LMFDB - Embedded newform 804.2.e.a.535.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.14
Character	$\chi$	$=$	804.535
Dual form			804.2.e.a.535.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483740 + 1.32891i) q^{2} -1.00000 q^{3} +(-1.53199 - 1.28569i) q^{4} -3.80010i q^{5} +(0.483740 - 1.32891i) q^{6} +0.504221 q^{7} +(2.44965 - 1.41393i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.483740 + 1.32891i) q^{2} -1.00000 q^{3} +(-1.53199 - 1.28569i) q^{4} -3.80010i q^{5} +(0.483740 - 1.32891i) q^{6} +0.504221 q^{7} +(2.44965 - 1.41393i) q^{8} +1.00000 q^{9} +(5.04998 + 1.83826i) q^{10} +0.340071 q^{11} +(1.53199 + 1.28569i) q^{12} -4.62451i q^{13} +(-0.243912 + 0.670063i) q^{14} +3.80010i q^{15} +(0.693993 + 3.93934i) q^{16} -5.54179 q^{17} +(-0.483740 + 1.32891i) q^{18} +5.66175i q^{19} +(-4.88575 + 5.82171i) q^{20} -0.504221 q^{21} +(-0.164506 + 0.451923i) q^{22} -2.26733i q^{23} +(-2.44965 + 1.41393i) q^{24} -9.44073 q^{25} +(6.14555 + 2.23706i) q^{26} -1.00000 q^{27} +(-0.772462 - 0.648273i) q^{28} +2.67950 q^{29} +(-5.04998 - 1.83826i) q^{30} -3.48870 q^{31} +(-5.57073 - 0.983362i) q^{32} -0.340071 q^{33} +(2.68078 - 7.36452i) q^{34} -1.91609i q^{35} +(-1.53199 - 1.28569i) q^{36} +3.22313 q^{37} +(-7.52395 - 2.73882i) q^{38} +4.62451i q^{39} +(-5.37309 - 9.30891i) q^{40} -5.82399i q^{41} +(0.243912 - 0.670063i) q^{42} -10.1339 q^{43} +(-0.520986 - 0.437226i) q^{44} -3.80010i q^{45} +(3.01308 + 1.09680i) q^{46} -4.07078i q^{47} +(-0.693993 - 3.93934i) q^{48} -6.74576 q^{49} +(4.56686 - 12.5459i) q^{50} +5.54179 q^{51} +(-5.94570 + 7.08471i) q^{52} +2.30104i q^{53} +(0.483740 - 1.32891i) q^{54} -1.29230i q^{55} +(1.23517 - 0.712935i) q^{56} -5.66175i q^{57} +(-1.29618 + 3.56081i) q^{58} +4.68692i q^{59} +(4.88575 - 5.82171i) q^{60} +5.81766i q^{61} +(1.68762 - 4.63616i) q^{62} +0.504221 q^{63} +(4.00158 - 6.92729i) q^{64} -17.5736 q^{65} +(0.164506 - 0.451923i) q^{66} +(1.18570 + 8.09902i) q^{67} +(8.48997 + 7.12503i) q^{68} +2.26733i q^{69} +(2.54631 + 0.926889i) q^{70} -9.21056i q^{71} +(2.44965 - 1.41393i) q^{72} +10.5523 q^{73} +(-1.55916 + 4.28324i) q^{74} +9.44073 q^{75} +(7.27927 - 8.67376i) q^{76} +0.171471 q^{77} +(-6.14555 - 2.23706i) q^{78} -9.58435 q^{79} +(14.9699 - 2.63724i) q^{80} +1.00000 q^{81} +(7.73954 + 2.81730i) q^{82} -16.5312i q^{83} +(0.772462 + 0.648273i) q^{84} +21.0593i q^{85} +(4.90216 - 13.4670i) q^{86} -2.67950 q^{87} +(0.833055 - 0.480838i) q^{88} -9.37374 q^{89} +(5.04998 + 1.83826i) q^{90} -2.33178i q^{91} +(-2.91509 + 3.47354i) q^{92} +3.48870 q^{93} +(5.40969 + 1.96920i) q^{94} +21.5152 q^{95} +(5.57073 + 0.983362i) q^{96} +0.449792i q^{97} +(3.26320 - 8.96449i) q^{98} +0.340071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.483740	+	1.32891i	−0.342056	+	0.939680i
$2$	−0.483740	+	1.32891i	−0.342056	+	0.939680i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.53199	−	1.28569i	−0.765996	−	0.642846i
$5$		−	3.80010i		−	1.69945i	−0.527222	−	0.849727i	$-0.676767\pi$
$5$		−	3.80010i		−	1.69945i	0.527222	−	0.849727i	$-0.323233\pi$
$6$	0.483740	−	1.32891i	0.197486	−	0.542524i
$7$	0.504221			0.190578			0.0952888	−	0.995450i	$-0.469623\pi$
$7$	0.504221			0.190578			0.0952888	+	0.995450i	$0.469623\pi$
$8$	2.44965	−	1.41393i	0.866082	−	0.499901i
$9$	1.00000			0.333333
$10$	5.04998	+	1.83826i	1.59694	+	0.581308i
$11$	0.340071			0.102535			0.0512676	−	0.998685i	$-0.483674\pi$
$11$	0.340071			0.102535			0.0512676	+	0.998685i	$0.483674\pi$
$12$	1.53199	+	1.28569i	0.442248	+	0.371147i
$13$		−	4.62451i		−	1.28261i	−0.767287	−	0.641304i	$-0.778394\pi$
$13$		−	4.62451i		−	1.28261i	0.767287	−	0.641304i	$-0.221606\pi$
$14$	−0.243912	+	0.670063i	−0.0651882	+	0.179082i
$15$			3.80010i			0.981181i
$16$	0.693993	+	3.93934i	0.173498	+	0.984834i
$17$	−5.54179			−1.34408			−0.672040	−	0.740514i	$-0.734582\pi$
$17$	−5.54179			−1.34408			−0.672040	+	0.740514i	$0.734582\pi$
$18$	−0.483740	+	1.32891i	−0.114019	+	0.313227i
$19$			5.66175i			1.29890i	0.760406	+	0.649448i	$0.225000\pi$
$19$			5.66175i			1.29890i	−0.760406	+	0.649448i	$0.775000\pi$
$20$	−4.88575	+	5.82171i	−1.09249	+	1.30177i
$21$	−0.504221			−0.110030
$22$	−0.164506	+	0.451923i	−0.0350728	+	0.0963503i
$23$		−	2.26733i		−	0.472772i	−0.971659	−	0.236386i	$-0.924037\pi$
$23$		−	2.26733i		−	0.472772i	0.971659	−	0.236386i	$-0.0759630\pi$
$24$	−2.44965	+	1.41393i	−0.500033	+	0.288618i
$25$	−9.44073			−1.88815
$26$	6.14555	+	2.23706i	1.20524	+	0.438724i
$27$	−1.00000			−0.192450
$28$	−0.772462	−	0.648273i	−0.145982	−	0.122512i
$29$	2.67950			0.497571			0.248785	−	0.968559i	$-0.419969\pi$
$29$	2.67950			0.497571			0.248785	+	0.968559i	$0.419969\pi$
$30$	−5.04998	−	1.83826i	−0.921995	−	0.335619i
$31$	−3.48870			−0.626589			−0.313295	−	0.949656i	$-0.601433\pi$
$31$	−3.48870			−0.626589			−0.313295	+	0.949656i	$0.601433\pi$
$32$	−5.57073	−	0.983362i	−0.984775	−	0.173836i
$33$	−0.340071			−0.0591987
$34$	2.68078	−	7.36452i	0.459751	−	1.26301i
$35$		−	1.91609i		−	0.323878i
$36$	−1.53199	−	1.28569i	−0.255332	−	0.214282i
$37$	3.22313			0.529879			0.264939	−	0.964265i	$-0.414648\pi$
$37$	3.22313			0.529879			0.264939	+	0.964265i	$0.414648\pi$
$38$	−7.52395	−	2.73882i	−1.22055	−	0.444295i
$39$			4.62451i			0.740514i
$40$	−5.37309	−	9.30891i	−0.849559	−	1.47187i
$41$		−	5.82399i		−	0.909554i	−0.890605	−	0.454777i	$-0.849719\pi$
$41$		−	5.82399i		−	0.909554i	0.890605	−	0.454777i	$-0.150281\pi$
$42$	0.243912	−	0.670063i	0.0376364	−	0.103393i
$43$	−10.1339			−1.54540			−0.772701	−	0.634771i	$-0.781095\pi$
$43$	−10.1339			−1.54540			−0.772701	+	0.634771i	$0.781095\pi$
$44$	−0.520986	−	0.437226i	−0.0785415	−	0.0659143i
$45$		−	3.80010i		−	0.566485i
$46$	3.01308	+	1.09680i	0.444254	+	0.161714i
$47$		−	4.07078i		−	0.593784i	−0.954911	−	0.296892i	$-0.904050\pi$
$47$		−	4.07078i		−	0.593784i	0.954911	−	0.296892i	$-0.0959501\pi$
$48$	−0.693993	−	3.93934i	−0.100169	−	0.568594i
$49$	−6.74576			−0.963680
$50$	4.56686	−	12.5459i	0.645852	−	1.77425i
$51$	5.54179			0.776005
$52$	−5.94570	+	7.08471i	−0.824520	+	0.982472i
$53$			2.30104i			0.316072i	0.987433	+	0.158036i	$0.0505162\pi$
$53$			2.30104i			0.316072i	−0.987433	+	0.158036i	$0.949484\pi$
$54$	0.483740	−	1.32891i	0.0658287	−	0.180841i
$55$		−	1.29230i		−	0.174254i
$56$	1.23517	−	0.712935i	0.165056	−	0.0952700i
$57$		−	5.66175i		−	0.749918i
$58$	−1.29618	+	3.56081i	−0.170197	+	0.467557i
$59$			4.68692i			0.610185i	0.952323	+	0.305092i	$0.0986874\pi$
$59$			4.68692i			0.610185i	−0.952323	+	0.305092i	$0.901313\pi$
$60$	4.88575	−	5.82171i	0.630748	−	0.751580i
$61$			5.81766i			0.744875i	0.928057	+	0.372437i	$0.121478\pi$
$61$			5.81766i			0.744875i	−0.928057	+	0.372437i	$0.878522\pi$
$62$	1.68762	−	4.63616i	0.214329	−	0.588793i
$63$	0.504221			0.0635259
$64$	4.00158	−	6.92729i	0.500198	−	0.865911i
$65$	−17.5736			−2.17973
$66$	0.164506	−	0.451923i	0.0202493	−	0.0556278i
$67$	1.18570	+	8.09902i	0.144856	+	0.989453i
$67$	1.18570	+	8.09902i	0.144856	+	0.989453i
$68$	8.48997	+	7.12503i	1.02956	+	0.864037i
$69$			2.26733i			0.272955i
$70$	2.54631	+	0.926889i	0.304342	+	0.110784i
$71$		−	9.21056i		−	1.09309i	−0.837429	−	0.546546i	$-0.815942\pi$
$71$		−	9.21056i		−	1.09309i	0.837429	−	0.546546i	$-0.184058\pi$
$72$	2.44965	−	1.41393i	0.288694	−	0.166634i
$73$	10.5523			1.23505			0.617525	−	0.786551i	$-0.288135\pi$
$73$	10.5523			1.23505			0.617525	+	0.786551i	$0.288135\pi$
$74$	−1.55916	+	4.28324i	−0.181248	+	0.497916i
$75$	9.44073			1.09012
$76$	7.27927	−	8.67376i	0.834989	−	0.994948i
$77$	0.171471			0.0195409
$78$	−6.14555	−	2.23706i	−0.695846	−	0.253297i
$79$	−9.58435			−1.07832			−0.539162	−	0.842202i	$-0.681259\pi$
