LMFDB - Embedded newform 756.2.ci.a.95.19

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			95.19
Character	$\chi$	$=$	756.95
Dual form			756.2.ci.a.191.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32113 - 0.504600i) q^{2} +(0.893683 + 1.48369i) q^{3} +(1.49076 + 1.33328i) q^{4} +(3.15348 + 0.556044i) q^{5} +(-0.431999 - 2.41109i) q^{6} +(1.10140 - 2.40560i) q^{7} +(-1.29670 - 2.51367i) q^{8} +(-1.40266 + 2.65189i) q^{9} +O(q^{10})$	\(q+(-1.32113 - 0.504600i) q^{2} +(0.893683 + 1.48369i) q^{3} +(1.49076 + 1.33328i) q^{4} +(3.15348 + 0.556044i) q^{5} +(-0.431999 - 2.41109i) q^{6} +(1.10140 - 2.40560i) q^{7} +(-1.29670 - 2.51367i) q^{8} +(-1.40266 + 2.65189i) q^{9} +(-3.88557 - 2.32585i) q^{10} +(0.904764 + 5.13117i) q^{11} +(-0.645914 + 3.40335i) q^{12} +(-1.08679 + 6.16349i) q^{13} +(-2.66896 + 2.62233i) q^{14} +(1.99322 + 5.17571i) q^{15} +(0.444711 + 3.97520i) q^{16} +(0.814654 - 0.470341i) q^{17} +(3.19124 - 2.79571i) q^{18} +(-6.33439 - 3.65716i) q^{19} +(3.95971 + 5.03341i) q^{20} +(4.55347 - 0.515702i) q^{21} +(1.39388 - 7.23548i) q^{22} +(-1.97765 - 1.65944i) q^{23} +(2.57067 - 4.17033i) q^{24} +(4.93681 + 1.79685i) q^{25} +(4.54589 - 7.59437i) q^{26} +(-5.18812 + 0.288837i) q^{27} +(4.84927 - 2.11768i) q^{28} +(8.24184 - 1.45326i) q^{29} +(-0.0216266 - 7.84356i) q^{30} +(0.993208 + 0.175129i) q^{31} +(1.41837 - 5.47615i) q^{32} +(-6.80449 + 5.92803i) q^{33} +(-1.31360 + 0.210305i) q^{34} +(4.81088 - 6.97359i) q^{35} +(-5.62675 + 2.08318i) q^{36} -2.56387 q^{37} +(6.52314 + 8.02792i) q^{38} +(-10.1159 + 3.89575i) q^{39} +(-2.69142 - 8.64785i) q^{40} +(5.45806 + 0.962404i) q^{41} +(-6.27593 - 1.61637i) q^{42} +(-3.63752 - 4.33503i) q^{43} +(-5.49252 + 8.85564i) q^{44} +(-5.89784 + 7.58276i) q^{45} +(1.77537 + 3.19026i) q^{46} +(0.501039 + 2.84153i) q^{47} +(-5.50053 + 4.21238i) q^{48} +(-4.57382 - 5.29908i) q^{49} +(-5.61546 - 4.86498i) q^{50} +(1.42588 + 0.788358i) q^{51} +(-9.83782 + 7.73927i) q^{52} +(-0.206079 - 0.118980i) q^{53} +(6.99991 + 2.23634i) q^{54} +16.6842i q^{55} +(-7.47509 + 0.350780i) q^{56} +(-0.234846 - 12.6666i) q^{57} +(-11.6218 - 2.23890i) q^{58} +(11.9175 - 4.33762i) q^{59} +(-3.92929 + 10.3733i) q^{60} +(-0.930103 - 5.27488i) q^{61} +(-1.22378 - 0.732541i) q^{62} +(4.83449 + 6.29505i) q^{63} +(-4.63711 + 6.51899i) q^{64} +(-6.85435 + 18.8322i) q^{65} +(11.9809 - 4.39813i) q^{66} +(2.23927 - 2.66866i) q^{67} +(1.84155 + 0.385001i) q^{68} +(0.694708 - 4.41723i) q^{69} +(-9.87466 + 6.78543i) q^{70} +(-1.77382 + 3.07235i) q^{71} +(8.48483 + 0.0871146i) q^{72} +7.47691 q^{73} +(3.38720 + 1.29373i) q^{74} +(1.74597 + 8.93050i) q^{75} +(-4.56700 - 13.8975i) q^{76} +(13.3401 + 3.47500i) q^{77} +(15.3303 - 0.0422692i) q^{78} +(2.97392 + 3.54418i) q^{79} +(-0.807999 + 12.7830i) q^{80} +(-5.06508 - 7.43942i) q^{81} +(-6.72517 - 4.02560i) q^{82} +(-1.16631 - 6.61447i) q^{83} +(7.47569 + 5.30227i) q^{84} +(2.83053 - 1.03023i) q^{85} +(2.61817 + 7.56262i) q^{86} +(9.52178 + 10.9296i) q^{87} +(11.7249 - 8.92790i) q^{88} +(1.04925 + 0.605782i) q^{89} +(11.6181 - 7.04174i) q^{90} +(13.6299 + 9.40288i) q^{91} +(-0.735684 - 5.11059i) q^{92} +(0.627775 + 1.63012i) q^{93} +(0.771903 - 4.00685i) q^{94} +(-17.9419 - 15.0550i) q^{95} +(9.39247 - 2.78952i) q^{96} +(-1.28566 + 1.07880i) q^{97} +(3.36868 + 9.30871i) q^{98} +(-14.8764 - 4.79797i) 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 $

$2$	−1.32113	−	0.504600i	−0.934178	−	0.356806i
$2$	−1.32113	−	0.504600i	−0.934178	−	0.356806i
$3$	0.893683	+	1.48369i	0.515968	+	0.856608i
$3$	0.893683	+	1.48369i	0.515968	+	0.856608i
$4$	1.49076	+	1.33328i	0.745378	+	0.666642i
$5$	3.15348	+	0.556044i	1.41028	+	0.248671i	0.826361	−	0.563141i	$-0.190407\pi$
$5$	3.15348	+	0.556044i	1.41028	+	0.248671i	0.583920	+	0.811811i	$0.301518\pi$
$6$	−0.431999	−	2.41109i	−0.176363	−	0.984325i
$7$	1.10140	−	2.40560i	0.416292	−	0.909231i
$7$	1.10140	−	2.40560i	0.416292	−	0.909231i
$8$	−1.29670	−	2.51367i	−0.458454	−	0.888718i
$9$	−1.40266	+	2.65189i	−0.467554	+	0.883964i
$10$	−3.88557	−	2.32585i	−1.22873	−	0.735500i
$11$	0.904764	+	5.13117i	0.272797	+	1.54711i	0.745875	+	0.666086i	$0.232032\pi$
$11$	0.904764	+	5.13117i	0.272797	+	1.54711i	−0.473078	+	0.881021i	$0.656857\pi$
$12$	−0.645914	+	3.40335i	−0.186459	+	0.982463i
$13$	−1.08679	+	6.16349i	−0.301421	+	1.70945i	0.338467	+	0.940978i	$0.390091\pi$
$13$	−1.08679	+	6.16349i	−0.301421	+	1.70945i	−0.639889	+	0.768467i	$0.721020\pi$
$14$	−2.66896	+	2.62233i	−0.713310	+	0.700848i
$15$	1.99322	+	5.17571i	0.514646	+	1.33636i
$16$	0.444711	+	3.97520i	0.111178	+	0.993801i
$17$	0.814654	−	0.470341i	0.197583	−	0.114074i	−0.397945	−	0.917409i	$-0.630276\pi$
$17$	0.814654	−	0.470341i	0.197583	−	0.114074i	0.595527	+	0.803335i	$0.296943\pi$
$18$	3.19124	−	2.79571i	0.752183	−	0.658954i
$19$	−6.33439	−	3.65716i	−1.45321	−	0.839011i	−0.454547	−	0.890723i	$-0.650199\pi$
$19$	−6.33439	−	3.65716i	−1.45321	−	0.839011i	−0.998662	+	0.0517118i	$0.983532\pi$
$20$	3.95971	+	5.03341i	0.885418	+	1.12551i
$21$	4.55347	−	0.515702i	0.993648	−	0.112535i
$22$	1.39388	−	7.23548i	0.297177	−	1.54261i
$23$	−1.97765	−	1.65944i	−0.412368	−	0.346018i	0.412883	−	0.910784i	$-0.364522\pi$
$23$	−1.97765	−	1.65944i	−0.412368	−	0.346018i	−0.825251	+	0.564766i	$0.808966\pi$
$24$	2.57067	−	4.17033i	0.524735	−	0.851266i
$25$	4.93681	+	1.79685i	0.987361	+	0.359370i
$26$	4.54589	−	7.59437i	0.891522	−	1.48938i
$27$	−5.18812	+	0.288837i	−0.998454	+	0.0555867i
$28$	4.84927	−	2.11768i	0.916426	−	0.400204i
$29$	8.24184	−	1.45326i	1.53047	−	0.269863i	0.655933	−	0.754819i	$-0.272275\pi$
$29$	8.24184	−	1.45326i	1.53047	−	0.269863i	0.874539	+	0.484956i	$0.161164\pi$
$30$	−0.0216266	−	7.84356i	−0.00394846	−	1.43203i
$31$	0.993208	+	0.175129i	0.178385	+	0.0314541i	0.262127	−	0.965033i	$-0.415576\pi$
$31$	0.993208	+	0.175129i	0.178385	+	0.0314541i	−0.0837419	+	0.996487i	$0.526687\pi$
$32$	1.41837	−	5.47615i	0.250735	−	0.968056i
$33$	−6.80449	+	5.92803i	−1.18451	+	1.03194i
$34$	−1.31360	+	0.210305i	−0.225280	+	0.0360671i
$35$	4.81088	−	6.97359i	0.813187	−	1.17875i
$36$	−5.62675	+	2.08318i	−0.937792	+	0.347197i
$37$	−2.56387			−0.421497			−0.210749	−	0.977540i	$-0.567590\pi$
$37$	−2.56387			−0.421497			−0.210749	+	0.977540i	$0.567590\pi$
$38$	6.52314	+	8.02792i	1.05819	+	1.30230i
$39$	−10.1159	+	3.89575i	−1.61985	+	0.623819i
$40$	−2.69142	−	8.64785i	−0.425551	−	1.36735i
$41$	5.45806	+	0.962404i	0.852406	+	0.150302i	0.582747	−	0.812654i	$-0.301978\pi$
$41$	5.45806	+	0.962404i	0.852406	+	0.150302i	0.269659	+	0.962956i	$0.413089\pi$
$42$	−6.27593	−	1.61637i	−0.968398	−	0.249412i
$43$	−3.63752	−	4.33503i	−0.554717	−	0.661086i	0.413703	−	0.910412i	$-0.364235\pi$
$43$	−3.63752	−	4.33503i	−0.554717	−	0.661086i	−0.968420	+	0.249326i	$0.919791\pi$
$44$	−5.49252	+	8.85564i	−0.828029	+	1.33504i
$45$	−5.89784	+	7.58276i	−0.879198	+	1.13037i
$46$	1.77537	+	3.19026i	0.261764	+	0.470378i
$47$	0.501039	+	2.84153i	0.0730841	+	0.414480i	0.999297	+	0.0374805i	$0.0119332\pi$
$47$	0.501039	+	2.84153i	0.0730841	+	0.414480i	−0.926213	+	0.377000i	$0.876956\pi$
$48$	−5.50053	+	4.21238i	−0.793933	+	0.608005i
$49$	−4.57382	−	5.29908i	−0.653402	−	0.757011i
$50$	−5.61546	−	4.86498i	−0.794146	−	0.688013i
$51$	1.42588	+	0.788358i	0.199663	+	0.110392i
$52$	−9.83782	+	7.73927i	−1.36426	+	1.07324i
$53$	−0.206079	−	0.118980i	−0.0283072	−	0.0163432i	0.485780	−	0.874081i	$-0.338536\pi$
$53$	−0.206079	−	0.118980i	−0.0283072	−	0.0163432i	−0.514087	+	0.857738i	$0.671869\pi$
$54$	6.99991	+	2.23634i	0.952568	+	0.304327i
$55$			16.6842i			2.24969i
$56$	−7.47509	+	0.350780i	−0.998901	+	0.0468749i
$57$	−0.234846	−	12.6666i	−0.0311061	−	1.67773i
$58$	−11.6218	−	2.23890i	−1.52602	−	0.293982i
$59$	11.9175	−	4.33762i	1.55153	−	0.564710i	0.582752	−	0.812650i	$-0.301976\pi$
$59$	11.9175	−	4.33762i	1.55153	−	0.564710i	0.968775	+	0.247941i	$0.0797538\pi$
$60$	−3.92929	+	10.3733i	−0.507269	+	1.33918i
$61$	−0.930103	−	5.27488i	−0.119087	−	0.675379i	−0.984645	−	0.174569i	$-0.944147\pi$
$61$	−0.930103	−	5.27488i	−0.119087	−	0.675379i	0.865557	−	0.500810i	$-0.166964\pi$
$62$	−1.22378	−	0.732541i	−0.155421	−	0.0930328i
$63$	4.83449	+	6.29505i	0.609089	+	0.793102i
$64$	−4.63711	+	6.51899i	−0.579639	+	0.814873i
$65$	−6.85435	+	18.8322i	−0.850177	+	2.33584i
$66$	11.9809	−	4.39813i	1.47475	−	0.541373i
$67$	2.23927	−	2.66866i	0.273570	−	0.326028i	−0.611714	−	0.791079i	$-0.709520\pi$
$67$	2.23927	−	2.66866i	0.273570	−	0.326028i	0.885284	+	0.465051i	$0.153964\pi$
$68$	1.84155	+	0.385001i	0.223321	+	0.0466882i
$69$	0.694708	−	4.41723i	0.0836330	−	0.531772i
$70$	−9.87466	+	6.78543i	−1.18025	+	0.811014i
$71$	−1.77382	+	3.07235i	−0.210514	+	0.364620i	−0.951875	−	0.306485i	$-0.900847\pi$
$71$	−1.77382	+	3.07235i	−0.210514	+	0.364620i	0.741362	+	0.671106i	$0.234180\pi$
$72$	8.48483	+	0.0871146i	0.999947	+	0.0102666i
$73$	7.47691			0.875106			0.437553	−	0.899193i	$-0.355845\pi$
$73$	7.47691			0.875106			0.437553	+	0.899193i	$0.355845\pi$
$74$	3.38720	+	1.29373i	0.393754	+	0.150393i
$75$	1.74597	+	8.93050i	0.201608	+	1.03121i
$76$	−4.56700	−	13.8975i	−0.523871	−	1.59415i
$77$	13.3401	+	3.47500i	1.52024	+	0.396013i
$78$	15.3303	−	0.0422692i	1.73581	−	0.00478605i
$79$	2.97392	+	3.54418i	0.334592	+	0.398751i	0.906940	−	0.421259i	$-0.138412\pi$
