	+	6.28526i	0.193328	+	0.330346i
$363$	3.08557	−	8.94343i	0.161951	−	0.469408i
$364$	−14.7083	+	25.8852i	−0.770923	+	1.35675i
$365$	20.7925	+	3.66627i	1.08833	+	0.191902i
$366$	25.4492	+	13.9317i	1.33025	+	0.728220i
$367$	−23.0936	+	4.07202i	−1.20548	+	0.212558i	−0.740064	−	0.672536i	$-0.765205\pi$
$367$	−23.0936	+	4.07202i	−1.20548	+	0.212558i	−0.465412	+	0.885094i	$0.654094\pi$
$368$	3.57474	+	2.85884i	0.186346	+	0.149028i
$369$	0.159263	+	4.72602i	0.00829089	+	0.246027i
$370$	22.5384	+	3.83743i	1.17172	+	0.199499i
$371$	−14.0225	−	16.8785i	−0.728012	−	0.876287i
$372$	7.53005	−	6.69485i	0.390415	−	0.347112i
$373$	2.74101	−	15.5451i	0.141924	−	0.804892i	−0.827861	−	0.560933i	$-0.810443\pi$
$373$	2.74101	−	15.5451i	0.141924	−	0.804892i	0.969785	−	0.243959i	$-0.0784464\pi$
$374$	−7.54991	−	8.89078i	−0.390396	−	0.459731i
$375$	−18.5729	+	7.11648i	−0.959102	+	0.367494i
$376$	2.52247	+	12.9624i	0.130087	+	0.668483i
$377$		−	54.3443i		−	2.79887i
$378$	13.2477	+	14.2302i	0.681386	+	0.731924i
$379$		−	6.43954i		−	0.330777i	−0.986229	−	0.165388i	$-0.947112\pi$
$379$		−	6.43954i		−	0.330777i	0.986229	−	0.165388i	$-0.0528878\pi$
$380$	24.9840	+	20.4676i	1.28165	+	1.04996i
$381$	−4.53060	+	28.4925i	−0.232110	+	1.45972i
$382$	−7.25482	+	6.16068i	−0.371189	+	0.315208i
$383$	0.209492	−	1.18809i	0.0107045	−	0.0607084i	−0.978988	−	0.203920i	$-0.934632\pi$
$383$	0.209492	−	1.18809i	0.0107045	−	0.0607084i	0.989692	+	0.143211i	$0.0457429\pi$
$384$	−11.7037	+	15.7170i	−0.597252	+	0.802054i
$385$	−4.68219	+	12.6709i	−0.238626	+	0.645768i
$386$	−3.08452	+	18.1163i	−0.156998	+	0.922096i
$387$	6.06625	−	7.74495i	0.308365	−	0.393698i
$388$	6.94833	−	5.97118i	0.352748	−	0.303141i
$389$	−31.4973	+	5.55383i	−1.59698	+	0.281590i	−0.900128	−	0.435626i	$-0.856527\pi$
$389$	−31.4973	+	5.55383i	−1.59698	+	0.281590i	−0.696850	+	0.717217i	$0.745416\pi$
$390$	−15.5353	−	25.5486i	−0.786660	−	1.29371i
$391$	3.94968	+	0.696435i	0.199744	+	0.0352202i
$392$	−15.2667	−	12.6067i	−0.771083	−	0.636735i
$393$	10.2382	−	1.98362i	0.516447	−	0.100060i
$394$	5.88429	−	3.44365i	0.296446	−	0.173489i
$395$	−17.5102	−	30.3286i	−0.881035	−	1.52600i
$396$	13.0349	−	5.42718i	0.655027	−	0.272726i
$397$	−1.08619	+	1.88133i	−0.0545142	+	0.0944213i	−0.891995	−	0.452046i	$-0.850694\pi$
$397$	−1.08619	+	1.88133i	−0.0545142	+	0.0944213i	0.837481	+	0.546467i	$0.184028\pi$
$398$	8.42056	−	4.92795i	0.422085	−	0.247016i
$399$	34.1063	−	0.407530i	1.70745	−	0.0204020i
$400$	−1.10967	−	0.374533i	−0.0554833	−	0.0187267i
$401$	−2.71641	+	3.23729i	−0.135651	+	0.161663i	−0.829593	−	0.558368i	$-0.811428\pi$
$401$	−2.71641	+	3.23729i	−0.135651	+	0.161663i	0.693942	+	0.720030i	$0.255872\pi$
$402$	1.90344	+	9.52370i	0.0949350	+	0.474999i
$403$	−5.59723	+	15.3783i	−0.278818	+	0.766045i
$404$	10.0196	+	11.6593i	0.498494	+	0.580070i
$405$	−18.9579	+	4.67763i	−0.942028	+	0.232434i
$406$	35.5971	+	6.24028i	1.76666	+	0.309700i
$407$	−3.04489	−	17.2685i	−0.150930	−	0.855965i
$408$	−2.39635	+	17.0018i	−0.118637	+	0.841712i
$409$	−0.0607695	+	0.344641i	−0.00300486	+	0.0170414i	−0.986273	−	0.165121i	$-0.947199\pi$
$409$	−0.0607695	+	0.344641i	−0.00300486	+	0.0170414i	0.983268	+	0.182162i	$0.0583097\pi$
$410$	4.55434	+	1.62734i	0.224923	+	0.0803686i
$411$	−1.73076	−	2.88445i	−0.0853719	−	0.142279i
$412$	−0.641345	−	0.105315i	−0.0315968	−	0.00518848i
$413$	4.14375	+	0.0202835i	0.203901	+	0.000998087i
$414$	−2.25924	+	4.29728i	−0.111035	+	0.211200i
$415$		−	10.3936i		−	0.510200i
$416$	4.60175	−	31.4933i	0.225619	−	1.54409i
$417$	4.13071	+	1.42514i	0.202282	+	0.0697893i
$418$	8.33491	−	23.3264i	0.407674	−	1.14093i
$419$	−3.66930	+	20.8096i	−0.179257	+	1.01662i	0.753858	+	0.657038i	$0.228191\pi$
$419$	−3.66930	+	20.8096i	−0.179257	+	1.01662i	−0.933115	+	0.359579i	$0.882920\pi$
$420$	18.5190	−	7.24236i	0.903635	−	0.353391i
$421$	3.21904	−	2.70109i	0.156886	−	0.131643i	−0.560966	−	0.827839i	$-0.689570\pi$
$421$	3.21904	−	2.70109i	0.156886	−	0.131643i	0.717852	+	0.696196i	$0.245126\pi$
$422$	−19.3920	+	23.3888i	−0.943986	+	1.13855i
$423$	−12.9931	+	5.23111i	−0.631744	+	0.254345i
$424$	20.5197	+	11.3686i	0.996524	+	0.552107i
$425$	−1.01058	+	0.178192i	−0.0490203	+	0.00864360i
$426$	7.97630	+	20.4556i	0.386453	+	0.991078i
$427$	5.59272	−	30.8345i	0.270651	−	1.49219i
$428$	0.163649	+	0.275894i	0.00791029	+	0.0133358i
$429$	−14.4431	+	17.8135i	−0.697319	+	0.860043i
$430$	−5.08213	−	8.68402i	−0.245082	−	0.418780i
$431$	2.08203	−	3.60618i	0.100288	−	0.173703i	−0.811515	−	0.584331i	$-0.801357\pi$
$431$	2.08203	−	3.60618i	0.100288	−	0.173703i	0.911803	+	0.410628i	$0.134690\pi$
$432$	−18.7198	−	9.03153i	−0.900657	−	0.434530i
$433$	−7.51729			−0.361258			−0.180629	−	0.983551i	$-0.557813\pi$
$433$	−7.51729			−0.361258			−0.180629	+	0.983551i	$0.557813\pi$
$434$	−9.43049	−	5.43221i	−0.452678	−	0.260755i
$435$	−22.8594	+	28.1938i	−1.09602	+	1.35179i
$436$	12.8517	−	22.8779i	0.615487	−	1.09565i
$437$	2.91311	+	8.00372i	0.139353	+	0.382870i
$438$	−14.9030	+	18.6036i	−0.712094	+	0.888915i
$439$	4.21698	−	0.743568i	0.201266	−	0.0354885i	−0.0721064	−	0.997397i	$-0.522972\pi$
$439$	4.21698	−	0.743568i	0.201266	−	0.0354885i	0.273372	+	0.961908i	$0.411861\pi$
$440$	−0.255083	−	14.4387i	−0.0121606	−	0.688339i
$441$	10.0624	−	18.4322i	0.479164	−	0.877725i
$442$	−9.69213	−	26.1488i	−0.461007	−	1.24377i
$443$	9.88193	+	3.59673i	0.469505	+	0.170886i	0.565928	−	0.824455i	$-0.308518\pi$
$443$	9.88193	+	3.59673i	0.469505	+	0.170886i	−0.0964233	+	0.995340i	$0.530740\pi$
$444$	−16.0191	+	20.2399i	−0.760230	+	0.960542i
$445$	−16.4426	−	13.7970i	−0.779454	−	0.654040i
$446$	2.25839	−	6.32043i	0.106938	−	0.299281i
$447$	18.6122	+	6.42140i	0.880326	+	0.303722i