$79$	−9.58435			−1.07832			−0.539162	+	0.842202i	$0.681259\pi$
$80$	14.9699	−	2.63724i	1.67368	−	0.294853i
$81$	1.00000			0.111111
$82$	7.73954	+	2.81730i	0.854690	+	0.311118i
$83$		−	16.5312i		−	1.81454i	−0.420554	−	0.907268i	$-0.638164\pi$
$83$		−	16.5312i		−	1.81454i	0.420554	−	0.907268i	$-0.361836\pi$
$84$	0.772462	+	0.648273i	0.0842825	+	0.0707324i
$85$			21.0593i			2.28420i
$86$	4.90216	−	13.4670i	0.528614	−	1.45218i
$87$	−2.67950			−0.287273
$88$	0.833055	−	0.480838i	0.0888040	−	0.0512575i
$89$	−9.37374			−0.993614			−0.496807	−	0.867861i	$-0.665494\pi$
$89$	−9.37374			−0.993614			−0.496807	+	0.867861i	$0.665494\pi$
$90$	5.04998	+	1.83826i	0.532314	+	0.193769i
$91$		−	2.33178i		−	0.244437i
$92$	−2.91509	+	3.47354i	−0.303920	+	0.362141i
$93$	3.48870			0.361761
$94$	5.40969	+	1.96920i	0.557967	+	0.203107i
$95$	21.5152			2.20741
$96$	5.57073	+	0.983362i	0.568560	+	0.100364i
$97$			0.449792i			0.0456695i	0.999739	+	0.0228347i	$0.00726916\pi$
$97$			0.449792i			0.0456695i	−0.999739	+	0.0228347i	$0.992731\pi$
$98$	3.26320	−	8.96449i	0.329632	−	0.905551i
$99$	0.340071			0.0341784
$100$	14.4631	+	12.1379i	1.44631	+	1.21379i
$101$		−	5.32681i		−	0.530038i	−0.964243	−	0.265019i	$-0.914622\pi$
$101$		−	5.32681i		−	0.530038i	0.964243	−	0.265019i	$-0.0853782\pi$
$102$	−2.68078	+	7.36452i	−0.265437	+	0.729196i
$103$			1.81617i			0.178953i	0.995989	+	0.0894763i	$0.0285193\pi$
$103$			1.81617i			0.178953i	−0.995989	+	0.0894763i	$0.971481\pi$
$104$	−6.53875	−	11.3284i	−0.641177	−	1.11084i
$105$			1.91609i			0.186991i
$106$	−3.05787	−	1.11310i	−0.297006	−	0.108114i
$107$		−	3.66598i		−	0.354404i	−0.984175	−	0.177202i	$-0.943295\pi$
$107$		−	3.66598i		−	0.354404i	0.984175	−	0.177202i	$-0.0567045\pi$
$108$	1.53199	+	1.28569i	0.147416	+	0.123716i
$109$			6.47504i			0.620196i	0.950705	+	0.310098i	$0.100362\pi$
$109$			6.47504i			0.620196i	−0.950705	+	0.310098i	$0.899638\pi$
$110$	1.71735	+	0.625138i	0.163743	+	0.0596046i
$111$	−3.22313			−0.305926
$112$	0.349926	+	1.98630i	0.0330649	+	0.187687i
$113$		−	12.8033i		−	1.20444i	−0.798332	−	0.602218i	$-0.794284\pi$
$113$		−	12.8033i		−	1.20444i	0.798332	−	0.602218i	$-0.205716\pi$
$114$	7.52395	+	2.73882i	0.704682	+	0.256514i
$115$	−8.61609			−0.803455
$116$	−4.10497	−	3.44501i	−0.381137	−	0.319861i
$117$		−	4.62451i		−	0.427536i
$118$	−6.22848	−	2.26725i	−0.573378	−	0.208717i
$119$	−2.79429			−0.256152
$120$	5.37309	+	9.30891i	0.490493	+	0.849783i
$121$	−10.8844			−0.989487
$122$	−7.73113	−	2.81423i	−0.699944	−	0.254789i
$123$			5.82399i			0.525131i
$124$	5.34466	+	4.48539i	0.479965	+	0.402800i
$125$			16.8752i			1.50936i
$126$	−0.243912	+	0.670063i	−0.0217294	+	0.0596940i
$127$			13.0192i			1.15527i	0.816295	+	0.577635i	$0.196024\pi$
$127$			13.0192i			1.15527i	−0.816295	+	0.577635i	$0.803976\pi$
$128$	7.27000	+	8.66874i	0.642584	+	0.766216i
$129$	10.1339			0.892238
$130$	8.50105	−	23.3537i	0.745591	−	2.04825i
$131$			18.9830i			1.65855i	0.558840	+	0.829276i	$0.311247\pi$
$131$			18.9830i			1.65855i	−0.558840	+	0.829276i	$0.688753\pi$
$132$	0.520986	+	0.437226i	0.0453460	+	0.0380557i
$133$			2.85478i			0.247540i
$134$	−11.3364	−	2.34213i	−0.979317	−	0.202330i
$135$			3.80010i			0.327060i
$136$	−13.5754	+	7.83572i	−1.16408	+	0.671908i
$137$			0.648578i			0.0554118i	0.999616	+	0.0277059i	$0.00882018\pi$
$137$			0.648578i			0.0554118i	−0.999616	+	0.0277059i	$0.991180\pi$
$138$	−3.01308	−	1.09680i	−0.256490	−	0.0933659i
$139$	−15.1383			−1.28402			−0.642009	−	0.766697i	$-0.721899\pi$
$139$	−15.1383			−1.28402			−0.642009	+	0.766697i	$0.721899\pi$
$140$	−2.46350	+	2.93543i	−0.208204	+	0.248089i
$141$			4.07078i			0.342821i
$142$	12.2400	+	4.45552i	1.02716	+	0.373899i
$143$		−	1.57266i		−	0.131513i
$144$	0.693993	+	3.93934i	0.0578328	+	0.328278i
$145$		−	10.1824i		−	0.845599i
$146$	−5.10456	+	14.0230i	−0.422456	+	1.16055i
$147$	6.74576			0.556381
$148$	−4.93780	−	4.14395i	−0.405885	−	0.340631i
$149$	−16.4646			−1.34883			−0.674414	−	0.738353i	$-0.735604\pi$
$149$	−16.4646			−1.34883			−0.674414	+	0.738353i	$0.735604\pi$
$150$	−4.56686	+	12.5459i	−0.372883	+	1.02437i
$151$		−	22.4874i		−	1.83000i	−0.403459	−	0.914998i	$-0.632192\pi$
$151$		−	22.4874i		−	1.83000i	0.403459	−	0.914998i	$-0.367808\pi$
$152$	8.00535	+	13.8693i	0.649319	+	1.12495i
$153$	−5.54179			−0.448027
$154$	−0.0829473	+	0.227869i	−0.00668409	+	0.0183622i
$155$			13.2574i			1.06486i
$156$	5.94570	−	7.08471i	0.476037	−	0.567231i
$157$	4.28597			0.342058			0.171029	−	0.985266i	$-0.445291\pi$
$157$	4.28597			0.342058			0.171029	+	0.985266i	$0.445291\pi$
$158$	4.63634	−	12.7367i	0.368847	−	1.01328i
$159$		−	2.30104i		−	0.182484i
$160$	−3.73687	+	21.1693i	−0.295426	+	1.67358i
$161$		−	1.14324i		−	0.0900998i
$162$	−0.483740	+	1.32891i	−0.0380062	+	0.104409i
$163$			1.28405i			0.100574i	0.998735	+	0.0502871i	$0.0160136\pi$
$163$			1.28405i			0.100574i	−0.998735	+	0.0502871i	$0.983986\pi$
$164$	−7.48786	+	8.92230i	−0.584703	+	0.696715i
$165$			1.29230i			0.100606i
$166$	21.9684	+	7.99681i	1.70508	+	0.620672i
$167$		−	2.23120i		−	0.172655i	−0.996267	−	0.0863275i	$-0.972487\pi$
$167$		−	2.23120i		−	0.172655i	0.996267	−	0.0863275i	$-0.0275132\pi$
$168$	−1.23517	+	0.712935i	−0.0952951	+	0.0550042i
$169$	−8.38610			−0.645084
$170$	−27.9859	−	10.1872i	−2.14642	−	0.781326i
$171$			5.66175i			0.432965i
$172$	15.5250	+	13.0290i	1.18377	+	0.993455i
$173$	8.76686			0.666532			0.333266	−	0.942833i	$-0.391849\pi$
$173$	8.76686			0.666532			0.333266	+	0.942833i	$0.391849\pi$
$174$	1.29618	−	3.56081i	0.0982633	−	0.269944i
$175$	−4.76022			−0.359839
$176$	0.236007	+	1.33965i	0.0177897	+	0.100980i
$177$		−	4.68692i		−	0.352290i
$178$	4.53445	−	12.4568i	0.339872	−	0.933679i
$179$	18.6985			1.39759			0.698795	−	0.715322i	$-0.253720\pi$
$179$	18.6985			1.39759			0.698795	+	0.715322i	$0.253720\pi$
$180$	−4.88575	+	5.82171i	−0.364162	+	0.433925i
$181$	15.0472			1.11845			0.559225	−	0.829016i	$-0.311099\pi$
$181$	15.0472			1.11845			0.559225	+	0.829016i	$0.311099\pi$
$182$	3.09871	+	1.12797i	0.229692	+	0.0836110i
$183$		−	5.81766i		−	0.430054i
$184$	−3.20586	−	5.55418i	−0.236339	−	0.409460i
$185$		−	12.2482i		−	0.900505i
$186$	−1.68762	+	4.63616i	−0.123743	+	0.339940i
$187$	−1.88460			−0.137816
$188$	−5.23377	+	6.23640i	−0.381712	+	0.454836i
$189$	−0.504221			−0.0366767
$190$	−10.4078	+	28.5917i	−0.755059	+	2.07426i
$191$	−15.4232			−1.11599			−0.557993	−	0.829846i	$-0.688428\pi$
$191$	−15.4232			−1.11599			−0.557993	+	0.829846i	$0.688428\pi$
$192$	−4.00158	+	6.92729i	−0.288789	+	0.499934i
$193$	20.7634			1.49458			0.747291	−	0.664497i	$-0.231354\pi$
$193$	20.7634			1.49458			0.747291	+	0.664497i	$0.231354\pi$
$194$	−0.597733	−	0.217583i	−0.0429147	−	0.0156215i
$195$	17.5736			1.25847
$196$	10.3344	+	8.67297i	0.738175	+	0.619498i
$197$		−	19.2813i		−	1.37374i	−0.726781	−	0.686869i	$-0.758985\pi$
$197$		−	19.2813i		−	1.37374i	0.726781	−	0.686869i	$-0.241015\pi$
$198$	−0.164506	+	0.451923i	−0.0116909	+	0.0321168i
$199$			3.70408i			0.262575i	0.991344	+	0.131288i	$0.0419112\pi$
$199$			3.70408i			0.262575i	−0.991344	+	0.131288i	$0.958089\pi$
$200$	−23.1265	+	13.3486i	−1.63529	+	0.943886i
$201$	−1.18570	−	8.09902i	−0.0836328	−	0.571261i
$202$	7.07884	+	2.57679i	0.498066	+	0.181302i
$203$	1.35106			0.0948259
$204$	−8.48997	−	7.12503i	−0.594417	−	0.498852i
$205$	−22.1317			−1.54575
$206$	−2.41352	−	0.878554i	−0.168158	−	0.0612118i
$207$		−	2.26733i		−	0.157591i
$208$	18.2175	−	3.20938i	1.26316	−	0.222530i
$209$			1.92540i			0.133183i
$210$	−2.54631	−	0.926889i	−0.175712	−	0.0639614i
$211$			8.23671i			0.567039i	0.958967	+	0.283519i	$0.0915020\pi$