$79$	2.97392	+	3.54418i	0.334592	+	0.398751i	−0.572348	+	0.820011i	$0.693967\pi$
$80$	−0.807999	+	12.7830i	−0.0903371	+	1.42918i
$81$	−5.06508	−	7.43942i	−0.562786	−	0.826603i
$82$	−6.72517	−	4.02560i	−0.742671	−	0.444553i
$83$	−1.16631	−	6.61447i	−0.128019	−	0.726032i	−0.979469	−	0.201596i	$-0.935387\pi$
$83$	−1.16631	−	6.61447i	−0.128019	−	0.726032i	0.851450	−	0.524436i	$-0.175724\pi$
$84$	7.47569	+	5.30227i	0.815664	+	0.578526i
$85$	2.83053	−	1.03023i	0.307014	−	0.111744i
$86$	2.61817	+	7.56262i	0.282325	+	0.815498i
$87$	9.52178	+	10.9296i	1.02084	+	1.17177i
$88$	11.7249	−	8.92790i	1.24988	−	0.951717i
$89$	1.04925	+	0.605782i	0.111220	+	0.0642128i	0.554578	−	0.832132i	$-0.312880\pi$
$89$	1.04925	+	0.605782i	0.111220	+	0.0642128i	−0.443358	+	0.896345i	$0.646213\pi$
$90$	11.6181	−	7.04174i	1.22465	−	0.742264i
$91$	13.6299	+	9.40288i	1.42880	+	0.985690i
$92$	−0.735684	−	5.11059i	−0.0767003	−	0.532816i
$93$	0.627775	+	1.63012i	0.0650972	+	0.169036i
$94$	0.771903	−	4.00685i	0.0796157	−	0.413276i
$95$	−17.9419	−	15.0550i	−1.84080	−	1.54461i
$96$	9.39247	−	2.78952i	0.958615	−	0.284705i
$97$	−1.28566	+	1.07880i	−0.130539	+	0.109535i	−0.705720	−	0.708491i	$-0.749376\pi$
$97$	−1.28566	+	1.07880i	−0.130539	+	0.109535i	0.575181	+	0.818026i	$0.304932\pi$
$98$	3.36868	+	9.30871i	0.340288	+	0.940321i
$99$	−14.8764	−	4.79797i	−1.49513	−	0.482214i
$100$	4.96387	+	9.26083i	0.496387	+	0.926083i
$101$	7.54936	+	8.99698i	0.751190	+	0.895233i	0.997257	−	0.0740199i	$-0.0235828\pi$
$101$	7.54936	+	8.99698i	0.751190	+	0.895233i	−0.246067	+	0.969253i	$0.579138\pi$
$102$	−1.48597	−	1.76102i	−0.147133	−	0.174367i
$103$	−13.3667	−	2.35691i	−1.31706	−	0.232234i	−0.529417	−	0.848362i	$-0.677589\pi$
$103$	−13.3667	−	2.35691i	−1.31706	−	0.232234i	−0.787646	+	0.616128i	$0.788700\pi$
$104$	16.9023	−	5.26039i	1.65740	−	0.515824i
$105$	14.6460	+	0.905672i	1.42931	+	0.0883845i
$106$	0.212220	+	0.261176i	0.0206126	+	0.0253676i
$107$	−3.17010	−	5.49078i	−0.306465	−	0.530813i	0.671121	−	0.741348i	$-0.265813\pi$
$107$	−3.17010	−	5.49078i	−0.306465	−	0.530813i	−0.977586	+	0.210534i	$0.932480\pi$
$108$	−8.11932	−	6.48665i	−0.781282	−	0.624178i
$109$	2.30805	−	3.99767i	0.221072	−	0.382907i	−0.734062	−	0.679082i	$-0.762378\pi$
$109$	2.30805	−	3.99767i	0.221072	−	0.382907i	0.955134	+	0.296175i	$0.0957112\pi$
$110$	8.41883	−	22.0419i	0.802704	−	2.10161i
$111$	−2.29128	−	3.80398i	−0.217479	−	0.361058i
$112$	10.0526	+	3.30851i	0.949877	+	0.312625i
$113$	−0.844020	+	1.00586i	−0.0793987	+	0.0946237i	−0.804281	−	0.594249i	$-0.797450\pi$
$113$	−0.844020	+	1.00586i	−0.0793987	+	0.0946237i	0.724883	+	0.688872i	$0.241894\pi$
$114$	−6.08132	+	16.8527i	−0.569567	+	1.57840i
$115$	−5.31376	−	6.33269i	−0.495510	−	0.590526i
$116$	14.2242	+	8.82225i	1.32068	+	0.819126i
$117$	−14.8205	−	11.5274i	−1.37016	−	1.06570i
$118$	−17.9333	−	0.283033i	−1.65089	−	0.0260553i
$119$	−0.234188	−	2.47777i	−0.0214680	−	0.227137i
$120$	10.4254	−	11.7217i	0.951708	−	1.07004i
$121$	−15.1737	+	5.52278i	−1.37943	+	0.502071i
$122$	−1.43292	+	7.43812i	−0.129731	+	0.673415i
$123$	3.44987	+	8.95815i	0.311064	+	0.807729i
$124$	1.24713	+	1.58530i	0.111996	+	0.142364i
$125$	0.703378	+	0.406095i	0.0629120	+	0.0363223i
$126$	−3.21050	−	10.7561i	−0.286014	−	0.958225i
$127$	1.44010	−	0.831444i	0.127788	−	0.0737787i	−0.434743	−	0.900555i	$-0.643161\pi$
$127$	1.44010	−	0.831444i	0.127788	−	0.0737787i	0.562532	+	0.826776i	$0.309827\pi$
$128$	9.41570	−	6.27252i	0.832239	−	0.554418i
$129$	3.18104	−	9.27109i	0.280075	−	0.816274i
$130$	18.5582	−	21.4210i	1.62766	−	1.87875i
$131$	7.08106	+	5.94172i	0.618675	+	0.519130i	0.897387	−	0.441245i	$-0.145463\pi$
$131$	7.08106	+	5.94172i	0.618675	+	0.519130i	−0.278712	+	0.960375i	$0.589907\pi$
$132$	−18.0476	−	0.235065i	−1.57084	−	0.0204597i
$133$	−15.7744	+	11.2100i	−1.36781	+	0.972030i
$134$	−4.30497	+	2.39570i	−0.371892	+	0.206957i
$135$	−16.5212	−	1.97398i	−1.42192	−	0.169893i
$136$	−2.23865	−	1.43788i	−0.191963	−	0.123297i
$137$	−4.52497	+	12.4323i	−0.386594	+	1.06216i	0.581930	+	0.813239i	$0.302298\pi$
$137$	−4.52497	+	12.4323i	−0.386594	+	1.06216i	−0.968524	+	0.248920i	$0.919924\pi$
$138$	−3.14673	+	5.48518i	−0.267868	+	0.466929i
$139$	−1.01099	−	2.77767i	−0.0857510	−	0.235599i	0.889404	−	0.457122i	$-0.151120\pi$
$139$	−1.01099	−	2.77767i	−0.0857510	−	0.235599i	−0.975155	+	0.221523i	$0.928897\pi$
$140$	16.4696	−	3.98166i	1.39194	−	0.336511i
$141$	−3.76818	+	3.28282i	−0.317338	+	0.276463i
$142$	3.89375	−	3.16389i	0.326756	−	0.265508i
$143$	−32.6092			−2.72692
$144$	−11.1656	−	4.39654i	−0.930466	−	0.366378i
$145$	26.7986			2.22550
$146$	−9.87795	−	3.77285i	−0.817505	−	0.312244i
$147$	3.77464	−	11.5218i	0.311327	−	0.950303i
$148$	−3.82210	−	3.41836i	−0.314175	−	0.280988i
$149$	−0.417063	−	1.14587i	−0.0341671	−	0.0938733i	0.921436	−	0.388530i	$-0.127017\pi$
$149$	−0.417063	−	1.14587i	−0.0341671	−	0.0938733i	−0.955603	+	0.294657i	$0.904795\pi$
$150$	2.19968	−	12.6793i	0.179603	−	1.03526i
$151$	15.6907	−	2.76669i	1.27689	−	0.225150i	0.506231	−	0.862398i	$-0.331038\pi$
$151$	15.6907	−	2.76669i	1.27689	−	0.225150i	0.770659	+	0.637248i	$0.219927\pi$
$152$	−0.979081	+	20.6649i	−0.0794140	+	1.67614i
$153$	0.104609	+	2.82011i	0.00845711	+	0.227992i
$154$	−15.8704	−	11.3223i	−1.27888	−	0.912378i
$155$	3.03468	+	1.10453i	0.243752	+	0.0887183i
$156$	−20.2746	−	7.67981i	−1.62326	−	0.614877i
$157$	22.4854	−	8.18402i	1.79453	−	0.653156i	0.795655	−	0.605750i	$-0.207127\pi$
$157$	22.4854	−	8.18402i	1.79453	−	0.653156i	0.998876	−	0.0474059i	$-0.0150954\pi$
$158$	−2.14053	−	6.18296i	−0.170292	−	0.491890i
$159$	−0.00764035	−	0.412088i	−0.000605919	−	0.0326807i
$160$	7.51778	−	16.4803i	0.594333	−	1.30288i
$161$	−6.17015	+	2.92971i	−0.486276	+	0.230894i
$162$	2.93768	+	12.3843i	0.230806	+	0.973000i
$163$	3.71184	−	2.14303i	0.290734	−	0.167855i	−0.347539	−	0.937666i	$-0.612983\pi$
$163$	3.71184	−	2.14303i	0.290734	−	0.167855i	0.638273	+	0.769810i	$0.279649\pi$
$164$	6.85349	+	8.71185i	0.535167	+	0.680281i
$165$	−24.7541	+	14.9103i	−1.92710	+	1.16077i
$166$	−1.79682	+	9.32708i	−0.139460	+	0.723922i
$167$	2.39302	+	2.00799i	0.185178	+	0.155383i	0.730664	−	0.682737i	$-0.239211\pi$
$167$	2.39302	+	2.00799i	0.185178	+	0.155383i	−0.545486	+	0.838120i	$0.683655\pi$
$168$	−7.20081	−	10.7772i	−0.555554	−	0.831480i
$169$	−24.5915	−	8.95059i	−1.89166	−	0.688507i
$170$	−4.25934	−	0.0672232i	−0.326677	−	0.00515578i
$171$	18.5834	−	11.6684i	1.42111	−	0.892302i
$172$	0.357163	−	11.3123i	0.0272334	−	0.862556i
$173$	7.43620	−	20.4308i	0.565363	−	1.55332i	−0.246297	−	0.969194i	$-0.579214\pi$
$173$	7.43620	−	20.4308i	0.565363	−	1.55332i	0.811661	−	0.584129i	$-0.198564\pi$
$174$	−7.06441	−	19.2441i	−0.535552	−	1.45889i
$175$	9.75992	−	9.89692i	0.737781	−	0.748137i
$176$	−19.9951	+	5.87851i	−1.50719	+	0.443109i
$177$	17.0861	+	13.8054i	1.28427	+	1.03768i
$178$	−1.08051	−	1.32977i	−0.0809876	−	0.0996702i
$179$	2.47824	+	4.29244i	0.185232	+	0.320832i	0.943655	−	0.330931i	$-0.107363\pi$
$179$	2.47824	+	4.29244i	0.185232	+	0.320832i	−0.758422	+	0.651763i	$0.774030\pi$
$180$	−18.9022	+	3.44055i	−1.40889	+	0.256444i
$181$	2.18921	+	3.79182i	0.162723	+	0.281844i	0.935844	−	0.352414i	$-0.114639\pi$
$181$	2.18921	+	3.79182i	0.162723	+	0.281844i	−0.773122	+	0.634258i	$0.781306\pi$
$182$	−13.2621	−	19.3001i	−0.983055	−	1.43062i
$183$	6.99506	−	6.09405i	0.517089	−	0.450485i
$184$	−1.60688	+	7.12297i	−0.118460	+	0.525113i
$185$	−8.08512	−	1.42562i	−0.594430	−	0.104814i
$186$	−0.00681142	−	2.47037i	−0.000499437	−	0.181137i
$187$	3.15047	+	3.75458i	0.230385	+	0.274562i
$188$	−3.04164	+	4.90406i	−0.221835	+	0.357666i
$189$	−5.01939	+	12.7987i	−0.365107	+	0.930966i
$190$	16.1067	+	28.9431i	1.16850	+	2.09975i
$191$	−5.35326	+	4.49192i	−0.387348	+	0.325024i	−0.815579	−	0.578646i	$-0.803581\pi$
$191$	−5.35326	+	4.49192i	−0.387348	+	0.325024i	0.428231	+	0.903669i	$0.359137\pi$
$192$	−13.8163	−	1.05413i	−0.997102	−	0.0760752i
$193$	−0.517483	+	2.93479i	−0.0372493	+	0.211251i	−0.997752	−	0.0670210i	$-0.978651\pi$
$193$	−0.517483	+	2.93479i	−0.0372493	+	0.211251i	0.960502	+	0.278272i	$0.0897617\pi$
$194$	2.24288	−	0.776484i	0.161030	−	0.0557483i
$195$	−34.0667	+	6.66027i	−2.43957	+	0.476951i
$196$	0.246721	−	13.9978i	0.0176229	−	0.999845i
$197$	−1.75643	+	1.01407i	−0.125140	+	0.0722497i	−0.561263	−	0.827637i	$-0.689685\pi$
$197$	−1.75643	+	1.01407i	−0.125140	+	0.0722497i	0.436123	+	0.899887i	$0.356351\pi$
$198$	17.2326	+	13.8454i	1.22467	+	0.983947i
$199$	−14.1934	+	8.19456i	−1.00614	+	0.580897i	−0.910060	−	0.414476i	$-0.863965\pi$
$199$	−14.1934	+	8.19456i	−1.00614	+	0.580897i	−0.0960831	+	0.995373i	$0.530631\pi$
$200$	−1.88488	−	14.7395i	−0.133281	−	1.04224i
$201$	5.96065	+	0.937445i	0.420432	+	0.0661223i
$202$	−5.43379	−	15.6956i	−0.382320	−	1.10434i
$203$	5.58164	−	21.4272i	0.391754	−	1.50389i
$204$	1.07454	+	3.07635i	0.0752327	+	0.215388i
$205$	16.6768	+	6.06985i	1.16476	+	0.423937i
$206$	16.4698	+	9.85864i	1.14751	+	0.686884i
$207$	7.17464	−	2.91687i	0.498672	−	0.202737i
$208$	−24.9844	−	1.57924i	−1.73236	−	0.109500i
$209$	13.0344	−	35.8117i	0.901609	−	2.47715i
$210$	−18.8923	−	8.58690i	−1.30369	−	0.592553i
$211$	13.8800	−	16.5416i	0.955539	−	1.13877i	−0.0347011	−	0.999398i	$-0.511048\pi$
