LMFDB - Embedded newform 169.2.h.a.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(12,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([21]))

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.h (of order $26$, degree $12$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	169.25
Dual form			169.2.h.a.142.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.622921 - 0.236243i) q^{2} +(-1.59376 - 2.30896i) q^{3} +(-1.16480 - 1.03192i) q^{4} +(3.47190 + 0.421565i) q^{5} +(0.447311 + 1.81481i) q^{6} +(-1.63679 - 3.11863i) q^{7} +(1.10100 + 2.09779i) q^{8} +(-1.72740 + 4.55479i) q^{9} +O(q^{10})$	\(q+(-0.622921 - 0.236243i) q^{2} +(-1.59376 - 2.30896i) q^{3} +(-1.16480 - 1.03192i) q^{4} +(3.47190 + 0.421565i) q^{5} +(0.447311 + 1.81481i) q^{6} +(-1.63679 - 3.11863i) q^{7} +(1.10100 + 2.09779i) q^{8} +(-1.72740 + 4.55479i) q^{9} +(-2.06313 - 1.08281i) q^{10} +(-4.16859 + 1.58094i) q^{11} +(-0.526257 + 4.33412i) q^{12} +(-1.62040 - 3.22092i) q^{13} +(0.282833 + 2.32934i) q^{14} +(-4.56000 - 8.68835i) q^{15} +(0.184897 + 1.52276i) q^{16} +(0.291510 - 0.152996i) q^{17} +(2.15207 - 2.42919i) q^{18} +1.89876i q^{19} +(-3.60906 - 4.07378i) q^{20} +(-4.59215 + 8.74962i) q^{21} +2.97019 q^{22} +5.94018 q^{23} +(3.08897 - 5.88554i) q^{24} +(7.02169 + 1.73069i) q^{25} +(0.248465 + 2.38918i) q^{26} +(5.09769 - 1.25647i) q^{27} +(-1.31166 + 5.32163i) q^{28} +(2.40046 - 6.32950i) q^{29} +(0.787959 + 6.48942i) q^{30} +(-1.59005 - 6.45110i) q^{31} +(1.37852 - 5.59288i) q^{32} +(10.2941 + 7.10547i) q^{33} +(-0.217732 + 0.0264374i) q^{34} +(-4.36805 - 11.5176i) q^{35} +(6.71228 - 3.52288i) q^{36} +(-0.381270 - 1.54687i) q^{37} +(0.448568 - 1.18278i) q^{38} +(-4.85443 + 8.87480i) q^{39} +(2.93823 + 7.74747i) q^{40} +(-2.97928 + 2.05645i) q^{41} +(4.92758 - 4.36546i) q^{42} +(4.78503 + 1.17940i) q^{43} +(6.48699 + 2.46019i) q^{44} +(-7.91753 + 15.0856i) q^{45} +(-3.70027 - 1.40333i) q^{46} +(-6.93071 - 7.82316i) q^{47} +(3.22132 - 2.85384i) q^{48} +(-3.07036 + 4.44819i) q^{49} +(-3.96509 - 2.73691i) q^{50} +(-0.817858 - 0.429245i) q^{51} +(-1.43629 + 5.42386i) q^{52} +(3.28768 - 1.72551i) q^{53} +(-3.47229 - 0.421612i) q^{54} +(-15.1394 + 3.73153i) q^{55} +(4.74013 - 6.86726i) q^{56} +(4.38415 - 3.02616i) q^{57} +(-2.99060 + 3.37569i) q^{58} +(9.68905 + 1.17646i) q^{59} +(-3.65423 + 14.8258i) q^{60} +(-5.92446 - 3.10940i) q^{61} +(-0.533548 + 4.39417i) q^{62} +(17.0321 - 2.06807i) q^{63} +(-0.437224 + 0.633429i) q^{64} +(-4.26806 - 11.8658i) q^{65} +(-4.73377 - 6.85804i) q^{66} +(6.40769 + 7.23278i) q^{67} +(-0.497432 - 0.122606i) q^{68} +(-9.46722 - 13.7156i) q^{69} +8.20648i q^{70} +(2.32404 - 1.60417i) q^{71} +(-11.4569 + 1.39112i) q^{72} +(6.70968 - 2.54465i) q^{73} +(-0.127937 + 1.05365i) q^{74} +(-7.19478 - 18.9711i) q^{75} +(1.95937 - 2.21167i) q^{76} +(11.7535 + 10.4127i) q^{77} +(5.12053 - 4.38148i) q^{78} +(-0.665946 + 0.589977i) q^{79} +5.36483i q^{80} +(-0.0868336 - 0.0769278i) q^{81} +(2.34168 - 0.577172i) q^{82} +(2.63349 + 1.81776i) q^{83} +(14.3779 - 5.45281i) q^{84} +(1.07659 - 0.408298i) q^{85} +(-2.70207 - 1.86510i) q^{86} +(-18.4403 + 4.54513i) q^{87} +(-7.90612 - 7.00421i) q^{88} -2.61048i q^{89} +(8.49585 - 7.52667i) q^{90} +(-7.39260 + 10.3254i) q^{91} +(-6.91914 - 6.12982i) q^{92} +(-12.3612 + 13.9529i) q^{93} +(2.46912 + 6.51054i) q^{94} +(-0.800450 + 6.59230i) q^{95} +(-15.1108 + 5.73075i) q^{96} +(-10.4348 + 1.26701i) q^{97} +(2.96344 - 2.04552i) q^{98} -21.7180i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{26}\right)$

Coefficient data

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

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

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

$2$	−0.622921	−	0.236243i	−0.440472	−	0.167049i	0.124392	−	0.992233i	$-0.460302\pi$
$2$	−0.622921	−	0.236243i	−0.440472	−	0.167049i	−0.564864	+	0.825184i	$0.691071\pi$
$3$	−1.59376	−	2.30896i	−0.920157	−	1.33308i	−0.942809	−	0.333334i	$-0.891826\pi$
$3$	−1.59376	−	2.30896i	−0.920157	−	1.33308i	0.0226520	−	0.999743i	$-0.492789\pi$
$4$	−1.16480	−	1.03192i	−0.582401	−	0.515962i
$5$	3.47190	+	0.421565i	1.55268	+	0.188530i	0.851463	−	0.524415i	$-0.175716\pi$
$5$	3.47190	+	0.421565i	1.55268	+	0.188530i	0.701220	+	0.712945i	$0.252639\pi$
$6$	0.447311	+	1.81481i	0.182614	+	0.740894i
$7$	−1.63679	−	3.11863i	−0.618647	−	1.17873i	−0.970141	−	0.242543i	$-0.922018\pi$
$7$	−1.63679	−	3.11863i	−0.618647	−	1.17873i	0.351494	−	0.936190i	$-0.385674\pi$
$8$	1.10100	+	2.09779i	0.389264	+	0.741681i
$9$	−1.72740	+	4.55479i	−0.575802	+	1.51826i
$10$	−2.06313	−	1.08281i	−0.652419	−	0.342416i
$11$	−4.16859	+	1.58094i	−1.25688	+	0.476671i	−0.891005	−	0.453994i	$-0.849999\pi$
$11$	−4.16859	+	1.58094i	−1.25688	+	0.476671i	−0.365873	+	0.930665i	$0.619230\pi$
$12$	−0.526257	+	4.33412i	−0.151917	+	1.25115i
$13$	−1.62040	−	3.22092i	−0.449419	−	0.893321i
$13$	−1.62040	−	3.22092i	−0.449419	−	0.893321i
$14$	0.282833	+	2.32934i	0.0755904	+	0.622543i
$15$	−4.56000	−	8.68835i	−1.17739	−	2.24332i
$16$	0.184897	+	1.52276i	0.0462242	+	0.380691i
$17$	0.291510	−	0.152996i	0.0707016	−	0.0371070i	−0.429002	−	0.903304i	$-0.641135\pi$
$17$	0.291510	−	0.152996i	0.0707016	−	0.0371070i	0.499703	+	0.866197i	$0.333442\pi$
$18$	2.15207	−	2.42919i	0.507249	−	0.572565i
$19$			1.89876i			0.435605i	0.975993	+	0.217802i	$0.0698888\pi$
$19$			1.89876i			0.435605i	−0.975993	+	0.217802i	$0.930111\pi$
$20$	−3.60906	−	4.07378i	−0.807009	−	0.910925i
$21$	−4.59215	+	8.74962i	−1.00209	+	1.90932i
$22$	2.97019			0.633247
$23$	5.94018			1.23861			0.619307	−	0.785149i	$-0.287414\pi$
$23$	5.94018			1.23861			0.619307	+	0.785149i	$0.287414\pi$
$24$	3.08897	−	5.88554i	0.630534	−	1.20138i
$25$	7.02169	+	1.73069i	1.40434	+	0.346138i
$26$	0.248465	+	2.38918i	0.0487280	+	0.468558i
$27$	5.09769	−	1.25647i	0.981050	−	0.241807i
$28$	−1.31166	+	5.32163i	−0.247881	+	1.00569i
$29$	2.40046	−	6.32950i	0.445755	−	1.17536i	−0.504369	−	0.863488i	$-0.668275\pi$
$29$	2.40046	−	6.32950i	0.445755	−	1.17536i	0.950124	−	0.311871i	$-0.100956\pi$
$30$	0.787959	+	6.48942i	0.143861	+	1.18480i
$31$	−1.59005	−	6.45110i	−0.285582	−	1.15865i	−0.921963	−	0.387277i	$-0.873416\pi$
$31$	−1.59005	−	6.45110i	−0.285582	−	1.15865i	0.636381	−	0.771375i	$-0.280431\pi$
$32$	1.37852	−	5.59288i	0.243690	−	0.988691i
$33$	10.2941	+	7.10547i	1.79196	+	1.23690i
$34$	−0.217732	+	0.0264374i	−0.0373407	+	0.00453399i
$35$	−4.36805	−	11.5176i	−0.738336	−	1.94683i
$36$	6.71228	−	3.52288i	1.11871	−	0.587146i
$37$	−0.381270	−	1.54687i	−0.0626805	−	0.254305i	0.931240	−	0.364407i	$-0.118728\pi$
$37$	−0.381270	−	1.54687i	−0.0626805	−	0.254305i	−0.993920	+	0.110102i	$0.964882\pi$
$38$	0.448568	−	1.18278i	0.0727673	−	0.191871i
$39$	−4.85443	+	8.87480i	−0.777330	+	1.42111i
$40$	2.93823	+	7.74747i	0.464575	+	1.22498i
$41$	−2.97928	+	2.05645i	−0.465286	+	0.321164i	−0.777538	−	0.628835i	$-0.783532\pi$
$41$	−2.97928	+	2.05645i	−0.465286	+	0.321164i	0.312252	+	0.949999i	$0.398917\pi$
$42$	4.92758	−	4.36546i	0.760343	−	0.673605i
$43$	4.78503	+	1.17940i	0.729710	+	0.179857i	0.586632	−	0.809854i	$-0.300454\pi$
$43$	4.78503	+	1.17940i	0.729710	+	0.179857i	0.143079	+	0.989711i	$0.454300\pi$