$448$	20.1006	+	6.63061i	0.949665	+	0.313267i
$449$	−6.35459	−	3.66882i	−0.299892	−	0.173143i	0.342503	−	0.939517i	$-0.388725\pi$
$449$	−6.35459	−	3.66882i	−0.299892	−	0.173143i	−0.642394	+	0.766374i	$0.722059\pi$
$450$	0.167138	−	1.23092i	0.00787897	−	0.0580259i
$451$		−	3.70929i		−	0.174664i
$452$	16.8525	−	20.5712i	0.792674	−	0.967588i
$453$	6.95954	−	12.5373i	0.326988	−	0.589054i
$454$	−4.86447	−	26.6685i	−0.228301	−	1.25162i
$455$	−20.8809	+	24.6390i	−0.978912	+	1.15509i
$456$	−33.8140	+	13.6461i	−1.58349	+	0.639036i
$457$	12.9591	−	10.8740i	0.606201	−	0.508663i	−0.287231	−	0.957861i	$-0.592735\pi$
$457$	12.9591	−	10.8740i	0.606201	−	0.508663i	0.893432	+	0.449198i	$0.148290\pi$
$458$	−14.3238	+	5.30915i	−0.669306	+	0.248080i
$459$	−18.1881	+	0.919819i	−0.848947	+	0.0429335i
$460$	3.23633	+	3.76594i	0.150895	+	0.175588i
$461$	12.9286	−	2.27966i	0.602143	−	0.106174i	0.135737	−	0.990745i	$-0.456660\pi$
$461$	12.9286	−	2.27966i	0.602143	−	0.106174i	0.466406	+	0.884571i	$0.345549\pi$
$462$	−10.0099	−	11.5061i	−0.465702	−	0.535314i
$463$	11.6002	+	31.8713i	0.539107	+	1.48118i	0.847953	+	0.530072i	$0.177835\pi$
$463$	11.6002	+	31.8713i	0.539107	+	1.48118i	−0.308846	+	0.951112i	$0.599943\pi$
$464$	−37.8797	+	7.60315i	−1.75852	+	0.352967i
$465$	9.37255	−	5.62382i	0.434642	−	0.260798i
$466$	−0.163273	−	27.7283i	−0.00756348	−	1.28449i
$467$	0.519468	−	0.899745i	0.0240381	−	0.0416353i	−0.853756	−	0.520673i	$-0.825681\pi$
$467$	0.519468	−	0.899745i	0.0240381	−	0.0416353i	0.877794	+	0.479038i	$0.159014\pi$
$468$	33.7235	−	1.53422i	1.55887	−	0.0709196i
$469$	9.11036	−	5.20058i	0.420677	−	0.240140i
$470$	0.0843513	+	14.3252i	0.00389083	+	0.660771i
$471$	−12.1066	+	35.0906i	−0.557844	+	1.61689i
$472$	−4.13534	+	1.58841i	−0.190345	+	0.0731126i
$473$	−4.96041	+	5.91158i	−0.228080	+	0.271815i
$474$	39.5279	−	0.898681i	1.81558	−	0.0412778i
$475$	−1.40082	−	1.66943i	−0.0642740	−	0.0765988i
$476$	18.2412	−	3.34600i	0.836082	−	0.153364i
$477$	−7.71768	+	23.6543i	−0.353368	+	1.08306i
$478$	−16.9364	+	6.27751i	−0.774651	+	0.287127i
$479$	26.7512	−	22.4469i	1.22229	−	1.02563i	0.223593	−	0.974683i	$-0.428221\pi$
$479$	26.7512	−	22.4469i	1.22229	−	1.02563i	0.998701	−	0.0509443i	$-0.0162231\pi$
$480$	−15.6347	+	14.4030i	−0.713624	+	0.657405i
$481$	7.28002	−	41.2871i	0.331940	−	1.88253i
$482$	10.2203	+	3.65189i	0.465523	+	0.166339i
$483$	5.17481	+	0.848838i	0.235462	+	0.0386235i
$484$	10.2208	−	3.85697i	0.464582	−	0.175317i
$485$	8.60701	−	4.96926i	0.390824	−	0.225642i
$486$	5.64532	−	21.3103i	0.256077	−	0.966656i
$487$	23.7114	+	13.6898i	1.07447	+	0.620344i	0.929398	−	0.369078i	$-0.120326\pi$
$487$	23.7114	+	13.6898i	1.07447	+	0.620344i	0.145068	+	0.989422i	$0.453660\pi$
$488$	6.39931	+	32.8845i	0.289683	+	1.48861i
$489$	−3.95050	+	24.8444i	−0.178648	+	1.12350i
$490$	−13.7415	−	16.5069i	−0.620779	−	0.745705i
$491$	10.4127	+	8.73731i	0.469919	+	0.394309i	0.846765	−	0.531967i	$-0.178547\pi$
$491$	10.4127	+	8.73731i	0.469919	+	0.394309i	−0.376846	+	0.926276i	$0.622991\pi$
$492$	−4.08064	+	3.62803i	−0.183969	+	0.163564i
$493$	−25.9321	+	21.7596i	−1.16792	+	0.980003i
$494$	37.8009	−	45.5919i	1.70074	−	2.05128i
$495$	14.9861	−	3.16629i	0.673577	−	0.142314i
$496$	11.5022	+	1.74992i	0.516465	+	0.0785738i
$497$	18.2411	−	15.1545i	0.818223	−	0.679773i
$498$	10.2930	+	5.63467i	0.461239	+	0.252496i
$499$	6.43227	+	17.6725i	0.287948	+	0.791130i	0.996353	+	0.0853243i	$0.0271926\pi$
$499$	6.43227	+	17.6725i	0.287948	+	0.791130i	−0.708405	+	0.705806i	$0.750585\pi$
$500$	−20.0235	−	11.2483i	−0.895478	−	0.503038i
$501$	−17.8273	+	3.45398i	−0.796464	+	0.154313i
$502$	7.29495	+	12.4651i	0.325590	+	0.556347i
$503$	16.3766	−	28.3652i	0.730198	−	1.26474i	−0.226601	−	0.973988i	$-0.572761\pi$
$503$	16.3766	−	28.3652i	0.730198	−	1.26474i	0.956799	−	0.290752i	$-0.0939054\pi$
$504$	−2.86746	+	22.2661i	−0.127727	+	0.991809i
$505$	8.33838	+	14.4425i	0.371053	+	0.642683i
$506$	1.88472	−	3.30927i	0.0837858	−	0.147115i
$507$	−27.7084	+	16.6259i	−1.23057	+	0.738382i
$508$	−28.6523	+	16.9954i	−1.27124	+	0.754051i
$509$	−10.9376	+	13.0350i	−0.484802	+	0.577764i	−0.951887	−	0.306448i	$-0.900859\pi$
$509$	−10.9376	+	13.0350i	−0.484802	+	0.577764i	0.467086	+	0.884212i	$0.345304\pi$
$510$	−5.97096	+	17.6429i	−0.264398	+	0.781240i
$511$	24.1506	+	8.92422i	1.06836	+	0.394784i
$512$	−22.5957	+	1.19856i	−0.998596	+	0.0529695i
$513$	−21.0049	−	32.4746i	−0.927387	−	1.43379i
$514$	4.19512	+	11.3182i	0.185039	+	0.499224i
$515$	−0.662533	−	0.241142i	−0.0291947	−	0.0106260i
$516$	11.3551	−	0.325069i	0.499882	−	0.0143104i
$517$	10.3244	−	3.75779i	0.454068	−	0.165267i
$518$	26.2083	+	9.50956i	1.15153	+	0.417826i
$519$	−5.54469	−	9.24068i	−0.243385	−	0.405621i
$520$	11.2339	−	32.6482i	0.492641	−	1.43172i
$521$			3.61439i			0.158349i	0.996861	+	0.0791746i	$0.0252285\pi$
$521$			3.61439i			0.158349i	−0.996861	+	0.0791746i	$0.974772\pi$
$522$	−15.5281	−	37.9229i	−0.679648	−	1.65984i
$523$		−	7.39361i		−	0.323300i	−0.986848	−	0.161650i	$-0.948318\pi$
$523$		−	7.39361i		−	0.323300i	0.986848	−	0.161650i	$-0.0516816\pi$
$524$	9.31511	+	7.63119i	0.406933	+	0.333370i
$525$	−1.31848	+	0.248762i	−0.0575432	+	0.0108569i
$526$	−2.30922	+	1.96095i	−0.100687	+	0.0855015i
$527$	9.57935	−	3.48660i	0.417283	−	0.151879i
$528$	14.4373	+	7.57506i	0.628301	+	0.329662i
$529$	−3.76652	−	21.3610i	−0.163762	−	0.928739i
$530$	19.5902	+	16.2425i	0.850944	+	0.705530i
$531$	−2.48503	−	3.98770i	−0.107841	−	0.173051i
$532$	25.5234	+	29.9960i	1.10658	+	1.30049i
$533$	3.03322	−	8.33369i	0.131383	−	0.360972i
$534$	22.5775	−	8.80369i	0.977023	−	0.380973i
$535$	0.119017	+	0.326996i	0.00514554	+	0.0141373i