$211$	13.8800	−	16.5416i	0.955539	−	1.13877i	0.990240	−	0.139370i	$-0.0445076\pi$
$212$	−0.148580	−	0.452132i	−0.0102045	−	0.0310526i
$213$	−6.14363	+	0.113906i	−0.420955	+	0.00780474i
$214$	1.41746	+	8.85365i	0.0968956	+	0.605223i
$215$	−9.06039	−	15.6931i	−0.617914	−	1.07026i
$216$	7.45350	+	12.6667i	0.507146	+	0.861860i
$217$	1.51521	−	2.19637i	0.102859	−	0.149099i
$218$	−5.06646	+	4.11678i	−0.343144	+	0.278824i
$219$	6.68199	+	11.0934i	0.451527	+	0.749623i
$220$	−22.2447	+	24.8720i	−1.49974	+	1.67687i
$221$	2.01358	+	5.53228i	0.135448	+	0.372141i
$222$	1.10759	+	6.18173i	0.0743365	+	0.414891i
$223$	−1.83167	+	5.03247i	−0.122658	+	0.336999i	−0.985791	−	0.167977i	$-0.946277\pi$
$223$	−1.83167	+	5.03247i	−0.122658	+	0.336999i	0.863133	+	0.504976i	$0.168499\pi$
$224$	−11.6112	−	9.44348i	−0.775808	−	0.630969i
$225$	−11.6897	+	10.5715i	−0.779315	+	0.704767i
$226$	1.62262	−	0.902981i	0.107935	−	0.0600654i
$227$	−3.49113	−	19.7992i	−0.231714	−	1.31412i	−0.849424	−	0.527711i	$-0.823051\pi$
$227$	−3.49113	−	19.7992i	−0.231714	−	1.31412i	0.617710	−	0.786406i	$-0.288061\pi$
$228$	16.5381	−	19.1959i	1.09526	−	1.27128i
$229$	−14.2686	+	5.19333i	−0.942893	+	0.343185i	−0.767308	−	0.641279i	$-0.778404\pi$
$229$	−14.2686	+	5.19333i	−0.942893	+	0.343185i	−0.175585	+	0.984464i	$0.556182\pi$
$230$	3.82467	+	11.0476i	0.252192	+	0.728458i
$231$	6.76597	+	22.8980i	0.445168	+	1.50658i
$232$	−14.3403	−	18.8329i	−0.941484	−	1.23644i
$233$		−	25.9256i		−	1.69844i	−0.528039	−	0.849220i	$-0.677073\pi$
$233$		−	25.9256i		−	1.69844i	0.528039	−	0.849220i	$-0.322927\pi$
$234$	13.7631	+	22.7076i	0.899722	+	1.48444i
$235$			9.23933i			0.602708i
$236$	23.5494	+	9.42308i	1.53293	+	0.613390i
$237$	−2.60072	+	7.57974i	−0.168935	+	0.492357i
$238$	−0.940890	+	3.39162i	−0.0609889	+	0.219846i
$239$	−13.4498	+	4.89532i	−0.869994	+	0.316652i	−0.738165	−	0.674621i	$-0.764307\pi$
$239$	−13.4498	+	4.89532i	−0.869994	+	0.316652i	−0.131829	+	0.991272i	$0.542085\pi$
$240$	−19.6881	+	10.2251i	−1.27086	+	0.660030i
$241$	−6.85618	−	2.49545i	−0.441646	−	0.160746i	0.111620	−	0.993751i	$-0.464396\pi$
$241$	−6.85618	−	2.49545i	−0.441646	−	0.160746i	−0.553265	+	0.833005i	$0.686618\pi$
$242$	22.8332	+	0.360366i	1.46778	+	0.0231652i
$243$	6.51122	−	14.1635i	0.417695	−	0.908587i
$244$	5.64635	−	9.10365i	0.361470	−	0.582801i
$245$	−11.4769	−	19.2538i	−0.733234	−	1.23008i
$246$	−0.0374314	−	13.5757i	−0.00238654	−	0.865553i
$247$	29.4251	−	35.0674i	1.87227	−	2.23129i
$248$	−0.847679	−	2.72369i	−0.0538277	−	0.172955i
$249$	8.77150	−	7.64168i	0.555871	−	0.484272i
$250$	−0.724336	−	0.891429i	−0.0458110	−	0.0563789i
$251$	6.01180	+	10.4127i	0.379461	+	0.657246i	0.990984	−	0.133981i	$-0.0427760\pi$
$251$	6.01180	+	10.4127i	0.379461	+	0.657246i	−0.611523	+	0.791227i	$0.709443\pi$
$252$	−1.18603	+	15.8301i	−0.0747130	+	0.997205i
$253$	6.72559	−	11.6491i	0.422834	−	0.732370i
$254$	−2.32211	+	0.371767i	−0.145702	+	0.0233267i
$255$	4.05813	+	3.27893i	0.254130	+	0.205334i
$256$	−15.6045	+	3.53563i	−0.975279	+	0.220977i
$257$	−5.31621	−	14.6062i	−0.331616	−	0.911108i	−0.987692	−	0.156413i	$-0.950007\pi$
$257$	−5.31621	−	14.6062i	−0.331616	−	0.911108i	0.656076	−	0.754695i	$-0.272215\pi$
$258$	−8.88076	+	10.6431i	−0.552892	+	0.662613i
$259$	−2.82386	+	6.16764i	−0.175466	+	0.383239i
$260$	−35.3268	+	18.9354i	−2.19087	+	1.17432i
$261$	−7.70664	+	23.8949i	−0.477029	+	1.47906i
$262$	−6.35679	−	11.4229i	−0.392724	−	0.705707i
$263$	11.7752	−	9.88053i	0.726088	−	0.609260i	−0.202974	−	0.979184i	$-0.565061\pi$
$263$	11.7752	−	9.88053i	0.726088	−	0.609260i	0.929062	+	0.369924i	$0.120616\pi$
$264$	23.7245	+	9.41737i	1.46014	+	0.579599i
$265$	−0.583710	−	0.489791i	−0.0358570	−	0.0300876i
$266$	26.4966	−	6.85007i	1.62461	−	0.420005i
$267$	0.0389006	+	2.09813i	0.00238068	+	0.128404i
$268$	6.89628	−	0.992738i	0.421257	−	0.0606411i
$269$	−11.2207	−	6.47825i	−0.684135	−	0.394986i	0.117276	−	0.993099i	$-0.462584\pi$
$269$	−11.2207	−	6.47825i	−0.684135	−	0.394986i	−0.801411	+	0.598114i	$0.795917\pi$
$270$	20.8306	+	10.9445i	1.26771	+	0.666062i
$271$	−3.09030	+	1.78419i	−0.187723	+	0.108382i	−0.590916	−	0.806733i	$-0.701234\pi$
$271$	−3.09030	+	1.78419i	−0.187723	+	0.108382i	0.403193	+	0.915115i	$0.367900\pi$
$272$	2.23199	+	3.02925i	0.135334	+	0.183675i
$273$	−1.77014	+	28.6257i	−0.107134	+	1.73251i
$274$	12.2514	−	14.1413i	0.740133	−	0.854307i
$275$	−4.75331	+	26.9573i	−0.286635	+	1.62559i
$276$	6.92506	−	5.65877i	0.416840	−	0.340618i
$277$	−5.88630	+	4.93919i	−0.353674	+	0.296767i	−0.802263	−	0.596971i	$-0.796371\pi$
$277$	−5.88630	+	4.93919i	−0.353674	+	0.296767i	0.448590	+	0.893738i	$0.351926\pi$
$278$	−0.0659678	+	4.17980i	−0.00395649	+	0.250688i
$279$	−1.85756	+	2.38823i	−0.111209	+	0.142980i
$280$	−23.7676	−	3.05030i	−1.42039	−	0.182290i
$281$	11.4483	+	13.6436i	0.682948	+	0.813906i	0.990484	−	0.137630i	$-0.0439486\pi$
$281$	11.4483	+	13.6436i	0.682948	+	0.813906i	−0.307535	+	0.951537i	$0.599504\pi$
$282$	6.63476	−	2.43559i	0.395094	−	0.145037i
$283$	3.32350	−	3.96080i	0.197562	−	0.235445i	−0.658164	−	0.752875i	$-0.728667\pi$
$283$	3.32350	−	3.96080i	0.197562	−	0.235445i	0.855726	+	0.517430i	$0.173111\pi$
$284$	−6.74064	+	2.21512i	−0.399983	+	0.131443i
$285$	6.30261	−	40.0745i	0.373334	−	2.37381i
$286$	43.0810	+	16.4546i	2.54743	+	0.972983i
$287$	8.32669	−	12.0699i	0.491509	−	0.712465i
$288$	12.5327	+	11.4426i	0.738495	+	0.674259i
$289$	−8.05756	+	13.9561i	−0.473974	+	0.820947i
$290$	−35.4044	−	13.5226i	−2.07902	−	0.794073i
$291$	−2.74957	−	0.943418i	−0.161183	−	0.0553041i
$292$	11.1463	+	9.96884i	0.652285	+	0.583382i
$293$	−8.18169	−	22.4790i	−0.477979	−	1.31324i	−0.911206	−	0.411952i	$-0.864847\pi$
$293$	−8.18169	−	22.4790i	−0.477979	−	1.31324i	0.433226	−	0.901285i	$-0.357375\pi$
$294$	−10.8007	+	13.3171i	−0.629909	+	0.776669i
$295$	39.9936	−	7.05194i	2.32851	−	0.410580i
$296$	3.32458	+	6.44473i	0.193237	+	0.374592i
$297$	−6.17610	−	26.3598i	−0.358373	−	1.52955i
$298$	−0.0272137	+	1.72429i	−0.00157644	+	0.0998855i
$299$	12.3773	−	10.3858i	0.715796	−	0.600624i
$300$	−9.30406	+	15.6411i	−0.537170	+	0.903038i
$301$	−14.4347	+	3.97580i	−0.832004	+	0.229161i
$302$	−22.1255	−	4.26237i	−1.27318	−	0.245272i
$303$	−6.60198	+	19.2413i	−0.379274	+	1.10539i
$304$	11.7210	−	26.8069i	0.672245	−	1.53748i
$305$		−	17.1514i		−	0.982087i
$306$	1.28483	−	3.77851i	0.0734486	−	0.216003i
$307$	14.3886	+	8.30729i	0.821203	+	0.474122i	0.850831	−	0.525439i	$-0.176099\pi$
$307$	14.3886	+	8.30729i	0.821203	+	0.474122i	−0.0296280	+	0.999561i	$0.509432\pi$
$308$	15.2536	+	22.9665i	0.869156	+	1.30864i
$309$	−8.44868	−	21.9384i	−0.480629	−	1.24803i
$310$	−3.45186	−	2.99053i	−0.196052	−	0.169851i
$311$	0.419559	+	0.352052i	0.0237910	+	0.0199630i	0.654606	−	0.755971i	$-0.272835\pi$
$311$	0.419559	+	0.352052i	0.0237910	+	0.0199630i	−0.630815	+	0.775934i	$0.717279\pi$
$312$	22.9100	+	20.3766i	1.29703	+	1.15360i
$313$	10.4235	+	3.79384i	0.589171	+	0.214441i	0.619365	−	0.785103i	$-0.287390\pi$
$313$	10.4235	+	3.79384i	0.589171	+	0.214441i	−0.0301939	+	0.999544i	$0.509612\pi$
$314$	−33.8358	−	0.534014i	−1.90946	−	0.0301361i
$315$	11.7452	+	22.5395i	0.661765	+	1.26996i
$316$	−0.292005	+	9.24859i	−0.0164266	+	0.520274i
$317$	−18.6294	+	3.28487i	−1.04633	+	0.184496i	−0.670285	−	0.742104i	$-0.733828\pi$
$317$	−18.6294	+	3.28487i	−1.04633	+	0.184496i	−0.376047	+	0.926601i	$0.622717\pi$
$318$	−0.197846	+	0.548276i	−0.0110946	+	0.0307458i
$319$	14.9138	+	40.9755i	0.835015	+	2.29419i
$320$	−18.2479	+	17.9791i	−1.02009	+	1.00506i
$321$	5.31354	−	9.61045i	0.296573	−	0.536403i
$322$	9.62989	−	0.757063i	0.536653	−	0.0421894i
$323$	−6.88045			−0.382839
$324$	2.36806	−	17.8435i	0.131559	−	0.991308i
$325$	−16.4402	+	28.4752i	−0.911936	+	1.57952i
$326$	−5.98519	+	0.958223i	−0.331489	+	0.0530710i
$327$	7.99396	−	0.148213i	0.442067	−	0.00819618i
$328$	−4.65832	−	14.9677i	−0.257213	−	0.826455i
$329$	7.38744	+	1.92438i	0.407283	+	0.106094i
$330$	40.2271	−	7.20754i	2.21443	−	0.396762i
$331$	−21.2402	+	3.74523i	−1.16747	+	0.205856i	−0.723590	−	0.690230i	$-0.757509\pi$
$331$	−21.2402	+	3.74523i	−1.16747	+	0.205856i	−0.443879	+	0.896087i	$0.646398\pi$
$332$	7.08028	−	11.4156i	0.388581	−	0.626512i
$333$	3.59624	−	6.79911i	0.197073	−	0.372589i
$334$	−2.14826	−	3.86033i	−0.117548	−	0.211228i
$335$	8.54539	−	7.17043i	0.466884	−	0.391763i
$336$	4.07499	+	17.8716i	0.222309	+	0.974976i
$337$	0.302888	−	1.71776i	0.0164994	−	0.0935725i	−0.975446	−	0.220238i	$-0.929316\pi$
$337$	0.302888	−	1.71776i	0.0164994	−	0.0935725i	0.991945	+	0.126666i	$0.0404276\pi$
$338$	27.9721	+	24.2338i	1.52148	+	1.31814i
$339$	−2.24667	−	0.353339i	−0.122023	−	0.0191908i
$340$	5.59322	+	2.23808i	0.303335	+	0.121377i
$341$			5.25477i			0.284562i
$342$	−30.4389	+	6.03820i	−1.64595	+	0.326508i
$343$	−17.7851	+	5.16635i	−0.960304	+	0.278956i
$344$	−6.18006	+	14.7648i	−0.333206	+	0.796064i
$345$	4.64693	−	13.5434i	0.250182	−	0.729151i
$346$	−20.1335	+	23.2394i	−1.08239	+	1.24936i
$347$	−2.10529	+	11.9397i	−0.113018	+	0.640956i	0.874695	+	0.484675i	$0.161062\pi$
$347$	−2.10529	+	11.9397i	−0.113018	+	0.640956i	−0.987712	+	0.156282i	$0.950049\pi$
$348$	−0.377568	+	28.9886i	−0.0202397	+	1.55395i
$349$	−5.12326	−	29.0555i	−0.274242	−	1.55530i	−0.741360	−	0.671108i	$-0.765819\pi$