$44$	6.48699	+	2.46019i	0.977951	+	0.370888i
$45$	−7.91753	+	15.0856i	−1.18028	+	2.24883i
$46$	−3.70027	−	1.40333i	−0.545574	−	0.206909i
$47$	−6.93071	−	7.82316i	−1.01095	−	1.14112i	−0.989960	−	0.141345i	$-0.954857\pi$
$47$	−6.93071	−	7.82316i	−1.01095	−	1.14112i	−0.0209880	−	0.999780i	$-0.506681\pi$
$48$	3.22132	−	2.85384i	0.464957	−	0.411916i
$49$	−3.07036	+	4.44819i	−0.438623	+	0.635455i
$50$	−3.96509	−	2.73691i	−0.560749	−	0.387057i
$51$	−0.817858	−	0.429245i	−0.114523	−	0.0601064i
$52$	−1.43629	+	5.42386i	−0.199178	+	0.752154i
$53$	3.28768	−	1.72551i	0.451598	−	0.237017i	−0.223560	−	0.974690i	$-0.571768\pi$
$53$	3.28768	−	1.72551i	0.451598	−	0.237017i	0.675158	+	0.737673i	$0.264075\pi$
$54$	−3.47229	−	0.421612i	−0.472518	−	0.0573741i
$55$	−15.1394	+	3.73153i	−2.04140	+	0.503160i
$56$	4.74013	−	6.86726i	0.633427	−	0.917677i
$57$	4.38415	−	3.02616i	0.580695	−	0.400825i
$58$	−2.99060	+	3.37569i	−0.392685	+	0.443250i
$59$	9.68905	+	1.17646i	1.26141	+	0.153163i	0.723786	−	0.690024i	$-0.242400\pi$
$59$	9.68905	+	1.17646i	1.26141	+	0.153163i	0.537621	+	0.843187i	$0.319323\pi$
$60$	−3.65423	+	14.8258i	−0.471759	+	1.91400i
$61$	−5.92446	−	3.10940i	−0.758550	−	0.398118i	0.0406575	−	0.999173i	$-0.487055\pi$
$61$	−5.92446	−	3.10940i	−0.758550	−	0.398118i	−0.799207	+	0.601055i	$0.794747\pi$
$62$	−0.533548	+	4.39417i	−0.0677607	+	0.558060i
$63$	17.0321	−	2.06807i	2.14585	−	0.260553i
$64$	−0.437224	+	0.633429i	−0.0546531	+	0.0791786i
$65$	−4.26806	−	11.8658i	−0.529387	−	1.47177i
$66$	−4.73377	−	6.85804i	−0.582686	−	0.844167i
$67$	6.40769	+	7.23278i	0.782823	+	0.883625i	0.995622	−	0.0934711i	$-0.0297963\pi$
$67$	6.40769	+	7.23278i	0.782823	+	0.883625i	−0.212799	+	0.977096i	$0.568258\pi$
$68$	−0.497432	−	0.122606i	−0.0603225	−	0.0148682i
$69$	−9.46722	−	13.7156i	−1.13972	−	1.65117i
$70$			8.20648i			0.980862i
$71$	2.32404	−	1.60417i	0.275813	−	0.190380i	−0.422126	−	0.906537i	$-0.638716\pi$
$71$	2.32404	−	1.60417i	0.275813	−	0.190380i	0.697939	+	0.716157i	$0.254101\pi$
$72$	−11.4569	+	1.39112i	−1.35021	+	0.163945i
$73$	6.70968	−	2.54465i	0.785309	−	0.297828i	0.0708328	−	0.997488i	$-0.477434\pi$
$73$	6.70968	−	2.54465i	0.785309	−	0.297828i	0.714476	+	0.699660i	$0.246665\pi$
$74$	−0.127937	+	1.05365i	−0.0148723	+	0.122485i
$75$	−7.19478	−	18.9711i	−0.830782	−	2.19059i
$76$	1.95937	−	2.21167i	0.224755	−	0.253696i
$77$	11.7535	+	10.4127i	1.33943	+	1.18663i
$78$	5.12053	−	4.38148i	0.579786	−	0.496105i
$79$	−0.665946	+	0.589977i	−0.0749248	+	0.0663776i	−0.699754	−	0.714384i	$-0.746707\pi$
$79$	−0.665946	+	0.589977i	−0.0749248	+	0.0663776i	0.624829	+	0.780761i	$0.285169\pi$
$80$			5.36483i			0.599807i
$81$	−0.0868336	−	0.0769278i	−0.00964817	−	0.00854753i
$82$	2.34168	−	0.577172i	0.258595	−	0.0637380i
$83$	2.63349	+	1.81776i	0.289063	+	0.199526i	0.703767	−	0.710431i	$-0.251500\pi$
$83$	2.63349	+	1.81776i	0.289063	+	0.199526i	−0.414705	+	0.909956i	$0.636115\pi$
$84$	14.3779	−	5.45281i	1.56876	−	0.594951i
$85$	1.07659	−	0.408298i	0.116773	−	0.0442861i
$86$	−2.70207	−	1.86510i	−0.291372	−	0.201119i
$87$	−18.4403	+	4.54513i	−1.97701	+	0.487289i
$88$	−7.90612	−	7.00421i	−0.842795	−	0.746651i
$89$		−	2.61048i		−	0.276710i	−0.990383	−	0.138355i	$-0.955818\pi$
$89$		−	2.61048i		−	0.276710i	0.990383	−	0.138355i	$-0.0441815\pi$
$90$	8.49585	−	7.52667i	0.895542	−	0.793381i
$91$	−7.39260	+	10.3254i	−0.774956	+	1.08240i
$92$	−6.91914	−	6.12982i	−0.721370	−	0.639078i
$93$	−12.3612	+	13.9529i	−1.28179	+	1.44684i
$94$	2.46912	+	6.51054i	0.254671	+	0.671511i
$95$	−0.800450	+	6.59230i	−0.0821244	+	0.676356i
$96$	−15.1108	+	5.73075i	−1.54223	+	0.584893i
$97$	−10.4348	+	1.26701i	−1.05949	+	0.128645i	−0.631685	−	0.775225i	$-0.717636\pi$
$97$	−10.4348	+	1.26701i	−1.05949	+	0.128645i	−0.427805	+	0.903871i	$0.640713\pi$
$98$	2.96344	−	2.04552i	0.299353	−	0.206628i
$99$		−	21.7180i		−	2.18274i
$100$	−6.39293	−	9.26176i	−0.639293	−	0.926176i
$101$	−1.65603	−	0.408175i	−0.164781	−	0.0406150i	0.156062	−	0.987747i	$-0.450120\pi$
$101$	−1.65603	−	0.408175i	−0.164781	−	0.0406150i	−0.320843	+	0.947132i	$0.603966\pi$
$102$	0.408055	+	0.460599i	0.0404035	+	0.0456061i
$103$	3.60809	+	5.22722i	0.355515	+	0.515053i	0.959411	−	0.282010i	$-0.0910012\pi$
$103$	3.60809	+	5.22722i	0.355515	+	0.515053i	−0.603896	+	0.797063i	$0.706386\pi$
$104$	4.97273	−	6.94551i	0.487616	−	0.681063i
$105$	−19.6321	+	28.4419i	−1.91589	+	2.77565i
$106$	−2.45561	+	0.298165i	−0.238510	+	0.0289603i
$107$	−0.354291	+	2.91785i	−0.0342506	+	0.282079i	0.965513	+	0.260354i	$0.0838391\pi$
$107$	−0.354291	+	2.91785i	−0.0342506	+	0.282079i	−0.999764	+	0.0217257i	$0.993084\pi$
$108$	−7.23437	−	3.79689i	−0.696128	−	0.365356i
$109$	−0.521958	+	2.11767i	−0.0499945	+	0.202836i	−0.990628	−	0.136589i	$-0.956386\pi$
$109$	−0.521958	+	2.11767i	−0.0499945	+	0.202836i	0.940633	+	0.339424i	$0.110232\pi$
$110$	10.3122	+	1.25213i	0.983231	+	0.119386i
$111$	−2.96402	+	3.34568i	−0.281332	+	0.317558i
$112$	4.44631	−	3.06906i	0.420136	−	0.289999i
$113$	8.16294	−	11.8261i	0.767905	−	1.11250i	−0.222585	−	0.974913i	$-0.571449\pi$
$113$	8.16294	−	11.8261i	0.767905	−	1.11250i	0.990489	−	0.137589i	$-0.0439352\pi$
$114$	−3.44589	+	0.849335i	−0.322737	+	0.0795475i
$115$	20.6237	+	2.50418i	1.92317	+	0.233516i
$116$	−9.32763	+	4.89552i	−0.866049	+	0.454538i
$117$	17.4697	−	1.81677i	1.61507	−	0.167961i
$118$	−5.75758	−	3.02181i	−0.530029	−	0.278180i
$119$	−0.954279	−	0.658691i	−0.0874786	−	0.0603821i
$120$	13.2058	−	19.1318i	1.20551	−	1.74649i
$121$	6.64419	−	5.88624i	0.604017	−	0.535112i
$122$	2.95590	+	3.33652i	0.267615	+	0.302074i
$123$	9.49652	+	3.60155i	0.856272	+	0.324741i
$124$	−4.80495	+	9.15507i	−0.431497	+	0.822149i
$125$	7.29838	+	2.76791i	0.652787	+	0.247569i
$126$	−11.0982	−	2.73547i	−0.988709	−	0.243695i
$127$	14.0643	−	12.4599i	1.24801	−	1.10564i	0.257774	−	0.966205i	$-0.417011\pi$
$127$	14.0643	−	12.4599i	1.24801	−	1.10564i	0.990232	−	0.139431i	$-0.0445275\pi$
$128$	−9.05921	+	6.25312i	−0.800729	+	0.552703i
$129$	−4.90299	−	12.9281i	−0.431684	−	1.13826i
$130$	−0.144551	+	8.39976i	−0.0126779	+	0.736708i
$131$	−2.53158	+	6.67522i	−0.221185	+	0.583217i	−0.998973	−	0.0453100i	$-0.985572\pi$
$131$	−2.53158	+	6.67522i	−0.221185	+	0.583217i	0.777788	+	0.628527i	$0.216342\pi$
$132$	−4.65822	−	18.8991i	−0.405446	−	1.64496i
$133$	5.92153	−	3.10786i	0.513462	−	0.269485i
$134$	−2.28279	−	6.01922i	−0.197203	−	0.519982i
$135$	18.2284	−	2.21332i	1.56885	−	0.190493i
$136$	0.641908	+	0.443077i	0.0550432	+	0.0379935i
$137$	−4.21554	+	17.1031i	−0.360158	+	1.46122i	0.459404	+	0.888227i	$0.348063\pi$
$137$	−4.21554	+	17.1031i	−0.360158	+	1.46122i	−0.819562	+	0.572990i	$0.805783\pi$
$138$	2.65711	+	10.7803i	0.226188	+	0.917682i
$139$	1.61503	+	13.3010i	0.136985	+	1.12818i	0.885362	+	0.464902i	$0.153910\pi$
$139$	1.61503	+	13.3010i	0.136985	+	1.12818i	−0.748377	+	0.663274i	$0.769166\pi$
$140$	−6.79738	+	17.9232i	−0.574484	+	1.51479i
$141$	−7.01746	+	28.4709i	−0.590977	+	2.39769i
$142$	−1.82667	+	0.450234i	−0.153291	+	0.0377828i
$143$	11.8469	+	10.8649i	0.990685	+	0.908571i
$144$	−7.25526	−	1.78826i	−0.604605	−	0.149022i
$145$	11.0025	−	20.9635i	0.913706	−	1.74092i
