LMFDB - Embedded newform 552.2.f.c.277.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{16} - 2 x^{15} + 5 x^{14} + 2 x^{13} + 6 x^{12} + 24 x^{11} - 12 x^{10} - 88 x^{9} + \cdots + 512 $ x^18 - 4x^16 - 2x^15 + 5x^14 + 2x^13 + 6x^12 + 24x^11 - 12x^10 - 88x^9 - 24x^8 + 96x^7 + 48x^6 + 32x^5 + 160x^4 - 128x^3 - 512*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.18
Root			$0.293513 - 1.38342i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.c.277.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38342 + 0.293513i) q^{2} +1.00000i q^{3} +(1.82770 + 0.812103i) q^{4} -1.32391i q^{5} +(-0.293513 + 1.38342i) q^{6} +0.191941 q^{7} +(2.29011 + 1.65993i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.38342 + 0.293513i) q^{2} +1.00000i q^{3} +(1.82770 + 0.812103i) q^{4} -1.32391i q^{5} +(-0.293513 + 1.38342i) q^{6} +0.191941 q^{7} +(2.29011 + 1.65993i) q^{8} -1.00000 q^{9} +(0.388583 - 1.83152i) q^{10} +2.99907i q^{11} +(-0.812103 + 1.82770i) q^{12} +3.25908i q^{13} +(0.265535 + 0.0563371i) q^{14} +1.32391 q^{15} +(2.68098 + 2.96856i) q^{16} +5.88617 q^{17} +(-1.38342 - 0.293513i) q^{18} -2.93015i q^{19} +(1.07515 - 2.41970i) q^{20} +0.191941i q^{21} +(-0.880265 + 4.14897i) q^{22} -1.00000 q^{23} +(-1.65993 + 2.29011i) q^{24} +3.24727 q^{25} +(-0.956582 + 4.50868i) q^{26} -1.00000i q^{27} +(0.350810 + 0.155876i) q^{28} -10.0792i q^{29} +(1.83152 + 0.388583i) q^{30} -10.0137 q^{31} +(2.83760 + 4.89367i) q^{32} -2.99907 q^{33} +(8.14304 + 1.72767i) q^{34} -0.254112i q^{35} +(-1.82770 - 0.812103i) q^{36} -2.32566i q^{37} +(0.860036 - 4.05362i) q^{38} -3.25908 q^{39} +(2.19760 - 3.03189i) q^{40} -6.73538 q^{41} +(-0.0563371 + 0.265535i) q^{42} +9.95924i q^{43} +(-2.43555 + 5.48140i) q^{44} +1.32391i q^{45} +(-1.38342 - 0.293513i) q^{46} +3.66477 q^{47} +(-2.96856 + 2.68098i) q^{48} -6.96316 q^{49} +(4.49234 + 0.953117i) q^{50} +5.88617i q^{51} +(-2.64671 + 5.95662i) q^{52} -8.44683i q^{53} +(0.293513 - 1.38342i) q^{54} +3.97048 q^{55} +(0.439567 + 0.318609i) q^{56} +2.93015 q^{57} +(2.95837 - 13.9437i) q^{58} -2.35929i q^{59} +(2.41970 + 1.07515i) q^{60} -7.37232i q^{61} +(-13.8532 - 2.93916i) q^{62} -0.191941 q^{63} +(2.48924 + 7.60287i) q^{64} +4.31472 q^{65} +(-4.14897 - 0.880265i) q^{66} -8.74836i q^{67} +(10.7582 + 4.78018i) q^{68} -1.00000i q^{69} +(0.0745851 - 0.351543i) q^{70} -1.06807 q^{71} +(-2.29011 - 1.65993i) q^{72} -15.7994 q^{73} +(0.682611 - 3.21736i) q^{74} +3.24727i q^{75} +(2.37958 - 5.35543i) q^{76} +0.575644i q^{77} +(-4.50868 - 0.956582i) q^{78} +2.11498 q^{79} +(3.93010 - 3.54936i) q^{80} +1.00000 q^{81} +(-9.31786 - 1.97692i) q^{82} -5.07343i q^{83} +(-0.155876 + 0.350810i) q^{84} -7.79273i q^{85} +(-2.92317 + 13.7778i) q^{86} +10.0792 q^{87} +(-4.97825 + 6.86821i) q^{88} +11.7235 q^{89} +(-0.388583 + 1.83152i) q^{90} +0.625551i q^{91} +(-1.82770 - 0.812103i) q^{92} -10.0137i q^{93} +(5.06991 + 1.07566i) q^{94} -3.87924 q^{95} +(-4.89367 + 2.83760i) q^{96} -10.5062 q^{97} +(-9.63297 - 2.04378i) q^{98} -2.99907i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	1.38342	+	0.293513i	0.978225	+	0.207545i
$2$	1.38342	+	0.293513i	0.978225	+	0.207545i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.82770	+	0.812103i	0.913850	+	0.406052i
$5$		−	1.32391i		−	0.592069i	−0.955177	−	0.296034i	$-0.904336\pi$
$5$		−	1.32391i		−	0.592069i	0.955177	−	0.296034i	$-0.0956643\pi$
$6$	−0.293513	+	1.38342i	−0.119826	+	0.564779i
$7$	0.191941			0.0725468			0.0362734	−	0.999342i	$-0.488451\pi$
$7$	0.191941			0.0725468			0.0362734	+	0.999342i	$0.488451\pi$
$8$	2.29011	+	1.65993i	0.809678	+	0.586875i
$9$	−1.00000			−0.333333
$10$	0.388583	−	1.83152i	0.122881	−	0.579177i
$11$			2.99907i			0.904253i	0.891954	+	0.452126i	$0.149334\pi$
$11$			2.99907i			0.904253i	−0.891954	+	0.452126i	$0.850666\pi$
$12$	−0.812103	+	1.82770i	−0.234434	+	0.527612i
$13$			3.25908i			0.903906i	0.892042	+	0.451953i	$0.149273\pi$
$13$			3.25908i			0.903906i	−0.892042	+	0.451953i	$0.850727\pi$
$14$	0.265535	+	0.0563371i	0.0709672	+	0.0150567i
$15$	1.32391			0.341831
$16$	2.68098	+	2.96856i	0.670244	+	0.742141i
$17$	5.88617			1.42761			0.713803	−	0.700347i	$-0.246971\pi$
$17$	5.88617			1.42761			0.713803	+	0.700347i	$0.246971\pi$
$18$	−1.38342	−	0.293513i	−0.326075	−	0.0691817i
$19$		−	2.93015i		−	0.672222i	−0.941822	−	0.336111i	$-0.890888\pi$
$19$		−	2.93015i		−	0.672222i	0.941822	−	0.336111i	$-0.109112\pi$
$20$	1.07515	−	2.41970i	0.240410	−	0.541062i
$21$			0.191941i			0.0418849i
$22$	−0.880265	+	4.14897i	−0.187673	+	0.884563i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	−1.65993	+	2.29011i	−0.338832	+	0.467468i
$25$	3.24727			0.649455
$26$	−0.956582	+	4.50868i	−0.187601	+	0.884224i
$27$		−	1.00000i		−	0.192450i
$28$	0.350810	+	0.155876i	0.0662969	+	0.0294578i
$29$		−	10.0792i		−	1.87165i	−0.352460	−	0.935827i	$-0.614655\pi$
$29$		−	10.0792i		−	1.87165i	0.352460	−	0.935827i	$-0.385345\pi$
$30$	1.83152	+	0.388583i	0.334388	+	0.0709453i
$31$	−10.0137			−1.79852			−0.899259	−	0.437416i	$-0.855894\pi$
$31$	−10.0137			−1.79852			−0.899259	+	0.437416i	$0.855894\pi$
$32$	2.83760	+	4.89367i	0.501622	+	0.865087i
$33$	−2.99907			−0.522071
$34$	8.14304	+	1.72767i	1.39652	+	0.296292i
$35$		−	0.254112i		−	0.0429527i
$36$	−1.82770	−	0.812103i	−0.304617	−	0.135351i
$37$		−	2.32566i		−	0.382336i	−0.981557	−	0.191168i	$-0.938772\pi$
$37$		−	2.32566i		−	0.382336i	0.981557	−	0.191168i	$-0.0612275\pi$
$38$	0.860036	−	4.05362i	0.139516	−	0.657585i
$39$	−3.25908			−0.521871
$40$	2.19760	−	3.03189i	0.347470	−	0.479385i
$41$	−6.73538			−1.05189			−0.525945	−	0.850519i	$-0.676288\pi$
$41$	−6.73538			−1.05189			−0.525945	+	0.850519i	$0.676288\pi$
$42$	−0.0563371	+	0.265535i	−0.00869301	+	0.0409729i
$43$			9.95924i			1.51877i	0.650641	+	0.759385i	$0.274500\pi$
$43$			9.95924i			1.51877i	−0.650641	+	0.759385i	$0.725500\pi$
$44$	−2.43555	+	5.48140i	−0.367173	+	0.826352i
$45$			1.32391i			0.197356i
$46$	−1.38342	−	0.293513i	−0.203974	−	0.0432761i
$47$	3.66477			0.534561			0.267281	−	0.963619i	$-0.413875\pi$
$47$	3.66477			0.534561			0.267281	+	0.963619i	$0.413875\pi$
$48$	−2.96856	+	2.68098i	−0.428475	+	0.386966i
$49$	−6.96316			−0.994737
$50$	4.49234	+	0.953117i	0.635313	+	0.134791i
$51$			5.88617i			0.824229i
$52$	−2.64671	+	5.95662i	−0.367033	+	0.826035i
$53$		−	8.44683i		−	1.16026i	−0.814523	−	0.580131i	$-0.803001\pi$
$53$		−	8.44683i		−	1.16026i	0.814523	−	0.580131i	$-0.196999\pi$
$54$	0.293513	−	1.38342i	0.0399421	−	0.188260i
$55$	3.97048			0.535380
$56$	0.439567	+	0.318609i	0.0587396	+	0.0425759i
$57$	2.93015			0.388108
$58$	2.95837	−	13.9437i	0.388452	−	1.83090i
$59$		−	2.35929i		−	0.307153i	−0.988137	−	0.153577i	$-0.950921\pi$
$59$		−	2.35929i		−	0.307153i	0.988137	−	0.153577i	$-0.0490792\pi$
$60$	2.41970	+	1.07515i	0.312382	+	0.138801i
$61$		−	7.37232i		−	0.943929i	−0.881618	−	0.471964i	$-0.843545\pi$
$61$		−	7.37232i		−	0.943929i	0.881618	−	0.471964i	$-0.156455\pi$
$62$	−13.8532	−	2.93916i	−1.75936	−	0.373274i
$63$	−0.191941			−0.0241823
$64$	2.48924	+	7.60287i	0.311155	+	0.950359i
$65$	4.31472			0.535175
$66$	−4.14897	−	0.880265i	−0.510703	−	0.108353i
$67$		−	8.74836i		−	1.06878i	−0.845237	−	0.534391i	$-0.820541\pi$
$67$		−	8.74836i		−	1.06878i	0.845237	−	0.534391i	$-0.179459\pi$
$68$	10.7582	+	4.78018i	1.30462	+	0.579682i
$69$		−	1.00000i		−	0.120386i
$70$	0.0745851	−	0.351543i	0.00891462	−	0.0420174i
$71$	−1.06807			−0.126757			−0.0633784	−	0.997990i	$-0.520188\pi$
$71$	−1.06807			−0.126757			−0.0633784	+	0.997990i	$0.520188\pi$
$72$	−2.29011	−	1.65993i	−0.269893	−	0.195625i
$73$	−15.7994			−1.84919			−0.924593	−	0.380957i	$-0.875594\pi$