$211$			8.23671i			0.567039i	−0.958967	+	0.283519i	$0.908498\pi$
$212$	2.95842	−	3.52517i	0.203185	−	0.242110i
$213$			9.21056i			0.631097i
$214$	4.87175	+	1.77338i	0.333026	+	0.121226i
$215$			38.5097i			2.62634i
$216$	−2.44965	+	1.41393i	−0.166678	+	0.0962060i
$217$	−1.75908			−0.119414
$218$	−8.60473	−	3.13224i	−0.582786	−	0.212142i
$219$	−10.5523			−0.713057
$220$	−1.66150	+	1.97980i	−0.112018	+	0.133478i
$221$			25.6281i			1.72393i
$222$	1.55916	−	4.28324i	0.104644	−	0.287472i
$223$		−	28.5150i		−	1.90951i	−0.297401	−	0.954753i	$-0.596120\pi$
$223$		−	28.5150i		−	1.90951i	0.297401	−	0.954753i	$-0.403880\pi$
$224$	−2.80888	−	0.495832i	−0.187676	−	0.0331292i
$225$	−9.44073			−0.629382
$226$	17.0144	+	6.19348i	1.13178	+	0.411984i
$227$		−	22.6375i		−	1.50250i	−0.660017	−	0.751251i	$-0.729451\pi$
$227$		−	22.6375i		−	1.50250i	0.660017	−	0.751251i	$-0.270549\pi$
$228$	−7.27927	+	8.67376i	−0.482081	+	0.574433i
$229$		−	23.6814i		−	1.56491i	−0.622708	−	0.782455i	$-0.713967\pi$
$229$		−	23.6814i		−	1.56491i	0.622708	−	0.782455i	$-0.286033\pi$
$230$	4.16795	−	11.4500i	0.274826	−	0.754990i
$231$	−0.171471			−0.0112820
$232$	6.56384	−	3.78864i	0.430937	−	0.248736i
$233$			5.29881i			0.347136i	0.984822	+	0.173568i	$0.0555297\pi$
$233$			5.29881i			0.347136i	−0.984822	+	0.173568i	$0.944470\pi$
$234$	6.14555	+	2.23706i	0.401747	+	0.146241i
$235$	−15.4693			−1.00911
$236$	6.02593	−	7.18032i	0.392255	−	0.467399i
$237$	9.58435			0.622571
$238$	1.35171	−	3.71335i	0.0876182	−	0.240701i
$239$	2.32000			0.150068			0.0750341	−	0.997181i	$-0.476093\pi$
$239$	2.32000			0.150068			0.0750341	+	0.997181i	$0.476093\pi$
$240$	−14.9699	+	2.63724i	−0.966300	+	0.170233i
$241$	−3.69645			−0.238109			−0.119055	−	0.992888i	$-0.537986\pi$
$241$	−3.69645			−0.238109			−0.119055	+	0.992888i	$0.537986\pi$
$242$	5.26520	−	14.4643i	0.338460	−	0.929800i
$243$	−1.00000			−0.0641500
$244$	7.47972	−	8.91260i	0.478840	−	0.570571i
$245$			25.6345i			1.63773i
$246$	−7.73954	−	2.81730i	−0.493455	−	0.179624i
$247$	26.1828			1.66597
$248$	−8.54610	+	4.93279i	−0.542678	+	0.313233i
$249$			16.5312i			1.04762i
$250$	−22.4256	−	8.16321i	−1.41832	−	0.516287i
$251$	5.87230			0.370656			0.185328	−	0.982677i	$-0.440665\pi$
$251$	5.87230			0.370656			0.185328	+	0.982677i	$0.440665\pi$
$252$	−0.772462	−	0.648273i	−0.0486605	−	0.0408374i
$253$		−	0.771055i		−	0.0484758i
$254$	−17.3014	−	6.29792i	−1.08558	−	0.395167i
$255$		−	21.0593i		−	1.31879i
$256$	−15.0367	+	5.46775i	−0.939797	+	0.341734i
$257$	19.7965			1.23487			0.617437	−	0.786620i	$-0.288171\pi$
$257$	19.7965			1.23487			0.617437	+	0.786620i	$0.288171\pi$
$258$	−4.90216	+	13.4670i	−0.305195	+	0.838418i
$259$	1.62517			0.100983
$260$	26.9226	+	22.5942i	1.66967	+	1.40123i
$261$	2.67950			0.165857
$262$	−25.2266	−	9.18283i	−1.55851	−	0.567317i
$263$			22.7728i			1.40423i	0.712062	+	0.702116i	$0.247761\pi$
$263$			22.7728i			1.40423i	−0.712062	+	0.702116i	$0.752239\pi$
$264$	−0.833055	+	0.480838i	−0.0512710	+	0.0295935i
$265$	8.74416			0.537150
$266$	−3.79373	−	1.38097i	−0.232609	−	0.0846727i
$267$	9.37374			0.573663
$268$	8.59636	−	13.9321i	0.525106	−	0.851037i
$269$	25.2625			1.54028			0.770142	−	0.637872i	$-0.220185\pi$
$269$	25.2625			1.54028			0.770142	+	0.637872i	$0.220185\pi$
$270$	−5.04998	−	1.83826i	−0.307332	−	0.111873i
$271$	28.1672			1.71103			0.855517	−	0.517774i	$-0.173239\pi$
$271$	28.1672			1.71103			0.855517	+	0.517774i	$0.173239\pi$
$272$	−3.84596	−	21.8310i	−0.233196	−	1.32370i
$273$			2.33178i			0.141125i
$274$	−0.861900	−	0.313743i	−0.0520693	−	0.0189539i
$275$	−3.21052			−0.193601
$276$	2.91509	−	3.47354i	0.175468	−	0.209082i
$277$	−11.1117			−0.667640			−0.333820	−	0.942637i	$-0.608338\pi$
$277$	−11.1117			−0.667640			−0.333820	+	0.942637i	$0.608338\pi$
$278$	7.32302	−	20.1175i	0.439206	−	1.20656i
$279$	−3.48870			−0.208863
$280$	−2.70922	−	4.69375i	−0.161907	−	0.280505i
$281$			17.7385i			1.05819i	0.848563	+	0.529094i	$0.177468\pi$
$281$			17.7385i			1.05819i	−0.848563	+	0.529094i	$0.822532\pi$
$282$	−5.40969	−	1.96920i	−0.322142	−	0.117264i
$283$			1.11568i			0.0663202i	0.999450	+	0.0331601i	$0.0105571\pi$
$283$			1.11568i			0.0663202i	−0.999450	+	0.0331601i	$0.989443\pi$
$284$	−11.8419	+	14.1105i	−0.702690	+	0.837304i
$285$	−21.5152			−1.27445
$286$	2.08992	+	0.760759i	0.123580	+	0.0449846i
$287$		−	2.93658i		−	0.173341i
$288$	−5.57073	−	0.983362i	−0.328258	−	0.0579452i
$289$	13.7114			0.806553
$290$	13.5314	+	4.92561i	0.794592	+	0.289242i
$291$		−	0.449792i		−	0.0263673i
$292$	−16.1660	−	13.5670i	−0.946043	−	0.793947i
$293$	14.1069			0.824134			0.412067	−	0.911154i	$-0.364807\pi$
$293$	14.1069			0.824134			0.412067	+	0.911154i	$0.364807\pi$
$294$	−3.26320	+	8.96449i	−0.190313	+	0.522820i
$295$	17.8107			1.03698
$296$	7.89554	−	4.55729i	0.458919	−	0.264887i
$297$	−0.340071			−0.0197329
$298$	7.96456	−	21.8799i	0.461375	−	1.26747i
$299$	−10.4853			−0.606381
$300$	−14.4631	−	12.1379i	−0.835028	−	0.700780i
$301$	−5.10971			−0.294519
$302$	29.8836	+	10.8780i	1.71961	+	0.625961i
$303$			5.32681i			0.306017i
$304$	−22.3036	+	3.92922i	−1.27920	+	0.225356i
$305$	22.1077			1.26588
$306$	2.68078	−	7.36452i	0.153250	−	0.421002i
$307$		−	9.22285i		−	0.526376i	−0.964745	−	0.263188i	$-0.915226\pi$
$307$		−	9.22285i		−	0.526376i	0.964745	−	0.263188i	$-0.0847739\pi$
$308$	−0.262692	−	0.220459i	−0.0149683	−	0.0125618i
$309$		−	1.81617i		−	0.103318i
$310$	−17.6179	−	6.41314i	−1.00063	−	0.364242i
$311$	−12.4064			−0.703503			−0.351752	−	0.936093i	$-0.614414\pi$
$311$	−12.4064			−0.703503			−0.351752	+	0.936093i	$0.614414\pi$
$312$	6.53875	+	11.3284i	0.370184	+	0.641346i
$313$		−	24.7560i		−	1.39929i	−0.714490	−	0.699646i	$-0.753341\pi$
$313$		−	24.7560i		−	1.39929i	0.714490	−	0.699646i	$-0.246659\pi$
$314$	−2.07330	+	5.69566i	−0.117003	+	0.321425i
$315$		−	1.91609i		−	0.107959i
$316$	14.6831	+	12.3225i	0.825991	+	0.693196i
$317$	−9.58106			−0.538126			−0.269063	−	0.963123i	$-0.586714\pi$
$317$	−9.58106			−0.538126			−0.269063	+	0.963123i	$0.586714\pi$
$318$	3.05787	+	1.11310i	0.171477	+	0.0624198i
$319$	0.911220			0.0510185
$320$	−26.3244	−	15.2064i	−1.47158	−	0.850063i
$321$			3.66598i			0.204615i
$322$	1.51926	+	0.553030i	0.0846649	+	0.0308192i
$323$		−	31.3762i		−	1.74582i
$324$	−1.53199	−	1.28569i	−0.0851106	−	0.0714273i
$325$			43.6588i			2.42175i
$326$	−1.70638	−	0.621144i	−0.0945075	−	0.0344020i
$327$		−	6.47504i		−	0.358070i
$328$	−8.23474	−	14.2667i	−0.454687	−	0.787749i
$329$		−	2.05257i		−	0.113162i
$330$	−1.71735	−	0.625138i	−0.0945370	−	0.0344127i
$331$	5.90506			0.324572			0.162286	−	0.986744i	$-0.448113\pi$
$331$	5.90506			0.324572			0.162286	+	0.986744i	$0.448113\pi$
$332$	−21.2540	+	25.3257i	−1.16647	+	1.38993i
$333$	3.22313			0.176626
$334$	2.96505	+	1.07932i	0.162240	+	0.0590577i
$335$	30.7771	−	4.50577i	1.68153	−	0.246177i
$336$	−0.349926	−	1.98630i	−0.0190900	−	0.108361i
$337$			30.3217i			1.65173i	0.563869	+	0.825864i	$0.309312\pi$
$337$			30.3217i			1.65173i	−0.563869	+	0.825864i	$0.690688\pi$
$338$	4.05669	−	11.1443i	0.220655	−	0.606173i
$339$			12.8033i			0.695381i
$340$	27.0758	−	32.2627i	1.46839	−	1.74969i
$341$	−1.18641			−0.0642475
$342$	−7.52395	−	2.73882i	−0.406848	−	0.148098i
$343$	−6.93090			−0.374234
$344$	−24.8245	+	14.3286i	−1.33845	+	0.772548i
$345$	8.61609			0.463875
$346$	−4.24088	+	11.6504i	−0.227991	+	0.626327i
$347$	25.4209			1.36466			0.682331	−	0.731043i	$-0.260966\pi$
$347$	25.4209			1.36466			0.682331	+	0.731043i	$0.260966\pi$
$348$	4.10497	+	3.44501i	0.220049	+	0.184672i
$349$	28.2378			1.51154			0.755768	−	0.654840i	$-0.227264\pi$