$146$	−4.78076			−0.395658
$147$	15.1641			1.25071
$148$	−1.15215	+	2.19524i	−0.0947064	+	0.180448i
$149$	6.01963	+	6.79476i	0.493148	+	0.556649i	0.941415	−	0.337251i	$-0.109497\pi$
$149$	6.01963	+	6.79476i	0.493148	+	0.556649i	−0.448267	+	0.893900i	$0.647959\pi$
$150$			13.5172i			1.10367i
$151$	−6.46328	+	7.29554i	−0.525975	+	0.593703i	−0.950117	−	0.311893i	$-0.899037\pi$
$151$	−6.46328	+	7.29554i	−0.525975	+	0.593703i	0.424143	+	0.905595i	$0.360575\pi$
$152$	−3.98319	+	2.09054i	−0.323080	+	0.169565i
$153$	0.193310	+	1.59205i	0.0156282	+	0.128710i
$154$	−4.86156	−	9.26294i	−0.391756	−	0.746429i
$155$	−2.80095	−	23.0679i	−0.224978	−	1.85286i
$156$	14.8126	−	5.32798i	1.18595	−	0.426580i
$157$	2.37792	−	19.5839i	0.189779	−	1.56297i	−0.517282	−	0.855815i	$-0.673056\pi$
$157$	2.37792	−	19.5839i	0.189779	−	1.56297i	0.707061	−	0.707153i	$-0.250021\pi$
$158$	0.554210	−	0.210184i	0.0440906	−	0.0167213i
$159$	−9.22390	−	4.84108i	−0.731503	−	0.383922i
$160$	7.14386	−	18.8368i	0.564772	−	1.48918i
$161$	−9.72281	−	18.5253i	−0.766265	−	1.46000i
$162$	0.0359168	+	0.0684337i	0.00282189	+	0.00537666i
$163$	3.03823	+	12.3266i	0.237973	+	0.965493i	0.961414	+	0.275107i	$0.0887132\pi$
$163$	3.03823	+	12.3266i	0.237973	+	0.965493i	−0.723441	+	0.690386i	$0.757441\pi$
$164$	5.59238	+	0.679037i	0.436691	+	0.0530239i
$165$	32.7445	+	29.0091i	2.54916	+	2.25836i
$166$	−1.21102	−	1.75447i	−0.0939934	−	0.136173i
$167$	−3.18964	−	1.20967i	−0.246822	−	0.0936073i	0.228092	−	0.973640i	$-0.426751\pi$
$167$	−3.18964	−	1.20967i	−0.246822	−	0.0936073i	−0.474914	+	0.880032i	$0.657521\pi$
$168$	−23.4108			−1.80619
$169$	−7.74859	+	10.4384i	−0.596045	+	0.802951i
$170$	−0.767090			−0.0588331
$171$	−8.64844	−	3.27992i	−0.661363	−	0.250822i
$172$	−4.35655	−	6.31156i	−0.332184	−	0.481252i
$173$	6.17638	+	5.47180i	0.469582	+	0.416013i	0.864445	−	0.502727i	$-0.167670\pi$
$173$	6.17638	+	5.47180i	0.469582	+	0.416013i	−0.394864	+	0.918740i	$0.629208\pi$
$174$	12.5606	+	1.52513i	0.952218	+	0.115620i
$175$	−6.09561	−	24.7308i	−0.460785	−	1.86948i
$176$	−3.17816	−	6.05547i	−0.239563	−	0.456448i
$177$	−12.7256	−	24.2466i	−0.956515	−	1.82249i
$178$	−0.616707	+	1.62612i	−0.0462241	+	0.121883i
$179$	5.80049	+	3.04433i	0.433549	+	0.227544i	0.667356	−	0.744739i	$-0.267426\pi$
$179$	5.80049	+	3.04433i	0.433549	+	0.227544i	−0.233807	+	0.972283i	$0.575118\pi$
$180$	24.7895	−	9.40143i	1.84770	−	0.700741i
$181$	0.152389	−	1.25504i	0.0113270	−	0.0932862i	−0.985949	−	0.167047i	$-0.946577\pi$
$181$	0.152389	−	1.25504i	0.0113270	−	0.0932862i	0.997276	+	0.0737605i	$0.0235000\pi$
$182$	7.04431	−	4.68545i	0.522159	−	0.347309i
$183$	2.26269	+	18.6350i	0.167263	+	1.37754i
$184$	6.54017	+	12.4613i	0.482148	+	0.918656i
$185$	−0.671625	−	5.53133i	−0.0493789	−	0.406671i
$186$	10.9963	−	5.77130i	0.806287	−	0.423172i
$187$	−0.973309	+	1.09864i	−0.0711754	+	0.0803404i
$188$			16.2644i			1.18620i
$189$	−12.2623	−	13.8413i	−0.891950	−	1.00680i
$190$	2.05600	−	3.91738i	0.149158	−	0.284197i
$191$	8.79548			0.636418			0.318209	−	0.948021i	$-0.396919\pi$
$191$	8.79548			0.636418			0.318209	+	0.948021i	$0.396919\pi$
$192$	2.15939			0.155841
$193$	5.12319	−	9.76142i	0.368775	−	0.702642i	−0.628389	−	0.777899i	$-0.716285\pi$
$193$	5.12319	−	9.76142i	0.368775	−	0.702642i	0.997164	+	0.0752570i	$0.0239777\pi$
$194$	6.79936	+	1.67589i	0.488165	+	0.120322i
$195$	−20.5954	+	28.7660i	−1.47487	+	2.05998i
$196$	8.16655	−	2.01287i	0.583325	−	0.143777i
$197$	−2.87410	+	11.6607i	−0.204771	+	0.830790i	0.775210	+	0.631703i	$0.217644\pi$
$197$	−2.87410	+	11.6607i	−0.204771	+	0.830790i	−0.979982	+	0.199087i	$0.936202\pi$
$198$	−5.13072	+	13.5286i	−0.364624	+	0.961436i
$199$	−0.542092	−	4.46453i	−0.0384279	−	0.316482i	−0.999230	−	0.0392457i	$-0.987505\pi$
$199$	−0.542092	−	4.46453i	−0.0384279	−	0.316482i	0.960802	−	0.277237i	$-0.0894186\pi$
$200$	4.10029	+	16.6355i	0.289934	+	1.17631i
$201$	6.48788	−	26.3224i	0.457620	−	1.85664i
$202$	0.935149	+	0.645487i	0.0657969	+	0.0454163i
$203$	−23.6685	+	2.87387i	−1.66120	+	0.201706i
$204$	0.509694	+	1.34395i	0.0356857	+	0.0940956i
$205$	−11.2107	+	5.88384i	−0.782990	+	0.410945i
$206$	−1.01266	−	4.10853i	−0.0705554	−	0.286255i
$207$	−10.2611	+	27.0563i	−0.713196	+	1.88054i
$208$	4.60508	−	3.06303i	0.319305	−	0.212383i
$209$	−3.00182	−	7.91514i	−0.207640	−	0.547502i
$210$	18.9484	−	13.0791i	1.30757	−	0.902547i
$211$	−8.96675	+	7.94385i	−0.617297	+	0.546877i	−0.912770	−	0.408474i	$-0.866061\pi$
$211$	−8.96675	+	7.94385i	−0.617297	+	0.546877i	0.295473	+	0.955351i	$0.404523\pi$
$212$	−5.61009	−	1.38276i	−0.385303	−	0.0949686i
$213$	−7.40793	−	2.80946i	−0.507583	−	0.192501i
$214$	0.910016	−	1.73389i	0.0622074	−	0.118526i
$215$	16.1160	+	6.11198i	1.09910	+	0.416833i
$216$	8.24838	+	9.31050i	0.561231	+	0.633499i
$217$	−17.5160	+	15.5179i	−1.18907	+	1.05342i
$218$	0.825422	−	1.19583i	0.0559046	−	0.0809919i
$219$	−16.5691	−	11.4368i	−1.11964	−	0.772829i
$220$	21.4851	+	11.2762i	1.44852	+	0.760244i
$221$	−0.965152	−	0.691014i	−0.0649231	−	0.0464826i
$222$	2.63674	−	1.38387i	0.176966	−	0.0928791i
$223$	20.0948	+	2.43995i	1.34565	+	0.163391i	0.761453	−	0.648221i	$-0.224487\pi$
$223$	20.0948	+	2.43995i	1.34565	+	0.163391i	0.584197	+	0.811612i	$0.301410\pi$
$224$	−19.6985	+	4.85524i	−1.31616	+	0.324405i
$225$	−20.0122	+	28.9927i	−1.33415	+	1.93285i
$226$	−7.87869	+	5.43826i	−0.524082	+	0.361748i
$227$	−3.40679	+	3.84547i	−0.226116	+	0.255233i	−0.850610	−	0.525797i	$-0.823767\pi$
$227$	−3.40679	+	3.84547i	−0.226116	+	0.255233i	0.624493	+	0.781030i	$0.285305\pi$
$228$	−8.22943	−	0.999234i	−0.545007	−	0.0661759i
$229$	−5.33166	+	21.6314i	−0.352326	+	1.42944i	0.481030	+	0.876704i	$0.340263\pi$
$229$	−5.33166	+	21.6314i	−0.352326	+	1.42944i	−0.833355	+	0.552737i	$0.813583\pi$
$230$	−12.2554	−	6.43212i	−0.808095	−	0.424121i
$231$	5.31021	−	43.7335i	0.349386	−	2.87745i
$232$	15.9209	−	1.93315i	1.04526	−	0.126917i
$233$	6.16182	−	8.92694i	0.403674	−	0.584823i	−0.567447	−	0.823410i	$-0.692069\pi$
$233$	6.16182	−	8.92694i	0.403674	−	0.584823i	0.971121	+	0.238587i	$0.0766842\pi$
$234$	−11.3114	−	2.99538i	−0.739452	−	0.195814i
$235$	−20.7648	−	30.0830i	−1.35455	−	1.96240i
$236$	−10.0718	−	11.3687i	−0.655619	−	0.740040i
$237$	2.42359	+	0.597361i	0.157429	+	0.0388028i
$238$	0.438829	+	0.635754i	0.0284451	+	0.0412098i
$239$		−	6.59963i		−	0.426895i	−0.976955	−	0.213447i	$-0.931531\pi$
$239$		−	6.59963i		−	0.426895i	0.976955	−	0.213447i	$-0.0684692\pi$
$240$	12.3872	−	8.55025i	0.799589	−	0.551916i
$241$	1.56261	−	0.189736i	0.100657	−	0.0122220i	−0.0700532	−	0.997543i	$-0.522317\pi$
$241$	1.56261	−	0.189736i	0.100657	−	0.0122220i	0.170710	+	0.985321i	$0.445394\pi$
$242$	−5.52939	+	2.09702i	−0.355442	+	0.134802i
$243$	1.85931	−	15.3128i	0.119275	−	0.982317i
$244$	3.69216	+	9.73543i	0.236366	+	0.623247i
$245$	−12.5352	+	14.1493i	−0.800844	+	0.903966i
$246$	−5.06474	−	4.48697i	−0.322916	−	0.286079i
$247$	6.11573	−	3.07675i	0.389135	−	0.195769i
$248$	11.7824	−	10.4383i	0.748183	−	0.662832i
$249$		−	8.97768i		−	0.568938i
$250$	−3.89241	−	3.44838i	−0.246178	−	0.218095i
$251$	20.6435	−	5.08818i	1.30301	−	0.321163i	0.474062	−	0.880491i	$-0.342787\pi$