$73$	−15.7994			−1.84919			−0.924593	+	0.380957i	$0.875594\pi$
$74$	0.682611	−	3.21736i	0.0793519	−	0.374011i
$75$			3.24727i			0.374963i
$76$	2.37958	−	5.35543i	0.272957	−	0.614310i
$77$			0.575644i			0.0656007i
$78$	−4.50868	−	0.956582i	−0.510507	−	0.108312i
$79$	2.11498			0.237954			0.118977	−	0.992897i	$-0.462039\pi$
$79$	2.11498			0.237954			0.118977	+	0.992897i	$0.462039\pi$
$80$	3.93010	−	3.54936i	0.439398	−	0.396831i
$81$	1.00000			0.111111
$82$	−9.31786	−	1.97692i	−1.02899	−	0.218315i
$83$		−	5.07343i		−	0.556881i	−0.960453	−	0.278441i	$-0.910182\pi$
$83$		−	5.07343i		−	0.556881i	0.960453	−	0.278441i	$-0.0898175\pi$
$84$	−0.155876	+	0.350810i	−0.0170074	+	0.0382766i
$85$		−	7.79273i		−	0.845241i
$86$	−2.92317	+	13.7778i	−0.315213	+	1.48570i
$87$	10.0792			1.08060
$88$	−4.97825	+	6.86821i	−0.530683	+	0.732153i
$89$	11.7235			1.24269			0.621343	−	0.783539i	$-0.286587\pi$
$89$	11.7235			1.24269			0.621343	+	0.783539i	$0.286587\pi$
$90$	−0.388583	+	1.83152i	−0.0409603	+	0.193059i
$91$			0.625551i			0.0655756i
$92$	−1.82770	−	0.812103i	−0.190551	−	0.0846676i
$93$		−	10.0137i		−	1.03838i
$94$	5.06991	+	1.07566i	0.522922	+	0.110946i
$95$	−3.87924			−0.398002
$96$	−4.89367	+	2.83760i	−0.499458	+	0.289612i
$97$	−10.5062			−1.06674			−0.533371	−	0.845881i	$-0.679075\pi$
$97$	−10.5062			−1.06674			−0.533371	+	0.845881i	$0.679075\pi$
$98$	−9.63297	−	2.04378i	−0.973077	−	0.206453i
$99$		−	2.99907i		−	0.301418i
$100$	5.93504	+	2.63712i	0.593504	+	0.263712i
$101$		−	2.79457i		−	0.278070i	−0.990287	−	0.139035i	$-0.955600\pi$
$101$		−	2.79457i		−	0.278070i	0.990287	−	0.139035i	$-0.0444000\pi$
$102$	−1.72767	+	8.14304i	−0.171065	+	0.806281i
$103$	8.85663			0.872669			0.436335	−	0.899784i	$-0.356276\pi$
$103$	8.85663			0.872669			0.436335	+	0.899784i	$0.356276\pi$
$104$	−5.40986	+	7.46367i	−0.530480	+	0.731873i
$105$	0.254112			0.0247988
$106$	2.47925	−	11.6855i	0.240807	−	1.13500i
$107$			8.81728i			0.852398i	0.904629	+	0.426199i	$0.140148\pi$
$107$			8.81728i			0.852398i	−0.904629	+	0.426199i	$0.859852\pi$
$108$	0.812103	−	1.82770i	0.0781447	−	0.175871i
$109$		−	2.16292i		−	0.207171i	−0.994621	−	0.103585i	$-0.966969\pi$
$109$		−	2.16292i		−	0.207171i	0.994621	−	0.103585i	$-0.0330315\pi$
$110$	5.49284	+	1.16539i	0.523722	+	0.111115i
$111$	2.32566			0.220742
$112$	0.514589	+	0.569789i	0.0486241	+	0.0538400i
$113$	14.5509			1.36883			0.684415	−	0.729093i	$-0.260058\pi$
$113$	14.5509			1.36883			0.684415	+	0.729093i	$0.260058\pi$
$114$	4.05362	+	0.860036i	0.379657	+	0.0805498i
$115$			1.32391i			0.123455i
$116$	8.18532	−	18.4217i	0.759988	−	1.71041i
$117$		−	3.25908i		−	0.301302i
$118$	0.692482	−	3.26389i	0.0637481	−	0.300465i
$119$	1.12980			0.103568
$120$	3.03189	+	2.19760i	0.276773	+	0.200612i
$121$	2.00559			0.182327
$122$	2.16387	−	10.1990i	0.195908	−	0.923375i
$123$		−	6.73538i		−	0.607309i
$124$	−18.3021	−	8.13218i	−1.64358	−	0.730291i
$125$		−	10.9186i		−	0.976590i
$126$	−0.265535	−	0.0563371i	−0.0236557	−	0.00501891i
$127$	−13.5359			−1.20112			−0.600560	−	0.799580i	$-0.705056\pi$
$127$	−13.5359			−1.20112			−0.600560	+	0.799580i	$0.705056\pi$
$128$	1.21213	+	11.2486i	0.107138	+	0.994244i
$129$	−9.95924			−0.876862
$130$	5.96906	+	1.26642i	0.523521	+	0.111073i
$131$		−	4.70732i		−	0.411281i	−0.978628	−	0.205640i	$-0.934072\pi$
$131$		−	4.70732i		−	0.411281i	0.978628	−	0.205640i	$-0.0659277\pi$
$132$	−5.48140	−	2.43555i	−0.477094	−	0.211988i
$133$		−	0.562415i		−	0.0487676i
$134$	2.56776	−	12.1027i	0.221820	−	1.04551i
$135$	−1.32391			−0.113944
$136$	13.4800	+	9.77065i	1.15590	+	0.837826i
$137$	−1.70413			−0.145594			−0.0727970	−	0.997347i	$-0.523193\pi$
$137$	−1.70413			−0.145594			−0.0727970	+	0.997347i	$0.523193\pi$
$138$	0.293513	−	1.38342i	0.0249855	−	0.117765i
$139$			8.87285i			0.752585i	0.926501	+	0.376293i	$0.122801\pi$
$139$			8.87285i			0.752585i	−0.926501	+	0.376293i	$0.877199\pi$
$140$	0.206365	−	0.464440i	0.0174410	−	0.0392523i
$141$			3.66477i			0.308629i
$142$	−1.47759	−	0.313493i	−0.123997	−	0.0263077i
$143$	−9.77420			−0.817360
$144$	−2.68098	−	2.96856i	−0.223415	−	0.247380i
$145$	−13.3439			−1.10815
$146$	−21.8573	−	4.63734i	−1.80892	−	0.383789i
$147$		−	6.96316i		−	0.574312i
$148$	1.88867	−	4.25061i	0.155248	−	0.349398i
$149$			15.3033i			1.25369i	0.779142	+	0.626847i	$0.215655\pi$
$149$			15.3033i			1.25369i	−0.779142	+	0.626847i	$0.784345\pi$
$150$	−0.953117	+	4.49234i	−0.0778217	+	0.366798i
$151$	5.30515			0.431727			0.215864	−	0.976424i	$-0.430743\pi$
$151$	5.30515			0.431727			0.215864	+	0.976424i	$0.430743\pi$
$152$	4.86385	−	6.71037i	0.394510	−	0.544283i
$153$	−5.88617			−0.475869
$154$	−0.168959	+	0.796357i	−0.0136151	+	0.0641723i
$155$			13.2572i			1.06485i
$156$	−5.95662	−	2.64671i	−0.476912	−	0.211906i
$157$			18.8258i			1.50246i	0.660040	+	0.751231i	$0.270539\pi$
$157$			18.8258i			1.50246i	−0.660040	+	0.751231i	$0.729461\pi$
$158$	2.92591	+	0.620774i	0.232773	+	0.0493862i
$159$	8.44683			0.669877
$160$	6.47876	−	3.75672i	0.512191	−	0.296995i
$161$	−0.191941			−0.0151271
$162$	1.38342	+	0.293513i	0.108692	+	0.0230606i
$163$			13.0149i			1.01941i	0.860350	+	0.509703i	$0.170245\pi$
$163$			13.0149i			1.01941i	−0.860350	+	0.509703i	$0.829755\pi$
$164$	−12.3103	−	5.46983i	−0.961270	−	0.427122i
$165$			3.97048i			0.309102i
$166$	1.48912	−	7.01868i	0.115578	−	0.544755i
$167$	10.8117			0.836632			0.418316	−	0.908302i	$-0.362620\pi$
$167$	10.8117			0.836632			0.418316	+	0.908302i	$0.362620\pi$
$168$	−0.318609	+	0.439567i	−0.0245812	+	0.0339133i
$169$	2.37839			0.182953
$170$	2.28727	−	10.7806i	0.175425	−	0.826836i
$171$			2.93015i			0.224074i
$172$	−8.08793	+	18.2025i	−0.616699	+	1.38793i
$173$		−	19.9680i		−	1.51814i	−0.651012	−	0.759068i	$-0.725655\pi$
$173$		−	19.9680i		−	1.51814i	0.651012	−	0.759068i	$-0.274345\pi$
$174$	13.9437	+	2.95837i	1.05707	+	0.224273i
$175$	0.623285			0.0471159
$176$	−8.90292	+	8.04043i	−0.671083	+	0.606070i
$177$	2.35929			0.177335
$178$	16.2185	+	3.44099i	1.21563	+	0.257913i
$179$		−	0.692156i		−	0.0517341i	−0.999665	−	0.0258671i	$-0.991765\pi$
$179$		−	0.692156i		−	0.0517341i	0.999665	−	0.0258671i	$-0.00823466\pi$
$180$	−1.07515	+	2.41970i	−0.0801368	+	0.180354i
$181$			4.88487i			0.363090i	0.983383	+	0.181545i	$0.0581098\pi$
$181$			4.88487i			0.363090i	−0.983383	+	0.181545i	$0.941890\pi$
$182$	−0.183607	+	0.865400i	−0.0136099	+	0.0641477i
$183$	7.37232			0.544978
$184$	−2.29011	−	1.65993i	−0.168829	−	0.122372i
$185$	−3.07895			−0.226369
$186$	2.93916	−	13.8532i	0.215510	−	1.01577i
$187$			17.6530i			1.29092i
$188$	6.69810	+	2.97617i	0.488509	+	0.217060i
$189$		−	0.191941i		−	0.0139616i
$190$	−5.36662	−	1.13861i	−0.389335	−	0.0826032i
$191$	7.04783			0.509963			0.254982	−	0.966946i	$-0.417931\pi$
$191$	7.04783			0.509963			0.254982	+	0.966946i	$0.417931\pi$
$192$	−7.60287	+	2.48924i	−0.548690	+	0.179646i
$193$	−15.4361			−1.11112			−0.555559	−	0.831477i	$-0.687496\pi$
$193$	−15.4361			−1.11112			−0.555559	+	0.831477i	$0.687496\pi$
$194$	−14.5345	−	3.08370i	−1.04351	−	0.221397i
$195$			4.31472i			0.308983i
$196$	−12.7266	−	5.65480i	−0.909041	−	0.403915i
$197$		−	6.67456i		−	0.475543i	−0.971321	−	0.237771i	$-0.923583\pi$
$197$		−	6.67456i		−	0.475543i	0.971321	−	0.237771i	$-0.0764169\pi$
$198$	0.880265	−	4.14897i	0.0625577	−	0.294854i
$199$	−20.3114			−1.43984			−0.719918	−	0.694059i	$-0.755821\pi$
$199$	−20.3114			−1.43984			−0.719918	+	0.694059i	$0.755821\pi$
$200$	7.43663	+	5.39026i	0.525849	+	0.381149i
$201$	8.74836			0.617062
$202$	0.820241	−	3.86606i	0.0577120	−	0.272015i
$203$		−	1.93460i		−	0.135783i
$204$	−4.78018	+	10.7582i	−0.334679	+	0.753221i
$205$			8.91701i			0.622791i
$206$	12.2524	+	2.59953i	0.853667	+	0.181118i