$536$	−7.05568	+	8.71681i	−0.304759	+	0.376509i
$537$	0.992366	+	0.157796i	0.0428238	+	0.00680940i
$538$	−36.5727	−	20.8291i	−1.57676	−	0.898006i
$539$	−8.37568	+	14.1846i	−0.360766	+	0.610973i
$540$	−18.1411	−	13.3895i	−0.780669	−	0.576193i
$541$	8.59183	+	14.8815i	0.369392	+	0.639805i	0.989471	−	0.144734i	$-0.0462327\pi$
$541$	8.59183	+	14.8815i	0.369392	+	0.639805i	−0.620079	+	0.784539i	$0.712899\pi$
$542$	32.0658	−	18.7658i	1.37734	−	0.806060i
$543$	−8.80851	−	1.40064i	−0.378009	−	0.0601072i
$544$	−16.8706	+	10.4141i	−0.723319	+	0.446502i
$545$	18.2975	−	21.8061i	0.783779	−	0.934071i
$546$	−13.0803	−	34.0363i	−0.559785	−	1.45662i
$547$	−3.74295	+	10.2837i	−0.160037	+	0.439698i	−0.993631	−	0.112679i	$-0.964057\pi$
$547$	−3.74295	+	10.2837i	−0.160037	+	0.439698i	0.833595	+	0.552377i	$0.186279\pi$
$548$	1.28542	−	3.66539i	0.0549103	−	0.156578i
$549$	−32.9624	+	13.2709i	−1.40680	+	0.566388i
$550$	−0.163552	+	0.960592i	−0.00697389	+	0.0409598i
$551$	−67.5561	−	24.5884i	−2.87799	−	1.04750i
$552$	−5.48400	+	1.16337i	−0.233414	+	0.0495165i
$553$	−14.4097	−	40.2016i	−0.612763	−	1.70954i
$554$	16.7914	−	14.2590i	0.713398	−	0.605806i
$555$	−21.1439	+	18.3574i	−0.897507	+	0.779230i
$556$	1.78142	+	4.72069i	0.0755492	+	0.200202i
$557$	−39.9475	+	23.0637i	−1.69263	+	0.977239i	−0.740244	+	0.672339i	$0.765290\pi$
$557$	−39.9475	+	23.0637i	−1.69263	+	0.977239i	−0.952384	+	0.304900i	$0.901377\pi$
$558$	0.488237	+	12.3307i	0.0206687	+	0.521999i
$559$	−15.9787	+	9.22529i	−0.675826	+	0.390188i
$560$	20.0955	+	11.1075i	0.849191	+	0.469378i
$561$	14.2833	−	0.240599i	0.603042	−	0.0101581i
$562$	−17.5477	−	20.6642i	−0.740205	−	0.871666i
$563$	−3.96181	+	22.4686i	−0.166970	+	0.946937i	0.780039	+	0.625731i	$0.215199\pi$
$563$	−3.96181	+	22.4686i	−0.166970	+	0.946937i	−0.947009	+	0.321206i	$0.895912\pi$
$564$	−14.2322	−	7.68258i	−0.599286	−	0.323495i
$565$	22.0989	−	18.5432i	0.929708	−	0.780118i
$566$	−23.4022	+	28.2255i	−0.983668	+	1.18641i
$567$	−23.7653	+	1.48674i	−0.998049	+	0.0624372i
$568$	−12.2863	+	22.1762i	−0.515523	+	0.930493i
$569$	−23.4242	−	27.9159i	−0.981995	−	1.17030i	−0.985392	−	0.170301i	$-0.945526\pi$
$569$	−23.4242	−	27.9159i	−0.981995	−	1.17030i	0.00339752	−	0.999994i	$-0.498919\pi$
$570$	−38.7889	+	7.75249i	−1.62469	+	0.324716i
$571$	38.1525	+	6.72731i	1.59663	+	0.281529i	0.899997	−	0.435896i	$-0.143568\pi$
$571$	38.1525	+	6.72731i	1.59663	+	0.281529i	0.696635	+	0.717425i	$0.254680\pi$
$572$	−26.4789	+	0.311844i	−1.10714	+	0.0130388i
$573$	−0.196327	−	11.6551i	−0.00820169	−	0.486898i
$574$	5.11051	+	2.94379i	0.213309	+	0.122872i
$575$	−0.167525	−	0.290162i	−0.00698628	−	0.0121006i
$576$	−5.78756	−	23.2917i	−0.241148	−	0.970488i
$577$	−21.0213	−	36.4100i	−0.875129	−	1.51577i	−0.856625	−	0.515939i	$-0.827443\pi$
$577$	−21.0213	−	36.4100i	−0.875129	−	1.51577i	−0.0185036	−	0.999829i	$-0.505890\pi$
$578$	3.30105	−	5.79614i	0.137306	−	0.241088i
$579$	−14.7557	−	16.9954i	−0.613224	−	0.706304i
$580$	−41.9088	+	0.493562i	−1.74017	+	0.0204940i
$581$	2.26198	−	12.4711i	0.0938428	−	0.517387i
$582$	0.255038	+	11.2177i	0.0105717	+	0.464988i
$583$	6.67540	−	18.3405i	0.276467	−	0.759586i
$584$	−27.5201	+	0.486187i	−1.13879	+	0.0201186i
$585$	36.2586	+	5.14094i	1.49911	+	0.212552i
$586$	−10.3385	−	27.8928i	−0.427081	−	1.15224i
$587$	−22.7101	−	8.26581i	−0.937347	−	0.341167i	−0.172230	−	0.985057i	$-0.555097\pi$
$587$	−22.7101	−	8.26581i	−0.937347	−	0.341167i	−0.765118	+	0.643890i	$0.777319\pi$
$588$	23.7968	−	4.65963i	0.981364	−	0.192160i
$589$	16.5844	+	13.9160i	0.683349	+	0.573398i
$590$	−4.72759	+	0.862334i	−0.194632	+	0.0355017i
$591$	−1.31129	+	8.24658i	−0.0539392	+	0.339219i
$592$	−29.7969	+	0.701937i	−1.22465	+	0.0288495i
$593$	14.8692	−	8.58473i	0.610604	−	0.352532i	−0.162598	−	0.986692i	$-0.551987\pi$
$593$	14.8692	−	8.58473i	0.610604	−	0.352532i	0.773202	+	0.634160i	$0.218654\pi$
$594$	−4.98880	+	16.5576i	−0.204693	+	0.679368i
$595$	20.1180	+	0.0984769i	0.824758	+	0.00403716i
$596$	8.02675	+	21.2705i	0.328788	+	0.871275i
$597$	−1.87648	+	11.8010i	−0.0767993	+	0.482985i
$598$	6.94051	−	5.89377i	0.283818	−	0.241014i
$599$	36.3700	−	13.2376i	1.48604	−	0.540873i	0.533634	−	0.845715i	$-0.320826\pi$
$599$	36.3700	−	13.2376i	1.48604	−	0.540873i	0.952403	+	0.304842i	$0.0986037\pi$
$600$	1.21673	−	0.759622i	0.0496727	−	0.0310114i
$601$	5.24770	+	1.91001i	0.214058	+	0.0779109i	0.446824	−	0.894622i	$-0.352555\pi$
$601$	5.24770	+	1.91001i	0.214058	+	0.0779109i	−0.232765	+	0.972533i	$0.574777\pi$
$602$	−4.20803	−	11.5258i	−0.171507	−	0.469758i
$603$	−10.4957	−	5.59708i	−0.427416	−	0.227931i
$604$	16.2712	−	3.06705i	0.662066	−	0.124796i
$605$	11.6707	−	2.05786i	0.474483	−	0.0836641i
$606$	−18.8232	+	0.427952i	−0.764640	+	0.0173844i
$607$	−3.32105	−	9.12452i	−0.134797	−	0.370353i	0.853868	−	0.520490i	$-0.174251\pi$
$607$	−3.32105	−	9.12452i	−0.134797	−	0.370353i	−0.988665	+	0.150137i	$0.952028\pi$
$608$	−37.0676	−	19.9698i	−1.50329	−	0.809884i
$609$	−33.5645	+	28.8543i	−1.36010	+	1.16923i
$610$	0.213992	+	36.3418i	0.00866429	+	1.47144i
$611$	26.2689			1.06272
$612$	−14.2351	−	15.4779i	−0.575419	−	0.625658i
$613$	−10.1617			−0.410427			−0.205214	−	0.978717i	$-0.565789\pi$
$613$	−10.1617			−0.410427			−0.205214	+	0.978717i	$0.565789\pi$
$614$	32.2134	+	18.3463i	1.30003	+	0.740398i
$615$	−5.07912	+	3.04763i	−0.204810	+	0.122892i
$616$	2.83627	−	17.3803i	0.114277	−	0.700272i
$617$	1.11588	+	3.06585i	0.0449236	+	0.123426i	0.960126	−	0.279569i	$-0.0901914\pi$
$617$	1.11588	+	3.06585i	0.0449236	+	0.123426i	−0.915202	+	0.402995i	$0.867969\pi$
$618$	0.597987	−	0.525389i	0.0240546	−	0.0211343i
$619$	8.11193	−	22.2873i	0.326046	−	0.895804i	−0.663056	−	0.748570i	$-0.730741\pi$