$251$	20.6435	−	5.08818i	1.30301	−	0.321163i	0.828946	+	0.559328i	$0.188941\pi$
$252$	−21.9731	−	15.1670i	−1.38418	−	0.955429i
$253$	−24.7622	+	9.39107i	−1.55679	+	0.590412i
$254$	−11.7045	+	4.43894i	−0.734407	+	0.278524i
$255$	−2.65857	−	1.83508i	−0.166486	−	0.114917i
$256$	8.61504	−	2.12342i	0.538440	−	0.132714i
$257$	13.0451	+	11.5570i	0.813733	+	0.720905i	0.963469	−	0.267821i	$-0.0863037\pi$
$257$	13.0451	+	11.5570i	0.813733	+	0.720905i	−0.149735	+	0.988726i	$0.547842\pi$
$258$			9.21149i			0.573482i
$259$	−4.20008	+	3.72094i	−0.260980	+	0.231208i
$260$	−7.27318	+	18.2256i	−0.451063	+	1.13031i
$261$	24.6830	+	21.8672i	1.52784	+	1.35355i
$262$	3.15394	−	3.56007i	0.194851	−	0.219942i
$263$	−6.74978	−	17.7977i	−0.416209	−	1.09745i	−0.965174	−	0.261608i	$-0.915747\pi$
$263$	−6.74978	−	17.7977i	−0.416209	−	1.09745i	0.548965	−	0.835845i	$-0.315022\pi$
$264$	−3.57198	+	29.4179i	−0.219840	+	1.81055i
$265$	12.1419	−	4.60483i	0.745873	−	0.282872i
$266$	−4.42285	+	0.537032i	−0.271183	+	0.0329275i
$267$	−6.02749	+	4.16047i	−0.368876	+	0.254617i
$268$		−	15.0370i		−	0.918531i
$269$	−0.527716	−	0.764529i	−0.0321754	−	0.0466141i	0.806566	−	0.591144i	$-0.201323\pi$
$269$	−0.527716	−	0.764529i	−0.0321754	−	0.0466141i	−0.838741	+	0.544530i	$0.816708\pi$
$270$	−11.8777	−	2.92759i	−0.722854	−	0.178168i
$271$	−16.9943	−	19.1826i	−1.03233	−	1.16526i	−0.986070	−	0.166329i	$-0.946809\pi$
$271$	−16.9943	−	19.1826i	−1.03233	−	1.16526i	−0.0462590	−	0.998929i	$-0.514730\pi$
$272$	0.286876	+	0.415612i	0.0173944	+	0.0252002i
$273$	35.6229	+	0.613032i	2.15600	+	0.0371024i
$274$	6.66643	−	9.65800i	0.402734	−	0.583461i
$275$	−32.0067	+	3.88631i	−1.93008	+	0.234354i
$276$	−3.12606	+	25.7454i	−0.188167	+	1.54969i
$277$	−26.1723	−	13.7363i	−1.57254	−	0.825332i	−0.999985	−	0.00546470i	$-0.998261\pi$
$277$	−26.1723	−	13.7363i	−1.57254	−	0.825332i	−0.572554	−	0.819867i	$-0.694047\pi$
$278$	2.13623	−	8.66701i	0.128122	−	0.519813i
$279$	32.1301	+	3.90130i	1.92358	+	0.233565i
$280$	19.3523	−	21.8442i	1.15652	−	1.30544i
$281$	−5.06359	+	3.49515i	−0.302069	+	0.208503i	−0.709451	−	0.704755i	$-0.751057\pi$
$281$	−5.06359	+	3.49515i	−0.302069	+	0.208503i	0.407382	+	0.913258i	$0.366442\pi$
$282$	11.0974	−	16.0773i	0.660839	−	0.957391i
$283$	−20.6275	+	5.08423i	−1.22618	+	0.302226i	−0.798661	−	0.601781i	$-0.794458\pi$
$283$	−20.6275	+	5.08423i	−1.22618	+	0.302226i	−0.427518	+	0.904007i	$0.640612\pi$
$284$	−4.36243	−	0.529695i	−0.258863	−	0.0314316i
$285$	16.4971	−	8.65833i	0.977202	−	0.512875i
$286$	−4.81290	−	9.56673i	−0.284593	−	0.565693i
$287$	11.2898	+	5.92533i	0.666414	+	0.349761i
$288$	23.0931	+	15.9400i	1.36078	+	0.939276i
$289$	−9.59553	+	13.9015i	−0.564443	+	0.817737i
$290$	−11.8061	+	10.4593i	−0.693281	+	0.614193i
$291$	19.5560	+	22.0741i	1.14639	+	1.29401i
$292$	−10.4413	−	3.95987i	−0.611033	−	0.231734i
$293$	12.2255	−	23.2938i	0.714222	−	1.36084i	−0.209513	−	0.977806i	$-0.567188\pi$
$293$	12.2255	−	23.2938i	0.714222	−	1.36084i	0.923735	−	0.383031i	$-0.125120\pi$
$294$	−9.44603	−	3.58241i	−0.550903	−	0.208930i
$295$	33.1435	+	8.16914i	1.92969	+	0.475626i
$296$	2.82524	−	2.50294i	0.164214	−	0.145481i
$297$	−19.2638	+	13.2968i	−1.11780	+	0.771560i
$298$	−2.14454	−	5.65470i	−0.124230	−	0.327568i
$299$	−9.62549	−	19.1328i	−0.556657	−	1.10648i
$300$	−11.1962	+	29.5220i	−0.646414	+	1.70445i
$301$	−4.15394	−	16.8532i	−0.239429	−	0.971402i
$302$	5.74963	−	3.01764i	0.330854	−	0.173646i
$303$	1.69686	+	4.47424i	0.0974819	+	0.257039i
$304$	−2.89136	+	0.351074i	−0.165831	+	0.0201355i
$305$	−19.2584	−	13.2931i	−1.10273	−	0.761160i
$306$	0.255694	−	1.03739i	0.0146171	−	0.0593038i
$307$	−3.19303	−	12.9546i	−0.182236	−	0.739360i	−0.988929	−	0.148389i	$-0.952591\pi$
$307$	−3.19303	−	12.9546i	−0.182236	−	0.739360i	0.806693	−	0.590970i	$-0.201255\pi$
$308$	−2.94538	−	24.2574i	−0.167828	−	1.38219i
$309$	6.31900	−	16.6618i	0.359476	−	0.947859i
$310$	−3.70486	+	15.0312i	−0.210422	+	0.853714i
$311$	30.6033	−	7.54304i	1.73536	−	0.427727i	0.760279	−	0.649596i	$-0.225062\pi$
$311$	30.6033	−	7.54304i	1.73536	−	0.427727i	0.975076	+	0.221869i	$0.0712159\pi$
$312$	−23.9622	−	0.412364i	−1.35659	−	0.0233455i
$313$	10.7658	+	2.65352i	0.608517	+	0.149986i	0.531520	−	0.847046i	$-0.321621\pi$
$313$	10.7658	+	2.65352i	0.608517	+	0.149986i	0.0769962	+	0.997031i	$0.475467\pi$
$314$	−6.10782	+	11.6375i	−0.344684	+	0.656741i
$315$	60.0057			3.38094
$316$	1.38451			0.0778846
$317$	−7.38353	+	14.0681i	−0.414700	+	0.790146i	−0.999783	−	0.0208280i	$-0.993370\pi$
$317$	−7.38353	+	14.0681i	−0.414700	+	0.790146i	0.585083	+	0.810974i	$0.301062\pi$
$318$	4.60209	+	5.19469i	0.258073	+	0.291304i
$319$			30.1801i			1.68976i
$320$	−1.78503	+	2.01489i	−0.0997864	+	0.112636i
$321$	7.30185	−	3.83230i	0.407549	−	0.213898i
$322$	1.68008	+	13.8367i	0.0936273	+	0.771090i
$323$	0.290503	+	0.553507i	0.0161640	+	0.0307979i
$324$	0.0217602	+	0.179211i	0.00120890	+	0.00995618i
$325$	−5.80356	−	25.4207i	−0.321923	−	1.41009i
$326$	1.01949	−	8.39625i	0.0564643	−	0.465025i
$327$	5.72148	−	2.16987i	0.316398	−	0.119994i
$328$	−7.59421	−	3.98575i	−0.419320	−	0.220076i
$329$	−13.0535	+	34.4192i	−0.719662	+	1.89759i
$330$	−13.5441	−	25.8061i	−0.745576	−	1.42058i
$331$	9.06722	+	17.2761i	0.498379	+	0.949582i	0.996589	+	0.0825258i	$0.0262987\pi$
$331$	9.06722	+	17.2761i	0.498379	+	0.949582i	−0.498210	+	0.867057i	$0.666009\pi$
$332$	−1.19169	−	4.83489i	−0.0654027	−	0.265349i
$333$	7.70430	+	0.935471i	0.422193	+	0.0512635i
$334$	1.70112	+	1.50706i	0.0930812	+	0.0824627i
$335$	19.1978	+	27.8128i	1.04889	+	1.51957i
$336$	−14.1727	−	5.37499i	−0.773183	−	0.293230i
$337$	−18.5098			−1.00829			−0.504146	−	0.863618i	$-0.668193\pi$
$337$	−18.5098			−1.00829			−0.504146	+	0.863618i	$0.668193\pi$
$338$	7.29275	−	4.67173i	0.396673	−	0.254108i
$339$	−40.3156			−2.18964
$340$	−1.67535	−	0.635376i	−0.0908586	−	0.0344581i
$341$	16.8271	+	24.3782i	0.911238	+	1.32016i
$342$	4.61244	+	4.08626i	0.249412	+	0.220960i
$343$	−5.57692	−	0.677160i	−0.301125	−	0.0365632i
$344$	2.79420	+	11.3365i	0.150653	+	0.611224i
$345$	−27.0872	−	51.6104i	−1.45833	−	2.77861i
$346$	−2.55473	−	4.86762i	−0.137343	−	0.261685i
$347$	2.31733	−	6.11029i	0.124401	−	0.328018i	−0.858319	−	0.513116i	$-0.828491\pi$
$347$	2.31733	−	6.11029i	0.124401	−	0.328018i	0.982720	+	0.185098i	$0.0592603\pi$
$348$	26.1695	+	13.7348i	1.40283	+	0.736264i
$349$	−7.65301	+	2.90240i	−0.409656	+	0.155362i	−0.550820	−	0.834624i	$-0.685685\pi$
$349$	−7.65301	+	2.90240i	−0.409656	+	0.155362i	0.141164	+	0.989986i	$0.454916\pi$
$350$	−2.04540	+	16.8454i	−0.109331	+	0.900425i
$351$	−12.3073	−	14.3832i	−0.656914	−	0.767720i
$352$	3.09551	+	25.4938i	0.164991	+	1.35882i
$353$	6.44599	+	12.2818i	0.343085	+	0.653695i	0.994466	−	0.105056i	$-0.0335023\pi$
$353$	6.44599	+	12.2818i	0.343085	+	0.653695i	−0.651381	+	0.758751i	$0.725810\pi$
$354$	2.19896	+	18.1101i	0.116873	+	0.962539i
$355$	8.74512	−	4.58979i	0.464143	−	0.243601i
$356$	−2.69382	+	3.04069i	−0.142772	+	0.161156i
$357$			3.25318i			0.172177i
$358$	−2.89405	−	3.26670i	−0.152955	−	0.172651i
$359$	1.82292	−	3.47328i	0.0962099	−	0.183313i	−0.832595	−	0.553883i	$-0.813145\pi$