$207$	1.00000			0.0695048
$208$	−9.67479	+	8.73752i	−0.670826	+	0.605838i
$209$	8.78771			0.607859
$210$	0.351543	+	0.0745851i	0.0242588	+	0.00514686i
$211$			21.6777i			1.49235i	0.665748	+	0.746176i	$0.268112\pi$
$211$			21.6777i			1.49235i	−0.665748	+	0.746176i	$0.731888\pi$
$212$	6.85970	−	15.4383i	0.471126	−	1.06031i
$213$		−	1.06807i		−	0.0731831i
$214$	−2.58799	+	12.1980i	−0.176911	+	0.833838i
$215$	13.1851			0.899216
$216$	1.65993	−	2.29011i	0.112944	−	0.155823i
$217$	−1.92204			−0.130477
$218$	0.634846	−	2.99223i	0.0429972	−	0.202660i
$219$		−	15.7994i		−	1.06763i
$220$	7.25685	+	3.22444i	0.489257	+	0.217392i
$221$			19.1835i			1.29042i
$222$	3.21736	+	0.682611i	0.215935	+	0.0458138i
$223$	−2.97465			−0.199198			−0.0995988	−	0.995028i	$-0.531756\pi$
$223$	−2.97465			−0.199198			−0.0995988	+	0.995028i	$0.531756\pi$
$224$	0.544652	+	0.939295i	0.0363911	+	0.0627593i
$225$	−3.24727			−0.216485
$226$	20.1299	+	4.27086i	1.33902	+	0.284094i
$227$		−	5.74197i		−	0.381108i	−0.981677	−	0.190554i	$-0.938972\pi$
$227$		−	5.74197i		−	0.381108i	0.981677	−	0.190554i	$-0.0610284\pi$
$228$	5.35543	+	2.37958i	0.354672	+	0.157592i
$229$		−	13.7652i		−	0.909631i	−0.890586	−	0.454816i	$-0.849705\pi$
$229$		−	13.7652i		−	0.909631i	0.890586	−	0.454816i	$-0.150295\pi$
$230$	−0.388583	+	1.83152i	−0.0256224	+	0.120767i
$231$	−0.575644			−0.0378746
$232$	16.7307	−	23.0824i	1.09843	−	1.51544i
$233$	27.3993			1.79499			0.897494	−	0.441027i	$-0.145386\pi$
$233$	27.3993			1.79499			0.897494	+	0.441027i	$0.145386\pi$
$234$	0.956582	−	4.50868i	0.0625338	−	0.294741i
$235$		−	4.85181i		−	0.316497i
$236$	1.91599	−	4.31207i	0.124720	−	0.280692i
$237$			2.11498i			0.137383i
$238$	1.56298	+	0.331610i	0.101313	+	0.0214951i
$239$	−8.75263			−0.566161			−0.283080	−	0.959096i	$-0.591356\pi$
$239$	−8.75263			−0.566161			−0.283080	+	0.959096i	$0.591356\pi$
$240$	3.54936	+	3.93010i	0.229110	+	0.253687i
$241$	−0.0992415			−0.00639271			−0.00319635	−	0.999995i	$-0.501017\pi$
$241$	−0.0992415			−0.00639271			−0.00319635	+	0.999995i	$0.501017\pi$
$242$	2.77458	+	0.588668i	0.178357	+	0.0378410i
$243$			1.00000i			0.0641500i
$244$	5.98708	−	13.4744i	0.383284	−	0.862609i
$245$			9.21857i			0.588953i
$246$	1.97692	−	9.31786i	0.126044	−	0.594085i
$247$	9.54959			0.607626
$248$	−22.9326	−	16.6221i	−1.45622	−	1.05551i
$249$	5.07343			0.321515
$250$	3.20475	−	15.1050i	0.202686	−	0.955326i
$251$			23.0894i			1.45739i	0.684840	+	0.728694i	$0.259872\pi$
$251$			23.0894i			1.45739i	−0.684840	+	0.728694i	$0.740128\pi$
$252$	−0.350810	−	0.155876i	−0.0220990	−	0.00981925i
$253$		−	2.99907i		−	0.188550i
$254$	−18.7259	−	3.97297i	−1.17497	−	0.249286i
$255$	7.79273			0.488000
$256$	−1.62473	+	15.9173i	−0.101545	+	0.994831i
$257$	−11.7476			−0.732795			−0.366398	−	0.930458i	$-0.619409\pi$
$257$	−11.7476			−0.732795			−0.366398	+	0.930458i	$0.619409\pi$
$258$	−13.7778	−	2.92317i	−0.857769	−	0.181988i
$259$		−	0.446389i		−	0.0277373i
$260$	7.88601	+	3.50399i	0.489069	+	0.217309i
$261$			10.0792i			0.623885i
$262$	1.38166	−	6.51220i	0.0853592	−	0.402325i
$263$	−26.6460			−1.64306			−0.821531	−	0.570164i	$-0.806880\pi$
$263$	−26.6460			−1.64306			−0.821531	+	0.570164i	$0.806880\pi$
$264$	−6.86821	−	4.97825i	−0.422709	−	0.306390i
$265$	−11.1828			−0.686955
$266$	0.165076	−	0.778057i	0.0101215	−	0.0477057i
$267$			11.7235i			0.717465i
$268$	7.10457	−	15.9894i	0.433981	−	0.976707i
$269$			16.3199i			0.995045i	0.867451	+	0.497522i	$0.165757\pi$
$269$			16.3199i			0.995045i	−0.867451	+	0.497522i	$0.834243\pi$
$270$	−1.83152	−	0.388583i	−0.111463	−	0.0236484i
$271$	7.41362			0.450346			0.225173	−	0.974319i	$-0.427705\pi$
$271$	7.41362			0.450346			0.225173	+	0.974319i	$0.427705\pi$
$272$	15.7807	+	17.4735i	0.956845	+	1.05948i
$273$	−0.625551			−0.0378601
$274$	−2.35753	−	0.500185i	−0.142424	−	0.0302173i
$275$			9.73879i			0.587271i
$276$	0.812103	−	1.82770i	0.0488829	−	0.110015i
$277$			15.3661i			0.923261i	0.887072	+	0.461631i	$0.152735\pi$
$277$			15.3661i			0.923261i	−0.887072	+	0.461631i	$0.847265\pi$
$278$	−2.60430	+	12.2749i	−0.156195	+	0.736198i
$279$	10.0137			0.599506
$280$	0.421808	−	0.581945i	0.0252079	−	0.0347778i
$281$	22.0697			1.31657			0.658284	−	0.752770i	$-0.271283\pi$
$281$	22.0697			1.31657			0.658284	+	0.752770i	$0.271283\pi$
$282$	−1.07566	+	5.06991i	−0.0640544	+	0.301909i
$283$		−	23.7862i		−	1.41394i	−0.707243	−	0.706971i	$-0.750061\pi$
$283$		−	23.7862i		−	1.41394i	0.707243	−	0.706971i	$-0.249939\pi$
$284$	−1.95212	−	0.867385i	−0.115837	−	0.0514698i
$285$		−	3.87924i		−	0.229786i
$286$	−13.5218	−	2.86886i	−0.799562	−	0.169639i
$287$	−1.29280			−0.0763113
$288$	−2.83760	−	4.89367i	−0.167207	−	0.288362i
$289$	17.6470			1.03806
$290$	−18.4602	−	3.91660i	−1.08402	−	0.229990i
$291$		−	10.5062i		−	0.615884i
$292$	−28.8767	−	12.8308i	−1.68988	−	0.750865i
$293$		−	20.7999i		−	1.21514i	−0.794265	−	0.607571i	$-0.792144\pi$
$293$		−	20.7999i		−	1.21514i	0.794265	−	0.607571i	$-0.207856\pi$
$294$	2.04378	−	9.63297i	0.119196	−	0.561806i
$295$	−3.12348			−0.181856
$296$	3.86044	−	5.32602i	0.224383	−	0.309569i
$297$	2.99907			0.174024
$298$	−4.49171	+	21.1709i	−0.260198	+	1.22640i
$299$		−	3.25908i		−	0.188478i
$300$	−2.63712	+	5.93504i	−0.152254	+	0.342660i
$301$			1.91159i			0.110182i
$302$	7.33925	+	1.55713i	0.422326	+	0.0896028i
$303$	2.79457			0.160544
$304$	8.69833	−	7.85566i	0.498883	−	0.450553i
$305$	−9.76026			−0.558871
$306$	−8.14304	−	1.72767i	−0.465507	−	0.0987641i
$307$		−	14.2896i		−	0.815549i	−0.913083	−	0.407774i	$-0.866305\pi$
$307$		−	14.2896i		−	0.815549i	0.913083	−	0.407774i	$-0.133695\pi$
$308$	−0.467482	+	1.05210i	−0.0266373	+	0.0599492i
$309$			8.85663i			0.503836i
$310$	−3.89117	+	18.3403i	−0.221004	+	1.04166i
$311$	−30.3745			−1.72238			−0.861189	−	0.508285i	$-0.830280\pi$
$311$	−30.3745			−1.72238			−0.861189	+	0.508285i	$0.830280\pi$
$312$	−7.46367	−	5.40986i	−0.422547	−	0.306273i
$313$	0.853858			0.0482629			0.0241314	−	0.999709i	$-0.492318\pi$
$313$	0.853858			0.0482629			0.0241314	+	0.999709i	$0.492318\pi$
$314$	−5.52561	+	26.0440i	−0.311828	+	1.46975i
$315$			0.254112i			0.0143176i
$316$	3.86555	+	1.71758i	0.217454	+	0.0966216i
$317$			17.0505i			0.957654i	0.877909	+	0.478827i	$0.158938\pi$
$317$			17.0505i			0.957654i	−0.877909	+	0.478827i	$0.841062\pi$
$318$	11.6855	+	2.47925i	0.655291	+	0.139030i
$319$	30.2281			1.69245
$320$	10.0655	−	3.29552i	0.562678	−	0.184225i
$321$	−8.81728			−0.492132
$322$	−0.265535	−	0.0563371i	−0.0147977	−	0.00313955i
$323$		−	17.2473i		−	0.959668i
$324$	1.82770	+	0.812103i	0.101539	+	0.0451168i
$325$			10.5831i			0.587046i
$326$	−3.82004	+	18.0051i	−0.211573	+	0.997209i
$327$	2.16292			0.119610
$328$	−15.4248	−	11.1803i	−0.851692	−	0.617328i
$329$	0.703419			0.0387808
$330$	−1.16539	+	5.49284i	−0.0641525	+	0.302371i
$331$		−	11.2123i		−	0.616283i	−0.951340	−	0.308142i	$-0.900293\pi$
$331$		−	11.2123i		−	0.616283i	0.951340	−	0.308142i	$-0.0997071\pi$
$332$	4.12015	−	9.27271i	0.226122	−	0.508906i
$333$			2.32566i			0.127445i
$334$	14.9571	+	3.17336i	0.818415	+	0.173639i
$335$	−11.5820			−0.632792
$336$	−0.569789	+	0.514589i	−0.0310845	+	0.0280731i
$337$	26.3971			1.43794			0.718970	−	0.695041i	$-0.244614\pi$
$337$	26.3971			1.43794			0.718970	+	0.695041i	$0.244614\pi$
$338$	3.29031	+	0.698088i	0.178969	+	0.0379710i
$339$			14.5509i			0.790294i
$340$	6.32850	−	14.2428i	0.343211	−	0.772423i
$341$		−	30.0318i		−	1.62632i
$342$	−0.860036	+	4.05362i	−0.0465054	+	0.219195i
$343$	−2.68010			−0.144712
$344$	−16.5317	+	22.8078i	−0.891328	+	1.22971i
$345$	−1.32391			−0.0712767
$346$	5.86085	−	27.6241i	0.315081	−	1.48508i