$349$	28.2378			1.51154			0.755768	+	0.654840i	$0.227264\pi$
$350$	2.30271	−	6.32589i	0.123085	−	0.338133i
$351$			4.62451i			0.246838i
$352$	−1.89444	−	0.334413i	−0.100974	−	0.0178243i
$353$		−	3.21842i		−	0.171299i	−0.996325	−	0.0856496i	$-0.972703\pi$
$353$		−	3.21842i		−	0.171299i	0.996325	−	0.0856496i	$-0.0272965\pi$
$354$	6.22848	+	2.26725i	0.331040	+	0.120503i
$355$	−35.0010			−1.85766
$356$	14.3605	+	12.0517i	0.761104	+	0.638741i
$357$	2.79429			0.147889
$358$	−9.04520	+	24.8485i	−0.478054	+	1.31329i
$359$		−	10.2583i		−	0.541410i	−0.962662	−	0.270705i	$-0.912743\pi$
$359$		−	10.2583i		−	0.541410i	0.962662	−	0.270705i	$-0.0872568\pi$
$360$	−5.37309	−	9.30891i	−0.283186	−	0.490623i
$361$	−13.0554			−0.687129
$362$	−7.27894	+	19.9964i	−0.382573	+	1.05099i
$363$	10.8844			0.571280
$364$	−2.99795	+	3.57226i	−0.157135	+	0.187237i
$365$		−	40.0997i		−	2.09891i
$366$	7.73113	+	2.81423i	0.404113	+	0.147102i
$367$	10.4326			0.544577			0.272288	−	0.962216i	$-0.412220\pi$
$367$	10.4326			0.544577			0.272288	+	0.962216i	$0.412220\pi$
$368$	8.93180	−	1.57352i	0.465602	−	0.0820251i
$369$		−	5.82399i		−	0.303185i
$370$	16.2767	+	5.92494i	0.846186	+	0.308023i
$371$			1.16023i			0.0602362i
$372$	−5.34466	−	4.48539i	−0.277108	−	0.232557i
$373$		−	18.9000i		−	0.978603i	−0.872115	−	0.489301i	$-0.837252\pi$
$373$		−	18.9000i		−	0.978603i	0.872115	−	0.489301i	$-0.162748\pi$
$374$	0.911657	−	2.50446i	0.0471406	−	0.129503i
$375$		−	16.8752i		−	0.871432i
$376$	−5.75581	−	9.97199i	−0.296833	−	0.514266i
$377$		−	12.3914i		−	0.638188i
$378$	0.243912	−	0.670063i	0.0125455	−	0.0344643i
$379$	−37.2326			−1.91251			−0.956255	−	0.292536i	$-0.905501\pi$
$379$	−37.2326			−1.91251			−0.956255	+	0.292536i	$0.905501\pi$
$380$	−32.9611	−	27.6619i	−1.69087	−	1.41903i
$381$		−	13.0192i		−	0.666995i
$382$	7.46083	−	20.4960i	0.381729	−	1.04867i
$383$	−27.8686			−1.42402			−0.712009	−	0.702171i	$-0.752214\pi$
$383$	−27.8686			−1.42402			−0.712009	+	0.702171i	$0.752214\pi$
$384$	−7.27000	−	8.66874i	−0.370996	−	0.442375i
$385$		−	0.651606i		−	0.0332089i
$386$	−10.0441	+	27.5926i	−0.511230	+	1.40443i
$387$	−10.1339			−0.515134
$388$	0.578294	−	0.689078i	0.0293584	−	0.0349826i
$389$	−31.7538			−1.60998			−0.804990	−	0.593288i	$-0.797829\pi$
$389$	−31.7538			−1.60998			−0.804990	+	0.593288i	$0.797829\pi$
$390$	−8.50105	+	23.3537i	−0.430467	+	1.18256i
$391$			12.5651i			0.635444i
$392$	−16.5248	+	9.53806i	−0.834626	+	0.481745i
$393$		−	18.9830i		−	0.957565i
$394$	25.6231	+	9.32715i	1.29087	+	0.469895i
$395$			36.4215i			1.83256i
$396$	−0.520986	−	0.437226i	−0.0261805	−	0.0219714i
$397$	30.5857			1.53505			0.767526	−	0.641018i	$-0.221488\pi$
$397$	30.5857			1.53505			0.767526	+	0.641018i	$0.221488\pi$
$398$	−4.92238	−	1.79181i	−0.246737	−	0.0898154i
$399$		−	2.85478i		−	0.142918i
$400$	−6.55180	−	37.1902i	−0.327590	−	1.85951i
$401$			1.33382i			0.0666076i	0.999445	+	0.0333038i	$0.0106029\pi$
$401$			1.33382i			0.0666076i	−0.999445	+	0.0333038i	$0.989397\pi$
$402$	11.3364	+	2.34213i	0.565409	+	0.116815i
$403$			16.1335i			0.803669i
$404$	−6.84864	+	8.16063i	−0.340732	+	0.406006i
$405$		−	3.80010i		−	0.188828i
$406$	−0.653562	+	1.79543i	−0.0324357	+	0.0891059i
$407$	1.09609			0.0543313
$408$	13.5754	−	7.83572i	0.672085	−	0.387926i
$409$		−	17.0811i		−	0.844607i	−0.906454	−	0.422304i	$-0.861222\pi$
$409$		−	17.0811i		−	0.844607i	0.906454	−	0.422304i	$-0.138778\pi$
$410$	10.7060	−	29.4110i	0.528732	−	1.45251i
$411$		−	0.648578i		−	0.0319920i
$412$	2.33503	−	2.78236i	0.115039	−	0.137077i
$413$			2.36324i			0.116288i
$414$	3.01308	+	1.09680i	0.148085	+	0.0539048i
$415$	−62.8202			−3.08372
$416$	−4.54757	+	25.7619i	−0.222963	+	1.26308i
$417$	15.1383			0.741328
$418$	−2.55868	−	0.931392i	−0.125149	−	0.0455559i
$419$		−	30.8172i		−	1.50552i	−0.658295	−	0.752760i	$-0.728722\pi$
$419$		−	30.8172i		−	1.50552i	0.658295	−	0.752760i	$-0.271278\pi$
$420$	2.46350	−	2.93543i	0.120206	−	0.143234i
$421$	−10.1332			−0.493861			−0.246930	−	0.969033i	$-0.579422\pi$
$421$	−10.1332			−0.493861			−0.246930	+	0.969033i	$0.579422\pi$
$422$	−10.9458	−	3.98443i	−0.532835	−	0.193959i
$423$		−	4.07078i		−	0.197928i
$424$	3.25351	+	5.63674i	0.158005	+	0.273744i
$425$	52.3185			2.53782
$426$	−12.2400	−	4.45552i	−0.593029	−	0.215871i
$427$			2.93339i			0.141957i
$428$	−4.71332	+	5.61625i	−0.227827	+	0.271472i
$429$			1.57266i			0.0759288i
$430$	−51.1758	−	18.6287i	−2.46792	−	0.898355i
$431$		−	21.3334i		−	1.02759i	−0.857912	−	0.513797i	$-0.828238\pi$
$431$		−	21.3334i		−	1.02759i	0.857912	−	0.513797i	$-0.171762\pi$
$432$	−0.693993	−	3.93934i	−0.0333898	−	0.189531i
$433$		−	35.9047i		−	1.72547i	−0.505655	−	0.862736i	$-0.668749\pi$
$433$		−	35.9047i		−	1.72547i	0.505655	−	0.862736i	$-0.331251\pi$
$434$	0.850936	−	2.33765i	0.0408462	−	0.112211i
$435$			10.1824i			0.488207i
$436$	8.32490	−	9.91970i	0.398691	−	0.475067i
$437$	12.8371			0.614081
$438$	5.10456	−	14.0230i	0.243905	−	0.670045i
$439$		−	15.4552i		−	0.737638i	−0.929501	−	0.368819i	$-0.879762\pi$
$439$		−	15.4552i		−	0.737638i	0.929501	−	0.368819i	$-0.120238\pi$
$440$	−1.82723	−	3.16569i	−0.0871098	−	0.150918i
$441$	−6.74576			−0.321227
$442$	−34.0573	−	12.3973i	−1.61994	−	0.589680i
$443$	0.526859			0.0250318			0.0125159	−	0.999922i	$-0.496016\pi$
$443$	0.526859			0.0250318			0.0125159	+	0.999922i	$0.496016\pi$
$444$	4.93780	+	4.14395i	0.234338	+	0.196663i
$445$			35.6211i			1.68860i
$446$	37.8938	+	13.7938i	1.79432	+	0.653158i
$447$	16.4646			0.778747
$448$	2.01768	−	3.49289i	0.0953265	−	0.165023i
$449$	8.56014			0.403978			0.201989	−	0.979388i	$-0.435259\pi$
$449$	8.56014			0.403978			0.201989	+	0.979388i	$0.435259\pi$
$450$	4.56686	−	12.5459i	0.215284	−	0.591418i
$451$		−	1.98057i		−	0.0932613i
$452$	−16.4611	+	19.6146i	−0.774267	+	0.922592i
$453$			22.4874i			1.05655i
$454$	30.0831	+	10.9506i	1.41187	+	0.513939i
$455$	−8.86097			−0.415409
$456$	−8.00535	−	13.8693i	−0.374885	−	0.649490i
$457$	38.8655			1.81805			0.909025	−	0.416741i	$-0.136828\pi$
$457$	38.8655			1.81805			0.909025	+	0.416741i	$0.136828\pi$
$458$	31.4704	+	11.4556i	1.47051	+	0.535286i
$459$	5.54179			0.258668
$460$	13.1998	+	11.0776i	0.615443	+	0.516498i
$461$	36.1291			1.68270			0.841350	−	0.540491i	$-0.181761\pi$
$461$	36.1291			1.68270			0.841350	+	0.540491i	$0.181761\pi$
$462$	0.0829473	−	0.227869i	0.00385906	−	0.0106014i
$463$	−34.8790			−1.62097			−0.810483	−	0.585762i	$-0.800795\pi$
$463$	−34.8790			−1.62097			−0.810483	+	0.585762i	$0.800795\pi$
$464$	1.85955	+	10.5555i	0.0863277	+	0.490025i
$465$		−	13.2574i		−	0.614797i
$466$	−7.04163	−	2.56325i	−0.326197	−	0.118740i
$467$		−	4.62628i		−	0.214079i	−0.994255	−	0.107039i	$-0.965863\pi$
$467$		−	4.62628i		−	0.214079i	0.994255	−	0.107039i	$-0.0341371\pi$
$468$	−5.94570	+	7.08471i	−0.274840	+	0.327491i
$469$	0.597855	+	4.08370i	0.0276064	+	0.188568i
$470$	7.48314	−	20.5573i	0.345172	−	0.948239i
$471$	−4.28597			−0.197487
$472$	6.62699	+	11.4813i	0.305032	+	0.528471i
$473$	−3.44624			−0.158458
$474$	−4.63634	+	12.7367i	−0.212954	+	0.585017i
$475$		−	53.4511i		−	2.45250i
$476$	4.28082	+	3.59259i	0.196211	+	0.164666i
$477$			2.30104i			0.105357i
$478$	−1.12228	+	3.08307i	−0.0513317	+	0.141016i
$479$		−	4.21394i		−	0.192540i	−0.995355	−	0.0962700i	$-0.969309\pi$
$479$		−	4.21394i		−	0.192540i	0.995355	−	0.0962700i	$-0.0306912\pi$
$480$	3.73687	−	21.1693i	0.170564	−	0.966242i
$481$		−	14.9054i		−	0.679627i
$482$	1.78812	−	4.91224i	0.0814467	−	0.223747i
$483$			1.14324i			0.0520191i
$484$	16.6747	+	13.9939i	0.757942	+	0.636087i
$485$	1.70925			0.0776132
$486$	0.483740	−	1.32891i	0.0219429	−	0.0602805i