$619$	8.11193	−	22.2873i	0.326046	−	0.895804i	0.989102	−	0.147234i	$-0.0470369\pi$
$620$	11.9101	+	4.17676i	0.478322	+	0.167743i
$621$	−2.31331	−	5.47766i	−0.0928297	−	0.219811i
$622$	−37.1138	−	30.7716i	−1.48813	−	1.23383i
$623$	−16.7265	−	20.1332i	−0.670133	−	0.806620i
$624$	26.2419	+	28.8248i	1.05052	+	1.15391i
$625$	−17.9640	−	15.0736i	−0.718559	−	0.602943i
$626$	33.4039	+	11.9358i	1.33509	+	0.477049i
$627$	15.6093	+	26.0142i	0.623376	+	1.03891i
$628$	−40.1025	+	15.1333i	−1.60027	+	0.603884i
$629$	−22.6163	+	13.0576i	−0.901773	+	0.520639i
$630$	−7.53100	+	23.1601i	−0.300042	+	0.922722i
$631$	15.9325	+	9.19860i	0.634261	+	0.366191i	0.782400	−	0.622776i	$-0.213995\pi$
$631$	15.9325	+	9.19860i	0.634261	+	0.366191i	−0.148139	+	0.988966i	$0.547328\pi$
$632$	29.9594	+	34.4497i	1.19172	+	1.37033i
$633$	−7.07782	−	36.5312i	−0.281318	−	1.45198i
$634$	27.5856	−	5.03174i	1.09556	−	0.199836i
$635$	−33.9594	+	12.3602i	−1.34764	+	0.490500i
$636$	−26.7058	+	10.5950i	−1.05895	+	0.420120i
$637$	−30.4169	+	25.0195i	−1.20516	+	0.991308i
$638$	11.1718	+	30.1408i	0.442295	+	1.19329i
$639$	−25.5639	−	8.34071i	−1.01129	−	0.329953i
$640$	−24.3285	−	3.26271i	−0.961670	−	0.128970i
$641$	20.4803	+	24.4075i	0.808923	+	0.964037i	0.999846	−	0.0175680i	$-0.00559236\pi$
$641$	20.4803	+	24.4075i	0.808923	+	0.964037i	−0.190922	+	0.981605i	$0.561148\pi$
$642$	−0.388353	−	0.0594097i	−0.0153271	−	0.00234471i
$643$	−20.0680	+	23.9161i	−0.791403	+	0.943157i	−0.999388	−	0.0349746i	$-0.988865\pi$
$643$	−20.0680	+	23.9161i	−0.791403	+	0.943157i	0.207985	+	0.978132i	$0.433309\pi$
$644$	3.06362	+	5.22301i	0.120724	+	0.205815i
$645$	12.1703	+	1.93519i	0.479204	+	0.0761981i
$646$	−36.8912	+	0.217227i	−1.45146	+	0.00854669i
$647$	5.49761	−	9.52215i	0.216133	−	0.374354i	−0.737489	−	0.675359i	$-0.763989\pi$
$647$	5.49761	−	9.52215i	0.216133	−	0.374354i	0.953623	+	0.301005i	$0.0973220\pi$
$648$	23.0948	−	10.7067i	0.907248	−	0.420597i
$649$	1.84285	+	3.19191i	0.0723382	+	0.125293i
$650$	−1.15296	+	2.02443i	−0.0452229	+	0.0794045i
$651$	12.4699	−	4.70814i	0.488733	−	0.184527i
$652$	−24.9837	+	14.8193i	−0.978437	+	0.580370i
$653$	−11.4786	−	2.02400i	−0.449194	−	0.0792051i	−0.0555251	−	0.998457i	$-0.517683\pi$
$653$	−11.4786	−	2.02400i	−0.449194	−	0.0792051i	−0.393669	+	0.919252i	$0.628794\pi$
$654$	11.6754	+	29.9421i	0.456545	+	1.17083i
$655$	8.39678	+	10.0069i	0.328089	+	0.391002i
$656$	−6.23322	−	0.948307i	−0.243366	−	0.0370252i
$657$	−6.03493	−	28.5635i	−0.235445	−	1.11437i
$658$	−3.01642	+	17.2069i	−0.117592	+	0.670794i
$659$	3.65071	−	3.06331i	0.142211	−	0.119330i	−0.568907	−	0.822402i	$-0.692633\pi$
$659$	3.65071	−	3.06331i	0.142211	−	0.119330i	0.711118	+	0.703072i	$0.248189\pi$
$660$	13.8684	+	10.9763i	0.539828	+	0.427252i
$661$	15.1994	+	12.7538i	0.591190	+	0.496067i	0.888600	−	0.458683i	$-0.151678\pi$
$661$	15.1994	+	12.7538i	0.591190	+	0.496067i	−0.297410	+	0.954750i	$0.596123\pi$
$662$	−27.5966	+	5.03376i	−1.07257	+	0.195643i
$663$	32.2871	+	11.1394i	1.25393	+	0.432618i
$664$	2.58821	+	13.3002i	0.100442	+	0.516146i
$665$	21.1813	+	37.1054i	0.821377	+	1.43889i
$666$	−6.71703	−	30.8913i	−0.260279	−	1.19702i
$667$	−9.57204	−	5.52642i	−0.370631	−	0.213984i
$668$	−16.2200	−	13.2879i	−0.627570	−	0.514123i
$669$	4.22943	+	7.04870i	0.163519	+	0.272518i
$670$	−9.27316	+	7.87461i	−0.358253	+	0.304223i
$671$	26.1923	−	9.53321i	1.01114	−	0.368025i
$672$	−21.8944	+	13.8793i	−0.844595	+	0.535406i
$673$	2.06105	+	11.6888i	0.0794478	+	0.450571i	0.998417	+	0.0562418i	$0.0179118\pi$
$673$	2.06105	+	11.6888i	0.0794478	+	0.450571i	−0.918969	+	0.394329i	$0.870977\pi$
$674$	3.87636	−	22.7670i	0.149312	−	0.876953i
$675$	1.03555	+	1.11457i	0.0398583	+	0.0428999i
$676$	−35.2103	−	12.3479i	−1.35424	−	0.474919i
$677$	18.5566	+	22.1148i	0.713186	+	0.849943i	0.993950	−	0.109834i	$-0.0350321\pi$
$677$	18.5566	+	22.1148i	0.713186	+	0.849943i	−0.280763	+	0.959777i	$0.590588\pi$
$678$	6.38321	+	31.9379i	0.245146	+	1.22657i
$679$	11.4089	−	4.08936i	0.437832	−	0.156935i
$680$	−20.0772	+	7.71178i	−0.769925	+	0.295733i
$681$	29.0285	+	16.1139i	1.11237	+	0.617486i
$682$	−0.0569980	−	9.67984i	−0.00218257	−	0.370660i
$683$	16.0797			0.615272			0.307636	−	0.951504i	$-0.400462\pi$
$683$	16.0797			0.615272			0.307636	+	0.951504i	$0.400462\pi$
$684$	13.3512	−	42.6163i	0.510496	−	1.62948i
$685$	2.10683	−	3.64913i	0.0804977	−	0.139426i
$686$	−12.8958	−	22.7969i	−0.492363	−	0.870390i
$687$	6.10193	−	17.6862i	0.232803	−	0.674771i
$688$	8.66585	+	9.84697i	0.330383	+	0.375412i
$689$	29.9953	−	35.7470i	1.14273	−	1.36185i
$690$	−6.07989	+	0.138228i	−0.231457	+	0.00526227i
$691$	2.44517	−	6.71806i	0.0930188	−	0.255567i	−0.884454	−	0.466627i	$-0.845469\pi$
$691$	2.44517	−	6.71806i	0.0930188	−	0.255567i	0.977473	+	0.211060i	$0.0676914\pi$
$692$	4.11799	−	11.7425i	0.156542	−	0.446384i
$693$	18.6707	−	0.537705i	0.709241	−	0.0204257i
$694$	7.69656	−	45.2043i	0.292158	−	1.71593i
$695$	0.950468	+	5.39037i	0.0360533	+	0.204468i
$696$	22.2313	−	41.7707i	0.842673	−	1.58332i
$697$	−5.19119	+	1.88944i	−0.196630	+	0.0715676i
$698$	−0.0858130	−	0.470454i	−0.00324807	−	0.0178070i
$699$	26.3794	+	21.3882i	0.997759	+	0.808978i
$700$	−1.19367	−	0.987686i	−0.0451163	−	0.0373310i
$701$		−	29.5557i		−	1.11630i	−0.829739	−	0.558152i	$-0.811511\pi$
$701$		−	29.5557i		−	1.11630i	0.829739	−	0.558152i	$-0.188489\pi$
$702$	−24.7481	+	33.1206i	−0.934057	+	1.25006i
$703$	−48.0306	−	27.7305i	−1.81151	−	1.04588i
$704$	3.92195	+	18.4130i	0.147814	+	0.693967i
$705$	−13.6283	−	11.0497i	−0.513271	−	0.416157i
$706$	−0.501033	+	1.40221i	−0.0188566	+	0.0527729i
$707$	6.86191	+	19.1440i	0.258069	+	0.719984i
$708$	1.70898	−	5.14933i	0.0642275	−	0.193524i