$347$			23.4240i			1.25746i	0.777622	+	0.628732i	$0.216426\pi$
$347$			23.4240i			1.25746i	−0.777622	+	0.628732i	$0.783574\pi$
$348$	18.4217	+	8.18532i	0.987506	+	0.438779i
$349$			5.59807i			0.299658i	0.988712	+	0.149829i	$0.0478723\pi$
$349$			5.59807i			0.299658i	−0.988712	+	0.149829i	$0.952128\pi$
$350$	0.862264	+	0.182942i	0.0460900	+	0.00977867i
$351$	3.25908			0.173957
$352$	−14.6764	+	8.51017i	−0.782257	+	0.453593i
$353$	1.72246			0.0916773			0.0458386	−	0.998949i	$-0.485404\pi$
$353$	1.72246			0.0916773			0.0458386	+	0.998949i	$0.485404\pi$
$354$	3.26389	+	0.692482i	0.173474	+	0.0368050i
$355$			1.41403i			0.0750487i
$356$	21.4270	+	9.52067i	1.13563	+	0.504595i
$357$			1.12980i			0.0597952i
$358$	0.203157	−	0.957542i	0.0107372	−	0.0506076i
$359$	−5.39866			−0.284931			−0.142465	−	0.989800i	$-0.545503\pi$
$359$	−5.39866			−0.284931			−0.142465	+	0.989800i	$0.545503\pi$
$360$	−2.19760	+	3.03189i	−0.115823	+	0.159795i
$361$	10.4142			0.548117
$362$	−1.43377	+	6.75783i	−0.0753575	+	0.355184i
$363$			2.00559i			0.105266i
$364$	−0.508012	+	1.14332i	−0.0266271	+	0.0599262i
$365$			20.9170i			1.09484i
$366$	10.1990	+	2.16387i	0.533111	+	0.113107i
$367$	35.5081			1.85351			0.926753	−	0.375672i	$-0.122588\pi$
$367$	35.5081			1.85351			0.926753	+	0.375672i	$0.122588\pi$
$368$	−2.68098	−	2.96856i	−0.139756	−	0.154747i
$369$	6.73538			0.350630
$370$	−4.25948	−	0.903712i	−0.221440	−	0.0469818i
$371$		−	1.62129i		−	0.0841733i
$372$	8.13218	−	18.3021i	0.421634	−	0.948919i
$373$			15.1214i			0.782957i	0.920187	+	0.391478i	$0.128036\pi$
$373$			15.1214i			0.782957i	−0.920187	+	0.391478i	$0.871964\pi$
$374$	−5.18139	+	24.4215i	−0.267923	+	1.26281i
$375$	10.9186			0.563835
$376$	8.39274	+	6.08327i	0.432822	+	0.313721i
$377$	32.8488			1.69180
$378$	0.0563371	−	0.265535i	0.00289767	−	0.0136576i
$379$			28.6883i			1.47362i	0.676101	+	0.736809i	$0.263668\pi$
$379$			28.6883i			1.47362i	−0.676101	+	0.736809i	$0.736332\pi$
$380$	−7.09009	−	3.15034i	−0.363714	−	0.161609i
$381$		−	13.5359i		−	0.693467i
$382$	9.75011	+	2.06863i	0.498859	+	0.105840i
$383$	−22.7218			−1.16103			−0.580515	−	0.814250i	$-0.697149\pi$
$383$	−22.7218			−1.16103			−0.580515	+	0.814250i	$0.697149\pi$
$384$	−11.2486	+	1.21213i	−0.574027	+	0.0618561i
$385$	0.762098			0.0388401
$386$	−21.3547	−	4.53071i	−1.08692	−	0.230607i
$387$		−	9.95924i		−	0.506257i
$388$	−19.2022	−	8.53211i	−0.974842	−	0.433152i
$389$			26.1031i			1.32348i	0.749734	+	0.661739i	$0.230181\pi$
$389$			26.1031i			1.32348i	−0.749734	+	0.661739i	$0.769819\pi$
$390$	−1.26642	+	5.96906i	−0.0641279	+	0.302255i
$391$	−5.88617			−0.297676
$392$	−15.9464	−	11.5584i	−0.805416	−	0.583786i
$393$	4.70732			0.237453
$394$	1.95907	−	9.23372i	0.0986965	−	0.465188i
$395$		−	2.80004i		−	0.140885i
$396$	2.43555	−	5.48140i	0.122391	−	0.275451i
$397$			10.1251i			0.508165i	0.967183	+	0.254082i	$0.0817734\pi$
$397$			10.1251i			0.508165i	−0.967183	+	0.254082i	$0.918227\pi$
$398$	−28.0992	−	5.96165i	−1.40848	−	0.298831i
$399$	0.562415			0.0281560
$400$	8.70587	+	9.63974i	0.435293	+	0.481987i
$401$	−8.40903			−0.419927			−0.209963	−	0.977709i	$-0.567334\pi$
$401$	−8.40903			−0.419927			−0.209963	+	0.977709i	$0.567334\pi$
$402$	12.1027	+	2.56776i	0.603625	+	0.128068i
$403$		−	32.6356i		−	1.62569i
$404$	2.26948	−	5.10763i	0.112911	−	0.254114i
$405$		−	1.32391i		−	0.0657854i
$406$	0.567831	−	2.67637i	0.0281810	−	0.132826i
$407$	6.97481			0.345728
$408$	−9.77065	+	13.4800i	−0.483719	+	0.667359i
$409$	−14.3542			−0.709770			−0.354885	−	0.934910i	$-0.615480\pi$
$409$	−14.3542			−0.709770			−0.354885	+	0.934910i	$0.615480\pi$
$410$	−2.61726	+	12.3360i	−0.129257	+	0.609230i
$411$		−	1.70413i		−	0.0840587i
$412$	16.1873	+	7.19249i	0.797489	+	0.354349i
$413$		−	0.452844i		−	0.0222830i
$414$	1.38342	+	0.293513i	0.0679914	+	0.0144254i
$415$	−6.71674			−0.329712
$416$	−15.9489	+	9.24798i	−0.781957	+	0.453420i
$417$	−8.87285			−0.434505
$418$	12.1571	+	2.57931i	0.594623	+	0.126158i
$419$			7.50638i			0.366711i	0.983047	+	0.183355i	$0.0586959\pi$
$419$			7.50638i			0.366711i	−0.983047	+	0.183355i	$0.941304\pi$
$420$	0.464440	+	0.206365i	0.0226624	+	0.0100696i
$421$		−	4.51794i		−	0.220191i	−0.993921	−	0.110095i	$-0.964884\pi$
$421$		−	4.51794i		−	0.220191i	0.993921	−	0.110095i	$-0.0351157\pi$
$422$	−6.36268	+	29.9893i	−0.309730	+	1.45986i
$423$	−3.66477			−0.178187
$424$	14.0212	−	19.3442i	0.680929	−	0.939438i
$425$	19.1140			0.927165
$426$	0.313493	−	1.47759i	0.0151888	−	0.0715895i
$427$		−	1.41505i		−	0.0684791i
$428$	−7.16054	+	16.1153i	−0.346118	+	0.778964i
$429$		−	9.77420i		−	0.471903i
$430$	18.2405	+	3.87000i	0.879636	+	0.186628i
$431$	−5.34229			−0.257329			−0.128664	−	0.991688i	$-0.541069\pi$
$431$	−5.34229			−0.257329			−0.128664	+	0.991688i	$0.541069\pi$
$432$	2.96856	−	2.68098i	0.142825	−	0.128989i
$433$	−11.1850			−0.537519			−0.268760	−	0.963207i	$-0.586614\pi$
$433$	−11.1850			−0.537519			−0.268760	+	0.963207i	$0.586614\pi$
$434$	−2.65899	−	0.564145i	−0.127636	−	0.0270798i
$435$		−	13.3439i		−	0.639789i
$436$	1.75652	−	3.95318i	0.0841220	−	0.189323i
$437$			2.93015i			0.140168i
$438$	4.63734	−	21.8573i	0.221581	−	1.04438i
$439$	1.47646			0.0704676			0.0352338	−	0.999379i	$-0.488782\pi$
$439$	1.47646			0.0704676			0.0352338	+	0.999379i	$0.488782\pi$
$440$	9.09286	+	6.59074i	0.433485	+	0.314201i
$441$	6.96316			0.331579
$442$	−5.63061	+	26.5388i	−0.267821	+	1.26232i
$443$		−	16.1473i		−	0.767181i	−0.923503	−	0.383591i	$-0.874687\pi$
$443$		−	16.1473i		−	0.767181i	0.923503	−	0.383591i	$-0.125313\pi$
$444$	4.25061	+	1.88867i	0.201725	+	0.0896325i
$445$		−	15.5208i		−	0.735755i
$446$	−4.11520	−	0.873100i	−0.194860	−	0.0413425i
$447$	−15.3033			−0.723821
$448$	0.477788	+	1.45930i	0.0225733	+	0.0689456i
$449$	−25.7616			−1.21576			−0.607881	−	0.794028i	$-0.707980\pi$
$449$	−25.7616			−1.21576			−0.607881	+	0.794028i	$0.707980\pi$
$450$	−4.49234	−	0.953117i	−0.211771	−	0.0449304i
$451$		−	20.1999i		−	0.951175i
$452$	26.5946	+	11.8168i	1.25090	+	0.555815i
$453$			5.30515i			0.249258i
$454$	1.68534	−	7.94356i	0.0790971	−	0.372810i
$455$	0.828171			0.0388252
$456$	6.71037	+	4.86385i	0.314242	+	0.227771i
$457$	−4.00181			−0.187197			−0.0935984	−	0.995610i	$-0.529837\pi$
$457$	−4.00181			−0.187197			−0.0935984	+	0.995610i	$0.529837\pi$
$458$	4.04027	−	19.0431i	0.188789	−	0.889825i
$459$		−	5.88617i		−	0.274743i
$460$	−1.07515	+	2.41970i	−0.0501290	+	0.112819i
$461$			26.3886i			1.22904i	0.788901	+	0.614521i	$0.210651\pi$
$461$			26.3886i			1.22904i	−0.788901	+	0.614521i	$0.789349\pi$
$462$	−0.796357	−	0.168959i	−0.0370499	−	0.00786068i
$463$	18.2533			0.848305			0.424152	−	0.905591i	$-0.360572\pi$
$463$	18.2533			0.848305			0.424152	+	0.905591i	$0.360572\pi$
$464$	29.9206	−	27.0220i	1.38903	−	1.25447i
$465$	−13.2572			−0.614789
$466$	37.9047	+	8.04205i	1.75590	+	0.372541i
$467$		−	38.6169i		−	1.78698i	−0.449086	−	0.893489i	$-0.648250\pi$
$467$		−	38.6169i		−	1.78698i	0.449086	−	0.893489i	$-0.351750\pi$
$468$	2.64671	−	5.95662i	0.122344	−	0.275345i
$469$		−	1.67917i		−	0.0775368i
$470$	1.42407	−	6.71209i	0.0656874	−	0.309606i
$471$	−18.8258			−0.867446
$472$	3.91626	−	5.40304i	0.180261	−	0.248695i
$473$	−29.8684			−1.37335
$474$	−0.620774	+	2.92591i	−0.0285131	+	0.134391i
$475$		−	9.51499i		−	0.436578i
$476$	2.06493	+	0.917512i	0.0946459	+	0.0420541i
$477$			8.44683i			0.386754i
$478$	−12.1086	−	2.56901i	−0.553833	−	0.117504i
$479$	26.1154			1.19324			0.596621	−	0.802523i	$-0.296510\pi$
$479$	26.1154			1.19324			0.596621	+	0.802523i	$0.296510\pi$
$480$	3.75672	+	6.47876i	0.171470	+	0.295713i
$481$	7.57951			0.345596
$482$	−0.137293	−	0.0291287i	−0.00625351	−	0.00132677i