$359$	1.82292	−	3.47328i	0.0962099	−	0.183313i	0.928804	+	0.370570i	$0.120838\pi$
$360$	−40.3636			−2.12735
$361$	15.3947			0.810249
$362$	−0.391420	+	0.745788i	−0.0205726	+	0.0391978i
$363$	−24.1803	−	5.95991i	−1.26914	−	0.312814i
$364$	19.2659	−	4.39843i	1.00981	−	0.230540i
$365$	24.3681	−	6.00620i	1.27548	−	0.314379i
$366$	2.99290	−	12.1427i	0.156441	−	0.634707i
$367$	9.98090	−	26.3175i	0.520999	−	1.37376i	−0.373890	−	0.927473i	$-0.621976\pi$
$367$	9.98090	−	26.3175i	0.520999	−	1.37376i	0.894889	−	0.446288i	$-0.147254\pi$
$368$	1.09832	+	9.04550i	0.0572540	+	0.471529i
$369$	−4.22028	−	17.1223i	−0.219699	−	0.891354i
$370$	−0.888367	+	3.60425i	−0.0461840	+	0.187376i
$371$	−10.7625	−	7.42880i	−0.558760	−	0.385684i
$372$	28.7966	−	3.49654i	1.49303	−	0.181287i
$373$	11.5296	+	30.4011i	0.596981	+	1.57411i	0.803268	+	0.595617i	$0.203092\pi$
$373$	11.5296	+	30.4011i	0.596981	+	1.57411i	−0.206288	+	0.978491i	$0.566138\pi$
$374$	0.865840	−	0.454428i	0.0447715	−	0.0234979i
$375$	−5.24086	−	21.2630i	−0.270637	−	1.09802i
$376$	8.78059	−	23.1525i	0.452824	−	1.19400i
$377$	−24.2765	+	2.52465i	−1.25030	+	0.130026i
$378$	4.36854	+	11.5189i	0.224693	+	0.592467i
$379$	−19.1627	+	13.2270i	−0.984321	+	0.679428i	−0.947454	−	0.319892i	$-0.896353\pi$
$379$	−19.1627	+	13.2270i	−0.984321	+	0.679428i	−0.0368672	+	0.999320i	$0.511738\pi$
$380$	7.73512	−	6.85272i	0.396803	−	0.351537i
$381$	−51.1845	−	12.6158i	−2.62226	−	0.646329i
$382$	−5.47889	−	2.07787i	−0.280324	−	0.106313i
$383$	−2.42483	+	4.62013i	−0.123903	+	0.236078i	−0.939505	−	0.342536i	$-0.888714\pi$
$383$	−2.42483	+	4.62013i	−0.123903	+	0.236078i	0.815601	+	0.578614i	$0.196406\pi$
$384$	28.8764	+	10.9514i	1.47359	+	0.558860i
$385$	36.4173	+	41.1066i	1.85600	+	2.09499i
$386$	−5.49740	+	4.87028i	−0.279811	+	0.247891i
$387$	−13.6376	+	19.7575i	−0.693239	+	1.00433i
$388$	13.4619	+	9.29207i	0.683424	+	0.471734i
$389$	11.5035	+	6.03750i	0.583250	+	0.306113i	0.730420	−	0.682998i	$-0.239324\pi$
$389$	11.5035	+	6.03750i	0.583250	+	0.306113i	−0.147170	+	0.989111i	$0.547016\pi$
$390$	19.6251	−	13.0534i	0.993754	−	0.660986i
$391$	1.73162	−	0.908826i	0.0875720	−	0.0459613i
$392$	−12.7118	−	1.54350i	−0.642045	−	0.0779584i
$393$	19.4475	−	4.79338i	0.980998	−	0.241794i
$394$	4.54509	−	6.58471i	0.228979	−	0.331733i
$395$	−2.56082	+	1.76760i	−0.128849	+	0.0889378i
$396$	−22.4113	+	25.2972i	−1.12621	+	1.27123i
$397$	−5.91016	−	0.717623i	−0.296622	−	0.0360165i	−0.0291274	−	0.999576i	$-0.509273\pi$
$397$	−5.91016	−	0.717623i	−0.296622	−	0.0360165i	−0.267495	+	0.963559i	$0.586196\pi$
$398$	−0.717033	+	2.90912i	−0.0359416	+	0.145821i
$399$	−16.6134	−	8.71938i	−0.831710	−	0.436515i
$400$	−1.33714	+	11.0124i	−0.0668572	+	0.550618i
$401$	14.0006	−	1.69998i	0.699157	−	0.0848930i	0.236763	−	0.971568i	$-0.423914\pi$
$401$	14.0006	−	1.69998i	0.699157	−	0.0848930i	0.462394	+	0.886674i	$0.346991\pi$
$402$	−10.2599	+	14.8640i	−0.511718	+	0.741351i
$403$	−18.2019	+	15.5748i	−0.906702	+	0.775837i
$404$	1.50774	+	2.18434i	0.0750131	+	0.108675i
$405$	−0.269048	−	0.303692i	−0.0133691	−	0.0150906i
$406$	15.4225	+	3.80131i	0.765406	+	0.188656i
$407$	4.03488	+	5.84553i	0.200001	+	0.289752i
$408$		−	2.18830i		−	0.108337i
$409$	10.8053	−	7.45834i	0.534286	−	0.368791i	−0.270161	−	0.962815i	$-0.587077\pi$
$409$	10.8053	−	7.45834i	0.534286	−	0.368791i	0.804447	+	0.594024i	$0.202462\pi$
$410$	8.37340	−	1.01672i	0.413533	−	0.0502120i
$411$	46.2089	−	17.5247i	2.27932	−	0.864431i
$412$	1.19139	−	9.81194i	0.0586954	−	0.483400i
$413$	−12.1899	−	32.1422i	−0.599828	−	1.58162i
$414$	12.7837	−	14.4298i	0.628285	−	0.709187i
$415$	8.37690	+	7.42129i	0.411206	+	0.364297i
$416$	−20.2480	+	4.62262i	−0.992738	+	0.226643i
$417$	28.1375	−	24.9276i	1.37790	−	1.22071i
$418$			5.63967i			0.275845i
$419$	11.2043	+	9.92618i	0.547368	+	0.484926i	0.890890	−	0.454219i	$-0.150082\pi$
$419$	11.2043	+	9.92618i	0.547368	+	0.484926i	−0.343522	+	0.939145i	$0.611620\pi$
$420$	52.2174	−	12.8704i	2.54795	−	0.628012i
$421$	20.6770	+	14.2723i	1.00773	+	0.695589i	0.953018	−	0.302913i	$-0.0979592\pi$
$421$	20.6770	+	14.2723i	1.00773	+	0.695589i	0.0547162	+	0.998502i	$0.482575\pi$
$422$	7.46226	−	2.83006i	0.363257	−	0.137765i
$423$	47.6050	−	18.0542i	2.31463	−	0.877825i
$424$	7.23951	+	4.99708i	0.351582	+	0.242679i
$425$	2.31168	−	0.569778i	0.112133	−	0.0276383i
$426$	3.95084	+	3.50014i	0.191419	+	0.169582i
$427$			23.5657i			1.14042i
$428$	3.42368	−	3.03311i	0.165490	−	0.146611i
$429$	6.20561	−	44.6700i	0.299610	−	2.15669i
$430$	−8.59506	−	7.61456i	−0.414491	−	0.367207i
$431$	15.6470	−	17.6618i	0.753689	−	0.850739i	−0.239053	−	0.971007i	$-0.576837\pi$
$431$	15.6470	−	17.6618i	0.753689	−	0.850739i	0.992741	+	0.120268i	$0.0383754\pi$
$432$	2.85585	+	7.53025i	0.137402	+	0.362300i
$433$	1.63831	−	13.4927i	0.0787322	−	0.648418i	−0.898909	−	0.438136i	$-0.855639\pi$
$433$	1.63831	−	13.4927i	0.0787322	−	0.648418i	0.977641	−	0.210282i	$-0.0674382\pi$
$434$	14.5771	−	5.52836i	0.699723	−	0.265370i
$435$	−65.9391	+	8.00645i	−3.16154	+	0.383880i
$436$	2.79325	−	1.92804i	0.133772	−	0.0923364i
$437$			11.2790i			0.539546i
$438$	7.61937	+	11.0386i	0.364068	+	0.527443i
$439$	−24.1992	−	5.96458i	−1.15497	−	0.284674i	−0.385098	−	0.922876i	$-0.625832\pi$
$439$	−24.1992	−	5.96458i	−1.15497	−	0.284674i	−0.769869	+	0.638202i	$0.779678\pi$
$440$	−24.4966	−	27.6509i	−1.16783	−	1.31820i
$441$	−14.9568	−	21.6687i	−0.712229	−	1.03184i
$442$	0.437966	+	0.658457i	0.0208319	+	0.0313196i
$443$	−6.16776	+	8.93555i	−0.293039	+	0.424541i	−0.941657	−	0.336574i	$-0.890732\pi$
$443$	−6.16776	+	8.93555i	−0.293039	+	0.424541i	0.648618	+	0.761114i	$0.275347\pi$
$444$	6.90498	−	0.838416i	0.327696	−	0.0397895i
$445$	1.10049	−	9.06333i	0.0521681	−	0.429643i
$446$	−11.9411	−	6.26716i	−0.565426	−	0.296759i
$447$	6.09498	−	24.7283i	0.288282	−	1.16961i
$448$	2.69108	+	0.326756i	0.127141	+	0.0154378i
$449$	20.7310	−	23.4005i	0.978358	−	1.10434i	−0.0161701	−	0.999869i	$-0.505147\pi$
$449$	20.7310	−	23.4005i	0.978358	−	1.10434i	0.994528	−	0.104469i	$-0.0333142\pi$
$450$	19.3154	−	13.3324i	0.910535	−	0.628497i
$451$	9.16830	−	13.2826i	0.431718	−	0.625452i
$452$	−21.7118	+	5.35148i	−1.02124	+	0.251712i
$453$	27.1460	+	3.29612i	1.27543	+	0.154865i
$454$	3.03062	−	1.59059i	0.142234	−	0.0746503i
$455$	−30.0192	+	32.7323i	−1.40732	+	1.53451i
$456$	11.1752	+	5.86521i	0.523327	+	0.274663i
$457$	19.0424	+	13.1440i	0.890765	+	0.614850i	0.923072	−	0.384628i	$-0.125670\pi$
$457$	19.0424	+	13.1440i	0.890765	+	0.614850i	−0.0323073	+	0.999478i	$0.510286\pi$
$458$	8.43146	−	12.2151i	0.393976	−	0.570773i
$459$	1.29379	−	1.14620i	0.0603890	−	0.0535000i
$460$	−21.4385	−	24.1990i	−0.999573	−	1.12828i
$461$	−20.0808	−	7.61562i	−0.935254	−	0.354695i	−0.160556	−	0.987027i	$-0.551329\pi$
$461$	−20.0808	−	7.61562i	−0.935254	−	0.354695i	−0.774698	+	0.632332i	$0.782098\pi$
$462$	−13.6396	+	25.9880i	−0.634570	+	1.20907i
$463$	−40.2005	−	15.2460i	−1.86827	−	0.708543i	−0.949514	−	0.313725i	$-0.898423\pi$
$463$	−40.2005	−	15.2460i	−1.86827	−	0.708543i	−0.918760	−	0.394817i	$-0.870808\pi$
$464$	10.0822	+	2.48503i	0.468053	+	0.115365i
$465$	−48.7988	+	43.2320i	−2.26299	+	2.00483i