$349$	−5.12326	−	29.0555i	−0.274242	−	1.55530i	0.467118	−	0.884195i	$-0.345292\pi$
$350$	−17.8881	+	8.15023i	−0.956159	+	0.435648i
$351$	3.85815	−	32.2908i	0.205933	−	1.72356i
$352$	29.3824	+	2.32327i	1.56609	+	0.123831i
$353$	−9.71205	+	26.6836i	−0.516920	+	1.42023i	0.356976	+	0.934114i	$0.383808\pi$
$353$	−9.71205	+	26.6836i	−0.516920	+	1.42023i	−0.873896	+	0.486113i	$0.838414\pi$
$354$	−15.6068	−	26.8604i	−0.829490	−	1.42761i
$355$	−7.30207	+	8.70227i	−0.387554	+	0.461868i
$356$	0.756491	+	2.30202i	0.0400939	+	0.122007i
$357$	3.46694	−	2.56180i	0.183490	−	0.135585i
$358$	−1.10811	−	6.92138i	−0.0585652	−	0.365806i
$359$	0.988027	−	1.71131i	0.0521461	−	0.0903197i	−0.838774	−	0.544480i	$-0.816727\pi$
$359$	0.988027	−	1.71131i	0.0521461	−	0.0903197i	0.890920	+	0.454160i	$0.150061\pi$
$360$	26.7083	+	4.99266i	1.40765	+	0.263136i
$361$	17.2497	+	29.8773i	0.907878	+	1.57249i
$362$	−0.978871	−	6.11416i	−0.0514483	−	0.321353i
$363$	−21.7546	−	17.5775i	−1.14182	−	0.922577i
$364$	7.78216	+	32.1899i	0.407896	+	1.68721i
$365$	23.5783	+	4.15749i	1.23415	+	0.217613i
$366$	−12.3164	+	4.52131i	−0.643790	+	0.236333i
$367$	12.9255	−	2.27912i	0.674706	−	0.118969i	0.174211	−	0.984708i	$-0.444262\pi$
$367$	12.9255	−	2.27912i	0.674706	−	0.118969i	0.500495	+	0.865739i	$0.333151\pi$
$368$	5.71714	−	8.59953i	0.298027	−	0.448281i
$369$	−10.2080	+	13.1243i	−0.531408	+	0.683222i
$370$	9.96210	+	5.96318i	0.517905	+	0.310011i
$371$	−0.513195	+	0.364699i	−0.0266438	+	0.0189342i
$372$	−1.23755	+	3.26712i	−0.0641641	+	0.169392i
$373$	5.03554	−	28.5580i	0.260730	−	1.47868i	−0.520193	−	0.854049i	$-0.674140\pi$
$373$	5.03554	−	28.5580i	0.260730	−	1.47868i	0.780923	−	0.624627i	$-0.214749\pi$
$374$	−2.26761	−	6.55001i	−0.117255	−	0.338693i
$375$	0.0260776	+	1.40651i	0.00134664	+	0.0726321i
$376$	6.49299	−	4.94408i	0.334851	−	0.254971i
$377$			52.3779i			2.69760i
$378$	13.0895	−	14.3759i	0.673250	−	0.739415i
$379$		−	2.93846i		−	0.150938i	−0.997148	−	0.0754692i	$-0.975955\pi$
$379$		−	2.93846i		−	0.150938i	0.997148	−	0.0754692i	$-0.0240455\pi$
$380$	−6.67435	−	46.3649i	−0.342387	−	2.37847i
$381$	2.52060	+	1.39362i	0.129134	+	0.0713972i
$382$	9.33897	−	3.23314i	0.477823	−	0.165422i
$383$	−0.120444	+	0.683074i	−0.00615442	+	0.0349034i	−0.987730	−	0.156169i	$-0.950085\pi$
$383$	−0.120444	+	0.683074i	−0.00615442	+	0.0349034i	0.981576	+	0.191073i	$0.0611966\pi$
$384$	17.7211	+	8.36433i	0.904327	+	0.426840i
$385$	40.1354	+	18.3760i	2.04549	+	0.936528i
$386$	2.16456	−	3.61611i	0.110173	−	0.184055i
$387$	16.5982	−	3.56573i	0.843736	−	0.181256i
$388$	−3.35495	−	0.105926i	−0.170322	−	0.00537755i
$389$	−11.0907	+	1.95559i	−0.562321	+	0.0991523i	−0.447581	−	0.894243i	$-0.647714\pi$
$389$	−11.0907	+	1.95559i	−0.562321	+	0.0991523i	−0.114739	+	0.993396i	$0.536603\pi$
$390$	48.3672	+	8.39100i	2.44917	+	0.424895i
$391$	−2.39160	−	0.421704i	−0.120949	−	0.0213265i
$392$	−7.38926	+	18.3684i	−0.373214	+	0.927745i
$393$	−2.48743	+	15.8161i	−0.125474	+	0.797817i
$394$	2.83216	−	0.453426i	0.142682	−	0.0228433i
$395$	7.40749	+	12.8301i	0.372711	+	0.645555i
$396$	−15.7800	−	26.9871i	−0.792977	−	1.35615i
$397$	14.5034	−	25.1206i	0.727904	−	1.26077i	−0.229863	−	0.973223i	$-0.573828\pi$
$397$	14.5034	−	25.1206i	0.727904	−	1.26077i	0.957767	−	0.287544i	$-0.0928388\pi$
$398$	22.8863	−	3.66407i	1.14718	−	0.183663i
$399$	−30.7294	−	13.3861i	−1.53840	−	0.670144i
$400$	−4.94739	+	20.4239i	−0.247370	+	1.02119i
$401$	11.0312	−	13.1465i	0.550872	−	0.656504i	−0.416716	−	0.909037i	$-0.636819\pi$
$401$	11.0312	−	13.1465i	0.550872	−	0.656504i	0.967588	+	0.252533i	$0.0812635\pi$
$402$	−7.40175	−	4.24623i	−0.369166	−	0.211783i
$403$	−2.15882	+	5.93130i	−0.107538	+	0.295459i
$404$	−0.741261	+	23.4777i	−0.0368791	+	1.16806i
$405$	−11.8360	−	26.2765i	−0.588135	−	1.30569i
$406$	−18.1862	+	25.4916i	−0.902568	+	1.26513i
$407$	−2.31970	−	13.1557i	−0.114983	−	0.652102i
$408$	0.132727	−	4.60647i	0.00657096	−	0.228054i
$409$	0.148256	−	0.840800i	0.00733078	−	0.0415749i	−0.980923	−	0.194397i	$-0.937725\pi$
$409$	0.148256	−	0.840800i	0.00733078	−	0.0415749i	0.988254	+	0.152822i	$0.0488361\pi$
$410$	−18.9693	−	16.4341i	−0.936827	−	0.811625i
$411$	−22.4895	+	4.39684i	−1.10932	+	0.216880i
$412$	−16.7841	−	21.3352i	−0.826893	−	1.05111i
$413$	2.69142	−	33.4462i	0.132436	−	1.64578i
$414$	−10.9505	+	0.233233i	−0.538187	+	0.0114628i
$415$		−	21.5071i		−	1.05574i
$416$	32.2108	+	14.6935i	1.57926	+	0.720410i
$417$	3.21769	−	3.98235i	0.157571	−	0.195016i
$418$	−35.2907	+	40.7347i	−1.72613	+	1.99240i
$419$	−1.71092	+	9.70311i	−0.0835839	+	0.474028i	0.914069	+	0.405558i	$0.132923\pi$
$419$	−1.71092	+	9.70311i	−0.0835839	+	0.474028i	−0.997653	+	0.0684699i	$0.978188\pi$
$420$	20.6262	+	20.8774i	1.00645	+	1.01872i
$421$	−16.0830	+	13.4953i	−0.783840	+	0.657719i	−0.944212	−	0.329337i	$-0.893175\pi$
$421$	−16.0830	+	13.4953i	−0.783840	+	0.657719i	0.160373	+	0.987057i	$0.448730\pi$
$422$	−26.6841	+	14.8496i	−1.29896	+	0.722869i
$423$	−8.23824	−	2.65701i	−0.400557	−	0.129188i
$424$	−0.0318528	+	0.672298i	−0.00154691	+	0.0326497i
$425$	4.86692	−	0.858170i	0.236080	−	0.0416274i
$426$	8.17400	+	2.94960i	0.396032	+	0.142908i
$427$	−13.7137	−	3.57232i	−0.663650	−	0.172877i
$428$	2.59491	−	12.4121i	0.125430	−	0.599959i
$429$	−29.1423	−	48.3820i	−1.40700	−	2.33590i
$430$	4.05121	+	25.3044i	0.195367	+	1.22029i
$431$	−3.77042	+	6.53056i	−0.181615	+	0.314566i	−0.942431	−	0.334402i	$-0.891466\pi$
$431$	−3.77042	+	6.53056i	−0.181615	+	0.314566i	0.760816	+	0.648968i	$0.224799\pi$
$432$	−3.45540	−	20.4954i	−0.166248	−	0.986084i
$433$	1.48785			0.0715013			0.0357506	−	0.999361i	$-0.488618\pi$
$433$	1.48785			0.0715013			0.0357506	+	0.999361i	$0.488618\pi$
$434$	−3.11008	+	2.13711i	−0.149289	+	0.102585i
$435$	23.9494	+	39.7608i	1.14829	+	1.90638i
$436$	8.77077	−	2.88226i	0.420044	−	0.138035i
$437$	6.45835	+	17.7442i	0.308945	+	0.848818i
$438$	−3.23002	−	18.0275i	−0.154336	−	0.861389i
$439$	−16.9615	+	2.99077i	−0.809529	+	0.142742i	−0.563068	−	0.826411i	$-0.690379\pi$
$439$	−16.9615	+	2.99077i	−0.809529	+	0.142742i	−0.246461	+	0.969153i	$0.579268\pi$
$440$	41.9385	−	21.6344i	1.99934	−	1.03138i
$441$	20.4681	−	4.69646i	0.974672	−	0.223641i
$442$	0.131388	−	8.32490i	0.00624949	−	0.395975i
$443$	9.91390	+	3.60836i	0.471024	+	0.171439i	0.566616	−	0.823982i	$-0.308252\pi$
$443$	9.91390	+	3.60836i	0.471024	+	0.171439i	−0.0955924	+	0.995421i	$0.530475\pi$
$444$	1.65604	−	8.72574i	0.0785921	−	0.414105i
$445$	2.97194	+	2.49375i	0.140883	+	0.118215i
$446$	4.95926	−	5.72428i	0.234828	−	0.271052i
$447$	1.32739	−	1.64284i	0.0627835	−	0.0777035i
$448$	10.5747	+	18.3351i	0.499609	+	0.866251i
$449$	16.5649	+	9.56377i	0.781748	+	0.451342i	0.837049	−	0.547127i	$-0.184279\pi$
$449$	16.5649	+	9.56377i	0.781748	+	0.451342i	−0.0553016	+	0.998470i	$0.517612\pi$
$450$	20.7780	−	8.06767i	0.979485	−	0.380314i
$451$			28.8770i			1.35977i
$452$	−2.59933	+	0.374180i	−0.122262	+	0.0176000i
$453$	18.1274	+	20.8075i	0.851699	+	0.977623i
$454$	−5.37844	+	27.9188i	−0.252423	+	1.31030i
$455$	37.7532	+	37.2307i	1.76990	+	1.74540i
$456$	−31.5352	+	17.0152i	−1.47677	+	0.796809i
$457$	−22.3959	+	18.7924i	−1.04764	+	0.879071i	−0.992843	−	0.119427i	$-0.961894\pi$
$457$	−22.3959	+	18.7924i	−1.04764	+	0.879071i	−0.0547932	+	0.998498i	$0.517450\pi$
$458$	21.4711	+	0.338869i	1.00328	+	0.0158343i
$459$	−4.09067	+	2.67549i	−0.190936	+	0.124881i
$460$	0.521750	−	16.5252i	0.0243267	−	0.770494i
$461$	−24.1855	+	4.26455i	−1.12643	+	0.198620i	−0.705662	−	0.708549i	$-0.749350\pi$
$461$	−24.1855	+	4.26455i	−1.12643	+	0.198620i	−0.420767	+	0.907169i	$0.638239\pi$
$462$	2.61565	−	33.6653i	0.121691	−	1.56625i
$463$	0.00451388	+	0.0124018i	0.000209778	+	0.000576360i	0.939797	−	0.341732i	$-0.111013\pi$
$463$	0.00451388	+	0.0124018i	0.000209778	+	0.000576360i	−0.939588	+	0.342308i	$0.888791\pi$
$464$	9.44224	+	32.1167i	0.438345	+	1.49098i
$465$	1.07326	+	5.48963i	0.0497712	+	0.254575i
$466$	−13.0820	+	34.2510i	−0.606014	+	1.58665i
$467$	17.0349	−	29.5053i	0.788280	−	1.36534i	−0.138741	−	0.990329i	$-0.544305\pi$
$467$	17.0349	−	29.5053i	0.788280	−	1.36534i	0.927020	−	0.375012i	$-0.122361\pi$
$468$	−6.72457	−	36.9444i	−0.310843	−	1.70776i
$469$	−3.95338	−	8.32605i	−0.182550	−	0.384461i
$470$	4.66217	−	12.2063i	0.215050	−	0.563036i
$471$	32.2374	+	26.0474i	1.48542	+	1.20020i
$472$	−26.3568	−	24.3321i	−1.21317	−	1.11998i
$473$	18.9527	−	22.5869i	0.871445	−	1.03855i
$474$	7.26062	−	8.70148i	0.333491	−	0.399672i
$475$	−24.7003	−	29.4367i	−1.13333	−	1.35065i
$476$	2.95445	−	4.00599i	0.135417	−	0.183614i
$477$	0.604582	−	0.379612i	0.0276819	−	0.0173812i
$478$	20.2391	+	0.319423i	0.925713	+	0.0146101i
$479$	−12.7108	+	10.6657i	−0.580773	+	0.487327i	−0.885201	−	0.465209i	$-0.845979\pi$
$479$	−12.7108	+	10.6657i	−0.580773	+	0.487327i	0.304428	+	0.952535i	$0.401535\pi$
$480$	31.1701	−	3.57409i	1.42271	−	0.163134i
$481$	2.78639	−	15.8024i	0.127048	−	0.720527i
$482$	7.79869	+	6.75644i	0.355221	+	0.307747i
$483$	−9.86093	−	6.53635i	−0.448688	−	0.297414i
$484$	−29.9838	−	11.9977i	−1.36290	−	0.545352i
$485$	−4.65417	+	2.68709i	−0.211335	+	0.122014i
$486$	−15.7490	+	15.4262i	−0.714391	+	0.699747i
$487$	−11.9113	−	6.87702i	−0.539755	−	0.311627i	0.205225	−	0.978715i	$-0.434207\pi$