$483$		−	0.191941i		−	0.00873361i
$484$	3.66562	+	1.62875i	0.166619	+	0.0740341i
$485$			13.9092i			0.631584i
$486$	−0.293513	+	1.38342i	−0.0133140	+	0.0627532i
$487$	−8.22313			−0.372626			−0.186313	−	0.982490i	$-0.559654\pi$
$487$	−8.22313			−0.372626			−0.186313	+	0.982490i	$0.559654\pi$
$488$	12.2376	−	16.8835i	0.553968	−	0.764278i
$489$	−13.0149			−0.588554
$490$	−2.70577	+	12.7531i	−0.122234	+	0.576128i
$491$			15.4881i			0.698968i	0.936942	+	0.349484i	$0.113643\pi$
$491$			15.4881i			0.698968i	−0.936942	+	0.349484i	$0.886357\pi$
$492$	5.46983	−	12.3103i	0.246599	−	0.554989i
$493$		−	59.3277i		−	2.67198i
$494$	13.2111	+	2.80293i	0.594395	+	0.126110i
$495$	−3.97048			−0.178460
$496$	−26.8466	−	29.7264i	−1.20545	−	1.33475i
$497$	−0.205007			−0.00919581
$498$	7.01868	+	1.48912i	0.314515	+	0.0667289i
$499$		−	25.2845i		−	1.13189i	−0.824443	−	0.565945i	$-0.808511\pi$
$499$		−	25.2845i		−	1.13189i	0.824443	−	0.565945i	$-0.191489\pi$
$500$	8.86704	−	19.9560i	0.396546	−	0.892457i
$501$			10.8117i			0.483030i
$502$	−6.77703	+	31.9423i	−0.302473	+	1.42565i
$503$	−11.9298			−0.531922			−0.265961	−	0.963984i	$-0.585689\pi$
$503$	−11.9298			−0.531922			−0.265961	+	0.963984i	$0.585689\pi$
$504$	−0.439567	−	0.318609i	−0.0195799	−	0.0141920i
$505$	−3.69974			−0.164636
$506$	0.880265	−	4.14897i	0.0391326	−	0.184444i
$507$			2.37839i			0.105628i
$508$	−24.7396	−	10.9926i	−1.09764	−	0.487717i
$509$			29.0843i			1.28914i	0.764546	+	0.644569i	$0.222963\pi$
$509$			29.0843i			1.28914i	−0.764546	+	0.644569i	$0.777037\pi$
$510$	10.7806	+	2.28727i	0.477374	+	0.101282i
$511$	−3.03256			−0.134153
$512$	−6.91961	+	21.5434i	−0.305806	+	0.952094i
$513$	−2.93015			−0.129369
$514$	−16.2519	−	3.44807i	−0.716839	−	0.152088i
$515$		−	11.7253i		−	0.516680i
$516$	−18.2025	−	8.08793i	−0.801321	−	0.356051i
$517$			10.9909i			0.483379i
$518$	0.131021	−	0.617543i	0.00575673	−	0.0271333i
$519$	19.9680			0.876496
$520$	9.88119	+	7.16214i	0.433319	+	0.314081i
$521$	−5.73265			−0.251152			−0.125576	−	0.992084i	$-0.540078\pi$
$521$	−5.73265			−0.251152			−0.125576	+	0.992084i	$0.540078\pi$
$522$	−2.95837	+	13.9437i	−0.129484	+	0.610300i
$523$		−	21.6326i		−	0.945926i	−0.881082	−	0.472963i	$-0.843184\pi$
$523$		−	21.6326i		−	0.945926i	0.881082	−	0.472963i	$-0.156816\pi$
$524$	3.82283	−	8.60357i	0.167001	−	0.375849i
$525$			0.623285i			0.0272024i
$526$	−36.8626	−	7.82094i	−1.60728	−	0.341009i
$527$	−58.9425			−2.56758
$528$	−8.04043	−	8.90292i	−0.349915	−	0.387450i
$529$	1.00000			0.0434783
$530$	−15.4705	−	3.28230i	−0.671996	−	0.142574i
$531$			2.35929i			0.102384i
$532$	0.456739	−	1.02793i	0.0198022	−	0.0445663i
$533$		−	21.9512i		−	0.950810i
$534$	−3.44099	+	16.2185i	−0.148906	+	0.701843i
$535$	11.6732			0.504678
$536$	14.5217	−	20.0347i	0.627242	−	0.865369i
$537$	0.692156			0.0298687
$538$	−4.79011	+	22.5773i	−0.206517	+	0.973378i
$539$		−	20.8830i		−	0.899494i
$540$	−2.41970	−	1.07515i	−0.104127	−	0.0462670i
$541$		−	19.4744i		−	0.837270i	−0.908155	−	0.418635i	$-0.862509\pi$
$541$		−	19.4744i		−	0.837270i	0.908155	−	0.418635i	$-0.137491\pi$
$542$	10.2562	+	2.17599i	0.440540	+	0.0934670i
$543$	−4.88487			−0.209630
$544$	16.7026	+	28.8050i	0.716119	+	1.23500i
$545$	−2.86351			−0.122659
$546$	−0.865400	−	0.183607i	−0.0370357	−	0.00785767i
$547$		−	9.24325i		−	0.395213i	−0.980281	−	0.197606i	$-0.936683\pi$
$547$		−	9.24325i		−	0.395213i	0.980281	−	0.197606i	$-0.0633168\pi$
$548$	−3.11465	−	1.38393i	−0.133051	−	0.0591187i
$549$			7.37232i			0.314643i
$550$	−2.85846	+	13.4728i	−0.121885	+	0.574484i
$551$	−29.5334			−1.25817
$552$	1.65993	−	2.29011i	0.0706515	−	0.0974737i
$553$	0.405951			0.0172628
$554$	−4.51016	+	21.2578i	−0.191618	+	0.903158i
$555$		−	3.07895i		−	0.130694i
$556$	−7.20567	+	16.2169i	−0.305588	+	0.687750i
$557$		−	34.2506i		−	1.45124i	−0.688093	−	0.725622i	$-0.741552\pi$
$557$		−	34.2506i		−	1.45124i	0.688093	−	0.725622i	$-0.258448\pi$
$558$	13.8532	+	2.93916i	0.586452	+	0.124425i
$559$	−32.4580			−1.37283
$560$	0.754346	−	0.681268i	0.0318770	−	0.0287888i
$561$	−17.6530			−0.745311
$562$	30.5316	+	6.47774i	1.28790	+	0.273247i
$563$		−	20.7594i		−	0.874904i	−0.899242	−	0.437452i	$-0.855881\pi$
$563$		−	20.7594i		−	0.874904i	0.899242	−	0.437452i	$-0.144119\pi$
$564$	−2.97617	+	6.69810i	−0.125319	+	0.282041i
$565$		−	19.2640i		−	0.810441i
$566$	6.98155	−	32.9063i	0.293456	−	1.38315i
$567$	0.191941			0.00806076
$568$	−2.44601	−	1.77293i	−0.102632	−	0.0743904i
$569$	−14.3303			−0.600757			−0.300379	−	0.953820i	$-0.597113\pi$
$569$	−14.3303			−0.600757			−0.300379	+	0.953820i	$0.597113\pi$
$570$	1.13861	−	5.36662i	0.0476910	−	0.224783i
$571$			23.6817i			0.991047i	0.868595	+	0.495523i	$0.165024\pi$
$571$			23.6817i			0.991047i	−0.868595	+	0.495523i	$0.834976\pi$
$572$	−17.8643	−	7.93766i	−0.746945	−	0.331890i
$573$			7.04783i			0.294427i
$574$	−1.78848	−	0.379452i	−0.0746497	−	0.0158380i
$575$	−3.24727			−0.135421
$576$	−2.48924	−	7.60287i	−0.103718	−	0.316786i
$577$	32.9829			1.37309			0.686547	−	0.727085i	$-0.259126\pi$
$577$	32.9829			1.37309			0.686547	+	0.727085i	$0.259126\pi$
$578$	24.4132	+	5.17962i	1.01546	+	0.215444i
$579$		−	15.4361i		−	0.641504i
$580$	−24.3886	−	10.8366i	−1.01268	−	0.449965i
$581$		−	0.973799i		−	0.0404000i
$582$	3.08370	−	14.5345i	0.127824	−	0.602473i
$583$	25.3326			1.04917
$584$	−36.1825	−	26.2260i	−1.49724	−	1.08524i
$585$	−4.31472			−0.178392
$586$	6.10504	−	28.7750i	0.252197	−	1.18868i
$587$		−	7.27362i		−	0.300214i	−0.988670	−	0.150107i	$-0.952038\pi$
$587$		−	7.27362i		−	0.300214i	0.988670	−	0.150107i	$-0.0479619\pi$
$588$	5.65480	−	12.7266i	0.233200	−	0.524835i
$589$			29.3417i			1.20900i
$590$	−4.32108	−	0.916781i	−0.177896	−	0.0377433i
$591$	6.67456			0.274555
$592$	6.90386	−	6.23504i	0.283747	−	0.256258i
$593$	−5.11990			−0.210249			−0.105125	−	0.994459i	$-0.533524\pi$
$593$	−5.11990			−0.210249			−0.105125	+	0.994459i	$0.533524\pi$
$594$	4.14897	+	0.880265i	0.170234	+	0.0361177i
$595$		−	1.49574i		−	0.0613195i
$596$	−12.4278	+	27.9698i	−0.509064	+	1.14569i
$597$		−	20.3114i		−	0.831290i
$598$	0.956582	−	4.50868i	0.0391176	−	0.184374i
$599$	−2.17574			−0.0888981			−0.0444491	−	0.999012i	$-0.514153\pi$
$599$	−2.17574			−0.0888981			−0.0444491	+	0.999012i	$0.514153\pi$
$600$	−5.39026	+	7.43663i	−0.220056	+	0.303599i
$601$	−8.68545			−0.354287			−0.177143	−	0.984185i	$-0.556686\pi$
$601$	−8.68545			−0.354287			−0.177143	+	0.984185i	$0.556686\pi$
$602$	−0.561075	+	2.64453i	−0.0228677	+	0.107783i
$603$			8.74836i			0.356261i
$604$	9.69623	+	4.30833i	0.394534	+	0.175303i
$605$		−	2.65522i		−	0.107950i
$606$	3.86606	+	0.820241i	0.157048	+	0.0333200i
$607$	−40.9496			−1.66209			−0.831046	−	0.556203i	$-0.812258\pi$
$607$	−40.9496			−1.66209			−0.831046	+	0.556203i	$0.812258\pi$
$608$	14.3392	−	8.31460i	0.581530	−	0.337202i
$609$	1.93460			0.0783941
$610$	−13.5025	−	2.86476i	−0.546701	−	0.115991i
$611$			11.9438i			0.483194i
$612$	−10.7582	−	4.78018i	−0.434873	−	0.193227i
$613$			39.7910i			1.60714i	0.595208	+	0.803571i	$0.297069\pi$
$613$			39.7910i			1.60714i	−0.595208	+	0.803571i	$0.702931\pi$
$614$	4.19417	−	19.7685i	0.169263	−	0.797791i
$615$	−8.91701			−0.359569
$616$	−0.955530	+	1.31829i	−0.0384994	+	0.0531154i
$617$	12.4760			0.502264			0.251132	−	0.967953i	$-0.419197\pi$
$617$	12.4760			0.502264			0.251132	+	0.967953i	$0.419197\pi$
$618$	−2.59953	+	12.2524i	−0.104569	+	0.492865i
$619$		−	1.92189i		−	0.0772471i	−0.999254	−	0.0386236i	$-0.987703\pi$
$619$		−	1.92189i		−	0.0772471i	0.999254	−	0.0386236i	$-0.0122973\pi$
$620$	−10.7662	+	24.2302i	−0.432383	+	0.973110i
$621$			1.00000i			0.0401286i
$622$	−42.0206	−	8.91530i	−1.68487	−	0.357471i