$466$	−5.94725	+	4.10509i	−0.275501	+	0.190165i
$467$	5.18068	+	13.6603i	0.239733	+	0.632124i	0.999844	−	0.0176691i	$-0.00562455\pi$
$467$	5.18068	+	13.6603i	0.239733	+	0.632124i	−0.760111	+	0.649794i	$0.774855\pi$
$468$	−22.2235	−	15.9112i	−1.02728	−	0.735496i
$469$	12.0684	−	31.8217i	0.557267	−	1.46939i
$470$	5.82794	+	23.6449i	0.268823	+	1.09066i
$471$	−49.0083	+	25.7215i	−2.25818	+	1.18519i
$472$	8.19972	+	21.6209i	0.377423	+	0.995182i
$473$	−21.8114	+	2.64838i	−1.00289	+	0.121773i
$474$	−1.36858	−	0.944664i	−0.0628611	−	0.0433899i
$475$	−3.28616	+	13.3325i	−0.150779	+	0.611736i
$476$	0.431826	+	1.75199i	0.0197927	+	0.0803022i
$477$	2.18018	+	17.9554i	0.0998234	+	0.822120i
$478$	−1.55911	+	4.11105i	−0.0713123	+	0.188035i
$479$	−8.74764	+	35.4906i	−0.399690	+	1.62161i	0.334314	+	0.942462i	$0.391495\pi$
$479$	−8.74764	+	35.4906i	−0.399690	+	1.62161i	−0.734004	+	0.679145i	$0.762351\pi$
$480$	−54.8790	+	13.5265i	−2.50487	+	0.617395i
$481$	−4.36454	+	3.73460i	−0.199006	+	0.170283i
$482$	−1.01821	−	0.250966i	−0.0463782	−	0.0114312i
$483$	−27.2782	+	51.9743i	−1.24120	+	2.36491i
$484$	−13.8133			−0.627878
$485$	−36.7626			−1.66931
$486$	−4.77574	+	9.09942i	−0.216632	+	0.412758i
$487$	−9.88887	−	11.1622i	−0.448108	−	0.505809i	0.480437	−	0.877029i	$-0.340478\pi$
$487$	−9.88887	−	11.1622i	−0.448108	−	0.505809i	−0.928545	+	0.371220i	$0.878940\pi$
$488$		−	15.8517i		−	0.717575i
$489$	23.6194	−	26.6607i	1.06810	−	1.20564i
$490$	11.1511	−	5.85255i	0.503756	−	0.264391i
$491$	3.71222	+	30.5729i	0.167530	+	1.37974i	0.797595	+	0.603193i	$0.206105\pi$
$491$	3.71222	+	30.5729i	0.167530	+	1.37974i	−0.630065	+	0.776543i	$0.716972\pi$
$492$	−7.34503	−	13.9948i	−0.331139	−	0.630933i
$493$	−0.268631	−	2.21238i	−0.0120985	−	0.0996404i
$494$	−4.53648	+	0.471775i	−0.204106	+	0.0212261i
$495$	9.15556	−	75.4028i	0.411512	−	3.38910i
$496$	9.52951	−	3.61406i	0.427887	−	0.162276i
$497$	−8.80678	−	4.62216i	−0.395038	−	0.207332i
$498$	−2.12091	+	5.59239i	−0.0950404	+	0.250601i
$499$	9.74369	+	18.5650i	0.436187	+	0.831085i	0.999987	+	0.00517365i	$0.00164683\pi$
$499$	9.74369	+	18.5650i	0.436187	+	0.831085i	−0.563799	+	0.825912i	$0.690661\pi$
$500$	−5.64489	−	10.7554i	−0.252447	−	0.480998i
$501$	2.29044	+	9.29268i	0.102329	+	0.415166i
$502$	−14.0613	−	1.70736i	−0.627588	−	0.0762030i
$503$	−26.6822	−	23.6384i	−1.18970	−	1.05398i	−0.997357	−	0.0726556i	$-0.976853\pi$
$503$	−26.6822	−	23.6384i	−1.18970	−	1.05398i	−0.192344	−	0.981328i	$-0.561609\pi$
$504$	23.0908	+	33.4529i	1.02855	+	1.49011i
$505$	−5.57751	−	2.11527i	−0.248196	−	0.0941284i
$506$	17.6435			0.784348
$507$	36.4511	+	1.25494i	1.61885	+	0.0557339i
$508$	−29.2398			−1.29731
$509$	−7.96748	−	3.02167i	−0.353152	−	0.133933i	0.171648	−	0.985158i	$-0.445091\pi$
$509$	−7.96748	−	3.02167i	−0.353152	−	0.133933i	−0.524800	+	0.851225i	$0.675860\pi$
$510$	1.22256	+	1.77118i	0.0541357	+	0.0784290i
$511$	−18.9181	−	16.7600i	−0.836889	−	0.741419i
$512$	15.9869	+	1.94116i	0.706526	+	0.0857878i
$513$	2.38572	+	9.67927i	0.105332	+	0.427350i
$514$	−5.39584	−	10.2809i	−0.238000	−	0.453471i
$515$	10.3233	+	19.6694i	0.454900	+	0.866739i
$516$	−7.62983	+	20.1182i	−0.335884	+	0.885654i
$517$	41.2593	+	21.6545i	1.81458	+	0.952365i
$518$	3.49536	−	1.32562i	0.153577	−	0.0582442i
$519$	2.79049	−	22.9817i	0.122489	−	1.00879i
$520$	20.1928	−	22.0178i	0.885514	−	0.965545i
$521$	0.308898	+	2.54400i	0.0135331	+	0.111455i	0.997910	−	0.0646192i	$-0.0205833\pi$
$521$	0.308898	+	2.54400i	0.0135331	+	0.111455i	−0.984377	+	0.176074i	$0.943660\pi$
$522$	−10.2096	−	19.4527i	−0.446861	−	0.851423i
$523$	−5.07556	−	41.8010i	−0.221939	−	1.82783i	−0.498563	−	0.866853i	$-0.666139\pi$
$523$	−5.07556	−	41.8010i	−0.221939	−	1.82783i	0.276624	−	0.960978i	$-0.410784\pi$
$524$	9.83710	−	5.16291i	0.429736	−	0.225543i
$525$	−47.3876	+	53.4895i	−2.06816	+	2.33447i
$526$			12.6811i			0.552924i
$527$	−1.45051	−	1.63729i	−0.0631853	−	0.0713214i
$528$	−8.91661	+	16.9892i	−0.388046	+	0.739360i
$529$	12.2858			0.534165
$530$	−8.65133			−0.375790
$531$	−22.0955	+	42.0994i	−0.958862	+	1.82696i
$532$	−10.1045	−	2.49053i	−0.438085	−	0.107978i
$533$	11.4513	+	6.26374i	0.496011	+	0.271313i
$534$	4.73753	−	1.16770i	0.205013	−	0.0505312i
$535$	−2.46013	+	9.98114i	−0.106361	+	0.431522i
$536$	−8.11796	+	21.4053i	−0.350643	+	0.924568i
$537$	−2.21535	−	18.2450i	−0.0955992	−	0.787331i
$538$	0.148111	+	0.600910i	0.00638552	+	0.0259071i
$539$	5.76678	−	23.3967i	0.248393	−	1.00777i
$540$	−23.5164	−	16.2322i	−1.01198	−	0.698523i
$541$	−20.7814	+	2.52332i	−0.893463	+	0.108486i	−0.554373	−	0.832268i	$-0.687042\pi$
$541$	−20.7814	+	2.52332i	−0.893463	+	0.108486i	−0.339090	+	0.940754i	$0.610119\pi$
$542$	6.05435	+	15.9640i	0.260057	+	0.685713i
$543$	−3.14070	+	1.64837i	−0.134780	+	0.0707382i
$544$	−0.453837	−	1.84129i	−0.0194581	−	0.0789446i
$545$	−2.70492	+	7.13230i	−0.115866	+	0.305514i
$546$	−22.0454	−	8.79753i	−0.943458	−	0.376499i
$547$	11.2588	+	29.6871i	0.481393	+	1.26933i	0.927323	+	0.374261i	$0.122104\pi$
$547$	11.2588	+	29.6871i	0.481393	+	1.26933i	−0.445930	+	0.895068i	$0.647127\pi$
$548$	22.5594	−	15.5716i	0.963689	−	0.665186i
$549$	24.3966	−	21.6135i	1.04122	−	0.922442i
$550$	20.8557	+	5.14048i	0.889292	+	0.219191i
$551$	12.0182	+	4.55790i	0.511992	+	0.194173i
$552$	18.3491	−	34.9612i	0.780988	−	1.48805i
$553$	2.92993	+	1.11118i	0.124593	+	0.0472521i
$554$	13.0582	+	14.7396i	0.554788	+	0.626226i
$555$	−11.7012	+	10.3664i	−0.496688	+	0.440027i
$556$	11.8444	−	17.1596i	0.502316	−	0.727730i
$557$	−22.3921	−	15.4561i	−0.948783	−	0.654898i	−0.0101989	−	0.999948i	$-0.503246\pi$
$557$	−22.3921	−	15.4561i	−0.948783	−	0.654898i	−0.938584	+	0.345050i	$0.887862\pi$
$558$	−19.0929	−	10.0207i	−0.808265	−	0.424210i
$559$	−3.95492	−	17.3233i	−0.167275	−	0.732697i
$560$	16.7310	−	8.78108i	0.707012	−	0.371068i
$561$	4.08793	+	0.496365i	0.172593	+	0.0209565i
$562$	3.97992	−	0.980963i	0.167883	−	0.0413794i
$563$	−18.4073	+	26.6675i	−0.775773	+	1.12390i	0.213373	+	0.976971i	$0.431555\pi$
$563$	−18.4073	+	26.6675i	−0.775773	+	1.12390i	−0.989147	+	0.146931i	$0.953060\pi$
$564$	37.5538	−	25.9215i	1.58130	−	1.09149i
$565$	33.3264	−	37.6177i	1.40205	−	1.58259i
$566$	14.0504	+	1.70603i	0.590584	+	0.0717098i
$567$	−0.0977818	+	0.396716i	−0.00410645	+	0.0166605i
$568$	5.92400	+	3.10915i	0.248565	+	0.130457i
$569$	0.983186	−	8.09727i	0.0412173	−	0.339455i	−0.957483	−	0.288489i	$-0.906847\pi$
$569$	0.983186	−	8.09727i	0.0412173	−	0.339455i	0.998700	−	0.0509657i	$-0.0162299\pi$
$570$	−12.3218	+	1.49614i	−0.516105	+	0.0626665i
$571$	0.565525	−	0.819304i	0.0236665	−	0.0342868i	−0.810972	−	0.585085i	$-0.801061\pi$
$571$	0.565525	−	0.819304i	0.0236665	−	0.0342868i	0.834639	+	0.550798i	$0.185677\pi$
$572$	−2.58747	−	24.8806i	−0.108188	−	1.04031i
$573$	−14.0179	−	20.3084i	−0.585605	−	0.848395i
$574$	−5.63282	−	6.35814i	−0.235109	−	0.265384i
$575$	41.7101	+	10.2806i	1.73943	+	0.428732i
$576$	−2.12987	−	3.08565i	−0.0887447	−	0.128569i
$577$			6.71593i			0.279588i	0.990181	+	0.139794i	$0.0446440\pi$
$577$			6.71593i			0.279588i	−0.990181	+	0.139794i	$0.955356\pi$
$578$	9.26139	−	6.39268i	0.385223	−	0.265900i