$487$	−11.9113	−	6.87702i	−0.539755	−	0.311627i	−0.744979	+	0.667087i	$0.767541\pi$
$488$	−12.0533	+	9.17793i	−0.545625	+	0.415465i
$489$	6.49680	+	3.59202i	0.293795	+	0.162437i
$490$	5.44702	+	31.2280i	0.246071	+	1.41074i
$491$	24.0833	+	20.2083i	1.08686	+	0.911988i	0.996473	−	0.0839182i	$-0.0267435\pi$
$491$	24.0833	+	20.2083i	1.08686	+	0.911988i	0.0903923	+	0.995906i	$0.471188\pi$
$492$	−6.80083	+	17.9541i	−0.306605	+	0.809432i
$493$	6.03072	−	5.06038i	0.271610	−	0.227908i
$494$	−56.5693	+	31.4806i	−2.54517	+	1.41638i
$495$	−44.2446	−	23.4022i	−1.98865	−	1.05185i
$496$	−0.254484	+	4.02608i	−0.0114267	+	0.180776i
$497$	5.43714	+	7.65099i	0.243889	+	0.343194i
$498$	−15.4443	+	5.66953i	−0.692074	+	0.254058i
$499$	12.4882	+	34.3109i	0.559047	+	1.53597i	0.821024	+	0.570894i	$0.193403\pi$
$499$	12.4882	+	34.3109i	0.559047	+	1.53597i	−0.261977	+	0.965074i	$0.584375\pi$
$500$	0.507125	+	1.54319i	0.0226793	+	0.0690136i
$501$	−0.840621	+	5.34500i	−0.0375562	+	0.238797i
$502$	−2.68808	−	16.7901i	−0.119975	−	0.749380i
$503$	−21.3042	+	36.8999i	−0.949905	+	1.64528i	−0.204286	+	0.978911i	$0.565487\pi$
$503$	−21.3042	+	36.8999i	−0.949905	+	1.64528i	−0.745619	+	0.666373i	$0.767846\pi$
$504$	9.55480	−	20.3152i	0.425604	−	0.904909i
$505$	18.8041	+	32.5696i	0.836770	+	1.44933i
$506$	−14.7635	+	11.9962i	−0.656317	+	0.533295i
$507$	−8.69715	−	44.4852i	−0.386254	−	1.97566i
$508$	3.25539	+	0.680585i	0.144435	+	0.0301961i
$509$	2.07731	−	2.47564i	0.0920752	−	0.109731i	−0.718040	−	0.696002i	$-0.754960\pi$
$509$	2.07731	−	2.47564i	0.0920752	−	0.109731i	0.810115	+	0.586271i	$0.199405\pi$
$510$	−3.70676	−	6.37961i	−0.164138	−	0.282494i
$511$	8.23510	−	17.9865i	0.364299	−	0.795674i
$512$	22.3996	+	3.20300i	0.989931	+	0.141554i
$513$	33.9199	+	17.1442i	1.49760	+	0.756935i
$514$	−0.346887	+	21.9792i	−0.0153005	+	0.969460i
$515$	−40.8412	−	14.8650i	−1.79968	−	0.655029i
$516$	17.1031	−	9.57971i	0.752924	−	0.421723i
$517$	−14.1271	+	5.14184i	−0.621308	+	0.226138i
$518$	6.84287	−	6.72332i	0.300658	−	0.295406i
$519$	36.9585	−	7.22564i	1.62230	−	0.317170i
$520$	56.2260	−	7.19016i	2.46567	−	0.315309i
$521$		−	40.2178i		−	1.76198i	−0.473139	−	0.880988i	$-0.656879\pi$
$521$		−	40.2178i		−	1.76198i	0.473139	−	0.880988i	$-0.343121\pi$
$522$	22.2388	−	27.6795i	0.973367	−	1.21150i
$523$		−	13.7791i		−	0.602516i	−0.953543	−	0.301258i	$-0.902593\pi$
$523$		−	13.7791i		−	0.602516i	0.953543	−	0.301258i	$-0.0974066\pi$
$524$	2.63415	+	18.2987i	0.115073	+	0.799383i
$525$	23.4062	+	5.63598i	1.02153	+	0.245974i
$526$	−20.5422	+	7.11169i	−0.895683	+	0.310085i
$527$	0.891491	−	0.324476i	0.0388340	−	0.0141344i
$528$	−26.5911	−	24.4130i	−1.15723	−	1.06244i
$529$	−2.83657	−	16.0870i	−0.123329	−	0.699434i
$530$	0.524006	+	0.941616i	0.0227614	+	0.0409012i
$531$	−5.21334	+	37.6882i	−0.226240	+	1.63553i
$532$	−38.4619	−	4.32037i	−1.66753	−	0.187312i
$533$	−11.8635	+	32.5948i	−0.513867	+	1.41184i
$534$	1.00733	−	2.79153i	0.0435912	−	0.120801i
$535$	−6.94375	−	19.0778i	−0.300204	−	0.824805i
$536$	−9.61180	−	2.16833i	−0.415167	−	0.0936577i
$537$	−4.15388	+	7.51301i	−0.179253	+	0.324210i
$538$	11.5550	+	14.2205i	0.498171	+	0.613091i
$539$	23.0522	−	28.2635i	0.992931	−	1.21739i
$540$	−21.9973	−	24.9702i	−0.946613	−	1.07455i
$541$	−9.13016	−	15.8139i	−0.392536	−	0.679893i	0.600247	−	0.799815i	$-0.295069\pi$
$541$	−9.13016	−	15.8139i	−0.392536	−	0.679893i	−0.992783	+	0.119922i	$0.961736\pi$
$542$	4.98299	−	0.797771i	0.214038	−	0.0342672i
$543$	−3.66943	+	6.63679i	−0.157470	+	0.284812i
$544$	−1.42018	−	5.12829i	−0.0608896	−	0.219873i
$545$	9.50129	−	11.3232i	0.406991	−	0.485033i
$546$	16.7831	−	36.9250i	0.718252	−	1.58024i
$547$	−7.50138	+	20.6099i	−0.320736	+	0.881215i	0.669624	+	0.742700i	$0.266455\pi$
$547$	−7.50138	+	20.6099i	−0.320736	+	0.881215i	−0.990360	+	0.138515i	$0.955767\pi$
$548$	−23.3213	+	12.5004i	−0.996239	+	0.533991i
$549$	15.2930	+	4.93234i	0.652691	+	0.210507i
$550$	19.8824	−	33.2156i	0.847789	−	1.41632i
$551$	−57.5219	−	20.9362i	−2.45051	−	0.891914i
$552$	−12.0043	+	3.98157i	−0.510937	+	0.169467i
$553$	11.8014	−	3.25049i	0.501845	−	0.138225i
$554$	10.2689	−	3.55507i	0.436283	−	0.151041i
$555$	−5.11035	−	13.2698i	−0.216922	−	0.563274i
$556$	2.19628	−	5.48877i	0.0931431	−	0.232775i
$557$	−34.7992	+	20.0913i	−1.47449	+	0.851298i	−0.999587	−	0.0287403i	$-0.990850\pi$
$557$	−34.7992	+	20.0913i	−1.47449	+	0.851298i	−0.474904	+	0.880038i	$0.657517\pi$
$558$	3.65918	−	2.21784i	0.154905	−	0.0938885i
$559$	30.6721	−	17.7086i	1.29729	−	0.748993i
$560$	29.8609	+	16.0230i	1.26185	+	0.677095i
$561$	−2.75511	+	8.02972i	−0.116321	+	0.339015i
$562$	−8.24012	−	23.8017i	−0.347589	−	1.00401i
$563$	−2.75919	+	15.6481i	−0.116286	+	0.659490i	0.869820	+	0.493370i	$0.164235\pi$
$563$	−2.75919	+	15.6481i	−0.116286	+	0.659490i	−0.986106	+	0.166120i	$0.946876\pi$
$564$	−9.99437	−	0.130174i	−0.420839	−	0.00548130i
$565$	−3.22091	+	2.70266i	−0.135505	+	0.113702i
$566$	−6.38939	+	3.55568i	−0.268566	+	0.149456i
$567$	−23.4750	+	3.99073i	−0.985856	+	0.167595i
$568$	10.0230	+	0.474880i	0.420555	+	0.0199255i
$569$	11.0646	+	13.1863i	0.463851	+	0.552797i	0.946368	−	0.323090i	$-0.104722\pi$
$569$	11.0646	+	13.1863i	0.463851	+	0.552797i	−0.482517	+	0.875887i	$0.660277\pi$
$570$	−28.5482	+	49.7633i	−1.19575	+	2.08435i
$571$	5.84776	+	1.03112i	0.244721	+	0.0431509i	0.294663	−	0.955601i	$-0.404793\pi$
$571$	5.84776	+	1.03112i	0.244721	+	0.0431509i	−0.0499421	+	0.998752i	$0.515904\pi$
$572$	−48.6124	−	43.4774i	−2.03259	−	1.81788i
$573$	−11.4487	−	3.92822i	−0.478277	−	0.164104i
$574$	−17.0911	+	11.7442i	−0.713369	+	0.490195i
$575$	−6.78150	−	11.7459i	−0.282808	−	0.489838i
$576$	−10.7833	−	21.4411i	−0.449306	−	0.893378i
$577$	−10.1488	−	17.5782i	−0.422500	−	0.731792i	0.573683	−	0.819077i	$-0.305514\pi$
$577$	−10.1488	−	17.5782i	−0.422500	−	0.731792i	−0.996183	+	0.0872853i	$0.972181\pi$
$578$	17.6873	−	14.3719i	0.735696	−	0.597794i
$579$	−4.81678	+	1.85499i	−0.200179	+	0.0770907i
$580$	39.9502	+	35.7301i	1.65884	+	1.48361i
$581$	−17.1963	−	4.47953i	−0.713424	−	0.185842i
$582$	3.15649	+	2.63381i	0.130841	+	0.109175i
$583$	0.424054	−	1.16508i	0.0175625	−	0.0482526i
$584$	−9.69534	−	18.7945i	−0.401196	−	0.777723i
$585$	−40.3266	−	44.5922i	−1.66730	−	1.84366i
$586$	−0.533861	+	33.8261i	−0.0220536	+	1.39734i
$587$	−25.6418	−	9.33284i	−1.05835	−	0.385208i	−0.246542	−	0.969132i	$-0.579294\pi$
$587$	−25.6418	−	9.33284i	−1.05835	−	0.385208i	−0.811808	+	0.583925i	$0.801516\pi$
$588$	20.9889	−	12.1436i	0.865568	−	0.500792i
$589$	−5.65089	−	4.74166i	−0.232841	−	0.195377i
$590$	−56.3950	−	10.8643i	−2.32175	−	0.447274i
$591$	−3.07425	−	1.69973i	−0.126458	−	0.0699175i
$592$	−1.14018	−	10.1919i	−0.0468611	−	0.418884i
$593$	−7.08780	+	4.09214i	−0.291061	+	0.168044i	−0.638420	−	0.769688i	$-0.720412\pi$
$593$	−7.08780	+	4.09214i	−0.291061	+	0.168044i	0.347359	+	0.937732i	$0.387078\pi$
$594$	−5.14176	+	37.9411i	−0.210969	+	1.55674i
$595$	0.639240	−	7.94382i	0.0262063	−	0.325665i
$596$	0.906031	−	2.26428i	0.0371125	−	0.0927484i
$597$	−24.8426	−	13.7352i	−1.01674	−	0.562146i
$598$	−21.5926	+	7.47534i	−0.882987	+	0.305689i
$599$	−16.8275	+	6.12470i	−0.687552	+	0.250249i	−0.662087	−	0.749427i	$-0.730329\pi$
$599$	−16.8275	+	6.12470i	−0.687552	+	0.250249i	−0.0254655	+	0.999676i	$0.508107\pi$
$600$	20.1844	−	15.9690i	0.824023	−	0.651933i
$601$	−39.0871	−	14.2265i	−1.59439	−	0.580312i	−0.616124	−	0.787649i	$-0.711298\pi$
$601$	−39.0871	−	14.2265i	−1.59439	−	0.580312i	−0.978270	+	0.207337i	$0.933520\pi$
$602$	21.0763	+	2.03123i	0.859006	+	0.0827868i
$603$	3.93605	+	9.68153i	0.160289	+	0.394262i
$604$	27.0798	+	16.7957i	1.10186	+	0.683406i
$605$	−50.9210	+	8.97874i	−2.07023	+	0.365038i
$606$	18.4313	−	22.0889i	0.748718	−	0.897301i
$607$	−10.3924	−	28.5529i	−0.421815	−	1.15893i	−0.950667	−	0.310213i	$-0.899600\pi$
$607$	−10.3924	−	28.5529i	−0.421815	−	1.15893i	0.528852	−	0.848714i	$-0.322623\pi$
$608$	−29.0117	+	29.5009i	−1.17658	+	1.19642i
$609$	36.7795	−	10.8677i	1.49038	−	0.440381i
$610$	−8.65461	+	22.6592i	−0.350415	+	0.917444i
$611$	−18.0583			−0.730561
$612$	−3.60405	+	4.34356i	−0.145685	+	0.175578i
$613$	−11.9832			−0.483996			−0.241998	−	0.970277i	$-0.577803\pi$
$613$	−11.9832			−0.483996			−0.241998	+	0.970277i	$0.577803\pi$
$614$	−14.8174	−	18.2355i	−0.597981	−	0.735925i
$615$	5.89798	+	30.1676i	0.237829	+	1.21648i
$616$	−8.56311	−	38.0386i	−0.345017	−	1.53262i
$617$	−9.34422	−	25.6730i	−0.376184	−	1.03356i	−0.972924	−	0.231123i	$-0.925760\pi$
$617$	−9.34422	−	25.6730i	−0.376184	−	1.03356i	0.596740	−	0.802434i	$-0.296462\pi$
$618$	0.0916690	+	33.2466i	0.00368747	+	1.33738i
$619$	6.98469	−	19.1903i	0.280738	−	0.771322i	−0.716537	−	0.697549i	$-0.754274\pi$
$619$	6.98469	−	19.1903i	0.280738	−	0.771322i	0.997275	−	0.0737727i	$-0.0235039\pi$
$620$	3.05132	+	5.69269i	0.122544	+	0.228624i
$621$	10.7396	+	8.03818i	0.430965	+	0.322561i
$622$	−0.376646	−	0.676816i	−0.0151021	−	0.0271378i
$623$	2.61291	−	1.85685i	0.104684	−	0.0743933i
$624$	−19.9851	−	38.4805i	−0.800043	−	1.54045i
$625$	−18.1303	−	15.2132i	−0.725213	−	0.608526i
$626$	−11.8564	−	10.2718i	−0.473877	−	0.410546i
$627$	64.7821	−	12.6653i	2.58715	−	0.505805i
$628$	44.4319	+	17.7790i	1.77303	+	0.709461i
$629$	−2.08867	+	1.20589i	−0.0832806	+	0.0480821i