$623$	2.25021			0.0901530
$624$	−8.73752	−	9.67479i	−0.349781	−	0.387301i
$625$	1.78116			0.0712462
$626$	1.18124	+	0.250618i	0.0472120	+	0.0100167i
$627$			8.78771i			0.350947i
$628$	−15.2885	+	34.4079i	−0.610077	+	1.37302i
$629$		−	13.6892i		−	0.545825i
$630$	−0.0745851	+	0.351543i	−0.00297154	+	0.0140058i
$631$	6.11572			0.243463			0.121731	−	0.992563i	$-0.461155\pi$
$631$	6.11572			0.243463			0.121731	+	0.992563i	$0.461155\pi$
$632$	4.84355	+	3.51073i	0.192666	+	0.139649i
$633$	−21.6777			−0.861610
$634$	−5.00456	+	23.5881i	−0.198756	+	0.936802i
$635$			17.9203i			0.711145i
$636$	15.4383	+	6.85970i	0.612168	+	0.272005i
$637$		−	22.6935i		−	0.899149i
$638$	41.8181	+	8.87234i	1.65560	+	0.351259i
$639$	1.06807			0.0422523
$640$	14.8921	−	1.60474i	0.588661	−	0.0634330i
$641$	−11.0821			−0.437718			−0.218859	−	0.975757i	$-0.570233\pi$
$641$	−11.0821			−0.437718			−0.218859	+	0.975757i	$0.570233\pi$
$642$	−12.1980	−	2.58799i	−0.481416	−	0.102140i
$643$		−	42.1115i		−	1.66072i	−0.557230	−	0.830358i	$-0.688136\pi$
$643$		−	42.1115i		−	1.66072i	0.557230	−	0.830358i	$-0.311864\pi$
$644$	−0.350810	−	0.155876i	−0.0138239	−	0.00614237i
$645$			13.1851i			0.519163i
$646$	5.06232	−	23.8603i	0.199174	−	0.938772i
$647$	31.9791			1.25723			0.628613	−	0.777718i	$-0.283623\pi$
$647$	31.9791			1.25723			0.628613	+	0.777718i	$0.283623\pi$
$648$	2.29011	+	1.65993i	0.0899642	+	0.0652083i
$649$	7.07567			0.277744
$650$	−3.10629	+	14.6409i	−0.121839	+	0.574264i
$651$		−	1.92204i		−	0.0753308i
$652$	−10.5694	+	23.7873i	−0.413931	+	0.931584i
$653$		−	46.8796i		−	1.83454i	−0.398264	−	0.917271i	$-0.630387\pi$
$653$		−	46.8796i		−	1.83454i	0.398264	−	0.917271i	$-0.369613\pi$
$654$	2.99223	+	0.634846i	0.117006	+	0.0248245i
$655$	−6.23205			−0.243506
$656$	−18.0574	−	19.9944i	−0.705023	−	0.780650i
$657$	15.7994			0.616395
$658$	0.973124	+	0.206463i	0.0379363	+	0.00804875i
$659$		−	32.9580i		−	1.28386i	−0.766763	−	0.641931i	$-0.778134\pi$
$659$		−	32.9580i		−	1.28386i	0.766763	−	0.641931i	$-0.221866\pi$
$660$	−3.22444	+	7.25685i	−0.125511	+	0.282473i
$661$		−	24.4629i		−	0.951498i	−0.879581	−	0.475749i	$-0.842177\pi$
$661$		−	24.4629i		−	0.951498i	0.879581	−	0.475749i	$-0.157823\pi$
$662$	3.29095	−	15.5113i	0.127907	−	0.602864i
$663$	−19.1835			−0.745026
$664$	8.42155	−	11.6187i	0.326820	−	0.450894i
$665$	−0.744585			−0.0288738
$666$	−0.682611	+	3.21736i	−0.0264506	+	0.124670i
$667$			10.0792i			0.390267i
$668$	19.7605	+	8.78019i	0.764556	+	0.339716i
$669$		−	2.97465i		−	0.115007i
$670$	−16.0228	−	3.39947i	−0.619014	−	0.131333i
$671$	22.1101			0.853550
$672$	−0.939295	+	0.544652i	−0.0362341	+	0.0210104i
$673$	20.7254			0.798906			0.399453	−	0.916754i	$-0.369200\pi$
$673$	20.7254			0.798906			0.399453	+	0.916754i	$0.369200\pi$
$674$	36.5182	+	7.74789i	1.40663	+	0.298437i
$675$		−	3.24727i		−	0.124988i
$676$	4.34698	+	1.93150i	0.167192	+	0.0742884i
$677$			14.0278i			0.539132i	0.962982	+	0.269566i	$0.0868802\pi$
$677$			14.0278i			0.539132i	−0.962982	+	0.269566i	$0.913120\pi$
$678$	−4.27086	+	20.1299i	−0.164022	+	0.773086i
$679$	−2.01657			−0.0773888
$680$	12.9354	−	17.8462i	0.496051	−	0.684372i
$681$	5.74197			0.220033
$682$	8.81474	−	41.5466i	0.337534	−	1.59090i
$683$		−	1.33122i		−	0.0509378i	−0.999676	−	0.0254689i	$-0.991892\pi$
$683$		−	1.33122i		−	0.0509378i	0.999676	−	0.0254689i	$-0.00810788\pi$
$684$	−2.37958	+	5.35543i	−0.0909856	+	0.204770i
$685$			2.25611i			0.0862016i
$686$	−3.70771	−	0.786644i	−0.141561	−	0.0300342i
$687$	13.7652			0.525176
$688$	−29.5646	+	26.7005i	−1.12714	+	1.01795i
$689$	27.5289			1.04877
$690$	−1.83152	−	0.388583i	−0.0697247	−	0.0147931i
$691$		−	49.9887i		−	1.90166i	−0.309715	−	0.950830i	$-0.600233\pi$
$691$		−	49.9887i		−	1.90166i	0.309715	−	0.950830i	$-0.399767\pi$
$692$	16.2160	−	36.4954i	0.616441	−	1.38735i
$693$		−	0.575644i		−	0.0218669i
$694$	−6.87523	+	32.4052i	−0.260980	+	1.23008i
$695$	11.7468			0.445582
$696$	23.0824	+	16.7307i	0.874937	+	0.634177i
$697$	−39.6456			−1.50168
$698$	−1.64311	+	7.74448i	−0.0621924	+	0.293133i
$699$			27.3993i			1.03634i
$700$	1.13918	+	0.506172i	0.0430569	+	0.0191315i
$701$			15.9504i			0.602437i	0.953555	+	0.301218i	$0.0973933\pi$
$701$			15.9504i			0.602437i	−0.953555	+	0.301218i	$0.902607\pi$
$702$	4.50868	+	0.956582i	0.170169	+	0.0361039i
$703$	−6.81452			−0.257015
$704$	−22.8015	+	7.46541i	−0.859365	+	0.281363i
$705$	4.85181			0.182730
$706$	2.38289	+	0.505564i	0.0896811	+	0.0190272i
$707$		−	0.536392i		−	0.0201731i
$708$	4.31207	+	1.91599i	0.162058	+	0.0720072i
$709$			32.6925i			1.22779i	0.789387	+	0.613896i	$0.210399\pi$
$709$			32.6925i			1.22779i	−0.789387	+	0.613896i	$0.789601\pi$
$710$	−0.415035	+	1.95619i	−0.0155760	+	0.0734146i
$711$	−2.11498			−0.0793180
$712$	26.8481	+	19.4602i	1.00617	+	0.729301i
$713$	10.0137			0.375017
$714$	−0.331610	+	1.56298i	−0.0124102	+	0.0584932i
$715$			12.9401i			0.483933i
$716$	0.562102	−	1.26505i	0.0210067	−	0.0472772i
$717$		−	8.75263i		−	0.326873i
$718$	−7.46862	−	1.58458i	−0.278726	−	0.0591359i
$719$	10.0521			0.374880			0.187440	−	0.982276i	$-0.439981\pi$
$719$	10.0521			0.374880			0.187440	+	0.982276i	$0.439981\pi$
$720$	−3.93010	+	3.54936i	−0.146466	+	0.132277i
$721$	1.69995			0.0633094
$722$	14.4073	+	3.05671i	0.536182	+	0.113759i
$723$		−	0.0992415i		−	0.00369083i
$724$	−3.96702	+	8.92808i	−0.147433	+	0.331810i
$725$		−	32.7298i		−	1.21555i
$726$	−0.588668	+	2.77458i	−0.0218475	+	0.102974i
$727$	19.6051			0.727113			0.363557	−	0.931572i	$-0.381562\pi$
$727$	19.6051			0.727113			0.363557	+	0.931572i	$0.381562\pi$
$728$	−1.03837	+	1.43258i	−0.0384847	+	0.0530951i
$729$	−1.00000			−0.0370370
$730$	−6.13940	+	28.9370i	−0.227230	+	1.07100i
$731$			58.6218i			2.16821i
$732$	13.4744	+	5.98708i	0.498028	+	0.221289i
$733$			33.0441i			1.22051i	0.792204	+	0.610256i	$0.208934\pi$
$733$			33.0441i			1.22051i	−0.792204	+	0.610256i	$0.791066\pi$
$734$	49.1225	+	10.4221i	1.81315	+	0.384686i
$735$	−9.21857			−0.340032
$736$	−2.83760	−	4.89367i	−0.104595	−	0.180383i
$737$	26.2369			0.966449
$738$	9.31786	+	1.97692i	0.342995	+	0.0727715i
$739$			8.05271i			0.296224i	0.988971	+	0.148112i	$0.0473196\pi$
$739$			8.05271i			0.296224i	−0.988971	+	0.148112i	$0.952680\pi$
$740$	−5.62740	−	2.50043i	−0.206867	−	0.0919175i
$741$			9.54959i			0.350813i
$742$	0.475870	−	2.24293i	0.0174698	−	0.0823405i
$743$	−17.9113			−0.657104			−0.328552	−	0.944486i	$-0.606561\pi$
$743$	−17.9113			−0.657104			−0.328552	+	0.944486i	$0.606561\pi$
$744$	16.6221	−	22.9326i	0.609396	−	0.840749i
$745$	20.2601			0.742273
$746$	−4.43833	+	20.9192i	−0.162499	+	0.765908i
$747$			5.07343i			0.185627i
$748$	−14.3361	+	32.2644i	−0.524179	+	1.17970i
$749$			1.69240i			0.0618388i
$750$	15.1050	+	3.20475i	0.551557	+	0.117021i
$751$	48.7216			1.77788			0.888939	−	0.458025i	$-0.151443\pi$
$751$	48.7216			1.77788			0.888939	+	0.458025i	$0.151443\pi$
$752$	9.82516	+	10.8791i	0.358287	+	0.396720i
$753$	−23.0894			−0.841423
$754$	45.4437	+	9.64155i	1.65496	+	0.351125i
$755$		−	7.02352i		−	0.255612i
$756$	0.155876	−	0.350810i	0.00566915	−	0.0127589i
$757$			9.00514i			0.327297i	0.986519	+	0.163649i	$0.0523264\pi$
$757$			9.00514i			0.327297i	−0.986519	+	0.163649i	$0.947674\pi$
$758$	−8.42038	+	39.6879i	−0.305842	+	1.44153i
$759$	2.99907			0.108859
$760$	−8.88390	−	6.43928i	−0.322253	−	0.233577i
$761$	−21.6058			−0.783208			−0.391604	−	0.920134i	$-0.628080\pi$
$761$	−21.6058			−0.783208			−0.391604	+	0.920134i	$0.628080\pi$
$762$	3.97297	−	18.7259i	0.143926	−	0.678367i
$763$		−	0.415154i		−	0.0150296i
$764$	12.8813	+	5.72357i	0.466030	+	0.207071i
$765$			7.79273i			0.281747i
$766$	−31.4338	−	6.66914i	−1.13575	−	0.240966i