$579$	−30.7038	+	3.72812i	−1.27601	+	0.154935i
$580$	−34.4484	+	13.0646i	−1.43039	+	0.542476i
$581$	1.35849	−	11.1882i	0.0563597	−	0.464164i
$582$	−6.96697	−	18.3704i	−0.288790	−	0.761477i
$583$	−10.9771	+	12.3906i	−0.454625	+	0.513165i
$584$	12.7255	+	11.2738i	0.526586	+	0.466515i
$585$	61.4190	+	1.05695i	2.53936	+	0.0436997i
$586$	−13.1185	+	11.6220i	−0.541921	+	0.480100i
$587$			2.20322i			0.0909367i	0.998966	+	0.0454683i	$0.0144780\pi$
$587$			2.20322i			0.0909367i	−0.998966	+	0.0454683i	$0.985522\pi$
$588$	−17.6631	−	15.6482i	−0.728416	−	0.645320i
$589$	12.2491	−	3.01912i	0.504714	−	0.124401i
$590$	−18.7159	−	12.9186i	−0.770521	−	0.531852i
$591$	31.5047	−	11.9481i	1.29593	−	0.491481i
$592$	2.28503	−	0.866597i	0.0939141	−	0.0356169i
$593$	9.33847	+	6.44588i	0.383485	+	0.264701i	0.744174	−	0.667985i	$-0.232843\pi$
$593$	9.33847	+	6.44588i	0.383485	+	0.264701i	−0.360689	+	0.932686i	$0.617459\pi$
$594$	15.1411	−	3.73195i	0.621247	−	0.153124i
$595$	−3.03548	−	2.68920i	−0.124443	−	0.110247i
$596$		−	14.1264i		−	0.578638i
$597$	−9.44445	+	8.36705i	−0.386536	+	0.342441i
$598$	1.47593	+	14.1922i	0.0603552	+	0.580362i
$599$	−13.0142	−	11.5296i	−0.531747	−	0.471087i	0.354006	−	0.935243i	$-0.384819\pi$
$599$	−13.0142	−	11.5296i	−0.531747	−	0.471087i	−0.885753	+	0.464156i	$0.846358\pi$
$600$	31.8758	−	35.9804i	1.30133	−	1.46889i
$601$	−1.25887	−	3.31936i	−0.0513502	−	0.135399i	0.906887	−	0.421374i	$-0.138452\pi$
$601$	−1.25887	−	3.31936i	−0.0513502	−	0.135399i	−0.958237	+	0.285974i	$0.907683\pi$
$602$	−1.39387	+	11.4795i	−0.0568098	+	0.467871i
$603$	−44.0125	+	16.6917i	−1.79233	+	0.679740i
$604$	15.0569	−	1.82824i	0.612656	−	0.0743899i
$605$	25.5494	−	17.6355i	1.03873	−	0.716985i
$606$		−	3.18797i		−	0.129502i
$607$	−17.3479	−	25.1328i	−0.704130	−	1.02011i	−0.997934	−	0.0642427i	$-0.979537\pi$
$607$	−17.3479	−	25.1328i	−0.704130	−	1.02011i	0.293804	−	0.955866i	$-0.405079\pi$
$608$	10.6195	+	2.61748i	0.430678	+	0.106153i
$609$	44.3574	+	50.0692i	1.79745	+	2.02891i
$610$	8.85604	+	12.8302i	0.358570	+	0.519479i
$611$	−13.9672	+	34.9999i	−0.565052	+	1.41594i
$612$	1.41771	−	2.05391i	0.0573076	−	0.0830243i
$613$	31.9690	−	3.88173i	1.29121	−	0.156782i	0.554043	−	0.832488i	$-0.313084\pi$
$613$	31.9690	−	3.88173i	1.29121	−	0.156782i	0.737171	+	0.675706i	$0.236161\pi$
$614$	−1.07143	+	8.82404i	−0.0432395	+	0.356109i
$615$	31.4527	+	16.5077i	1.26830	+	0.665653i
$616$	−8.90295	+	36.1207i	−0.358710	+	1.45534i
$617$	−3.27799	−	0.398020i	−0.131967	−	0.0160237i	0.0542866	−	0.998525i	$-0.482712\pi$
$617$	−3.27799	−	0.398020i	−0.131967	−	0.0160237i	−0.186254	+	0.982502i	$0.559635\pi$
$618$	−7.87248	+	8.88619i	−0.316678	+	0.357455i
$619$	−3.96110	+	2.73415i	−0.159210	+	0.109895i	−0.645006	−	0.764177i	$-0.723145\pi$
$619$	−3.96110	+	2.73415i	−0.159210	+	0.109895i	0.485796	+	0.874072i	$0.338530\pi$
$620$	−20.5418	+	29.7599i	−0.824978	+	1.19519i
$621$	30.2812	−	7.46365i	1.21514	−	0.299506i
$622$	−20.8454	−	2.53110i	−0.835826	−	0.101488i
$623$	−8.14113	+	4.27280i	−0.326168	+	0.171186i
$624$	−14.4118	−	5.75122i	−0.576933	−	0.230233i
$625$	−7.84494	−	4.11734i	−0.313797	−	0.164694i
$626$	−6.07934	−	4.19627i	−0.242979	−	0.167717i
$627$	−13.4916	+	19.5459i	−0.538801	+	0.780588i
$628$	−22.9789	+	20.3576i	−0.916959	+	0.812355i
$629$	−0.347810	−	0.392597i	−0.0138681	−	0.0156538i
$630$	−37.3788	−	14.1759i	−1.48921	−	0.564782i
$631$	−16.7021	+	31.8232i	−0.664900	+	1.26686i	0.286257	+	0.958153i	$0.407589\pi$
$631$	−16.7021	+	31.8232i	−0.664900	+	1.26686i	−0.951157	+	0.308708i	$0.900104\pi$
$632$	−1.97086	−	0.747448i	−0.0783965	−	0.0297319i
$633$	32.6328	+	8.04327i	1.29704	+	0.319691i
$634$	7.92285	−	7.01904i	0.314657	−	0.278762i
$635$	54.0826	−	37.3305i	2.14620	−	1.48142i
$636$	5.74839	+	15.1573i	0.227939	+	0.601025i
$637$	19.3024	+	2.68152i	0.764791	+	0.106246i
$638$	7.12984	−	18.7998i	0.282273	−	0.744292i
$639$	3.29210	+	13.3566i	0.130234	+	0.528378i
$640$	−34.0888	+	17.8912i	−1.34748	+	0.707211i
$641$	1.74980	+	4.61384i	0.0691128	+	0.182236i	0.965122	−	0.261799i	$-0.0843159\pi$
$641$	1.74980	+	4.61384i	0.0691128	+	0.182236i	−0.896010	+	0.444035i	$0.853547\pi$
$642$	−5.45383	+	0.662215i	−0.215245	+	0.0261355i
$643$	−1.87520	−	1.29435i	−0.0739505	−	0.0510443i	0.530516	−	0.847675i	$-0.321998\pi$
$643$	−1.87520	−	1.29435i	−0.0739505	−	0.0510443i	−0.604466	+	0.796631i	$0.706614\pi$
$644$	−7.79152	+	31.6115i	−0.307029	+	1.24567i
$645$	−11.5727	−	46.9521i	−0.455673	−	1.84874i
$646$	−0.0501983	−	0.413420i	−0.00197502	−	0.0162658i
$647$	5.21922	−	13.7619i	0.205189	−	0.541038i	−0.792434	−	0.609958i	$-0.791186\pi$
$647$	5.21922	−	13.7619i	0.205189	−	0.541038i	0.997622	+	0.0689203i	$0.0219554\pi$
$648$	0.0657742	−	0.266856i	0.00258385	−	0.0104831i
$649$	−42.2497	+	10.4136i	−1.65844	+	0.408770i
$650$	−2.39029	+	17.2061i	−0.0937551	+	0.674880i
$651$	63.7464	+	15.7121i	2.49842	+	0.615805i
$652$	9.18117	−	17.4933i	0.359562	−	0.685089i
$653$	−18.1282			−0.709410			−0.354705	−	0.934978i	$-0.615419\pi$
$653$	−18.1282			−0.709410			−0.354705	+	0.934978i	$0.615419\pi$
$654$	−4.07665			−0.159409
$655$	−11.6034	+	22.1085i	−0.453384	+	0.863850i
$656$	−3.68235	−	4.15651i	−0.143772	−	0.162285i
$657$			34.9568i			1.36380i
$658$	16.2626	−	18.3566i	0.633981	−	0.715617i
$659$	34.6939	−	18.2088i	1.35148	−	0.709312i	0.375430	−	0.926851i	$-0.377495\pi$
$659$	34.6939	−	18.2088i	1.35148	−	0.709312i	0.976052	+	0.217539i	$0.0698028\pi$
$660$	−8.20567	−	67.5798i	−0.319405	−	2.63054i
$661$	0.554569	+	1.05664i	0.0215702	+	0.0410986i	0.896003	−	0.444049i	$-0.146458\pi$
$661$	0.554569	+	1.05664i	0.0215702	+	0.0410986i	−0.874432	+	0.485147i	$0.838766\pi$
$662$	−1.56680	−	12.9037i	−0.0608953	−	0.501518i
$663$	−0.0573023	+	3.32980i	−0.00222544	+	0.129319i
$664$	−0.913806	+	7.52587i	−0.0354625	+	0.292060i
$665$	21.8691	−	8.29387i	0.848049	−	0.321622i
$666$	−4.57817	−	2.40281i	−0.177401	−	0.0931070i
$667$	14.2592	−	37.5984i	0.552118	−	1.45582i
$668$	2.46701	+	4.70050i	0.0954516	+	0.181868i
$669$	−26.3926	−	50.2868i	−1.02040	−	1.94420i
$670$	−5.38813	−	21.8605i	−0.208162	−	0.844545i
$671$	29.6125	+	3.59560i	1.14318	+	0.138807i
$672$	42.6052	+	37.7449i	1.64353	+	1.45604i
$673$	−27.0876	−	39.2432i	−1.04415	−	1.51272i	−0.846461	−	0.532451i	$-0.821271\pi$
$673$	−27.0876	−	39.2432i	−1.04415	−	1.51272i	−0.197691	−	0.980264i	$-0.563344\pi$
$674$	11.5301	+	4.37280i	0.444124	+	0.168434i
$675$	37.9689			1.46142
$676$	19.7972	−	4.16266i	0.761429	−	0.160102i
$677$	19.0165			0.730864			0.365432	−	0.930838i	$-0.380921\pi$
$677$	19.0165			0.730864			0.365432	+	0.930838i	$0.380921\pi$
$678$	25.1134	+	9.52427i	0.964476	+	0.365778i
$679$	21.0308	+	30.4684i	0.807089	+	1.16927i
$680$	2.04186	+	1.80893i	0.0783016	+	0.0693692i
$681$	14.3086	+	1.73738i	0.548307	+	0.0665766i
$682$	−4.72276	−	19.1610i	−0.180844	−	0.733712i
$683$	−19.0066	−	36.2141i	−0.727268	−	1.38569i	−0.914992	−	0.403471i	$-0.867804\pi$
$683$	−19.0066	−	36.2141i	−0.727268	−	1.38569i	0.187724	−	0.982222i	$-0.439889\pi$
$684$	6.68909	+	12.7450i	0.255764	+	0.487317i
$685$	−21.8460	+	57.6032i	−0.834694	+	2.20091i
$686$	3.31400	+	1.73932i	0.126529	+	0.0664077i
$687$	58.4433	−	22.1646i	2.22975	−	0.845633i