$630$	−4.14341	−	35.7042i	−0.165077	−	1.42249i
$631$	18.9005	+	10.9122i	0.752417	+	0.434408i	0.826567	−	0.562839i	$-0.190291\pi$
$631$	18.9005	+	10.9122i	0.752417	+	0.434408i	−0.0741495	+	0.997247i	$0.523624\pi$
$632$	5.05262	−	12.0712i	0.200982	−	0.480167i
$633$	36.9468	+	5.81071i	1.46850	+	0.230955i
$634$	26.2694	+	5.06068i	1.04329	+	0.200985i
$635$	5.00366	−	1.82118i	0.198564	−	0.0722715i
$636$	0.538040	−	0.624510i	0.0213347	−	0.0247634i
$637$	37.6316	−	22.4317i	1.49102	−	0.888777i
$638$	0.973140	−	61.6594i	0.0385270	−	2.44112i
$639$	−5.65946	−	9.01344i	−0.223885	−	0.356566i
$640$	33.1801	−	14.5447i	1.31156	−	0.574931i
$641$	8.21759	+	9.79334i	0.324575	+	0.386814i	0.903515	−	0.428557i	$-0.140978\pi$
$641$	8.21759	+	9.79334i	0.324575	+	0.386814i	−0.578940	+	0.815370i	$0.696533\pi$
$642$	−11.8693	+	10.0154i	−0.468444	+	0.395277i
$643$	10.5489	−	12.5717i	0.416008	−	0.495779i	−0.516823	−	0.856092i	$-0.672886\pi$
$643$	10.5489	−	12.5717i	0.416008	−	0.495779i	0.932832	+	0.360313i	$0.117330\pi$
$644$	−13.1043	−	3.85907i	−0.516383	−	0.152069i
$645$	15.1865	−	27.4674i	0.597968	−	1.08153i
$646$	9.08996	+	3.47188i	0.357640	+	0.136599i
$647$	−7.64754	+	13.2459i	−0.300656	+	0.520751i	−0.976285	−	0.216491i	$-0.930539\pi$
$647$	−7.64754	+	13.2459i	−0.300656	+	0.520751i	0.675629	+	0.737242i	$0.263872\pi$
$648$	−12.1324	+	22.3787i	−0.476605	+	0.879118i
$649$	33.0396	+	57.2263i	1.29692	+	2.24633i
$650$	36.0881	−	29.3236i	1.41549	−	1.15017i
$651$	4.61285	+	0.285247i	0.180792	+	0.0111797i
$652$	8.39072	+	1.75420i	0.328606	+	0.0686996i
$653$	43.6761	+	7.70128i	1.70918	+	0.301374i	0.940886	−	0.338724i	$-0.109995\pi$
$653$	43.6761	+	7.70128i	1.70918	+	0.301374i	0.768293	+	0.640098i	$0.221106\pi$
$654$	−10.6358	−	3.83795i	−0.415894	−	0.150076i
$655$	19.0262	+	22.6745i	0.743413	+	0.885965i
$656$	−1.39849	+	22.1249i	−0.0546018	+	0.863832i
$657$	−10.4876	+	19.8280i	−0.409160	+	0.773563i
$658$	−8.78871	−	6.27006i	−0.342620	−	0.244432i
$659$	28.2941	−	23.7415i	1.10218	−	0.924839i	0.104611	−	0.994513i	$-0.466640\pi$
$659$	28.2941	−	23.7415i	1.10218	−	0.924839i	0.997570	+	0.0696740i	$0.0221959\pi$
$660$	−56.7820	−	10.7765i	−2.21024	−	0.419476i
$661$	−33.5985	−	28.1925i	−1.30683	−	1.09656i	−0.988922	−	0.148438i	$-0.952576\pi$
$661$	−33.5985	−	28.1925i	−1.30683	−	1.09656i	−0.317907	−	0.948122i	$-0.602980\pi$
$662$	29.9509	+	5.76991i	1.16407	+	0.224254i
$663$	−6.40867	+	7.93163i	−0.248892	+	0.308039i
$664$	−15.1143	+	11.5087i	−0.586547	+	0.446625i
$665$	−55.9775	+	26.5793i	−2.17072	+	1.03070i
$666$	−8.18193	+	7.16782i	−0.317043	+	0.277747i
$667$	−18.7111	−	10.8028i	−0.724496	−	0.418288i
$668$	0.890203	+	6.18400i	0.0344430	+	0.239266i
$669$	−9.10356	+	1.77981i	−0.351964	+	0.0688113i
$670$	−14.9078	+	5.16105i	−0.575937	+	0.199389i
$671$	26.2248	−	9.54504i	1.01240	−	0.368482i
$672$	3.63443	−	25.6669i	0.140201	−	0.990123i
$673$	8.83692	+	50.1167i	0.340638	+	1.93186i	0.362229	+	0.932089i	$0.382016\pi$
$673$	8.83692	+	50.1167i	0.340638	+	1.93186i	−0.0215906	+	0.999767i	$0.506873\pi$
$674$	−1.26694	+	2.11655i	−0.0488006	+	0.0815264i
$675$	−26.1317	−	7.89634i	−1.00581	−	0.303930i
$676$	−24.7263	−	46.1306i	−0.951013	−	1.77426i
$677$	−7.91064	−	9.42753i	−0.304031	−	0.362330i	0.592299	−	0.805718i	$-0.298221\pi$
$677$	−7.91064	−	9.42753i	−0.304031	−	0.362330i	−0.896329	+	0.443389i	$0.853776\pi$
$678$	2.78985	+	1.60048i	0.107143	+	0.0614660i
$679$	1.17912	+	4.28098i	0.0452506	+	0.164289i
$680$	−6.26002	−	5.77912i	−0.240061	−	0.221619i
$681$	26.2558	−	22.8739i	1.00613	−	0.876530i
$682$	2.65156	−	6.94222i	0.101533	−	0.265831i
$683$	23.2520			0.889715			0.444857	−	0.895601i	$-0.353254\pi$
$683$	23.2520			0.889715			0.444857	+	0.895601i	$0.353254\pi$
$684$	43.2606	+	7.38227i	1.65411	+	0.282268i
$685$	−21.1823	+	36.6888i	−0.809334	+	1.40181i
$686$	26.1033	+	2.14895i	0.996628	+	0.0820474i
$687$	−20.4568	−	16.5289i	−0.780477	−	0.630617i
$688$	15.6150	−	16.3877i	0.595315	−	0.624776i
$689$	0.957297	−	1.14086i	0.0364701	−	0.0434634i
$690$	−12.9732	+	15.5477i	−0.493880	+	0.591890i
$691$	−8.32952	+	22.8852i	−0.316870	+	0.870592i	0.674355	+	0.738407i	$0.264422\pi$
$691$	−8.32952	+	22.8852i	−0.316870	+	0.870592i	−0.991225	+	0.132185i	$0.957801\pi$
$692$	38.3256	−	20.5428i	1.45692	−	0.780919i
$693$	−27.9269	+	30.5022i	−1.06086	+	1.15868i
$694$	8.80613	−	14.7115i	0.334276	−	0.558442i
$695$	−1.64363	−	9.32149i	−0.0623464	−	0.353584i
$696$	15.1265	−	38.1071i	0.573367	−	1.44444i
$697$	4.89909	−	1.78312i	0.185566	−	0.0675406i
$698$	−7.89292	+	40.9712i	−0.298751	+	1.55078i
$699$	38.4655	−	23.1692i	1.45490	−	0.876340i
$700$	27.7451	−	1.74116i	1.04867	−	0.0658095i
$701$			21.7762i			0.822475i	0.911528	+	0.411237i	$0.134903\pi$
$701$			21.7762i			0.822475i	−0.911528	+	0.411237i	$0.865097\pi$
$702$	−21.3911	+	40.7135i	−0.807354	+	1.53663i
$703$	16.2406	+	9.37649i	0.612524	+	0.353641i
$704$	−37.6455	−	17.8957i	−1.41882	−	0.674469i
$705$	−13.7083	+	8.25703i	−0.516284	+	0.310978i
$706$	26.2954	−	30.3518i	0.989642	−	1.14230i
$707$	29.9580	−	8.25143i	1.12669	−	0.310327i
$708$	7.06475	+	43.3612i	0.265510	+	1.62961i
$709$	7.21515	+	40.9192i	0.270971	+	1.53675i	0.751476	+	0.659760i	$0.229342\pi$
$709$	7.21515	+	40.9192i	0.270971	+	1.53675i	−0.480505	+	0.876992i	$0.659547\pi$
$710$	14.0381	−	7.81218i	0.526842	−	0.293186i
$711$	−13.5702	+	2.91523i	−0.508922	+	0.109330i
$712$	0.162178	−	3.42298i	0.00607786	−	0.128282i
$713$	−1.67360	−	1.99452i	−0.0626768	−	0.0746952i
$714$	−5.87296	+	1.63504i	−0.219790	+	0.0611899i
$715$	−102.833	−	18.1322i	−3.84572	−	0.678105i
$716$	−2.02858	+	9.70318i	−0.0758117	+	0.362625i
$717$	−19.2830	−	15.5804i	−0.720135	−	0.581861i
$718$	−2.16884	+	1.76230i	−0.0809404	+	0.0657686i
$719$	−9.51779			−0.354954			−0.177477	−	0.984125i	$-0.556793\pi$
$719$	−9.51779			−0.354954			−0.177477	+	0.984125i	$0.556793\pi$
$720$	−32.7658	−	20.0730i	−1.22111	−	0.748076i
$721$	−20.3920	+	29.5591i	−0.759436	+	1.10084i
$722$	−7.71292	−	48.1760i	−0.287045	−	1.79292i
$723$	−2.42479	−	12.4026i	−0.0901788	−	0.461257i
$724$	−1.79200	+	8.57153i	−0.0665990	+	0.318558i
$725$	43.2997	+	7.63490i	1.60811	+	0.283553i
$726$	19.8710	+	34.1994i	0.737481	+	1.26926i
$727$	3.01083	−	0.530890i	0.111665	−	0.0196896i	−0.117536	−	0.993069i	$-0.537500\pi$
$727$	3.01083	−	0.530890i	0.111665	−	0.0196896i	0.229202	+	0.973379i	$0.426389\pi$
$728$	5.96182	−	46.4539i	0.220960	−	1.72170i
$729$	26.8331	−	2.99704i	0.993820	−	0.111001i
$730$	−29.0521	−	17.3902i	−1.07527	−	0.643640i
$731$	−5.00226	−	1.82067i	−0.185015	−	0.0673401i
$732$	18.5530	+	0.241648i	0.685739	+	0.00893156i
$733$	3.00363	+	2.52035i	0.110942	+	0.0930911i	0.696571	−	0.717488i	$-0.254708\pi$
$733$	3.00363	+	2.52035i	0.110942	+	0.0930911i	−0.585629	+	0.810579i	$0.699153\pi$
$734$	−18.2263	−	3.51121i	−0.672745	−	0.129601i
$735$	18.3099	−	34.2350i	0.675370	−	1.26278i
$736$	−11.8924	+	8.47620i	−0.438360	+	0.312437i
$737$	15.7194	+	9.07557i	0.579030	+	0.334303i
$738$	20.1086	−	12.1879i	0.740208	−	0.448642i
$739$	−36.0623	+	20.8206i	−1.32657	+	0.765898i	−0.984768	−	0.173872i	$-0.944372\pi$
$739$	−36.0623	+	20.8206i	−1.32657	+	0.765898i	−0.341807	+	0.939770i	$0.611039\pi$
$740$	−10.1522	−	12.9050i	−0.373202	−	0.474398i
$741$	78.3258	+	12.3185i	2.87737	+	0.452530i
$742$	0.862023	−	0.222856i	0.0316459	−	0.00818130i
$743$	−6.07596	+	34.4585i	−0.222905	+	1.26416i	0.643744	+	0.765241i	$0.277380\pi$
$743$	−6.07596	+	34.4585i	−0.222905	+	1.26416i	−0.866649	+	0.498918i	$0.833731\pi$
$744$	3.28355	−	3.69181i	0.120381	−	0.135348i
$745$	−0.678046	−	3.84539i	−0.0248417	−	0.140884i
$746$	−21.0630	+	35.1878i	−0.771170	+	1.28832i
$747$	19.1768	+	6.18494i	0.701643	+	0.226295i
$748$	−0.309340	+	9.79764i	−0.0113106	+	0.358237i
$749$	−16.7002	+	1.57843i	−0.610211	+	0.0576745i
$750$	0.675276	−	1.87134i	0.0246576	−	0.0683318i
$751$	49.2861	+	8.69046i	1.79847	+	0.317120i	0.970036	−	0.242961i	$-0.0781187\pi$
$751$	49.2861	+	8.69046i	1.79847	+	0.317120i	0.828438	+	0.560080i	$0.189230\pi$
$752$	−11.0729	+	3.25539i	−0.403786	+	0.118712i
$753$	−10.0766	+	18.2253i	−0.367213	+	0.664168i
$754$	26.4299	−	69.1979i	0.962521	−	2.52004i
$755$	51.0187			1.85676
$756$	−24.5469	+	12.3874i	−0.892763	+	0.450526i
$757$	−43.9212			−1.59634			−0.798172	−	0.602429i	$-0.794200\pi$
$757$	−43.9212			−1.59634			−0.798172	+	0.602429i	$0.794200\pi$
$758$	−1.48275	+	3.88208i	−0.0538558	+	0.141003i
$759$	23.2941	−	0.431886i	0.845523	−	0.0156765i
$760$	−14.5781	+	64.6219i	−0.528803	+	2.34408i
$761$	−22.6138	−	3.98743i	−0.819751	−	0.144544i	−0.251982	−	0.967732i	$-0.581082\pi$
$761$	−22.6138	−	3.98743i	−0.819751	−	0.144544i	−0.567769	+	0.823188i	$0.692193\pi$
$762$	−2.62681	−	3.11304i	−0.0951594	−	0.112774i
$763$	−7.07469	−	9.95530i	−0.256121	−	0.360406i
$764$	−13.9694	−	0.441055i	−0.505396	−	0.0159568i
$765$	−1.23822	+	8.95132i	−0.0447680	+	0.323636i
$766$	0.503802	−	0.841652i	0.0182031	−	0.0304101i
$767$	13.7830	+	78.1675i	0.497677	+	2.82247i
$768$	−19.1912	−	19.9924i	−0.692503	−	0.721415i
$769$	7.55428	−	42.8424i	0.272414	−	1.54494i	−0.474643	−	0.880178i	$-0.657423\pi$
$769$	7.55428	−	42.8424i	0.272414	−	1.54494i	0.747057	−	0.664760i	$-0.231466\pi$
$770$	−43.7514	−	44.5294i	−1.57669	−	1.60473i
$771$	16.9200	−	20.9409i	0.609359	−	0.754167i
$772$	−4.68435	+	3.68511i	−0.168594	+	0.132630i