$709$	−0.0162956	−	0.0924168i	−0.000611993	−	0.00347079i	0.984500	−	0.175383i	$-0.0561165\pi$
$709$	−0.0162956	−	0.0924168i	−0.000611993	−	0.00347079i	−0.985112	+	0.171913i	$0.945005\pi$
$710$	−17.5538	+	21.1717i	−0.658781	+	0.794559i
$711$	−29.8594	+	38.1223i	−1.11981	+	1.42970i
$712$	24.4765	+	13.5608i	0.917297	+	0.508213i
$713$	2.13948	+	2.54974i	0.0801242	+	0.0954884i
$714$	−11.0041	+	19.8699i	−0.411819	+	0.743613i
$715$	−28.2900	−	4.98830i	−1.05799	−	0.186552i
$716$	0.591934	+	0.997932i	0.0221216	+	0.0372945i
$717$	7.21489	−	20.9121i	0.269445	−	0.780977i
$718$	9.12612	−	16.0241i	0.340584	−	0.598013i
$719$	−47.3095			−1.76435			−0.882174	−	0.470924i	$-0.843921\pi$
$719$	−47.3095			−1.76435			−0.882174	+	0.470924i	$0.843921\pi$
$720$	−1.48943	−	25.9927i	−0.0555079	−	0.968690i
$721$	−0.742481	−	0.433531i	−0.0276514	−	0.0161455i
$722$	−26.0009	−	44.4286i	−0.967651	−	1.65346i
$723$	−11.3980	+	6.83912i	−0.423895	+	0.254350i
$724$	−5.25416	−	8.85791i	−0.195269	−	0.329202i
$725$	2.78506	+	0.491081i	0.103434	+	0.0182383i
$726$	−4.28911	+	12.6734i	−0.159184	+	0.470354i
$727$	−5.83185	+	1.02831i	−0.216291	+	0.0381380i	−0.280744	−	0.959783i	$-0.590581\pi$
$727$	−5.83185	+	1.02831i	−0.216291	+	0.0381380i	0.0644523	+	0.997921i	$0.479470\pi$
$728$	20.5847	−	36.7291i	0.762920	−	1.36127i
$729$	15.7901	+	21.9014i	0.584820	+	0.811163i
$730$	−29.4350	−	5.01166i	−1.08944	−	0.185490i
$731$	10.8000	+	3.93089i	0.399454	+	0.145389i
$732$	−36.1061	−	19.4901i	−1.33452	−	0.720374i
$733$	−8.94290	−	7.50399i	−0.330314	−	0.277166i	0.462514	−	0.886612i	$-0.346947\pi$
$733$	−8.94290	−	7.50399i	−0.330314	−	0.277166i	−0.792828	+	0.609446i	$0.791392\pi$
$734$	32.6248	−	5.95092i	1.20420	−	0.219652i
$735$	26.3045	−	0.185537i	0.970255	−	0.00684365i
$736$	−5.07917	−	4.01318i	−0.187221	−	0.147928i
$737$	8.08046	+	4.66526i	0.297648	+	0.171847i
$738$	−0.264582	−	6.68217i	−0.00973941	−	0.245974i
$739$	−9.68487	+	5.59156i	−0.356264	+	0.205689i	−0.667441	−	0.744663i	$-0.732610\pi$
$739$	−9.68487	+	5.59156i	−0.356264	+	0.205689i	0.311177	+	0.950352i	$0.399277\pi$
$740$	−31.9055	−	5.23917i	−1.17287	−	0.192596i
$741$	13.7969	+	71.2106i	0.506840	+	2.61599i
$742$	19.9710	+	23.7526i	0.733160	+	0.871985i
$743$	−1.35795	+	7.70131i	−0.0498183	+	0.282534i	−0.999532	−	0.0305856i	$-0.990263\pi$
$743$	−1.35795	+	7.70131i	−0.0498183	+	0.282534i	0.949714	+	0.313119i	$0.101374\pi$
$744$	−10.5932	+	9.53048i	−0.388364	+	0.349404i
$745$	4.28262	+	24.2880i	0.156903	+	0.889842i
$746$	−3.74686	+	22.0065i	−0.137182	+	0.805714i
$747$	−13.3316	+	5.36742i	−0.487779	+	0.196384i
$748$	10.7510	+	12.5104i	0.393097	+	0.457425i
$749$	0.0716411	+	0.418258i	0.00261771	+	0.0152828i
$750$	26.2064	−	10.2187i	0.956922	−	0.373135i
$751$	0.996050	+	0.175631i	0.0363464	+	0.00640885i	0.191792	−	0.981436i	$-0.438570\pi$
$751$	0.996050	+	0.175631i	0.0363464	+	0.00640885i	−0.155445	+	0.987844i	$0.549681\pi$
$752$	−3.67520	−	18.3102i	−0.134021	−	0.667706i
$753$	−17.4693	−	2.77780i	−0.636618	−	0.101229i
$754$	0.452536	+	76.8531i	0.0164804	+	2.79882i
$755$	17.9619			0.653701
$756$	−18.8532	−	20.0139i	−0.685684	−	0.727899i
$757$	13.5888			0.493893			0.246947	−	0.969029i	$-0.420573\pi$
$757$	13.5888			0.493893			0.246947	+	0.969029i	$0.420573\pi$
$758$	0.0536233	+	9.10672i	0.00194769	+	0.330771i
$759$	1.66886	+	4.35546i	0.0605757	+	0.158093i
$760$	−35.5025	−	28.7369i	−1.28781	−	1.04240i
$761$	−24.6907	−	4.35364i	−0.895038	−	0.157819i	−0.292836	−	0.956163i	$-0.594599\pi$
$761$	−24.6907	−	4.35364i	−0.895038	−	0.157819i	−0.602202	+	0.798344i	$0.705710\pi$
$762$	6.16986	−	40.3316i	0.223510	−	1.46106i
$763$	26.7006	−	22.1826i	0.966625	−	0.803065i
$764$	10.2084	−	8.77277i	0.369326	−	0.317388i
$765$	−12.0649	−	19.3604i	−0.436207	−	0.699976i
$766$	−0.286368	+	1.68192i	−0.0103469	+	0.0607704i
$767$	1.53021	+	8.67825i	0.0552527	+	0.313353i
$768$	16.4204	−	22.3242i	0.592519	−	0.805556i
$769$	1.85220	−	10.5043i	0.0667920	−	0.378796i	−0.933028	−	0.359805i	$-0.882843\pi$
$769$	1.85220	−	10.5043i	0.0667920	−	0.378796i	0.999820	−	0.0189917i	$-0.00604559\pi$
$770$	6.51599	−	17.9580i	0.234820	−	0.647162i
$771$	−13.9751	−	4.82155i	−0.503301	−	0.173644i
$772$	4.21123	−	25.6456i	0.151566	−	0.923004i
$773$	38.8572	−	22.4342i	1.39760	−	0.806902i	0.403455	−	0.914999i	$-0.367809\pi$
$773$	38.8572	−	22.4342i	1.39760	−	0.806902i	0.994140	+	0.108097i	$0.0344759\pi$
$774$	−8.51433	+	11.0033i	−0.306041	+	0.395507i
$775$	−0.737532	−	0.425814i	−0.0264929	−	0.0152957i
$776$	−9.77653	+	8.50224i	−0.350957	+	0.305213i
$777$	−29.3653	+	17.4252i	−1.05348	+	0.625125i
$778$	44.4969	−	8.11645i	1.59529	−	0.290989i
$779$	−8.98733	−	7.54126i	−0.322004	−	0.270194i
$780$	22.1826	+	36.0012i	0.794264	+	1.28905i
$781$	19.8211	+	7.21429i	0.709255	+	0.258148i
$782$	−5.59139	−	0.952001i	−0.199948	−	0.0340435i
$783$	47.9687	+	14.7616i	1.71426	+	0.527535i
$784$	21.6949	+	17.7011i	0.774818	+	0.632184i
$785$	−45.7915	+	8.07428i	−1.63437	+	0.288183i
$786$	−14.4622	+	2.89046i	−0.515849	+	0.103099i
$787$	17.0020	+	2.99792i	0.606057	+	0.106864i	0.468252	−	0.883595i	$-0.344884\pi$
$787$	17.0020	+	2.99792i	0.606057	+	0.106864i	0.137805	+	0.990459i	$0.455995\pi$
$788$	−8.29283	+	4.91898i	−0.295420	+	0.175231i
$789$	−0.0624912	−	3.70982i	−0.00222474	−	0.132073i
$790$	25.0153	+	42.7446i	0.890006	+	1.52078i
$791$	30.5517	−	17.4402i	1.08629	−	0.620102i
$792$	−18.3886	+	7.78360i	−0.653410	+	0.276578i
$793$	66.6420			2.36653
$794$	1.52041	−	2.66960i	0.0539572	−	0.0947407i
$795$	−30.5982	+	5.92831i	−1.08521	+	0.210256i
$796$	−11.8672	+	7.03917i	−0.420623	+	0.249497i
$797$	3.42575	+	0.604052i	0.121346	+	0.0213966i	0.233991	−	0.972239i	$-0.424821\pi$