$487$	19.4897			0.883161			0.441580	−	0.897222i	$-0.354418\pi$
$487$	19.4897			0.883161			0.441580	+	0.897222i	$0.354418\pi$
$488$	8.22578	+	14.2512i	0.372364	+	0.645123i
$489$		−	1.28405i		−	0.0580665i
$490$	−34.0659	−	12.4005i	−1.53894	−	0.560195i
$491$			10.2182i			0.461142i	0.973055	+	0.230571i	$0.0740594\pi$
$491$			10.2182i			0.461142i	−0.973055	+	0.230571i	$0.925941\pi$
$492$	7.48786	−	8.92230i	0.337579	−	0.402248i
$493$	−14.8492			−0.668775
$494$	−12.6657	+	34.7946i	−0.569856	+	1.56548i
$495$		−	1.29230i		−	0.0580847i
$496$	−2.42113	−	13.7432i	−0.108712	−	0.617086i
$497$		−	4.64416i		−	0.208319i
$498$	−21.9684	−	7.99681i	−0.984429	−	0.358345i
$499$	38.0177			1.70191			0.850954	−	0.525241i	$-0.176025\pi$
$499$	38.0177			1.70191			0.850954	+	0.525241i	$0.176025\pi$
$500$	21.6963	−	25.8527i	0.970289	−	1.15617i
$501$			2.23120i			0.0996825i
$502$	−2.84066	+	7.80374i	−0.126785	+	0.348298i
$503$	−22.0210			−0.981867			−0.490933	−	0.871197i	$-0.663344\pi$
$503$	−22.0210			−0.981867			−0.490933	+	0.871197i	$0.663344\pi$
$504$	1.23517	−	0.712935i	0.0550187	−	0.0317567i
$505$	−20.2424			−0.900775
$506$	1.02466	+	0.372990i	0.0455517	+	0.0165814i
$507$	8.38610			0.372440
$508$	16.7387	−	19.9453i	0.742660	−	0.884932i
$509$	−13.9675			−0.619099			−0.309550	−	0.950883i	$-0.600178\pi$
$509$	−13.9675			−0.619099			−0.309550	+	0.950883i	$0.600178\pi$
$510$	27.9859	+	10.1872i	1.23924	+	0.451099i
$511$	5.32068			0.235373
$512$	0.00774800	−	22.6274i	0.000342417	−	1.00000i
$513$		−	5.66175i		−	0.249973i
$514$	−9.57638	+	26.3078i	−0.422396	+	1.16039i
$515$	6.90162			0.304122
$516$	−15.5250	−	13.0290i	−0.683450	−	0.573571i
$517$		−	1.38435i		−	0.0608838i
$518$	−0.786159	+	2.15970i	−0.0345419	+	0.0948918i
$519$	−8.76686			−0.384823
$520$	−43.0492	+	24.8479i	−1.88783	+	1.08965i
$521$		−	24.9200i		−	1.09177i	−0.837862	−	0.545883i	$-0.816194\pi$
$521$		−	24.9200i		−	1.09177i	0.837862	−	0.545883i	$-0.183806\pi$
$522$	−1.29618	+	3.56081i	−0.0567323	+	0.155852i
$523$		−	40.3900i		−	1.76613i	−0.469248	−	0.883066i	$-0.655475\pi$
$523$		−	40.3900i		−	1.76613i	0.469248	−	0.883066i	$-0.344525\pi$
$524$	24.4063	−	29.0818i	1.06619	−	1.27044i
$525$	4.76022			0.207753
$526$	−30.2630	−	11.0161i	−1.31953	−	0.480326i
$527$	19.3336			0.842187
$528$	−0.236007	−	1.33965i	−0.0102709	−	0.0583009i
$529$	17.8592			0.776487
$530$	−4.22990	+	11.6202i	−0.183735	+	0.504748i
$531$			4.68692i			0.203395i
$532$	3.67036	−	4.37349i	0.159130	−	0.189615i
$533$	−26.9331			−1.16660
$534$	−4.53445	+	12.4568i	−0.196225	+	0.539060i
$535$	−13.9311			−0.602293
$536$	14.3560	+	18.1633i	0.620086	+	0.784534i
$537$	−18.6985			−0.806899
$538$	−12.2205	+	33.5716i	−0.526863	+	1.44737i
$539$	−2.29404			−0.0988112
$540$	4.88575	−	5.82171i	0.210249	−	0.250527i
$541$			10.9995i			0.472906i	0.971643	+	0.236453i	$0.0759849\pi$
$541$			10.9995i			0.472906i	−0.971643	+	0.236453i	$0.924015\pi$
$542$	−13.6256	+	37.4316i	−0.585269	+	1.60782i
$543$	−15.0472			−0.645738
$544$	30.8718	+	5.44958i	1.32362	+	0.233649i
$545$	24.6058			1.05400
$546$	−3.09871	−	1.12797i	−0.132613	−	0.0482728i
$547$	−27.1656			−1.16152			−0.580758	−	0.814077i	$-0.697244\pi$
$547$	−27.1656			−1.16152			−0.580758	+	0.814077i	$0.697244\pi$
$548$	0.833871	−	0.993616i	0.0356212	−	0.0424452i
$549$			5.81766i			0.248292i
$550$	1.55306	−	4.26648i	0.0662225	−	0.181923i
$551$			15.1707i			0.646292i
$552$	3.20586	+	5.55418i	0.136451	+	0.236402i
$553$	−4.83263			−0.205504
$554$	5.37520	−	14.7665i	0.228370	−	0.627368i
$555$			12.2482i			0.519907i
$556$	23.1918	+	19.4632i	0.983552	+	0.825425i
$557$	−26.7154			−1.13197			−0.565984	−	0.824416i	$-0.691504\pi$
$557$	−26.7154			−1.13197			−0.565984	+	0.824416i	$0.691504\pi$
$558$	1.68762	−	4.63616i	0.0714428	−	0.196264i
$559$			46.8642i			1.98214i
$560$	7.54812	−	1.32975i	0.318966	−	0.0561923i
$561$	1.88460			0.0795679
$562$	−23.5728	−	8.58081i	−0.994358	−	0.361959i
$563$	−4.60311			−0.193998			−0.0969989	−	0.995284i	$-0.530924\pi$
$563$	−4.60311			−0.193998			−0.0969989	+	0.995284i	$0.530924\pi$
$564$	5.23377	−	6.23640i	0.220381	−	0.262600i
$565$	−48.6539			−2.04688
$566$	−1.48263	−	0.539698i	−0.0623197	−	0.0226852i
$567$	0.504221			0.0211753
$568$	−13.0231	−	22.5627i	−0.546438	−	0.946708i
$569$	−26.9989			−1.13185			−0.565927	−	0.824456i	$-0.691481\pi$
$569$	−26.9989			−1.13185			−0.565927	+	0.824456i	$0.691481\pi$
$570$	10.4078	−	28.5917i	0.435933	−	1.19758i
$571$			42.5338i			1.77998i	0.455978	+	0.889991i	$0.349290\pi$
$571$			42.5338i			1.77998i	−0.455978	+	0.889991i	$0.650710\pi$
$572$	−2.02196	+	2.40930i	−0.0845423	+	0.100738i
$573$	15.4232			0.644315
$574$	3.90244	+	1.42054i	0.162885	+	0.0592922i
$575$			21.4053i			0.892663i
$576$	4.00158	−	6.92729i	0.166733	−	0.288637i
$577$			20.8087i			0.866278i	0.901327	+	0.433139i	$0.142594\pi$
$577$			20.8087i			0.866278i	−0.901327	+	0.433139i	$0.857406\pi$
$578$	−6.63276	+	18.2212i	−0.275886	+	0.757902i
$579$	−20.7634			−0.862897
$580$	−13.0914	+	15.5993i	−0.543590	+	0.647725i
$581$		−	8.33538i		−	0.345810i
$582$	0.597733	+	0.217583i	0.0247768	+	0.00901909i
$583$			0.782516i			0.0324085i
$584$	25.8494	−	14.9202i	1.06966	−	0.617403i
$585$	−17.5736			−0.726578
$586$	−6.82408	+	18.7468i	−0.281900	+	0.774422i
$587$	22.3079			0.920746			0.460373	−	0.887726i	$-0.347716\pi$
$587$	22.3079			0.920746			0.460373	+	0.887726i	$0.347716\pi$
$588$	−10.3344	−	8.67297i	−0.426185	−	0.357667i
$589$		−	19.7522i		−	0.813874i
$590$	−8.61577	+	23.6688i	−0.354706	+	0.974431i
$591$			19.2813i			0.793128i
$592$	2.23683	+	12.6970i	0.0919331	+	0.521843i
$593$		−	16.7245i		−	0.686791i	−0.939191	−	0.343396i	$-0.888423\pi$
$593$		−	16.7245i		−	0.686791i	0.939191	−	0.343396i	$-0.111577\pi$
$594$	0.164506	−	0.451923i	0.00674976	−	0.0185426i
$595$			10.6186i			0.435318i
$596$	25.2235	+	21.1683i	1.03320	+	0.867089i
$597$		−	3.70408i		−	0.151598i
$598$	5.07217	−	13.9340i	0.207416	−	0.569804i
$599$	−34.0386			−1.39078			−0.695391	−	0.718632i	$-0.744769\pi$
$599$	−34.0386			−1.39078			−0.695391	+	0.718632i	$0.744769\pi$
$600$	23.1265	−	13.3486i	0.944135	−	0.544953i
$601$	−20.8952			−0.852334			−0.426167	−	0.904645i	$-0.640136\pi$
$601$	−20.8952			−0.852334			−0.426167	+	0.904645i	$0.640136\pi$
$602$	2.47177	−	6.79034i	0.100742	−	0.276753i
$603$	1.18570	+	8.09902i	0.0482854	+	0.329818i
$604$	−28.9118	+	34.4504i	−1.17641	+	1.40177i
$605$			41.3616i			1.68159i
$606$	−7.07884	−	2.57679i	−0.287558	−	0.104675i
$607$		−	17.6228i		−	0.715286i	−0.933858	−	0.357643i	$-0.883580\pi$
$607$		−	17.6228i		−	0.715286i	0.933858	−	0.357643i	$-0.116420\pi$
$608$	5.56755	−	31.5401i	0.225794	−	1.27912i
$609$	−1.35106			−0.0547477
$610$	−10.6944	+	29.3790i	−0.433002	+	1.18952i
$611$	−18.8254			−0.761592
$612$	8.48997	+	7.12503i	0.343187	+	0.288012i
$613$	−11.6404			−0.470150			−0.235075	−	0.971977i	$-0.575534\pi$
$613$	−11.6404			−0.470150			−0.235075	+	0.971977i	$0.575534\pi$
$614$	12.2563	+	4.46146i	0.494624	+	0.180050i
$615$	22.1317			0.892437
$616$	0.420044	−	0.242449i	0.0169241	−	0.00976853i
$617$	−24.5113			−0.986789			−0.493395	−	0.869806i	$-0.664244\pi$
$617$	−24.5113			−0.986789			−0.493395	+	0.869806i	$0.664244\pi$
$618$	2.41352	+	0.878554i	0.0970861	+	0.0353406i
$619$			12.3130i			0.494903i	0.968900	+	0.247452i	$0.0795931\pi$
$619$			12.3130i			0.494903i	−0.968900	+	0.247452i	$0.920407\pi$
$620$	17.0449	−	20.3102i	0.684541	−	0.815678i
$621$			2.26733i			0.0909850i
$622$	6.00148	−	16.4870i	0.240637	−	0.661068i
$623$	−4.72644			−0.189361
$624$	−18.2175	+	3.20938i	−0.729284	+	0.128478i
$625$	16.9238			0.676950
$626$	32.8984	+	11.9755i	1.31489	+	0.478636i
$627$		−	1.92540i		−	0.0768930i