$773$	2.58843	−	1.49443i	0.0930994	−	0.0537509i	−0.452728	−	0.891649i	$-0.649549\pi$
$773$	2.58843	−	1.49443i	0.0930994	−	0.0537509i	0.545827	+	0.837898i	$0.316216\pi$
$774$	−23.7277	−	3.66469i	−0.852874	−	0.131725i
$775$	4.58859	+	2.64923i	0.164827	+	0.0951630i
$776$	4.37887	+	1.83285i	0.157192	+	0.0657955i
$777$	−11.6745	+	1.32219i	−0.418820	+	0.0474333i
$778$	15.6390	+	3.01279i	0.560686	+	0.108014i
$779$	−31.0538	−	26.0573i	−1.11262	−	0.933599i
$780$	−59.6652	−	35.4917i	−2.13636	−	1.27081i
$781$	−17.3696	−	6.32203i	−0.621534	−	0.226220i
$782$	2.94682	+	1.76393i	0.105378	+	0.0630780i
$783$	−42.3399	+	9.92023i	−1.51310	+	0.354520i
$784$	19.0309	−	20.5384i	0.679674	−	0.733514i
$785$	75.4580	−	13.3053i	2.69321	−	0.474886i
$786$	11.2670	−	19.6399i	0.401882	−	0.700533i
$787$	−7.43419	−	1.31085i	−0.265000	−	0.0467267i	0.0395692	−	0.999217i	$-0.487401\pi$
$787$	−7.43419	−	1.31085i	−0.265000	−	0.0467267i	−0.304569	+	0.952490i	$0.598513\pi$
$788$	−3.97045	−	0.830077i	−0.141441	−	0.0295703i
$789$	25.1829	+	8.64061i	0.896535	+	0.307614i
$790$	−3.31214	−	20.6881i	−0.117841	−	0.736049i
$791$	1.49010	+	3.13824i	0.0529818	+	0.111583i
$792$	7.22977	+	43.6160i	0.256899	+	1.54983i
$793$	33.5225			1.19042
$794$	−31.8367	+	25.8691i	−1.12984	+	0.918060i
$795$	0.205045	−	1.30376i	0.00727221	−	0.0462396i
$796$	−32.0846	−	6.70772i	−1.13721	−	0.237749i
$797$	20.0151	+	3.52920i	0.708971	+	0.125011i	0.516494	−	0.856291i	$-0.327237\pi$
$797$	20.0151	+	3.52920i	0.708971	+	0.125011i	0.192477	+	0.981302i	$0.438348\pi$
$798$	33.8429	+	33.1909i	1.19803	+	1.17494i
$799$	1.74466	+	2.07921i	0.0617218	+	0.0735571i
$800$	16.8420	−	24.4861i	0.595456	−	0.865715i
$801$	−3.07821	+	1.93278i	−0.108763	+	0.0682914i
$802$	−21.2074	+	11.8018i	−0.748858	+	0.416737i
$803$	6.76484	+	38.3653i	0.238726	+	1.35388i
$804$	7.63600	+	9.34474i	0.269301	+	0.329564i
$805$	−21.0865	+	5.80792i	−0.743202	+	0.204702i
$806$	5.84501	−	6.74666i	0.205882	−	0.237641i
$807$	−0.416003	−	22.4374i	−0.0146440	−	0.789835i
$808$	12.8262	−	30.6431i	0.451224	−	1.07802i
$809$	22.8211	+	13.1758i	0.802347	+	0.463235i	0.844291	−	0.535884i	$-0.180022\pi$
$809$	22.8211	+	13.1758i	0.802347	+	0.463235i	−0.0419439	+	0.999120i	$0.513355\pi$
$810$	2.37771	+	40.6871i	0.0835442	+	1.42960i
$811$		−	31.3046i		−	1.09925i	−0.835411	−	0.549626i	$-0.814770\pi$
$811$		−	31.3046i		−	1.09925i	0.835411	−	0.549626i	$-0.185230\pi$
$812$	36.8894	−	24.5008i	1.29456	−	0.859810i
$813$	−5.40893	−	2.99055i	−0.189699	−	0.104883i
$814$	−3.57373	+	18.5508i	−0.125259	+	0.650206i
$815$	12.8968	−	4.69407i	0.451757	−	0.164426i
$816$	−2.49978	+	6.01876i	−0.0875096	+	0.210699i
$817$	7.18758	+	40.7628i	0.251462	+	1.42611i
$818$	−0.620133	+	1.03599i	−0.0216824	+	0.0362227i
$819$	−44.0536	+	22.9560i	−1.53936	+	0.802147i
$820$	16.7682	+	31.2835i	0.585570	+	1.09247i
$821$	1.46974	−	4.03807i	0.0512942	−	0.140930i	−0.911400	−	0.411522i	$-0.864997\pi$
$821$	1.46974	−	4.03807i	0.0512942	−	0.140930i	0.962694	+	0.270592i	$0.0872195\pi$
$822$	31.9301	+	5.53941i	1.11369	+	0.193209i
$823$	6.50028	−	7.74673i	0.226585	−	0.270034i	−0.640759	−	0.767742i	$-0.721380\pi$
$823$	6.50028	−	7.74673i	0.226585	−	0.270034i	0.867345	+	0.497708i	$0.165825\pi$
$824$	11.4082	+	36.6558i	0.397423	+	1.27697i
$825$	−44.2442	+	17.0389i	−1.54039	+	0.593218i
$826$	−20.4327	+	42.8286i	−0.710944	+	1.49020i
$827$	3.52238	−	6.10094i	0.122485	−	0.212150i	−0.798262	−	0.602310i	$-0.794247\pi$
$827$	3.52238	−	6.10094i	0.122485	−	0.212150i	0.920747	+	0.390160i	$0.127580\pi$
$828$	14.5847	+	5.21748i	0.506852	+	0.181320i
$829$	30.6838			1.06569			0.532847	−	0.846212i	$-0.321122\pi$
$829$	30.6838			1.06569			0.532847	+	0.846212i	$0.321122\pi$
$830$	−10.8525	+	28.4137i	−0.376696	+	0.986253i
$831$	−12.5887	−	4.31936i	−0.436697	−	0.149837i
$832$	−35.1402	−	35.6656i	−1.21827	−	1.23648i
$833$	−6.21845	−	2.16566i	−0.215457	−	0.0750357i
$834$	−6.26048	+	3.63754i	−0.216783	+	0.125958i
$835$	6.42983	+	7.66278i	0.222514	+	0.265181i
$836$	67.1783	−	36.0080i	2.32341	−	1.24536i
$837$	−5.20346	−	0.621717i	−0.179858	−	0.0214897i
$838$	7.15654	−	11.9557i	0.247219	−	0.413004i
$839$	7.02678	+	39.8508i	0.242591	+	1.37580i	0.826021	+	0.563640i	$0.190599\pi$
$839$	7.02678	+	39.8508i	0.242591	+	1.37580i	−0.583430	+	0.812164i	$0.698290\pi$
$840$	−16.7150	−	37.9897i	−0.576723	−	1.31077i
$841$	38.5649	−	14.0365i	1.32982	−	0.484017i
$842$	28.0575	−	9.71347i	0.966924	−	0.334748i
$843$	−10.0116	+	29.1787i	−0.344819	+	1.00497i
$844$	42.7463	−	6.15344i	1.47139	−	0.211810i
$845$	−72.5721	−	41.8995i	−2.49656	−	1.44139i
$846$	9.54303	+	7.66727i	0.328096	+	0.263606i
$847$	−3.42680	+	42.5847i	−0.117746	+	1.46323i
$848$	0.381324	−	0.872119i	0.0130947	−	0.0299487i
$849$	8.84674	+	1.39135i	0.303619	+	0.0477509i
$850$	−6.86286	−	1.32210i	−0.235394	−	0.0453477i
$851$	5.07043	+	4.25460i	0.173812	+	0.145846i
$852$	−9.31053	−	8.02140i	−0.318974	−	0.274809i
$853$	10.3491	−	8.68393i	0.354346	−	0.297332i	−0.448186	−	0.893940i	$-0.647930\pi$
$853$	10.3491	−	8.68393i	0.354346	−	0.297332i	0.802533	+	0.596608i	$0.203485\pi$
$854$	16.3149	+	11.6394i	0.558284	+	0.398292i
$855$	65.0906	−	26.4628i	2.22605	−	0.905009i
$856$	−9.69134	+	15.0885i	−0.331243	+	0.515715i
$857$	1.47829	+	1.76176i	0.0504974	+	0.0601804i	0.790702	−	0.612201i	$-0.209716\pi$
$857$	1.47829	+	1.76176i	0.0504974	+	0.0601804i	−0.740205	+	0.672382i	$0.765271\pi$
$858$	14.0872	+	78.6240i	0.480928	+	2.68418i
$859$	47.5118	+	8.37762i	1.62108	+	0.285841i	0.909169	−	0.416426i	$-0.136718\pi$
$859$	47.5118	+	8.37762i	1.62108	+	0.285841i	0.711914	+	0.702267i	$0.247829\pi$
$860$	7.41646	−	35.4746i	0.252899	−	1.20967i
$861$	25.3494	+	1.56754i	0.863906	+	0.0534216i
$862$	8.27654	−	6.72515i	0.281900	−	0.229060i
$863$	−28.5638	−	49.4739i	−0.972323	−	1.68411i	−0.688501	−	0.725236i	$-0.741731\pi$
$863$	−28.5638	−	49.4739i	−0.972323	−	1.68411i	−0.283822	−	0.958877i	$-0.591602\pi$
$864$	−5.77695	+	28.8206i	−0.196536	+	0.980497i
$865$	34.8103	−	60.2933i	1.18359	−	2.05003i
$866$	−1.96563	−	0.750768i	−0.0667950	−	0.0255121i
$867$	−27.9074	+	0.517419i	−0.947785	+	0.0175725i
$868$	5.18720	−	1.25405i	0.176065	−	0.0425651i
$869$	−15.4951	+	18.4663i	−0.525635	+	0.626428i
$870$	−11.5770	−	64.6139i	−0.392496	−	2.19062i
$871$	14.0146	+	16.7020i	0.474868	+	0.565925i
$872$	−13.0417	−	0.617903i	−0.441648	−	0.0209248i
$873$	−1.05751	−	4.92262i	−0.0357912	−	0.166606i
$874$	0.421412	−	26.7012i	0.0142545	−	0.903181i
$875$	1.75161	−	1.24477i	0.0592151	−	0.0420809i
$876$	−4.82944	+	25.4465i	−0.163172	+	0.859759i
$877$	−25.4233	+	9.25334i	−0.858485	+	0.312463i	−0.733495	−	0.679695i	$-0.762112\pi$
$877$	−25.4233	+	9.25334i	−0.858485	+	0.312463i	−0.124990	+	0.992158i	$0.539890\pi$
$878$	23.9175	+	4.60760i	0.807176	+	0.155499i
$879$	26.0400	−	32.2282i	0.878307	−	1.08703i
$880$	−66.3229	+	7.41963i	−2.23574	+	0.250116i
$881$	23.6909	+	13.6780i	0.798168	+	0.460823i	0.842830	−	0.538179i	$-0.180888\pi$
$881$	23.6909	+	13.6780i	0.798168	+	0.460823i	−0.0446619	+	0.999002i	$0.514221\pi$
$882$	−29.4108	−	4.12359i	−0.990314	−	0.138849i
$883$	−11.6678	+	6.73638i	−0.392651	+	0.226697i	−0.683308	−	0.730130i	$-0.739459\pi$
$883$	−11.6678	+	6.73638i	−0.392651	+	0.226697i	0.290657	+	0.956827i	$0.406126\pi$
$884$	−4.37433	+	10.9320i	−0.147125	+	0.367682i
$885$	46.2044	+	53.0358i	1.55315	+	1.78278i
$886$	−11.2767	−	9.76967i	−0.378850	−	0.328218i
$887$	3.21453	+	2.69731i	0.107933	+	0.0905668i	0.695157	−	0.718858i	$-0.255335\pi$
$887$	3.21453	+	2.69731i	0.107933	+	0.0905668i	−0.587224	+	0.809425i	$0.699779\pi$
$888$	−6.59085	+	10.6922i	−0.221174	+	0.358806i
$889$	−0.413985	−	4.38007i	−0.0138846	−	0.146903i
$890$	−2.66796	−	4.79421i	−0.0894302	−	0.160702i
$891$	33.5903	−	32.7207i	1.12532	−	1.09618i
$892$	−9.44029	+	5.06006i	−0.316084	+	0.169423i
$893$	7.21818	−	19.8318i	0.241547	−	0.663645i
$894$	−2.58263	+	1.50059i	−0.0863761	+	0.0501873i
$895$	5.42830	+	14.9141i	0.181448	+	0.498525i
$896$	−4.71868	−	29.5590i	−0.157640	−	0.987497i
$897$	26.4706	+	9.08243i	0.883827	+	0.303254i
$898$	−17.0585	−	20.9936i	−0.569250	−	0.700567i
$899$	8.44037			0.281502
$900$	−31.5214	+	0.173825i	−1.05071	+	0.00579418i
$901$	−0.223845			−0.00745734
$902$	14.5714	−	38.1502i	0.485173	−	1.27026i
$903$	−18.7989	−	17.8635i	−0.625589	−	0.594461i
$904$	3.62286	+	0.817283i	0.120494	+	0.0271824i
$905$	4.79522	+	13.1748i	0.159398	+	0.437944i
$906$	−13.4491	−	36.6365i	−0.446817	−	1.21717i
$907$	−44.3983	+	7.82862i	−1.47422	+	0.259945i	−0.852266	−	0.523108i	$-0.824772\pi$
$907$	−44.3983	+	7.82862i	−1.47422	+	0.259945i	−0.621955	+	0.783053i	$0.713661\pi$
$908$	21.1935	−	34.1704i	0.703330	−	1.13398i
$909$	−34.4482	+	7.40038i	−1.14258	+	0.245455i
$910$	−31.0903	−	68.2368i	−1.03063	−	2.26203i
$911$	−25.0160	−	9.10508i	−0.828818	−	0.301665i	−0.107444	−	0.994211i	$-0.534267\pi$
$911$	−25.0160	−	9.10508i	−0.828818	−	0.301665i	−0.721374	+	0.692546i	$0.756489\pi$
$912$	50.2479	−	6.56654i	1.66387	−	0.217440i
$913$	32.8848	−	11.9691i	1.08833	−	0.396118i
$914$	39.0705	−	13.5262i	1.29234	−	0.447406i
$915$	25.4474	−	15.3279i	0.841263	−	0.506725i
$916$	−28.1951	−	11.2820i	−0.931593	−	0.372769i
$917$	22.0925	−	10.4900i	0.729559	−	0.346409i
$918$	6.75435	−	1.47050i	0.222927	−	0.0485339i
$919$	−48.6105	+	28.0653i	−1.60351	+	0.925787i	−0.612733	+	0.790290i	$0.709930\pi$