$767$	7.68911			0.277638
$768$	−15.9173	−	1.62473i	−0.574366	−	0.0586273i
$769$	−7.24401			−0.261226			−0.130613	−	0.991433i	$-0.541695\pi$
$769$	−7.24401			−0.261226			−0.130613	+	0.991433i	$0.541695\pi$
$770$	1.05430	+	0.223686i	0.0379944	+	0.00806107i
$771$		−	11.7476i		−	0.423080i
$772$	−28.2126	−	12.5357i	−1.01540	−	0.451171i
$773$			28.8217i			1.03665i	0.855185	+	0.518323i	$0.173443\pi$
$773$			28.8217i			1.03665i	−0.855185	+	0.518323i	$0.826557\pi$
$774$	2.92317	−	13.7778i	0.105071	−	0.495233i
$775$	−32.5173			−1.16806
$776$	−24.0604	−	17.4396i	−0.863717	−	0.626044i
$777$	0.446389			0.0160141
$778$	−7.66159	+	36.1115i	−0.274681	+	1.29466i
$779$			19.7357i			0.707104i
$780$	−3.50399	+	7.88601i	−0.125463	+	0.282364i
$781$		−	3.20322i		−	0.114620i
$782$	−8.14304	−	1.72767i	−0.291195	−	0.0617812i
$783$	−10.0792			−0.360200
$784$	−18.6681	−	20.6706i	−0.666717	−	0.738235i
$785$	24.9236			0.889560
$786$	6.51220	+	1.38166i	0.232283	+	0.0492822i
$787$			36.3333i			1.29514i	0.762006	+	0.647570i	$0.224215\pi$
$787$			36.3333i			1.29514i	−0.762006	+	0.647570i	$0.775785\pi$
$788$	5.42043	−	12.1991i	0.193095	−	0.434575i
$789$		−	26.6460i		−	0.948622i
$790$	0.821847	−	3.87362i	0.0292400	−	0.137817i
$791$	2.79290			0.0993042
$792$	4.97825	−	6.86821i	0.176894	−	0.244051i
$793$	24.0270			0.853223
$794$	−2.97185	+	14.0073i	−0.105467	+	0.497100i
$795$		−	11.1828i		−	0.396613i
$796$	−37.1231	−	16.4949i	−1.31579	−	0.584648i
$797$			44.3607i			1.57134i	0.618648	+	0.785668i	$0.287681\pi$
$797$			44.3607i			1.57134i	−0.618648	+	0.785668i	$0.712319\pi$
$798$	0.778057	+	0.165076i	0.0275429	+	0.00584363i
$799$	21.5715			0.763143
$800$	9.21448	+	15.8911i	0.325781	+	0.561835i
$801$	−11.7235			−0.414229
$802$	−11.6332	−	2.46816i	−0.410783	−	0.0871537i
$803$		−	47.3836i		−	1.67213i
$804$	15.9894	+	7.10457i	0.563902	+	0.250559i
$805$			0.254112i			0.00895626i
$806$	9.57896	−	45.1487i	0.337404	−	1.59029i
$807$	−16.3199			−0.574489
$808$	4.63879	−	6.39987i	0.163192	−	0.225147i
$809$	−6.56801			−0.230919			−0.115460	−	0.993312i	$-0.536834\pi$
$809$	−6.56801			−0.230919			−0.115460	+	0.993312i	$0.536834\pi$
$810$	0.388583	−	1.83152i	0.0136534	−	0.0643530i
$811$			53.3049i			1.87179i	0.352280	+	0.935895i	$0.385406\pi$
$811$			53.3049i			1.87179i	−0.352280	+	0.935895i	$0.614594\pi$
$812$	1.57110	−	3.53588i	0.0551347	−	0.124085i
$813$			7.41362i			0.260007i
$814$	9.64909	+	2.04720i	0.338200	+	0.0717542i
$815$	17.2305			0.603558
$816$	−17.4735	+	15.7807i	−0.611694	+	0.552434i
$817$	29.1821			1.02095
$818$	−19.8579	−	4.21315i	−0.694315	−	0.147309i
$819$		−	0.625551i		−	0.0218585i
$820$	−7.24153	+	16.2976i	−0.252885	+	0.569138i
$821$		−	19.7133i		−	0.687998i	−0.938970	−	0.343999i	$-0.888218\pi$
$821$		−	19.7133i		−	0.687998i	0.938970	−	0.343999i	$-0.111782\pi$
$822$	0.500185	−	2.35753i	0.0174460	−	0.0822284i
$823$	21.2851			0.741952			0.370976	−	0.928642i	$-0.379023\pi$
$823$	21.2851			0.741952			0.370976	+	0.928642i	$0.379023\pi$
$824$	20.2827	+	14.7014i	0.706581	+	0.512148i
$825$	−9.73879			−0.339061
$826$	0.132916	−	0.626473i	0.00462472	−	0.0217978i
$827$		−	40.7445i		−	1.41682i	−0.705799	−	0.708412i	$-0.749412\pi$
$827$		−	40.7445i		−	1.41682i	0.705799	−	0.708412i	$-0.250588\pi$
$828$	1.82770	+	0.812103i	0.0635170	+	0.0282225i
$829$			15.1191i			0.525107i	0.964917	+	0.262554i	$0.0845647\pi$
$829$			15.1191i			0.525107i	−0.964917	+	0.262554i	$0.915435\pi$
$830$	−9.29207	−	1.97145i	−0.322533	−	0.0684300i
$831$	−15.3661			−0.533045
$832$	−24.7784	+	8.11264i	−0.859036	+	0.281255i
$833$	−40.9863			−1.42009
$834$	−12.2749	−	2.60430i	−0.425044	−	0.0901794i
$835$		−	14.3136i		−	0.495344i
$836$	16.0613	+	7.13653i	0.555492	+	0.246822i
$837$			10.0137i			0.346125i
$838$	−2.20322	+	10.3845i	−0.0761090	+	0.358726i
$839$	24.1826			0.834877			0.417439	−	0.908705i	$-0.362928\pi$
$839$	24.1826			0.834877			0.417439	+	0.908705i	$0.362928\pi$
$840$	0.581945	+	0.421808i	0.0200790	+	0.0145538i
$841$	−72.5896			−2.50309
$842$	1.32607	−	6.25021i	0.0456995	−	0.215396i
$843$			22.0697i			0.760120i
$844$	−17.6045	+	39.6203i	−0.605972	+	1.36379i
$845$		−	3.14876i		−	0.108321i
$846$	−5.06991	−	1.07566i	−0.174307	−	0.0369819i
$847$	0.384956			0.0132272
$848$	25.0750	−	22.6458i	0.861077	−	0.777659i
$849$	23.7862			0.816339
$850$	26.4427	+	5.61021i	0.906977	+	0.192429i
$851$			2.32566i			0.0797225i
$852$	0.867385	−	1.95212i	0.0297161	−	0.0668784i
$853$			23.5617i			0.806737i	0.915038	+	0.403369i	$0.132161\pi$
$853$			23.5617i			0.806737i	−0.915038	+	0.403369i	$0.867839\pi$
$854$	0.415335	−	1.95761i	0.0142125	−	0.0669880i
$855$	3.87924			0.132667
$856$	−14.6361	+	20.1926i	−0.500251	+	0.690168i
$857$	53.8027			1.83786			0.918932	−	0.394416i	$-0.129053\pi$
$857$	53.8027			1.83786			0.918932	+	0.394416i	$0.129053\pi$
$858$	2.86886	−	13.5218i	0.0979411	−	0.461628i
$859$		−	8.74277i		−	0.298300i	−0.988815	−	0.149150i	$-0.952346\pi$
$859$		−	8.74277i		−	0.298300i	0.988815	−	0.149150i	$-0.0476537\pi$
$860$	24.0984	+	10.7077i	0.821749	+	0.365128i
$861$		−	1.29280i		−	0.0440584i
$862$	−7.39062	−	1.56803i	−0.251726	−	0.0534073i
$863$	29.4074			1.00104			0.500519	−	0.865725i	$-0.333142\pi$
$863$	29.4074			1.00104			0.500519	+	0.865725i	$0.333142\pi$
$864$	4.89367	−	2.83760i	0.166486	−	0.0965373i
$865$	−26.4357			−0.898840
$866$	−15.4736	−	3.28296i	−0.525815	−	0.111559i
$867$			17.6470i			0.599323i
$868$	−3.51292	−	1.56090i	−0.119236	−	0.0529803i
$869$			6.34297i			0.215171i
$870$	3.91660	−	18.4602i	0.132785	−	0.625858i
$871$	28.5116			0.966079
$872$	3.59031	−	4.95334i	0.121583	−	0.167741i
$873$	10.5062			0.355581
$874$	−0.860036	+	4.05362i	−0.0290912	+	0.137116i
$875$		−	2.09573i		−	0.0708486i
$876$	12.8308	−	28.8767i	0.433512	−	0.975652i
$877$			37.5621i			1.26838i	0.773176	+	0.634192i	$0.218667\pi$
$877$			37.5621i			1.26838i	−0.773176	+	0.634192i	$0.781333\pi$
$878$	2.04256	+	0.433360i	0.0689332	+	0.0146252i
$879$	20.7999			0.701563
$880$	10.6448	+	11.7866i	0.358835	+	0.397327i
$881$	−49.1144			−1.65471			−0.827354	−	0.561681i	$-0.810155\pi$
$881$	−49.1144			−1.65471			−0.827354	+	0.561681i	$0.810155\pi$
$882$	9.63297	+	2.04378i	0.324359	+	0.0688176i
$883$			15.4901i			0.521284i	0.965435	+	0.260642i	$0.0839343\pi$
$883$			15.4901i			0.521284i	−0.965435	+	0.260642i	$0.916066\pi$
$884$	−15.5790	+	35.0617i	−0.523978	+	1.17925i
$885$		−	3.12348i		−	0.104994i
$886$	4.73944	−	22.3385i	0.159225	−	0.750476i
$887$	−16.3374			−0.548555			−0.274277	−	0.961651i	$-0.588439\pi$
$887$	−16.3374			−0.548555			−0.274277	+	0.961651i	$0.588439\pi$
$888$	5.32602	+	3.86044i	0.178730	+	0.129548i
$889$	−2.59810			−0.0871374
$890$	4.55555	−	21.4717i	0.152702	−	0.719735i
$891$			2.99907i			0.100473i
$892$	−5.43678	−	2.41573i	−0.182037	−	0.0808845i
$893$		−	10.7383i		−	0.359344i
$894$	−21.1709	−	4.49171i	−0.708060	−	0.150225i
$895$	−0.916349			−0.0306302
$896$	0.232657	+	2.15906i	0.00777251	+	0.0721293i
$897$	3.25908			0.108818
$898$	−35.6390	−	7.56135i	−1.18929	−	0.252325i
$899$			100.930i			3.36620i
$900$	−5.93504	−	2.63712i	−0.197835	−	0.0879040i
$901$		−	49.7195i		−	1.65640i
$902$	5.92892	−	27.9449i	0.197412	−	0.930463i
$903$	−1.91159			−0.0636136
$904$	33.3231	+	24.1534i	1.10831	+	0.803332i
$905$	6.46711			0.214974
$906$	−1.55713	+	7.33925i	−0.0517322	+	0.243830i
$907$		−	12.5162i		−	0.415594i	−0.978172	−	0.207797i	$-0.933371\pi$
$907$		−	12.5162i		−	0.415594i	0.978172	−	0.207797i	$-0.0666294\pi$
$908$	4.66307	−	10.4946i	0.154750	−	0.348276i
$909$			2.79457i			0.0926899i
$910$	1.14571	+	0.243079i	0.0379798	+	0.00805798i
$911$	49.8408			1.65130			0.825649	−	0.564184i	$-0.190809\pi$
$911$	49.8408			1.65130			0.825649	+	0.564184i	$0.190809\pi$