$628$	−6.56607	−	5.51044i	−0.262015	−	0.219890i
$629$	−17.8619			−0.712200
$630$	2.54631	+	0.926889i	0.101447	+	0.0369281i
$631$	44.6443			1.77726			0.888632	−	0.458622i	$-0.151657\pi$
$631$	44.6443			1.77726			0.888632	+	0.458622i	$0.151657\pi$
$632$	−23.4783	+	13.5516i	−0.933918	+	0.539055i
$633$		−	8.23671i		−	0.327380i
$634$	4.63474	−	12.7323i	0.184069	−	0.505666i
$635$	49.4743			1.96333
$636$	−2.95842	+	3.52517i	−0.117309	+	0.139782i
$637$			31.1958i			1.23602i
$638$	−0.440794	+	1.21093i	−0.0174512	+	0.0479411i
$639$		−	9.21056i		−	0.364364i
$640$	32.9420	−	27.6267i	1.30215	−	1.09204i
$641$		−	21.8812i		−	0.864257i	−0.901812	−	0.432129i	$-0.857763\pi$
$641$		−	21.8812i		−	0.864257i	0.901812	−	0.432129i	$-0.142237\pi$
$642$	−4.87175	−	1.77338i	−0.192273	−	0.0699898i
$643$			0.844350i			0.0332979i	0.999861	+	0.0166490i	$0.00529977\pi$
$643$			0.844350i			0.0332979i	−0.999861	+	0.0166490i	$0.994700\pi$
$644$	−1.46985	+	1.75143i	−0.0579203	+	0.0690160i
$645$		−	38.5097i		−	1.51632i
$646$	41.6961	+	15.1779i	1.64051	+	0.597168i
$647$	−38.2100			−1.50219			−0.751095	−	0.660194i	$-0.770474\pi$
$647$	−38.2100			−1.50219			−0.751095	+	0.660194i	$0.770474\pi$
$648$	2.44965	−	1.41393i	0.0962314	−	0.0555446i
$649$			1.59388i			0.0625654i
$650$	−58.0185	−	21.1195i	−2.27567	−	0.828375i
$651$	1.75908			0.0689437
$652$	1.65089	−	1.96715i	0.0646537	−	0.0770394i
$653$			7.95949i			0.311479i	0.987798	+	0.155740i	$0.0497761\pi$
$653$			7.95949i			0.311479i	−0.987798	+	0.155740i	$0.950224\pi$
$654$	8.60473	+	3.13224i	0.336471	+	0.122480i
$655$	72.1372			2.81863
$656$	22.9427	−	4.04181i	0.895760	−	0.157806i
$657$	10.5523			0.411684
$658$	2.72768	+	0.992911i	0.106336	+	0.0387077i
$659$		−	1.09591i		−	0.0426905i	−0.999772	−	0.0213453i	$-0.993205\pi$
$659$		−	1.09591i		−	0.0426905i	0.999772	−	0.0213453i	$-0.00679493\pi$
$660$	1.66150	−	1.97980i	0.0646739	−	0.0770634i
$661$		−	8.08616i		−	0.314515i	−0.987558	−	0.157258i	$-0.949735\pi$
$661$		−	8.08616i		−	0.314515i	0.987558	−	0.157258i	$-0.0502653\pi$
$662$	−2.85652	+	7.84728i	−0.111022	+	0.304993i
$663$		−	25.6281i		−	0.995311i
$664$	−23.3740	−	40.4957i	−0.907088	−	1.57154i
$665$	10.8484			0.420684
$666$	−1.55916	+	4.28324i	−0.0604161	+	0.165972i
$667$		−	6.07532i		−	0.235237i
$668$	−2.86863	+	3.41817i	−0.110991	+	0.132253i
$669$			28.5150i			1.10245i
$670$	−8.90034	+	43.0795i	−0.343850	+	1.66431i
$671$			1.97842i			0.0763759i
$672$	2.80888	+	0.495832i	0.108355	+	0.0191271i
$673$		−	21.3833i		−	0.824264i	−0.911124	−	0.412132i	$-0.864784\pi$
$673$		−	21.3833i		−	0.824264i	0.911124	−	0.412132i	$-0.135216\pi$
$674$	−40.2948	−	14.6678i	−1.55210	−	0.564984i
$675$	9.44073			0.363374
$676$	12.8474	+	10.7819i	0.494132	+	0.414690i
$677$			35.4808i			1.36364i	0.731520	+	0.681820i	$0.238811\pi$
$677$			35.4808i			1.36364i	−0.731520	+	0.681820i	$0.761189\pi$
$678$	−17.0144	−	6.19348i	−0.653436	−	0.237859i
$679$			0.226795i			0.00870359i
$680$	29.7765	+	51.5880i	1.14188	+	1.97831i
$681$			22.6375i			0.867470i
$682$	0.573912	−	1.57662i	0.0219762	−	0.0603720i
$683$	−1.55508			−0.0595035			−0.0297518	−	0.999557i	$-0.509472\pi$
$683$	−1.55508			−0.0595035			−0.0297518	+	0.999557i	$0.509472\pi$
$684$	7.27927	−	8.67376i	0.278330	−	0.331649i
$685$	2.46466			0.0941698
$686$	3.35276	−	9.21053i	0.128009	−	0.351660i
$687$			23.6814i			0.903501i
$688$	−7.03284	−	39.9207i	−0.268125	−	1.52196i
$689$	10.6412			0.405396
$690$	−4.16795	+	11.4500i	−0.158671	+	0.435894i
$691$		−	11.1474i		−	0.424069i	−0.977262	−	0.212034i	$-0.931991\pi$
$691$		−	11.1474i		−	0.424069i	0.977262	−	0.212034i	$-0.0680089\pi$
$692$	−13.4308	−	11.2715i	−0.510561	−	0.428477i
$693$	0.171471			0.00651364
$694$	−12.2971	+	33.7820i	−0.466791	+	1.28235i
$695$			57.5272i			2.18213i
$696$	−6.56384	+	3.78864i	−0.248802	+	0.143608i
$697$			32.2753i			1.22251i
$698$	−13.6598	+	37.5255i	−0.517030	+	1.42036i
$699$		−	5.29881i		−	0.200419i
$700$	7.29261	+	6.12017i	0.275635	+	0.231321i
$701$			25.9270i			0.979248i	0.871934	+	0.489624i	$0.162866\pi$
$701$			25.9270i			0.979248i	−0.871934	+	0.489624i	$0.837134\pi$
$702$	−6.14555	−	2.23706i	−0.231949	−	0.0844324i
$703$			18.2486i			0.688257i
$704$	1.36082	−	2.35577i	0.0512879	−	0.0887864i
$705$	15.4693			0.582609
$706$	4.27698	+	1.55688i	0.160966	+	0.0585939i
$707$		−	2.68589i		−	0.101013i
$708$	−6.02593	+	7.18032i	−0.226468	+	0.269853i
$709$	−28.4463			−1.06832			−0.534162	−	0.845382i	$-0.679373\pi$
$709$	−28.4463			−1.06832			−0.534162	+	0.845382i	$0.679373\pi$
$710$	16.9314	−	46.5131i	0.635424	−	1.74561i
$711$	−9.58435			−0.359441
$712$	−22.9624	+	13.2538i	−0.860552	+	0.496709i
$713$			7.91005i			0.296234i
$714$	−1.35171	+	3.71335i	−0.0505864	+	0.138969i
$715$	−5.97626			−0.223500
$716$	−28.6459	−	24.0405i	−1.07055	−	0.898435i
$717$	−2.32000			−0.0866420
$718$	13.6323	+	4.96233i	0.508752	+	0.185193i
$719$		−	19.2378i		−	0.717449i	−0.933444	−	0.358724i	$-0.883212\pi$
$719$		−	19.2378i		−	0.717449i	0.933444	−	0.358724i	$-0.116788\pi$
$720$	14.9699	−	2.63724i	0.557894	−	0.0982842i
$721$			0.915751i			0.0341044i
$722$	6.31544	−	17.3495i	0.235036	−	0.645681i
$723$	3.69645			0.137473
$724$	−23.0522	−	19.3461i	−0.856728	−	0.718991i
$725$	−25.2964			−0.939486
$726$	−5.26520	+	14.4643i	−0.195410	+	0.536820i
$727$	−14.4119			−0.534506			−0.267253	−	0.963626i	$-0.586116\pi$
$727$	−14.4119			−0.534506			−0.267253	+	0.963626i	$0.586116\pi$
$728$	−3.29698	−	5.71204i	−0.122194	−	0.211702i
$729$	1.00000			0.0370370
$730$	53.2888	+	19.3978i	1.97231	+	0.717945i
$731$	56.1598			2.07714
$732$	−7.47972	+	8.91260i	−0.276458	+	0.329419i
$733$			34.5142i			1.27481i	0.770528	+	0.637406i	$0.219992\pi$
$733$			34.5142i			1.27481i	−0.770528	+	0.637406i	$0.780008\pi$
$734$	−5.04666	+	13.8640i	−0.186276	+	0.511728i
$735$		−	25.6345i		−	0.945544i
$736$	−2.22961	+	12.6307i	−0.0821846	+	0.465574i
$737$	0.403222	+	2.75424i	0.0148529	+	0.101454i
$738$	7.73954	+	2.81730i	0.284897	+	0.103706i
$739$	38.1448			1.40318			0.701589	−	0.712582i	$-0.252474\pi$
$739$	38.1448			1.40318			0.701589	+	0.712582i	$0.252474\pi$
$740$	−15.7474	+	18.7641i	−0.578886	+	0.689783i
$741$	−26.1828			−0.961851
$742$	−1.54184	−	0.561250i	−0.0566027	−	0.0206042i
$743$			3.37379i			0.123772i	0.998083	+	0.0618862i	$0.0197116\pi$
$743$			3.37379i			0.123772i	−0.998083	+	0.0618862i	$0.980288\pi$
$744$	8.54610	−	4.93279i	0.313315	−	0.180845i
$745$			62.5669i			2.29227i
$746$	25.1163	+	9.14267i	0.919573	+	0.334737i
$747$		−	16.5312i		−	0.604845i
$748$	2.88719	+	2.42302i	0.105566	+	0.0885942i
$749$		−	1.84846i		−	0.0675414i
$750$	22.4256	+	8.16321i	0.818867	+	0.298078i
$751$		−	15.4907i		−	0.565265i	−0.959228	−	0.282632i	$-0.908792\pi$
$751$		−	15.4907i		−	0.565265i	0.959228	−	0.282632i	$-0.0912076\pi$
$752$	16.0362	−	2.82509i	0.584779	−	0.103021i
$753$	−5.87230			−0.213998
$754$	16.4670	+	5.99420i	0.599693	+	0.218296i
$755$	−85.4541			−3.10999
$756$	0.772462	+	0.648273i	0.0280942	+	0.0235775i
$757$		−	1.49878i		−	0.0544739i	−0.999629	−	0.0272370i	$-0.991329\pi$
$757$		−	1.49878i		−	0.0544739i	0.999629	−	0.0272370i	$-0.00867086\pi$
$758$	18.0109	−	49.4787i	0.654185	−	1.79715i
$759$			0.771055i			0.0279875i
$760$	52.7048	−	30.4211i	1.91180	−	1.10349i
$761$	−29.5458			−1.07103			−0.535517	−	0.844524i	$-0.679883\pi$
$761$	−29.5458			−1.07103			−0.535517	+	0.844524i	$0.679883\pi$
$762$	17.3014	+	6.29792i	0.626762	+	0.228150i
$763$			3.26485i			0.118196i
$764$	23.6282	+	19.8295i	0.854840	+	0.717407i
$765$			21.0593i			0.761401i
$766$	13.4811	−	37.0347i	0.487093	−	1.33812i
$767$	21.6747			0.782628
$768$	15.0367	−	5.46775i	0.542592	−	0.197300i