$797$	3.42575	+	0.604052i	0.121346	+	0.0213966i	−0.112645	+	0.993635i	$0.535932\pi$
$798$	−48.2293	+	0.860334i	−1.70730	+	0.0304555i
$799$	−10.5181	−	12.5350i	−0.372104	−	0.443457i
$800$	1.57240	+	0.520421i	0.0555926	+	0.0183996i
$801$	−9.20590	+	28.2156i	−0.325274	+	0.996951i
$802$	3.81456	−	4.60076i	0.134697	−	0.162458i
$803$	3.97661	+	22.5525i	0.140332	+	0.795860i
$804$	−2.77113	−	13.4525i	−0.0977303	−	0.474432i
$805$	2.21640	+	6.18351i	0.0781177	+	0.217940i
$806$	7.78748	−	21.7944i	0.274302	−	0.767674i
$807$	48.1348	−	18.4435i	1.69442	−	0.649243i
$808$	−14.2667	−	16.4050i	−0.501901	−	0.577124i
$809$	−3.15842	−	1.82352i	−0.111044	−	0.0641114i	0.443449	−	0.896299i	$-0.353755\pi$
$809$	−3.15842	−	1.82352i	−0.111044	−	0.0641114i	−0.554494	+	0.832188i	$0.687088\pi$
$810$	26.7712	−	6.77293i	0.940643	−	0.237976i
$811$			37.1856i			1.30576i	0.757460	+	0.652881i	$0.226440\pi$
$811$			37.1856i			1.30576i	−0.757460	+	0.652881i	$0.773560\pi$
$812$	−50.3930	−	8.52851i	−1.76845	−	0.299292i
$813$	−7.14571	+	44.9388i	−0.250611	+	1.57607i
$814$	4.44985	+	24.3955i	0.155967	+	0.855062i
$815$	−29.6113	+	10.7776i	−1.03724	+	0.377523i
$816$	3.24732	−	24.0636i	0.113679	−	0.842396i
$817$	4.23843	+	24.0374i	0.148284	+	0.840961i
$818$	0.0830697	−	0.487894i	0.00290446	−	0.0170588i
$819$	42.3872	+	14.0596i	1.48113	+	0.491282i
$820$	−6.45426	−	2.26344i	−0.225392	−	0.0790428i
$821$	17.5909	−	48.3307i	0.613927	−	1.68675i	−0.107451	−	0.994210i	$-0.534269\pi$
$821$	17.5909	−	48.3307i	0.613927	−	1.68675i	0.721378	−	0.692541i	$-0.243509\pi$
$822$	2.47164	+	4.06474i	0.0862082	+	0.141774i
$823$	10.2973	−	12.2718i	0.358940	−	0.427768i	−0.556110	−	0.831109i	$-0.687707\pi$
$823$	10.2973	−	12.2718i	0.358940	−	0.427768i	0.915050	+	0.403341i	$0.132151\pi$
$824$	0.907861	+	0.143594i	0.0316268	+	0.00500234i
$825$	−0.782398	−	0.901156i	−0.0272396	−	0.0313742i
$826$	−5.86022	+	0.00582115i	−0.203903	+	0.000202544i
$827$	−5.56965	+	9.64692i	−0.193676	+	0.335456i	−0.946466	−	0.322805i	$-0.895374\pi$
$827$	−5.56965	+	9.64692i	−0.193676	+	0.335456i	0.752790	+	0.658261i	$0.228708\pi$
$828$	3.15920	−	6.09598i	0.109790	−	0.211850i
$829$	8.14021			0.282721			0.141361	−	0.989958i	$-0.454852\pi$
$829$	8.14021			0.282721			0.141361	+	0.989958i	$0.454852\pi$
$830$	0.0865493	+	14.6985i	0.00300417	+	0.510191i
$831$	0.454403	+	26.9759i	0.0157631	+	0.935783i
$832$	−6.24549	+	44.5758i	−0.216524	+	1.54539i
$833$	24.1178	+	4.49650i	0.835633	+	0.155795i
$834$	−5.85347	−	1.98102i	−0.202689	−	0.0685970i
$835$	−14.6209	−	17.4246i	−0.505979	−	0.603002i
$836$	−11.5929	+	33.0574i	−0.400949	+	1.14331i
$837$	−12.0537	−	9.11777i	−0.416638	−	0.315156i
$838$	5.01579	−	29.4593i	0.173268	−	1.01765i
$839$	4.40658	+	24.9910i	0.152132	+	0.862784i	0.961361	+	0.275291i	$0.0887741\pi$
$839$	4.40658	+	24.9910i	0.152132	+	0.862784i	−0.809229	+	0.587493i	$0.800115\pi$
$840$	−26.1291	+	10.3963i	−0.901539	+	0.358706i
$841$	60.4153	−	21.9894i	2.08328	−	0.758254i
$842$	−4.52983	+	3.84666i	−0.156108	+	0.132565i
$843$	33.1976	−	0.559207i	1.14339	−	0.0192601i
$844$	27.2291	−	33.2376i	0.937266	−	1.14409i
$845$	−35.0541	−	20.2385i	−1.20590	−	0.696226i
$846$	18.3311	−	7.50597i	0.630236	−	0.258061i
$847$	14.4514	+	0.0707388i	0.496554	+	0.00243061i
$848$	−29.1134	−	15.9064i	−0.999757	−	0.546229i
$849$	−8.54150	−	44.0858i	−0.293143	−	1.51302i
$850$	1.42767	−	0.260413i	0.0489686	−	0.00893209i
$851$	−6.53185	−	5.48088i	−0.223909	−	0.187882i
$852$	−11.4503	−	28.8617i	−0.392282	−	0.988785i
$853$	13.9677	−	11.7203i	0.478245	−	0.401296i	−0.371546	−	0.928415i	$-0.621172\pi$
$853$	13.9677	−	11.7203i	0.478245	−	0.401296i	0.849792	+	0.527119i	$0.176728\pi$
$854$	−7.65240	+	43.6525i	−0.261860	+	1.49376i
$855$	22.7962	−	42.7475i	0.779614	−	1.46194i
$856$	−0.233729	−	0.388803i	−0.00798868	−	0.0132890i
$857$	−1.63335	−	1.94655i	−0.0557943	−	0.0664930i	0.737426	−	0.675428i	$-0.236041\pi$
$857$	−1.63335	−	1.94655i	−0.0557943	−	0.0664930i	−0.793220	+	0.608935i	$0.791597\pi$
$858$	20.2769	−	25.3119i	0.692242	−	0.864134i
$859$	47.8855	+	8.44351i	1.63383	+	0.288089i	0.913895	−	0.405950i	$-0.133059\pi$
$859$	47.8855	+	8.44351i	1.63383	+	0.288089i	0.719937	+	0.694039i	$0.244171\pi$
$860$	7.25941	+	12.2385i	0.247544	+	0.417330i
$861$	−6.75760	+	2.55141i	−0.230299	+	0.0869518i
$862$	−2.91435	+	5.11715i	−0.0992631	+	0.174291i
$863$	12.9596	+	22.4466i	0.441149	+	0.764092i	0.997775	−	0.0666708i	$-0.0212377\pi$
$863$	12.9596	+	22.4466i	0.441149	+	0.764092i	−0.556626	+	0.830763i	$0.687904\pi$
$864$	26.5486	+	12.6164i	0.903200	+	0.429219i
$865$	6.74948	−	11.6904i	0.229489	−	0.397487i
$866$	10.6309	−	0.0625980i	0.361252	−	0.00212717i
$867$	2.92298	+	7.62853i	0.0992696	+	0.259078i
$868$	13.3817	+	7.60365i	0.454205	+	0.258085i
$869$	24.4162	−	29.0981i	0.828262	−	0.987084i
$870$	32.0927	−	40.0617i	1.08805	−	1.35822i
$871$	14.3395	+	17.0891i	0.485875	+	0.579043i
$872$	−17.9843	+	32.4607i	−0.609024	+	1.09926i
$873$	−10.8188	−	8.47385i	−0.366161	−	0.286796i
$874$	−4.18634	−	11.2945i	−0.141605	−	0.382043i
$875$	−19.4150	−	23.3692i	−0.656346	−	0.790024i
$876$	20.9208	−	26.4331i	0.706847	−	0.893093i
$877$	8.64752	−	3.14744i	0.292006	−	0.106281i	−0.191864	−	0.981422i	$-0.561453\pi$
$877$	8.64752	−	3.14744i	0.292006	−	0.106281i	0.483870	+	0.875140i	$0.339231\pi$
$878$	−5.95742	+	1.08666i	−0.201053	+	0.0366730i
$879$	34.4405	+	11.8823i	1.16165	+	0.400781i
$880$	0.480970	+	20.4170i	0.0162135	+	0.688256i
$881$	9.10485	+	5.25669i	0.306750	+	0.177102i	0.645471	−	0.763785i	$-0.276661\pi$
$881$	9.10485	+	5.25669i	0.306750	+	0.177102i	−0.338721	+	0.940887i	$0.609994\pi$
$882$	−14.0767	+	26.1505i	−0.473988	+	0.880531i
$883$	0.251870	−	0.145417i	0.00847610	−	0.00489368i	−0.495756	−	0.868462i	$-0.665109\pi$