$919$	−48.6105	+	28.0653i	−1.60351	+	0.925787i	−0.990778	+	0.135498i	$0.956737\pi$
$920$	−9.02794	+	21.5687i	−0.297643	+	0.711098i
$921$	0.533456	+	28.7723i	0.0175780	+	0.948081i
$922$	34.1040	+	6.56998i	1.12315	+	0.216371i
$923$	−17.0086	−	14.2719i	−0.559845	−	0.469766i
$924$	−20.4432	+	43.1563i	−0.672530	+	1.41974i
$925$	−12.6573	−	4.60689i	−0.416170	−	0.151474i
$926$	0.000294534	−	0.0186620i	9.67899e−6	−	0.000613273i
$927$	24.9993	−	32.1412i	0.821084	−	1.05565i
$928$	3.73171	−	47.1948i	0.122499	−	1.54925i
$929$	2.69059	−	7.39233i	0.0882754	−	0.242535i	−0.887697	−	0.460427i	$-0.847696\pi$
$929$	2.69059	−	7.39233i	0.0882754	−	0.242535i	0.975973	+	0.217893i	$0.0699184\pi$
$930$	1.35216	−	7.79407i	0.0443390	−	0.255578i
$931$	9.59277	+	50.2936i	0.314390	+	1.64831i
$932$	34.5661	−	38.6487i	1.13225	−	1.26598i
$933$	−0.147383	+	0.937119i	−0.00482509	+	0.0306799i
$934$	−37.3936	+	30.3844i	−1.22356	+	0.994208i
$935$	7.84724	+	13.5918i	0.256632	+	0.444500i
$936$	−9.75817	+	52.2015i	−0.318956	+	1.70626i
$937$	−24.0535	−	41.6618i	−0.785792	−	1.36103i	−0.928525	−	0.371271i	$-0.878922\pi$
$937$	−24.0535	−	41.6618i	−0.785792	−	1.36103i	0.142732	−	0.989761i	$-0.454411\pi$
$938$	1.02159	+	12.9947i	0.0333560	+	0.424291i
$939$	3.68642	+	18.8557i	0.120302	+	0.615333i
$940$	−12.3186	+	13.7736i	−0.401790	+	0.449245i
$941$	−12.8917	−	2.27316i	−0.420258	−	0.0741028i	−0.0404797	−	0.999180i	$-0.512889\pi$
$941$	−12.8917	−	2.27316i	−0.420258	−	0.0741028i	−0.379778	+	0.925078i	$0.624000\pi$
$942$	−29.4461	−	50.6790i	−0.959406	−	1.65121i
$943$	−9.19708	−	10.9606i	−0.299498	−	0.356928i
$944$	22.5427	+	45.4455i	0.733704	+	1.47913i
$945$	−22.9452	+	37.5694i	−0.746407	+	1.22213i
$946$	−36.4363	+	20.2767i	−1.18465	+	0.659252i
$947$	−34.5715	+	29.0089i	−1.12342	+	0.942663i	−0.998772	−	0.0495379i	$-0.984225\pi$
$947$	−34.5715	+	29.0089i	−1.12342	+	0.942663i	−0.124650	+	0.992201i	$0.539781\pi$
$948$	−13.9830	+	7.83206i	−0.454146	+	0.254373i
$949$	−8.12583	+	46.0839i	−0.263776	+	1.49595i
$950$	17.7785	+	51.3534i	0.576810	+	1.66612i
$951$	−21.5225	−	24.7046i	−0.697915	−	0.801101i
$952$	−5.92463	+	3.80160i	−0.192018	+	0.123211i
$953$	17.1808	−	9.91932i	0.556540	−	0.321318i	−0.195216	−	0.980760i	$-0.562541\pi$
$953$	17.1808	−	9.91932i	0.556540	−	0.321318i	0.751755	+	0.659442i	$0.229207\pi$
$954$	−0.990282	+	0.196443i	−0.0320616	+	0.00636008i
$955$	−19.3791	+	11.1885i	−0.627094	+	0.362053i
$956$	−26.5772	−	10.6346i	−0.859568	−	0.343949i
$957$	−47.4666	+	58.7466i	−1.53438	+	1.89901i
$958$	22.1745	−	7.67681i	0.716427	−	0.248026i
$959$	24.9232	+	24.5782i	0.804812	+	0.793672i
$960$	−42.9832	−	11.0066i	−1.38728	−	0.355237i
$961$	−28.1747	−	10.2547i	−0.908861	−	0.330798i
$962$	−11.6551	+	19.4710i	−0.375774	+	0.627769i
$963$	19.0075	−	0.705063i	0.612509	−	0.0227204i
$964$	−6.89376	−	12.8613i	−0.222033	−	0.414236i
$965$	−3.26375	+	8.96708i	−0.105064	+	0.288660i
$966$	9.72931	+	13.6112i	0.313035	+	0.437933i
$967$	−17.8168	+	21.2332i	−0.572950	+	0.682815i	−0.972234	−	0.234013i	$-0.924814\pi$
$967$	−17.8168	+	21.2332i	−0.572950	+	0.682815i	0.399284	+	0.916827i	$0.369259\pi$
$968$	33.5583	+	30.9804i	1.07860	+	0.995747i
$969$	−6.14894	−	10.2084i	−0.197532	−	0.327943i
$970$	7.50466	−	1.20149i	0.240960	−	0.0385774i
$971$	12.8758	+	22.3016i	0.413205	+	0.715691i	0.995238	−	0.0974735i	$-0.0310761\pi$
$971$	12.8758	+	22.3016i	0.413205	+	0.715691i	−0.582034	+	0.813165i	$0.697743\pi$
$972$	28.5906	−	12.4330i	0.917043	−	0.398789i
$973$	−7.79547	−	0.627303i	−0.249911	−	0.0201104i
$974$	12.2663	+	15.0959i	0.393036	+	0.483703i
$975$	−56.9406	+	1.05571i	−1.82356	+	0.0338098i
$976$	20.5551	−	6.04314i	0.657952	−	0.193436i
$977$	−8.67065	−	23.8224i	−0.277399	−	0.762146i	−0.997655	−	0.0684388i	$-0.978198\pi$
$977$	−8.67065	−	23.8224i	−0.277399	−	0.762146i	0.720257	−	0.693708i	$-0.244024\pi$
$978$	−6.77057	−	8.02381i	−0.216499	−	0.256573i
$979$	−2.15905	+	5.93195i	−0.0690037	+	0.189586i
$980$	8.56144	−	44.0047i	0.273485	−	1.40568i
$981$	7.36397	+	11.7281i	0.235113	+	0.374449i
$982$	−21.6200	−	38.8502i	−0.689923	−	1.23976i
$983$	−2.53270	−	14.3637i	−0.0807807	−	0.458130i	−0.998188	−	0.0601795i	$-0.980833\pi$
$983$	−2.53270	−	14.3637i	−0.0807807	−	0.458130i	0.917407	−	0.397951i	$-0.130278\pi$
$984$	18.0444	−	20.2879i	0.575235	−	0.646755i
$985$	−6.10273	+	2.22121i	−0.194449	+	0.0707737i
$986$	−10.5208	+	3.64230i	−0.335051	+	0.115994i
$987$	3.74685	+	12.6804i	0.119264	+	0.403623i
$988$	90.6204	−	13.0450i	2.88302	−	0.415018i
$989$			14.6094i			0.464553i
$990$	46.6440	+	53.2432i	1.48244	+	1.69218i
$991$			28.1414i			0.893940i	0.894549	+	0.446970i	$0.147497\pi$
$991$			28.1414i			0.893940i	−0.894549	+	0.446970i	$0.852503\pi$
$992$	2.36777	−	5.19056i	0.0751767	−	0.164800i
$993$	−24.5388	−	28.1668i	−0.778715	−	0.893848i
$994$	−3.32246	−	12.8515i	−0.105382	−	0.407626i
$995$	−49.3152	+	17.9493i	−1.56340	+	0.569030i
$996$	23.2647	+	0.303016i	0.737170	+	0.00960143i
$997$	16.6472	+	6.05908i	0.527222	+	0.191893i	0.591897	−	0.806013i	$-0.298379\pi$
$997$	16.6472	+	6.05908i	0.527222	+	0.191893i	−0.0646757	+	0.997906i	$0.520601\pi$
$998$	0.814862	−	51.6306i	0.0257940	−	1.63434i
$999$	13.3017	−	0.740540i	0.420846	−	0.0234296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.95.19	yes	840
4.3	odd	2	inner	756.2.ci.a.95.61	yes	840
7.2	even	3		756.2.bs.a.527.75	yes	840
27.2	odd	18		756.2.bs.a.515.34	✓	840
28.23	odd	6		756.2.bs.a.527.34	yes	840
108.83	even	18		756.2.bs.a.515.75	yes	840
189.2	odd	18	inner	756.2.ci.a.191.61	yes	840
756.191	even	18	inner	756.2.ci.a.191.19	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.34	✓	840	27.2	odd	18
756.2.bs.a.515.75	yes	840	108.83	even	18
756.2.bs.a.527.34	yes	840	28.23	odd	6
756.2.bs.a.527.75	yes	840	7.2	even	3
756.2.ci.a.95.19	yes	840	1.1	even	1	trivial
756.2.ci.a.95.61	yes	840	4.3	odd	2	inner
756.2.ci.a.191.19	yes	840	756.191	even	18	inner
756.2.ci.a.191.61	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)

\(f(q)\)	\(=\)	\(q+(-1.32113 - 0.504600i) q^{2} +(0.893683 + 1.48369i) q^{3} +(1.49076 + 1.33328i) q^{4} +(3.15348 + 0.556044i) q^{5} +(-0.431999 - 2.41109i) q^{6} +(1.10140 - 2.40560i) q^{7} +(-1.29670 - 2.51367i) q^{8} +(-1.40266 + 2.65189i) q^{9} +O(q^{10})\)	\(q+(-1.32113 - 0.504600i) q^{2} +(0.893683 + 1.48369i) q^{3} +(1.49076 + 1.33328i) q^{4} +(3.15348 + 0.556044i) q^{5} +(-0.431999 - 2.41109i) q^{6} +(1.10140 - 2.40560i) q^{7} +(-1.29670 - 2.51367i) q^{8} +(-1.40266 + 2.65189i) q^{9} +(-3.88557 - 2.32585i) q^{10} +(0.904764 + 5.13117i) q^{11} +(-0.645914 + 3.40335i) q^{12} +(-1.08679 + 6.16349i) q^{13} +(-2.66896 + 2.62233i) q^{14} +(1.99322 + 5.17571i) q^{15} +(0.444711 + 3.97520i) q^{16} +(0.814654 - 0.470341i) q^{17} +(3.19124 - 2.79571i) q^{18} +(-6.33439 - 3.65716i) q^{19} +(3.95971 + 5.03341i) q^{20} +(4.55347 - 0.515702i) q^{21} +(1.39388 - 7.23548i) q^{22} +(-1.97765 - 1.65944i) q^{23} +(2.57067 - 4.17033i) q^{24} +(4.93681 + 1.79685i) q^{25} +(4.54589 - 7.59437i) q^{26} +(-5.18812 + 0.288837i) q^{27} +(4.84927 - 2.11768i) q^{28} +(8.24184 - 1.45326i) q^{29} +(-0.0216266 - 7.84356i) q^{30} +(0.993208 + 0.175129i) q^{31} +(1.41837 - 5.47615i) q^{32} +(-6.80449 + 5.92803i) q^{33} +(-1.31360 + 0.210305i) q^{34} +(4.81088 - 6.97359i) q^{35} +(-5.62675 + 2.08318i) q^{36} -2.56387 q^{37} +(6.52314 + 8.02792i) q^{38} +(-10.1159 + 3.89575i) q^{39} +(-2.69142 - 8.64785i) q^{40} +(5.45806 + 0.962404i) q^{41} +(-6.27593 - 1.61637i) q^{42} +(-3.63752 - 4.33503i) q^{43} +(-5.49252 + 8.85564i) q^{44} +(-5.89784 + 7.58276i) q^{45} +(1.77537 + 3.19026i) q^{46} +(0.501039 + 2.84153i) q^{47} +(-5.50053 + 4.21238i) q^{48} +(-4.57382 - 5.29908i) q^{49} +(-5.61546 - 4.86498i) q^{50} +(1.42588 + 0.788358i) q^{51} +(-9.83782 + 7.73927i) q^{52} +(-0.206079 - 0.118980i) q^{53} +(6.99991 + 2.23634i) q^{54} +16.6842i q^{55} +(-7.47509 + 0.350780i) q^{56} +(-0.234846 - 12.6666i) q^{57} +(-11.6218 - 2.23890i) q^{58} +(11.9175 - 4.33762i) q^{59} +(-3.92929 + 10.3733i) q^{60} +(-0.930103 - 5.27488i) q^{61} +(-1.22378 - 0.732541i) q^{62} +(4.83449 + 6.29505i) q^{63} +(-4.63711 + 6.51899i) q^{64} +(-6.85435 + 18.8322i) q^{65} +(11.9809 - 4.39813i) q^{66} +(2.23927 - 2.66866i) q^{67} +(1.84155 + 0.385001i) q^{68} +(0.694708 - 4.41723i) q^{69} +(-9.87466 + 6.78543i) q^{70} +(-1.77382 + 3.07235i) q^{71} +(8.48483 + 0.0871146i) q^{72} +7.47691 q^{73} +(3.38720 + 1.29373i) q^{74} +(1.74597 + 8.93050i) q^{75} +(-4.56700 - 13.8975i) q^{76} +(13.3401 + 3.47500i) q^{77} +(15.3303 - 0.0422692i) q^{78} +(2.97392 + 3.54418i) q^{79} +(-0.807999 + 12.7830i) q^{80} +(-5.06508 - 7.43942i) q^{81} +(-6.72517 - 4.02560i) q^{82} +(-1.16631 - 6.61447i) q^{83} +(7.47569 + 5.30227i) q^{84} +(2.83053 - 1.03023i) q^{85} +(2.61817 + 7.56262i) q^{86} +(9.52178 + 10.9296i) q^{87} +(11.7249 - 8.92790i) q^{88} +(1.04925 + 0.605782i) q^{89} +(11.6181 - 7.04174i) q^{90} +(13.6299 + 9.40288i) q^{91} +(-0.735684 - 5.11059i) q^{92} +(0.627775 + 1.63012i) q^{93} +(0.771903 - 4.00685i) q^{94} +(-17.9419 - 15.0550i) q^{95} +(9.39247 - 2.78952i) q^{96} +(-1.28566 + 1.07880i) q^{97} +(3.36868 + 9.30871i) q^{98} +(-14.8764 - 4.79797i) 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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