$769$		−	22.9587i		−	0.827914i	−0.910297	−	0.413957i	$-0.864146\pi$
$769$		−	22.9587i		−	0.827914i	0.910297	−	0.413957i	$-0.135854\pi$
$770$	0.865924	+	0.315208i	0.0312057	+	0.0113593i
$771$	−19.7965			−0.712955
$772$	−31.8093	−	26.6953i	−1.14484	−	0.960786i
$773$	−22.3753			−0.804784			−0.402392	−	0.915468i	$-0.631821\pi$
$773$	−22.3753			−0.804784			−0.402392	+	0.915468i	$0.631821\pi$
$774$	4.90216	−	13.4670i	0.176205	−	0.484061i
$775$	32.9359			1.18309
$776$	0.635977	+	1.10183i	0.0228302	+	0.0395535i
$777$	−1.62517			−0.0583026
$778$	15.3606	−	42.1978i	0.550703	−	1.51287i
$779$	32.9740			1.18142
$780$	−26.9226	−	22.5942i	−0.963983	−	0.809003i
$781$		−	3.13224i		−	0.112080i
$782$	−16.6978	−	6.07824i	−0.597114	−	0.217357i
$783$	−2.67950			−0.0957575
$784$	−4.68151	−	26.5738i	−0.167197	−	0.949065i
$785$		−	16.2871i		−	0.581312i
$786$	25.2266	+	9.18283i	0.899804	+	0.327541i
$787$	39.1227			1.39457			0.697287	−	0.716792i	$-0.254390\pi$
$787$	39.1227			1.39457			0.697287	+	0.716792i	$0.254390\pi$
$788$	−24.7899	+	29.5388i	−0.883102	+	1.05228i
$789$		−	22.7728i		−	0.810734i
$790$	−48.4008	−	17.6185i	−1.72202	−	0.626839i
$791$		−	6.45571i		−	0.229539i
$792$	0.833055	−	0.480838i	0.0296013	−	0.0170858i
$793$	26.9038			0.955383
$794$	−14.7955	+	40.6455i	−0.525073	+	1.44246i
$795$	−8.74416			−0.310123
$796$	4.76231	−	5.67462i	0.168795	−	0.201132i
$797$	−0.464601			−0.0164570			−0.00822850	−	0.999966i	$-0.502619\pi$
$797$	−0.464601			−0.0164570			−0.00822850	+	0.999966i	$0.502619\pi$
$798$	3.79373	+	1.38097i	0.134297	+	0.0488858i
$799$			22.5594i			0.798094i
$800$	52.5917	+	9.28366i	1.85940	+	0.328227i
$801$	−9.37374			−0.331205
$802$	−1.77252	−	0.645221i	−0.0625898	−	0.0227835i
$803$	3.58852			0.126636
$804$	−8.59636	+	13.9321i	−0.303170	+	0.491346i
$805$	−4.34442			−0.153121
$806$	−21.4400	−	7.80444i	−0.755191	−	0.274900i
$807$	−25.2625			−0.889284
$808$	−7.53176	−	13.0488i	−0.264966	−	0.459056i
$809$			40.9908i			1.44116i	0.693373	+	0.720579i	$0.256124\pi$
$809$			40.9908i			1.44116i	−0.693373	+	0.720579i	$0.743876\pi$
$810$	5.04998	+	1.83826i	0.177438	+	0.0645898i
$811$	−38.6909			−1.35862			−0.679310	−	0.733851i	$-0.737721\pi$
$811$	−38.6909			−1.35862			−0.679310	+	0.733851i	$0.737721\pi$
$812$	−2.06981	−	1.73705i	−0.0726362	−	0.0609584i
$813$	−28.1672			−0.987866
$814$	−0.530224	+	1.45660i	−0.0185843	+	0.0510540i
$815$	4.87950			0.170921
$816$	3.84596	+	21.8310i	0.134636	+	0.764237i
$817$		−	57.3755i		−	2.00731i
$818$	22.6992	+	8.26283i	0.793660	+	0.288903i
$819$		−	2.33178i		−	0.0814788i
$820$	33.9056	+	28.4546i	1.18403	+	0.993677i
$821$	45.8043			1.59858			0.799290	−	0.600946i	$-0.205209\pi$
$821$	45.8043			1.59858			0.799290	+	0.600946i	$0.205209\pi$
$822$	0.861900	+	0.313743i	0.0300622	+	0.0109430i
$823$			11.9886i			0.417898i	0.977927	+	0.208949i	$0.0670042\pi$
$823$			11.9886i			0.417898i	−0.977927	+	0.208949i	$0.932996\pi$
$824$	2.56794	+	4.44898i	0.0894586	+	0.154988i
$825$	3.21052			0.111776
$826$	−3.14053	−	1.14320i	−0.109273	−	0.0397769i
$827$		−	26.6854i		−	0.927944i	−0.885850	−	0.463972i	$-0.846424\pi$
$827$		−	26.6854i		−	0.927944i	0.885850	−	0.463972i	$-0.153576\pi$
$828$	−2.91509	+	3.47354i	−0.101307	+	0.120714i
$829$	7.27045			0.252513			0.126257	−	0.991998i	$-0.459704\pi$
$829$	7.27045			0.252513			0.126257	+	0.991998i	$0.459704\pi$
$830$	30.3886	−	83.4822i	1.05480	−	2.89771i
$831$	11.1117			0.385462
$832$	−32.0353	−	18.5054i	−1.11063	−	0.641558i
$833$	37.3836			1.29526
$834$	−7.32302	+	20.1175i	−0.253576	+	0.696611i
$835$	−8.47876			−0.293419
$836$	2.47547	−	2.94969i	0.0856158	−	0.102017i
$837$	3.48870			0.120587
$838$	40.9532	+	14.9075i	1.41471	+	0.514972i
$839$			13.5307i			0.467133i	0.972341	+	0.233566i	$0.0750396\pi$
$839$			13.5307i			0.467133i	−0.972341	+	0.233566i	$0.924960\pi$
$840$	2.70922	+	4.69375i	0.0934771	+	0.161950i
$841$	−21.8203			−0.752423
$842$	4.90182	−	13.4661i	0.168928	−	0.464071i
$843$		−	17.7385i		−	0.610945i
$844$	10.5899	−	12.6186i	0.364519	−	0.434349i
$845$			31.8680i			1.09629i
$846$	5.40969	+	1.96920i	0.185989	+	0.0677024i
$847$	−5.48812			−0.188574
$848$	−9.06456	+	1.59690i	−0.311278	+	0.0548379i
$849$		−	1.11568i		−	0.0382900i
$850$	−25.3086	+	69.5265i	−0.868077	+	2.38474i
$851$		−	7.30791i		−	0.250512i
$852$	11.8419	−	14.1105i	0.405698	−	0.483418i
$853$	5.84027			0.199967			0.0999835	−	0.994989i	$-0.468121\pi$
$853$	5.84027			0.199967			0.0999835	+	0.994989i	$0.468121\pi$
$854$	−3.89820	−	1.41900i	−0.133394	−	0.0485571i
$855$	21.5152			0.735805
$856$	−5.18345	−	8.98037i	−0.177167	−	0.306943i
$857$		−	6.89192i		−	0.235424i	−0.993048	−	0.117712i	$-0.962444\pi$
$857$		−	6.89192i		−	0.235424i	0.993048	−	0.117712i	$-0.0375559\pi$
$858$	−2.08992	−	0.760759i	−0.0713487	−	0.0259719i
$859$			40.0083i			1.36507i	0.730854	+	0.682533i	$0.239122\pi$
$859$			40.0083i			1.36507i	−0.730854	+	0.682533i	$0.760878\pi$
$860$	49.5116	−	58.9965i	1.68833	−	2.01176i
$861$			2.93658i			0.100078i
$862$	28.3501	+	10.3198i	0.965609	+	0.351495i
$863$			37.1959i			1.26616i	0.774085	+	0.633082i	$0.218210\pi$
$863$			37.1959i			1.26616i	−0.774085	+	0.633082i	$0.781790\pi$
$864$	5.57073	+	0.983362i	0.189520	+	0.0334547i
$865$		−	33.3149i		−	1.13274i
$866$	47.7141	+	17.3686i	1.62139	+	0.590208i
$867$	−13.7114			−0.465664
$868$	2.69489	+	2.26163i	0.0914705	+	0.0767647i
$869$	−3.25936			−0.110566
$870$	−13.5314	−	4.92561i	−0.458758	−	0.166994i
$871$	37.4540	−	5.48328i	1.26908	−	0.185794i
$872$	9.15528	+	15.8616i	0.310037	+	0.537141i
$873$			0.449792i			0.0152232i
$874$	−6.20982	+	17.0593i	−0.210050	+	0.577040i
$875$			8.50884i			0.287651i
$876$	16.1660	+	13.5670i	0.546198	+	0.458386i
$877$	−12.4486			−0.420359			−0.210179	−	0.977663i	$-0.567405\pi$
$877$	−12.4486			−0.420359			−0.210179	+	0.977663i	$0.567405\pi$
$878$	20.5386	+	7.47632i	0.693144	+	0.252313i
$879$	−14.1069			−0.475814
$880$	5.09081	−	0.896849i	0.171611	−	0.0302328i
$881$	−19.7625			−0.665817			−0.332908	−	0.942959i	$-0.608030\pi$
$881$	−19.7625			−0.665817			−0.332908	+	0.942959i	$0.608030\pi$
$882$	3.26320	−	8.96449i	0.109877	−	0.301850i
$883$	11.8604			0.399135			0.199567	−	0.979884i	$-0.436046\pi$
$883$	11.8604			0.399135			0.199567	+	0.979884i	$0.436046\pi$
$884$	32.9498	−	39.2619i	1.10822	−	1.32052i
$885$	−17.8107			−0.598702
$886$	−0.254863	+	0.700147i	−0.00856229	+	0.0235219i
$887$			13.2391i			0.444526i	0.974987	+	0.222263i	$0.0713444\pi$
$887$			13.2391i			0.444526i	−0.974987	+	0.222263i	$0.928656\pi$
$888$	−7.89554	+	4.55729i	−0.264957	+	0.152933i
$889$			6.56457i			0.220169i
$890$	−47.3372	−	17.2314i	−1.58674	−	0.577596i
$891$	0.340071			0.0113928
$892$	−36.6615	+	43.6847i	−1.22752	+	1.46267i
$893$	23.0477			0.771263
$894$	−7.96456	+	21.8799i	−0.266375	+	0.731772i
$895$		−	71.0560i		−	2.37514i
$896$	3.66569	+	4.37096i	0.122462	+	0.146024i
$897$	10.4853			0.350094
$898$	−4.14088	+	11.3756i	−0.138183	+	0.379610i
$899$	−9.34797			−0.311772
$900$	14.4631	+	12.1379i	0.482104	+	0.404596i
$901$		−	12.7519i		−	0.424826i
$902$	2.63199	+	0.958081i	0.0876358	+	0.0319006i
$903$	5.10971			0.170041
$904$	−18.1031	−	31.3637i	−0.602099	−	1.04314i
$905$		−	57.1809i		−	1.90076i
$906$	−29.8836	−	10.8780i	−0.992817	−	0.361399i
$907$			0.0597825i			0.00198505i	1.00000		0.000992523i	$0.000315930\pi$
$907$			0.0597825i			0.00198505i	−1.00000		0.000992523i	$0.999684\pi$
$908$	−29.1048	+	34.6804i	−0.965877	+	1.15091i
$909$		−	5.32681i		−	0.176679i
$910$	4.28641	−	11.7754i	0.142093	−	0.390351i
$911$			30.6924i			1.01689i	0.861096	+	0.508443i	$0.169779\pi$
$911$			30.6924i			1.01689i	−0.861096	+	0.508443i	$0.830221\pi$
$912$	22.3036	−	3.92922i	0.738544	−	0.130109i