$912$	7.85566	+	8.69833i	0.260127	+	0.288030i
$913$	15.2156			0.503561
$914$	−5.53618	−	1.17458i	−0.183121	−	0.0388518i
$915$		−	9.76026i		−	0.322664i
$916$	11.1788	−	25.1587i	0.369357	−	0.831267i
$917$		−	0.903528i		−	0.0298371i
$918$	1.72767	−	8.14304i	0.0570215	−	0.268760i
$919$	−12.0336			−0.396952			−0.198476	−	0.980106i	$-0.563599\pi$
$919$	−12.0336			−0.396952			−0.198476	+	0.980106i	$0.563599\pi$
$920$	−2.19760	+	3.03189i	−0.0724526	+	0.0999586i
$921$	14.2896			0.470857
$922$	−7.74541	+	36.5066i	−0.255081	+	1.20228i
$923$		−	3.48093i		−	0.114576i
$924$	−1.05210	−	0.467482i	−0.0346117	−	0.0153790i
$925$		−	7.55205i		−	0.248310i
$926$	25.2520	+	5.35759i	0.829833	+	0.176061i
$927$	−8.85663			−0.290890
$928$	49.3241	−	28.6007i	1.61914	−	0.938864i
$929$	−3.37137			−0.110611			−0.0553055	−	0.998469i	$-0.517613\pi$
$929$	−3.37137			−0.110611			−0.0553055	+	0.998469i	$0.517613\pi$
$930$	−18.3403	−	3.89117i	−0.601403	−	0.127596i
$931$			20.4031i			0.668684i
$932$	50.0777	+	22.2511i	1.64035	+	0.728858i
$933$		−	30.3745i		−	0.994415i
$934$	11.3346	−	53.4234i	0.370878	−	1.74807i
$935$	23.3709			0.764311
$936$	5.40986	−	7.46367i	0.176827	−	0.243958i
$937$	18.4301			0.602085			0.301043	−	0.953611i	$-0.402665\pi$
$937$	18.4301			0.602085			0.301043	+	0.953611i	$0.402665\pi$
$938$	0.492858	−	2.32299i	0.0160924	−	0.0758484i
$939$			0.853858i			0.0278646i
$940$	3.94017	−	8.86765i	0.128514	−	0.289231i
$941$		−	27.2409i		−	0.888027i	−0.896020	−	0.444013i	$-0.853554\pi$
$941$		−	27.2409i		−	0.888027i	0.896020	−	0.444013i	$-0.146446\pi$
$942$	−26.0440	−	5.52561i	−0.848558	−	0.180034i
$943$	6.73538			0.219334
$944$	7.00370	−	6.32520i	0.227951	−	0.205868i
$945$	−0.254112			−0.00826625
$946$	−41.3206	−	8.76677i	−1.34345	−	0.285032i
$947$			27.2844i			0.886623i	0.896368	+	0.443311i	$0.146196\pi$
$947$			27.2844i			0.886623i	−0.896368	+	0.443311i	$0.853804\pi$
$948$	−1.71758	+	3.86555i	−0.0557845	+	0.125547i
$949$		−	51.4917i		−	1.67149i
$950$	2.79277	−	13.1632i	0.0906095	−	0.427072i
$951$	−17.0505			−0.552902
$952$	2.58736	+	1.87539i	0.0838569	+	0.0607817i
$953$	−19.2257			−0.622782			−0.311391	−	0.950282i	$-0.600795\pi$
$953$	−19.2257			−0.622782			−0.311391	+	0.950282i	$0.600795\pi$
$954$	−2.47925	+	11.6855i	−0.0802688	+	0.378333i
$955$		−	9.33067i		−	0.301933i
$956$	−15.9972	−	7.10804i	−0.517386	−	0.229890i
$957$			30.2281i			0.977136i
$958$	36.1285	+	7.66520i	1.16726	+	0.247651i
$959$	−0.327093			−0.0105624
$960$	3.29552	+	10.0655i	0.106363	+	0.324862i
$961$	69.2747			2.23467
$962$	10.4856	+	2.22468i	0.338071	+	0.0717267i
$963$		−	8.81728i		−	0.284133i
$964$	−0.181384	−	0.0805943i	−0.00584198	−	0.00259577i
$965$			20.4360i			0.657858i
$966$	0.0563371	−	0.265535i	0.00181262	−	0.00854344i
$967$	−21.4557			−0.689968			−0.344984	−	0.938609i	$-0.612116\pi$
$967$	−21.4557			−0.689968			−0.344984	+	0.938609i	$0.612116\pi$
$968$	4.59304	+	3.32915i	0.147626	+	0.107003i
$969$	17.2473			0.554065
$970$	−4.08253	+	19.2423i	−0.131082	+	0.617832i
$971$			56.0901i			1.80002i	0.435874	+	0.900008i	$0.356439\pi$
$971$			56.0901i			1.80002i	−0.435874	+	0.900008i	$0.643561\pi$
$972$	−0.812103	+	1.82770i	−0.0260482	+	0.0586235i
$973$			1.70306i			0.0545977i
$974$	−11.3760	−	2.41360i	−0.364512	−	0.0773366i
$975$	−10.5831			−0.338931
$976$	21.8852	−	19.7650i	0.700528	−	0.632663i
$977$	−15.6208			−0.499755			−0.249877	−	0.968277i	$-0.580390\pi$
$977$	−15.6208			−0.499755			−0.249877	+	0.968277i	$0.580390\pi$
$978$	−18.0051	−	3.82004i	−0.575739	−	0.122152i
$979$			35.1595i			1.12370i
$980$	−7.48643	+	16.8488i	−0.239145	+	0.538214i
$981$			2.16292i			0.0690569i
$982$	−4.54596	+	21.4265i	−0.145067	+	0.683749i
$983$	−15.4826			−0.493818			−0.246909	−	0.969039i	$-0.579415\pi$
$983$	−15.4826			−0.493818			−0.246909	+	0.969039i	$0.579415\pi$
$984$	11.1803	−	15.4248i	0.356415	−	0.491724i
$985$	−8.83649			−0.281554
$986$	17.4134	−	82.0751i	0.554557	−	2.61380i
$987$			0.703419i			0.0223901i
$988$	17.4538	+	7.75525i	0.555279	+	0.246727i
$989$		−	9.95924i		−	0.316686i
$990$	−5.49284	−	1.16539i	−0.174574	−	0.0370385i
$991$	23.8697			0.758246			0.379123	−	0.925346i	$-0.376226\pi$
$991$	23.8697			0.758246			0.379123	+	0.925346i	$0.376226\pi$
$992$	−28.4150	−	49.0039i	−0.902177	−	1.55587i
$993$	11.2123			0.355811
$994$	−0.283610	−	0.0601721i	−0.00899557	−	0.00190854i
$995$			26.8904i			0.852482i
$996$	9.27271	+	4.12015i	0.293817	+	0.130552i
$997$			10.2001i			0.323041i	0.986869	+	0.161520i	$0.0516397\pi$
$997$			10.2001i			0.323041i	−0.986869	+	0.161520i	$0.948360\pi$
$998$	7.42133	−	34.9791i	0.234918	−	1.10724i
$999$	−2.32566			−0.0735806

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.c.277.18	yes	18
4.3	odd	2		2208.2.f.c.1105.3		18
8.3	odd	2		2208.2.f.c.1105.16		18
8.5	even	2	inner	552.2.f.c.277.17	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.c.277.17	✓	18	8.5	even	2	inner
552.2.f.c.277.18	yes	18	1.1	even	1	trivial
2208.2.f.c.1105.3		18	4.3	odd	2
2208.2.f.c.1105.16		18	8.3	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38342 + 0.293513i) q^{2} +1.00000i q^{3} +(1.82770 + 0.812103i) q^{4} -1.32391i q^{5} +(-0.293513 + 1.38342i) q^{6} +0.191941 q^{7} +(2.29011 + 1.65993i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.38342 + 0.293513i) q^{2} +1.00000i q^{3} +(1.82770 + 0.812103i) q^{4} -1.32391i q^{5} +(-0.293513 + 1.38342i) q^{6} +0.191941 q^{7} +(2.29011 + 1.65993i) q^{8} -1.00000 q^{9} +(0.388583 - 1.83152i) q^{10} +2.99907i q^{11} +(-0.812103 + 1.82770i) q^{12} +3.25908i q^{13} +(0.265535 + 0.0563371i) q^{14} +1.32391 q^{15} +(2.68098 + 2.96856i) q^{16} +5.88617 q^{17} +(-1.38342 - 0.293513i) q^{18} -2.93015i q^{19} +(1.07515 - 2.41970i) q^{20} +0.191941i q^{21} +(-0.880265 + 4.14897i) q^{22} -1.00000 q^{23} +(-1.65993 + 2.29011i) q^{24} +3.24727 q^{25} +(-0.956582 + 4.50868i) q^{26} -1.00000i q^{27} +(0.350810 + 0.155876i) q^{28} -10.0792i q^{29} +(1.83152 + 0.388583i) q^{30} -10.0137 q^{31} +(2.83760 + 4.89367i) q^{32} -2.99907 q^{33} +(8.14304 + 1.72767i) q^{34} -0.254112i q^{35} +(-1.82770 - 0.812103i) q^{36} -2.32566i q^{37} +(0.860036 - 4.05362i) q^{38} -3.25908 q^{39} +(2.19760 - 3.03189i) q^{40} -6.73538 q^{41} +(-0.0563371 + 0.265535i) q^{42} +9.95924i q^{43} +(-2.43555 + 5.48140i) q^{44} +1.32391i q^{45} +(-1.38342 - 0.293513i) q^{46} +3.66477 q^{47} +(-2.96856 + 2.68098i) q^{48} -6.96316 q^{49} +(4.49234 + 0.953117i) q^{50} +5.88617i q^{51} +(-2.64671 + 5.95662i) q^{52} -8.44683i q^{53} +(0.293513 - 1.38342i) q^{54} +3.97048 q^{55} +(0.439567 + 0.318609i) q^{56} +2.93015 q^{57} +(2.95837 - 13.9437i) q^{58} -2.35929i q^{59} +(2.41970 + 1.07515i) q^{60} -7.37232i q^{61} +(-13.8532 - 2.93916i) q^{62} -0.191941 q^{63} +(2.48924 + 7.60287i) q^{64} +4.31472 q^{65} +(-4.14897 - 0.880265i) q^{66} -8.74836i q^{67} +(10.7582 + 4.78018i) q^{68} -1.00000i q^{69} +(0.0745851 - 0.351543i) q^{70} -1.06807 q^{71} +(-2.29011 - 1.65993i) q^{72} -15.7994 q^{73} +(0.682611 - 3.21736i) q^{74} +3.24727i q^{75} +(2.37958 - 5.35543i) q^{76} +0.575644i q^{77} +(-4.50868 - 0.956582i) q^{78} +2.11498 q^{79} +(3.93010 - 3.54936i) q^{80} +1.00000 q^{81} +(-9.31786 - 1.97692i) q^{82} -5.07343i q^{83} +(-0.155876 + 0.350810i) q^{84} -7.79273i q^{85} +(-2.92317 + 13.7778i) q^{86} +10.0792 q^{87} +(-4.97825 + 6.86821i) q^{88} +11.7235 q^{89} +(-0.388583 + 1.83152i) q^{90} +0.625551i q^{91} +(-1.82770 - 0.812103i) q^{92} -10.0137i q^{93} +(5.06991 + 1.07566i) q^{94} -3.87924 q^{95} +(-4.89367 + 2.83760i) q^{96} -10.5062 q^{97} +(-9.63297 - 2.04378i) q^{98} -2.99907i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Introduction

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