$883$	0.251870	−	0.145417i	0.00847610	−	0.00489368i	0.504232	+	0.863568i	$0.331776\pi$
$884$	13.9242	+	36.8986i	0.468323	+	1.24104i
$885$	2.85655	−	5.14594i	0.0960218	−	0.172979i
$886$	−14.0049	−	5.00417i	−0.470503	−	0.168118i
$887$	−35.3550	−	29.6664i	−1.18710	−	0.996099i	−0.999905	−	0.0137766i	$-0.995615\pi$
$887$	−35.3550	−	29.6664i	−1.18710	−	0.996099i	−0.187199	−	0.982322i	$-0.559941\pi$
$888$	22.4854	−	28.7564i	0.754561	−	0.965001i
$889$	−43.4373	+	7.44012i	−1.45684	+	0.249534i
$890$	23.3678	+	19.3746i	0.783292	+	0.649439i
$891$	−11.8005	−	17.5873i	−0.395330	−	0.589197i
$892$	−3.14116	+	8.95709i	−0.105174	+	0.299906i
$893$	11.8855	−	32.6552i	0.397734	−	1.09276i
$894$	−26.3746	−	8.92608i	−0.882099	−	0.298533i
$895$	0.430494	+	1.18277i	0.0143898	+	0.0395357i
$896$	−28.4813	−	9.20956i	−0.951493	−	0.307670i
$897$	0.187821	+	11.1501i	0.00627118	+	0.372292i
$898$	9.01714	+	5.13549i	0.300906	+	0.171374i
$899$	−28.0940			−0.936989
$900$	−0.226115	+	1.74214i	−0.00753717	+	0.0580713i
$901$	−29.0680			−0.968395
$902$	0.0308880	+	5.24564i	0.00102846	+	0.174661i
$903$	14.1817	+	4.97065i	0.471938	+	0.165413i
$904$	−23.6613	+	29.2319i	−0.786963	+	0.972239i
$905$	−3.82118	−	10.4986i	−0.127020	−	0.348985i
$906$	−9.73771	+	17.7881i	−0.323514	+	0.590969i
$907$	−35.8528	+	6.32182i	−1.19047	+	0.209913i	−0.733577	−	0.679607i	$-0.762150\pi$
$907$	−35.8528	+	6.32182i	−1.19047	+	0.209913i	−0.456897	+	0.889519i	$0.651039\pi$
$908$	7.10135	+	37.6739i	0.235667	+	1.25025i
$909$	14.2191	−	18.1539i	0.471616	−	0.602126i
$910$	29.3244	−	35.0180i	0.972094	−	1.16084i
$911$	−46.2523	−	16.8345i	−1.53241	−	0.557751i	−0.568198	−	0.822892i	$-0.692359\pi$
$911$	−46.2523	−	16.8345i	−1.53241	−	0.557751i	−0.964210	+	0.265141i	$0.914581\pi$
$912$	47.7058	−	19.5797i	1.57970	−	0.648349i
$913$	10.5935	−	3.85571i	0.350593	−	0.127605i
$914$	−18.2361	+	15.4858i	−0.603196	+	0.512224i
$915$	−34.5738	−	28.0323i	−1.14298	−	0.926719i
$916$	20.2123	−	7.62741i	0.667833	−	0.252017i
$917$	7.89732	+	13.8345i	0.260792	+	0.456856i
$918$	25.7137	−	1.45225i	0.848679	−	0.0479315i
$919$	1.60265	−	0.925292i	0.0528667	−	0.0305226i	−0.473334	−	0.880883i	$-0.656950\pi$
$919$	1.60265	−	0.925292i	0.0528667	−	0.0305226i	0.526200	+	0.850361i	$0.323616\pi$
$920$	−4.60814	−	5.29880i	−0.151926	−	0.174696i
$921$	−42.3973	+	16.2451i	−1.39704	+	0.535295i
$922$	−18.2645	+	3.33152i	−0.601508	+	0.109718i
$923$	38.6328	+	32.4168i	1.27161	+	1.06701i
$924$	14.2517	+	16.1885i	0.468846	+	0.532563i
$925$	2.05011	+	0.746179i	0.0674072	+	0.0245342i
$926$	−16.6703	−	44.9754i	−0.547819	−	1.47798i
$927$	0.0328347	+	0.974349i	0.00107843	+	0.0320018i
$928$	53.5058	−	11.0677i	1.75641	−	0.363316i
$929$	−12.8053	+	35.1823i	−0.420129	+	1.15429i	0.531504	+	0.847056i	$0.321627\pi$
$929$	−12.8053	+	35.1823i	−0.420129	+	1.15429i	−0.951633	+	0.307238i	$0.900595\pi$
$930$	−13.2077	+	8.03119i	−0.433098	+	0.263353i
$931$	17.3397	+	49.1319i	0.568287	+	1.61023i
$932$	0.461798	+	39.2117i	0.0151267	+	1.28442i
$933$	57.9685	−	11.2312i	1.89780	−	0.367694i
$934$	−0.727134	+	1.27674i	−0.0237926	+	0.0417761i
$935$	8.94708	+	15.4968i	0.292601	+	0.506800i
$936$	−47.6786	+	2.45051i	−1.55842	+	0.0800973i
$937$	11.4204	+	19.7806i	0.373087	+	0.646206i	0.990039	−	0.140795i	$-0.0449660\pi$
$937$	11.4204	+	19.7806i	0.373087	+	0.646206i	−0.616952	+	0.787001i	$0.711633\pi$
$938$	−12.8405	+	7.43046i	−0.419256	+	0.242613i
$939$	−37.2528	+	22.3528i	−1.21570	+	0.729457i
$940$	−0.238577	−	20.2578i	−0.00778153	−	0.660737i
$941$	11.8118	+	2.08274i	0.385053	+	0.0678953i	0.362824	−	0.931858i	$-0.381813\pi$
$941$	11.8118	+	2.08274i	0.385053	+	0.0678953i	0.0222290	+	0.999753i	$0.492924\pi$
$942$	16.8288	−	49.7256i	0.548314	−	1.62015i
$943$	−1.15942	−	1.38174i	−0.0377558	−	0.0449956i
$944$	5.83493	−	2.28075i	0.189911	−	0.0742322i
$945$	−16.0765	−	25.1239i	−0.522967	−	0.817280i
$946$	6.96573	−	8.40140i	0.226475	−	0.273153i
$947$	9.13142	−	7.66217i	0.296731	−	0.248987i	−0.482251	−	0.876033i	$-0.660181\pi$
$947$	9.13142	−	7.66217i	0.296731	−	0.248987i	0.778982	+	0.627046i	$0.215736\pi$
$948$	−55.8924	+	1.60006i	−1.81530	+	0.0519676i
$949$	−9.50766	+	53.9206i	−0.308632	+	1.75034i
$950$	1.99493	+	2.34923i	0.0647239	+	0.0762190i
$951$	−16.6680	+	30.0267i	−0.540498	+	0.973682i
$952$	−25.7686	+	4.88377i	−0.835165	+	0.158284i
$953$	−33.4259	+	19.2984i	−1.08277	+	0.625137i	−0.931642	−	0.363377i	$-0.881624\pi$
$953$	−33.4259	+	19.2984i	−1.08277	+	0.625137i	−0.151128	+	0.988514i	$0.548290\pi$
$954$	10.7173	−	33.5159i	0.346985	−	1.08512i
$955$	12.6453	−	7.30076i	0.409192	−	0.236247i
$956$	23.8989	−	9.01862i	0.772947	−	0.291683i
$957$	−37.2163	−	12.8400i	−1.20303	−	0.415058i
$958$	−37.6444	+	31.9670i	−1.21623	+	1.03281i
$959$	3.32212	−	3.92001i	0.107277	−	0.126584i
$960$	21.9905	−	20.4988i	0.709741	−	0.661596i
$961$	−21.1805	−	7.70906i	−0.683241	−	0.248679i
$962$	−9.95152	+	58.4483i	−0.320850	+	1.88445i
$963$	0.357969	−	0.321527i	0.0115354	−	0.0103611i
$964$	−14.4839	−	5.07935i	−0.466494	−	0.163595i
$965$	9.64258	−	26.4928i	0.310406	−	0.852833i
$966$	−7.32523	−	1.15733i	−0.235685	−	0.0372363i
$967$	30.1047	−	35.8774i	0.968101	−	1.15374i	−0.0199793	−	0.999800i	$-0.506360\pi$
$967$	30.1047	−	35.8774i	0.968101	−	1.15374i	0.988081	−	0.153938i	$-0.0491955\pi$
$968$	−14.4220	+	5.53960i	−0.463541	+	0.178049i
$969$	28.4561	−	35.0965i	0.914140	−	1.12746i
$970$	−12.1306	+	7.09914i	−0.389489	+	0.227940i
$971$	−4.88427	−	8.45981i	−0.156744	−	0.271488i	0.776949	−	0.629564i	$-0.216766\pi$
$971$	−4.88427	−	8.45981i	−0.156744	−	0.271488i	−0.933693	+	0.358076i	$0.883433\pi$
$972$	−7.80610	+	30.1839i	−0.250381	+	0.968147i
$973$	−0.0326722	+	6.67466i	−0.00104742	+	0.213980i