$913$		−	5.62178i		−	0.186054i
$914$	−18.8008	+	51.6486i	−0.621875	+	1.70839i
$915$	−22.1077			−0.730857
$916$	−30.4470	+	36.2797i	−1.00600	+	1.19871i
$917$			9.57162i			0.316083i
$918$	−2.68078	+	7.36452i	−0.0884791	+	0.243065i
$919$	23.0564			0.760562			0.380281	−	0.924871i	$-0.375827\pi$
$919$	23.0564			0.760562			0.380281	+	0.924871i	$0.375827\pi$
$920$	−21.1064	+	12.1826i	−0.695858	+	0.401648i
$921$			9.22285i			0.303903i
$922$	−17.4771	+	48.0122i	−0.575577	+	1.58120i
$923$	−42.5943			−1.40201
$924$	0.262692	+	0.220459i	0.00864193	+	0.00725256i
$925$	−30.4287			−1.00049
$926$	16.8724	−	46.3510i	0.554461	−	1.52319i
$927$			1.81617i			0.0596508i
$928$	−14.9268	−	2.63492i	−0.489995	−	0.0864954i
$929$		−	49.8286i		−	1.63482i	−0.576053	−	0.817412i	$-0.695408\pi$
$929$		−	49.8286i		−	1.63482i	0.576053	−	0.817412i	$-0.304592\pi$
$930$	17.6179	+	6.41314i	0.577712	+	0.210295i
$931$		−	38.1928i		−	1.25172i
$932$	6.81263	−	8.11772i	0.223155	−	0.265905i
$933$	12.4064			0.406168
$934$	6.14790	+	2.23792i	0.201165	+	0.0732269i
$935$			7.16166i			0.234211i
$936$	−6.53875	−	11.3284i	−0.213726	−	0.370282i
$937$		−	29.8580i		−	0.975419i	−0.873006	−	0.487710i	$-0.837832\pi$
$937$		−	29.8580i		−	0.975419i	0.873006	−	0.487710i	$-0.162168\pi$
$938$	−5.71606	−	1.18095i	−0.186636	−	0.0385595i
$939$			24.7560i			0.807882i
$940$	23.6989	+	19.8888i	0.772973	+	0.648702i
$941$			55.5854i			1.81203i	0.423244	+	0.906016i	$0.360891\pi$
$941$			55.5854i			1.81203i	−0.423244	+	0.906016i	$0.639109\pi$
$942$	2.07330	−	5.69566i	0.0675517	−	0.185575i
$943$	−13.2049			−0.430012
$944$	−18.4634	+	3.25269i	−0.600931	+	0.105866i
$945$			1.91609i			0.0623304i
$946$	1.66708	−	4.57973i	0.0542015	−	0.148900i
$947$		−	3.89342i		−	0.126519i	−0.997997	−	0.0632596i	$-0.979850\pi$
$947$		−	3.89342i		−	0.126519i	0.997997	−	0.0632596i	$-0.0201496\pi$
$948$	−14.6831	−	12.3225i	−0.476886	−	0.400217i
$949$		−	48.7991i		−	1.58409i
$950$	71.0316	+	25.8564i	2.30457	+	0.838894i
$951$	9.58106			0.310687
$952$	−6.84503	+	3.95094i	−0.221849	+	0.128051i
$953$	14.6821			0.475599			0.237799	−	0.971314i	$-0.423574\pi$
$953$	14.6821			0.475599			0.237799	+	0.971314i	$0.423574\pi$
$954$	−3.05787	−	1.11310i	−0.0990020	−	0.0360381i
$955$			58.6098i			1.89657i
$956$	−3.55422	−	2.98280i	−0.114952	−	0.0964708i
$957$	−0.911220			−0.0294556
$958$	5.59994	+	2.03845i	0.180926	+	0.0658594i
$959$			0.327027i			0.0105602i
$960$	26.3244	+	15.2064i	0.849615	+	0.490784i
$961$	−18.8290			−0.607386
$962$	19.8079	+	7.21033i	0.638632	+	0.232471i
$963$		−	3.66598i		−	0.118135i
$964$	5.66293	+	4.75250i	0.182391	+	0.153068i
$965$		−	78.9029i		−	2.53997i
$966$	−1.51926	−	0.553030i	−0.0488813	−	0.0177935i
$967$		−	18.9050i		−	0.607945i	−0.952681	−	0.303973i	$-0.901687\pi$
$967$		−	18.9050i		−	0.607945i	0.952681	−	0.303973i	$-0.0983131\pi$
$968$	−26.6629	+	15.3898i	−0.856977	+	0.494645i
$969$			31.3762i			1.00795i
$970$	−0.826835	+	2.27144i	−0.0265481	+	0.0729316i
$971$			8.48442i			0.272278i	0.990690	+	0.136139i	$0.0434694\pi$
$971$			8.48442i			0.272278i	−0.990690	+	0.136139i	$0.956531\pi$
$972$	1.53199	+	1.28569i	0.0491386	+	0.0412386i
$973$	−7.63307			−0.244705
$974$	−9.42793	+	25.9000i	−0.302090	+	0.829888i
$975$		−	43.6588i		−	1.39820i
$976$	−22.9177	+	4.03742i	−0.733578	+	0.129235i
$977$	−11.8970			−0.380618			−0.190309	−	0.981724i	$-0.560949\pi$
$977$	−11.8970			−0.380618			−0.190309	+	0.981724i	$0.560949\pi$
$978$	1.70638	+	0.621144i	0.0545640	+	0.0198620i
$979$	−3.18773			−0.101880
$980$	32.9581	−	39.2719i	1.05281	−	1.25449i
$981$			6.47504i			0.206732i
$982$	−13.5791	−	4.94297i	−0.433326	−	0.157736i
$983$	38.2523			1.22006			0.610029	−	0.792379i	$-0.291158\pi$
$983$	38.2523			1.22006			0.610029	+	0.792379i	$0.291158\pi$
$984$	8.23474	+	14.2667i	0.262514	+	0.454807i
$985$	−73.2709			−2.33461
$986$	7.18316	−	19.7332i	0.228758	−	0.628434i
$987$			2.05257i			0.0653341i
$988$	−40.1119	−	33.6631i	−1.27613	−	1.07096i
$989$			22.9769i			0.730623i
$990$	1.71735	+	0.625138i	0.0545810	+	0.0198682i
$991$	−3.30855			−0.105100			−0.0525498	−	0.998618i	$-0.516735\pi$
$991$	−3.30855			−0.105100			−0.0525498	+	0.998618i	$0.516735\pi$
$992$	19.4346	+	3.43066i	0.617049	+	0.108923i
$993$	−5.90506			−0.187392
$994$	6.17166	+	2.24657i	0.195753	+	0.0712567i
$995$	14.0759			0.446235
$996$	21.2540	−	25.3257i	0.673460	−	0.802474i
$997$	21.9651			0.695642			0.347821	−	0.937561i	$-0.386922\pi$
$997$	21.9651			0.695642			0.347821	+	0.937561i	$0.386922\pi$
$998$	−18.3907	+	50.5221i	−0.582147	+	1.59925i
$999$	−3.22313			−0.101975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.a.535.14	yes	34
4.3	odd	2		804.2.e.b.535.22	yes	34
67.66	odd	2		804.2.e.b.535.21	yes	34
268.267	even	2	inner	804.2.e.a.535.13	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.13	✓	34	268.267	even	2	inner
804.2.e.a.535.14	yes	34	1.1	even	1	trivial
804.2.e.b.535.21	yes	34	67.66	odd	2
804.2.e.b.535.22	yes	34	4.3	odd	2

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.483740 + 1.32891i) q^{2} -1.00000 q^{3} +(-1.53199 - 1.28569i) q^{4} -3.80010i q^{5} +(0.483740 - 1.32891i) q^{6} +0.504221 q^{7} +(2.44965 - 1.41393i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.483740 + 1.32891i) q^{2} -1.00000 q^{3} +(-1.53199 - 1.28569i) q^{4} -3.80010i q^{5} +(0.483740 - 1.32891i) q^{6} +0.504221 q^{7} +(2.44965 - 1.41393i) q^{8} +1.00000 q^{9} +(5.04998 + 1.83826i) q^{10} +0.340071 q^{11} +(1.53199 + 1.28569i) q^{12} -4.62451i q^{13} +(-0.243912 + 0.670063i) q^{14} +3.80010i q^{15} +(0.693993 + 3.93934i) q^{16} -5.54179 q^{17} +(-0.483740 + 1.32891i) q^{18} +5.66175i q^{19} +(-4.88575 + 5.82171i) q^{20} -0.504221 q^{21} +(-0.164506 + 0.451923i) q^{22} -2.26733i q^{23} +(-2.44965 + 1.41393i) q^{24} -9.44073 q^{25} +(6.14555 + 2.23706i) q^{26} -1.00000 q^{27} +(-0.772462 - 0.648273i) q^{28} +2.67950 q^{29} +(-5.04998 - 1.83826i) q^{30} -3.48870 q^{31} +(-5.57073 - 0.983362i) q^{32} -0.340071 q^{33} +(2.68078 - 7.36452i) q^{34} -1.91609i q^{35} +(-1.53199 - 1.28569i) q^{36} +3.22313 q^{37} +(-7.52395 - 2.73882i) q^{38} +4.62451i q^{39} +(-5.37309 - 9.30891i) q^{40} -5.82399i q^{41} +(0.243912 - 0.670063i) q^{42} -10.1339 q^{43} +(-0.520986 - 0.437226i) q^{44} -3.80010i q^{45} +(3.01308 + 1.09680i) q^{46} -4.07078i q^{47} +(-0.693993 - 3.93934i) q^{48} -6.74576 q^{49} +(4.56686 - 12.5459i) q^{50} +5.54179 q^{51} +(-5.94570 + 7.08471i) q^{52} +2.30104i q^{53} +(0.483740 - 1.32891i) q^{54} -1.29230i q^{55} +(1.23517 - 0.712935i) q^{56} -5.66175i q^{57} +(-1.29618 + 3.56081i) q^{58} +4.68692i q^{59} +(4.88575 - 5.82171i) q^{60} +5.81766i q^{61} +(1.68762 - 4.63616i) q^{62} +0.504221 q^{63} +(4.00158 - 6.92729i) q^{64} -17.5736 q^{65} +(0.164506 - 0.451923i) q^{66} +(1.18570 + 8.09902i) q^{67} +(8.48997 + 7.12503i) q^{68} +2.26733i q^{69} +(2.54631 + 0.926889i) q^{70} -9.21056i q^{71} +(2.44965 - 1.41393i) q^{72} +10.5523 q^{73} +(-1.55916 + 4.28324i) q^{74} +9.44073 q^{75} +(7.27927 - 8.67376i) q^{76} +0.171471 q^{77} +(-6.14555 - 2.23706i) q^{78} -9.58435 q^{79} +(14.9699 - 2.63724i) q^{80} +1.00000 q^{81} +(7.73954 + 2.81730i) q^{82} -16.5312i q^{83} +(0.772462 + 0.648273i) q^{84} +21.0593i q^{85} +(4.90216 - 13.4670i) q^{86} -2.67950 q^{87} +(0.833055 - 0.480838i) q^{88} -9.37374 q^{89} +(5.04998 + 1.83826i) q^{90} -2.33178i q^{91} +(-2.91509 + 3.47354i) q^{92} +3.48870 q^{93} +(5.40969 + 1.96920i) q^{94} +21.5152 q^{95} +(5.57073 + 0.983362i) q^{96} +0.449792i q^{97} +(3.26320 - 8.96449i) q^{98} +0.340071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

Introduction

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