$974$	−33.6464	−	19.1625i	−1.07810	−	0.614006i
$975$	−1.02091	−	2.66443i	−0.0326954	−	0.0853299i
$976$	−9.32367	−	46.4516i	−0.298444	−	1.48688i
$977$	−0.250738	−	0.688897i	−0.00802182	−	0.0220398i	0.935617	−	0.353017i	$-0.114844\pi$
$977$	−0.250738	−	0.688897i	−0.00802182	−	0.0220398i	−0.943639	+	0.330977i	$0.892622\pi$
$978$	5.37987	−	35.1675i	0.172029	−	1.12453i
$979$	7.96263	−	21.8771i	0.254487	−	0.699197i
$980$	19.5706	+	23.2294i	0.625159	+	0.742036i
$981$	−37.4195	−	12.2088i	−1.19471	−	0.389798i
$982$	−14.7983	−	12.2695i	−0.472233	−	0.391535i
$983$	5.92057	+	33.5772i	0.188837	+	1.07095i	0.920926	+	0.389738i	$0.127434\pi$
$983$	5.92057	+	33.5772i	0.188837	+	1.07095i	−0.732089	+	0.681209i	$0.761454\pi$
$984$	5.74058	−	5.16470i	0.183003	−	0.164645i
$985$	−9.82885	+	3.57741i	−0.313173	+	0.113986i
$986$	36.4917	−	30.9881i	1.16213	−	0.986863i
$987$	−13.9475	−	16.2243i	−0.443955	−	0.516426i
$988$	−53.0780	+	64.7904i	−1.68864	+	2.06126i
$989$			3.75258i			0.119325i
$990$	−21.1669	+	4.60253i	−0.672727	+	0.146278i
$991$			33.1097i			1.05176i	0.850558	+	0.525882i	$0.176265\pi$
$991$			33.1097i			1.05176i	−0.850558	+	0.525882i	$0.823735\pi$
$992$	−16.2809	−	2.37894i	−0.516919	−	0.0755314i
$993$	16.6747	−	30.0387i	0.529156	−	0.953250i
$994$	−25.6701	+	21.5833i	−0.814206	+	0.684579i
$995$	−14.0653	+	5.11936i	−0.445900	+	0.162295i
$996$	−14.6031	−	7.88278i	−0.462718	−	0.249775i
$997$	36.0890	+	13.1353i	1.14295	+	0.416000i	0.842978	−	0.537948i	$-0.180800\pi$
$997$	36.0890	+	13.1353i	1.14295	+	0.416000i	0.299972	+	0.953948i	$0.403023\pi$
$998$	−9.24360	−	24.9387i	−0.292601	−	0.789421i
$999$	34.4658	+	17.6408i	1.09045	+	0.558129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.95.1	yes	840
4.3	odd	2	inner	756.2.ci.a.95.77	yes	840
7.2	even	3		756.2.bs.a.527.95	yes	840
27.2	odd	18		756.2.bs.a.515.17	✓	840
28.23	odd	6		756.2.bs.a.527.17	yes	840
108.83	even	18		756.2.bs.a.515.95	yes	840
189.2	odd	18	inner	756.2.ci.a.191.77	yes	840
756.191	even	18	inner	756.2.ci.a.191.1	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.17	✓	840	27.2	odd	18
756.2.bs.a.515.95	yes	840	108.83	even	18
756.2.bs.a.527.17	yes	840	28.23	odd	6
756.2.bs.a.527.95	yes	840	7.2	even	3
756.2.ci.a.95.1	yes	840	1.1	even	1	trivial
756.2.ci.a.95.77	yes	840	4.3	odd	2	inner
756.2.ci.a.191.1	yes	840	756.191	even	18	inner
756.2.ci.a.191.77	yes	840	189.2	odd	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41419 + 0.00832720i) q^{2} +(1.09084 - 1.34539i) q^{3} +(1.99986 - 0.0235525i) q^{4} +(2.13665 + 0.376749i) q^{5} +(-1.53144 + 1.91172i) q^{6} +(2.48173 + 0.917059i) q^{7} +(-2.82799 + 0.0499609i) q^{8} +(-0.620154 - 2.93520i) q^{9} +O(q^{10})\)	\(q+(-1.41419 + 0.00832720i) q^{2} +(1.09084 - 1.34539i) q^{3} +(1.99986 - 0.0235525i) q^{4} +(2.13665 + 0.376749i) q^{5} +(-1.53144 + 1.91172i) q^{6} +(2.48173 + 0.917059i) q^{7} +(-2.82799 + 0.0499609i) q^{8} +(-0.620154 - 2.93520i) q^{9} +(-3.02476 - 0.515002i) q^{10} +(0.408639 + 2.31751i) q^{11} +(2.14983 - 2.71629i) q^{12} +(-0.977014 + 5.54092i) q^{13} +(-3.51728 - 1.27623i) q^{14} +(2.83761 - 2.46366i) q^{15} +(3.99889 - 0.0942034i) q^{16} +(3.03522 - 1.75239i) q^{17} +(0.901457 + 4.14577i) q^{18} +(6.44594 + 3.72156i) q^{19} +(4.28187 + 0.703122i) q^{20} +(3.94097 - 2.33854i) q^{21} +(-0.597192 - 3.27399i) q^{22} +(0.876606 + 0.735560i) q^{23} +(-3.01765 + 3.85925i) q^{24} +(-0.275135 - 0.100141i) q^{25} +(1.33554 - 7.84404i) q^{26} +(-4.62548 - 2.36747i) q^{27} +(4.98472 + 1.77554i) q^{28} +(-9.51207 + 1.67723i) q^{29} +(-3.99240 + 3.50771i) q^{30} +(2.86446 + 0.505081i) q^{31} +(-5.65440 + 0.166521i) q^{32} +(3.56371 + 1.97824i) q^{33} +(-4.27778 + 2.50348i) q^{34} +(4.95709 + 2.89442i) q^{35} +(-1.30935 - 5.85539i) q^{36} -7.45130 q^{37} +(-9.14676 - 5.20932i) q^{38} +(6.38894 + 7.35870i) q^{39} +(-6.06124 - 0.958691i) q^{40} +(-1.55229 - 0.273710i) q^{41} +(-5.55380 + 3.33996i) q^{42} +(2.10789 + 2.51208i) q^{43} +(0.871805 + 4.62507i) q^{44} +(-0.219217 - 6.50514i) q^{45} +(-1.24581 - 1.03292i) q^{46} +(-0.810739 - 4.59793i) q^{47} +(4.23539 - 5.48283i) q^{48} +(5.31801 + 4.55179i) q^{49} +(0.389926 + 0.139327i) q^{50} +(0.953284 - 5.99512i) q^{51} +(-1.82339 + 11.1041i) q^{52} +(-7.18267 - 4.14692i) q^{53} +(6.56102 + 3.30954i) q^{54} +5.10566i q^{55} +(-7.06413 - 2.46944i) q^{56} +(12.0384 - 4.61269i) q^{57} +(13.4379 - 2.45114i) q^{58} +(1.47176 - 0.535676i) q^{59} +(5.61680 - 4.99380i) q^{60} +(-2.05678 - 11.6646i) q^{61} +(-4.05509 - 0.690427i) q^{62} +(1.15270 - 7.85311i) q^{63} +(7.99501 - 0.282577i) q^{64} +(-4.17507 + 11.4709i) q^{65} +(-5.05624 - 2.76793i) q^{66} +(2.54861 - 3.03731i) q^{67} +(6.02875 - 3.57602i) q^{68} +(1.94585 - 0.377003i) q^{69} +(-7.03437 - 4.05198i) q^{70} +(4.48169 - 7.76252i) q^{71} +(1.90043 + 8.26973i) q^{72} +9.73135 q^{73} +(10.5375 - 0.0620485i) q^{74} +(-0.434855 + 0.260926i) q^{75} +(12.9786 + 7.29079i) q^{76} +(-1.11116 + 6.12619i) q^{77} +(-9.09645 - 10.3534i) q^{78} +(-10.3755 - 12.3650i) q^{79} +(8.57972 + 1.30530i) q^{80} +(-8.23082 + 3.64055i) q^{81} +(2.19751 + 0.374152i) q^{82} +(-0.831866 - 4.71774i) q^{83} +(7.82631 - 4.76958i) q^{84} +(7.14541 - 2.60072i) q^{85} +(-3.00187 - 3.53501i) q^{86} +(-8.11957 + 14.6270i) q^{87} +(-1.27141 - 6.53347i) q^{88} +(-8.56772 - 4.94658i) q^{89} +(0.364184 + 9.19767i) q^{90} +(-7.50604 + 12.8551i) q^{91} +(1.77041 + 1.45037i) q^{92} +(3.80418 - 3.30285i) q^{93} +(1.18483 + 6.49559i) q^{94} +(12.3706 + 10.3802i) q^{95} +(-5.94399 + 7.78903i) q^{96} +(3.50909 - 2.94447i) q^{97} +(-7.55857 - 6.39281i) q^{98} +(6.54894 - 2.63665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Introduction

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