$688$	−0.911216	+	7.50454i	−0.0347398	+	0.286108i
$689$	−10.8851	−	7.79333i	−0.414689	−	0.296902i
$690$	4.68062	+	38.5484i	0.178188	+	1.46751i
$691$	5.90156	+	11.2445i	0.224506	+	0.427760i	0.971490	−	0.237082i	$-0.0761910\pi$
$691$	5.90156	+	11.2445i	0.224506	+	0.427760i	−0.746984	+	0.664842i	$0.768499\pi$
$692$	−1.54778	−	12.7471i	−0.0588378	−	0.484573i
$693$	−67.7305	+	35.5477i	−2.57287	+	1.35035i
$694$	−2.88703	+	3.25878i	−0.109590	+	0.123702i
$695$			46.8606i			1.77753i
$696$	−29.8376	−	33.6797i	−1.13099	−	1.27663i
$697$	−0.553862	+	1.05530i	−0.0209790	+	0.0399722i
$698$	5.45289			0.206395
$699$	−30.4324			−1.15106
$700$	−18.4202	+	35.0967i	−0.696218	+	1.32653i
$701$	−29.4923	−	7.26919i	−1.11391	−	0.274554i	−0.360926	−	0.932595i	$-0.617539\pi$
$701$	−29.4923	−	7.26919i	−1.11391	−	0.274554i	−0.752982	+	0.658041i	$0.771385\pi$
$702$	4.26853	+	11.8671i	0.161105	+	0.447896i
$703$	2.93714	−	0.723940i	0.110776	−	0.0273039i
$704$	0.821198	−	3.33173i	0.0309501	−	0.125569i
$705$	−36.3663	+	95.8901i	−1.36963	+	3.61143i
$706$	−1.11385	−	9.17341i	−0.0419205	−	0.345246i
$707$	1.43762	+	5.83266i	0.0540673	+	0.219360i
$708$	−10.1979	+	41.3744i	−0.383259	+	1.55494i
$709$	−20.9689	−	14.4738i	−0.787505	−	0.543576i	0.105075	−	0.994464i	$-0.466492\pi$
$709$	−20.9689	−	14.4738i	−0.787505	−	0.543576i	−0.892580	+	0.450889i	$0.851107\pi$
$710$	−6.53182	+	0.793107i	−0.245135	+	0.0297648i
$711$	−1.53686	−	4.05238i	−0.0576369	−	0.151976i
$712$	5.47624	−	2.87415i	0.205231	−	0.107713i
$713$	−9.44521	−	38.3207i	−0.353726	−	1.43512i
$714$	0.768541	−	2.02648i	0.0287619	−	0.0758390i
$715$	36.5509	+	42.7162i	1.36693	+	1.59750i
$716$	−3.61490	−	9.53171i	−0.135095	−	0.356217i
$717$	−15.2383	+	10.5182i	−0.569083	+	0.392810i
$718$	−1.95607	+	1.73293i	−0.0729999	+	0.0646723i
$719$	47.2119	+	11.6367i	1.76071	+	0.433976i	0.981291	−	0.192529i	$-0.0616691\pi$
$719$	47.2119	+	11.6367i	1.76071	+	0.433976i	0.779417	+	0.626505i	$0.215515\pi$
$720$	−24.4357	−	9.26724i	−0.910665	−	0.345370i
$721$	10.3961	−	19.8081i	0.387172	−	0.737694i
$722$	−9.58970	−	3.63689i	−0.356892	−	0.135351i
$723$	−2.92852	−	3.30562i	−0.108913	−	0.122937i
$724$	−1.47261	+	1.30462i	−0.0547290	+	0.0484857i
$725$	27.8097	−	40.2893i	1.03283	−	1.49631i
$726$	13.6544	+	9.42497i	0.506764	+	0.349794i
$727$	−30.5189	−	16.0176i	−1.13188	−	0.594059i	−0.208533	−	0.978015i	$-0.566869\pi$
$727$	−30.5189	−	16.0176i	−1.13188	−	0.594059i	−0.923351	+	0.383957i	$0.874561\pi$
$728$	−29.7998	−	4.13982i	−1.10445	−	0.153432i
$729$	−38.6281	+	20.2736i	−1.43067	+	0.750873i
$730$	−16.5983	−	2.01540i	−0.614332	−	0.0745934i
$731$	1.57533	−	0.388284i	0.0582656	−	0.0143612i
$732$	16.5943	−	24.0410i	0.613342	−	0.888580i
$733$	33.4470	−	23.0868i	1.23539	−	0.852729i	0.242315	−	0.970198i	$-0.422093\pi$
$733$	33.4470	−	23.0868i	1.23539	−	0.852729i	0.993077	+	0.117468i	$0.0374778\pi$
$734$	−12.4346	+	14.0358i	−0.458970	+	0.518071i
$735$	52.6482	+	6.39265i	1.94196	+	0.235797i
$736$	8.18867	−	33.2227i	0.301838	−	1.22461i
$737$	−38.1456	−	20.0204i	−1.40511	−	0.737460i
$738$	−1.41613	+	11.6629i	−0.0521285	+	0.429316i
$739$	2.09164	−	0.253971i	0.0769421	−	0.00934246i	−0.0819751	−	0.996634i	$-0.526123\pi$
$739$	2.09164	−	0.253971i	0.0769421	−	0.00934246i	0.158917	+	0.987292i	$0.449200\pi$
$740$	−4.92560	+	7.13597i	−0.181069	+	0.262323i
$741$	−16.8511	−	9.21737i	−0.619040	−	0.338609i
$742$	4.94917	+	7.17011i	0.181690	+	0.263223i
$743$	13.9329	+	15.7270i	0.511149	+	0.576968i	0.946259	−	0.323409i	$-0.104829\pi$
$743$	13.9329	+	15.7270i	0.511149	+	0.576968i	−0.435110	+	0.900377i	$0.643290\pi$
$744$	−42.8799	−	10.5689i	−1.57205	−	0.387476i
$745$	18.0352	+	26.1284i	0.660757	+	0.957272i
$746$		−	21.6613i		−	0.793075i
$747$	−12.8286	+	8.85497i	−0.469375	+	0.323986i
$748$	2.26742	−	0.275315i	0.0829052	−	0.0100665i
$749$	9.67961	−	3.67099i	0.353685	−	0.134135i
$750$	−1.75859	+	14.4833i	−0.0642147	+	0.528855i
$751$	−1.93814	−	5.11044i	−0.0707236	−	0.186483i	0.894994	−	0.446079i	$-0.147180\pi$
$751$	−1.93814	−	5.11044i	−0.0707236	−	0.186483i	−0.965717	+	0.259596i	$0.916411\pi$
$752$	10.6314	−	12.0003i	0.387685	−	0.437606i
$753$	−44.6492	−	39.5557i	−1.62711	−	1.44149i
$754$	15.7188	+	4.16249i	0.572444	+	0.151589i
$755$	−25.5154	+	22.6047i	−0.928602	+	0.822670i
$756$			28.7761i			1.04658i
$757$	22.9406	+	20.3236i	0.833792	+	0.738675i	0.967642	−	0.252326i	$-0.0811956\pi$
$757$	22.9406	+	20.3236i	0.833792	+	0.738675i	−0.133850	+	0.991002i	$0.542734\pi$
$758$	15.0616	−	3.71236i	0.547063	−	0.134839i
$759$	61.1486	+	42.2078i	2.21955	+	1.53205i
$760$	−14.7106	+	5.57898i	−0.533608	+	0.202371i
$761$	−22.0245	+	8.35277i	−0.798386	+	0.302788i	−0.719855	−	0.694124i	$-0.755792\pi$
$761$	−22.0245	+	8.35277i	−0.798386	+	0.302788i	−0.0785302	+	0.996912i	$0.525023\pi$
$762$	28.9035	+	19.9506i	1.04706	+	0.722735i
$763$	7.45856	−	1.83837i	0.270018	−	0.0665535i
$764$	−10.2450	−	9.07627i	−0.370651	−	0.328368i
$765$			5.60895i			0.202792i
$766$	2.60195	−	2.30513i	0.0940123	−	0.0832877i
$767$	−11.9109	−	33.1140i

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.h (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.622921 - 0.236243i) q^{2} +(-1.59376 - 2.30896i) q^{3} +(-1.16480 - 1.03192i) q^{4} +(3.47190 + 0.421565i) q^{5} +(0.447311 + 1.81481i) q^{6} +(-1.63679 - 3.11863i) q^{7} +(1.10100 + 2.09779i) q^{8} +(-1.72740 + 4.55479i) q^{9} +O(q^{10})\)	\(q+(-0.622921 - 0.236243i) q^{2} +(-1.59376 - 2.30896i) q^{3} +(-1.16480 - 1.03192i) q^{4} +(3.47190 + 0.421565i) q^{5} +(0.447311 + 1.81481i) q^{6} +(-1.63679 - 3.11863i) q^{7} +(1.10100 + 2.09779i) q^{8} +(-1.72740 + 4.55479i) q^{9} +(-2.06313 - 1.08281i) q^{10} +(-4.16859 + 1.58094i) q^{11} +(-0.526257 + 4.33412i) q^{12} +(-1.62040 - 3.22092i) q^{13} +(0.282833 + 2.32934i) q^{14} +(-4.56000 - 8.68835i) q^{15} +(0.184897 + 1.52276i) q^{16} +(0.291510 - 0.152996i) q^{17} +(2.15207 - 2.42919i) q^{18} +1.89876i q^{19} +(-3.60906 - 4.07378i) q^{20} +(-4.59215 + 8.74962i) q^{21} +2.97019 q^{22} +5.94018 q^{23} +(3.08897 - 5.88554i) q^{24} +(7.02169 + 1.73069i) q^{25} +(0.248465 + 2.38918i) q^{26} +(5.09769 - 1.25647i) q^{27} +(-1.31166 + 5.32163i) q^{28} +(2.40046 - 6.32950i) q^{29} +(0.787959 + 6.48942i) q^{30} +(-1.59005 - 6.45110i) q^{31} +(1.37852 - 5.59288i) q^{32} +(10.2941 + 7.10547i) q^{33} +(-0.217732 + 0.0264374i) q^{34} +(-4.36805 - 11.5176i) q^{35} +(6.71228 - 3.52288i) q^{36} +(-0.381270 - 1.54687i) q^{37} +(0.448568 - 1.18278i) q^{38} +(-4.85443 + 8.87480i) q^{39} +(2.93823 + 7.74747i) q^{40} +(-2.97928 + 2.05645i) q^{41} +(4.92758 - 4.36546i) q^{42} +(4.78503 + 1.17940i) q^{43} +(6.48699 + 2.46019i) q^{44} +(-7.91753 + 15.0856i) q^{45} +(-3.70027 - 1.40333i) q^{46} +(-6.93071 - 7.82316i) q^{47} +(3.22132 - 2.85384i) q^{48} +(-3.07036 + 4.44819i) q^{49} +(-3.96509 - 2.73691i) q^{50} +(-0.817858 - 0.429245i) q^{51} +(-1.43629 + 5.42386i) q^{52} +(3.28768 - 1.72551i) q^{53} +(-3.47229 - 0.421612i) q^{54} +(-15.1394 + 3.73153i) q^{55} +(4.74013 - 6.86726i) q^{56} +(4.38415 - 3.02616i) q^{57} +(-2.99060 + 3.37569i) q^{58} +(9.68905 + 1.17646i) q^{59} +(-3.65423 + 14.8258i) q^{60} +(-5.92446 - 3.10940i) q^{61} +(-0.533548 + 4.39417i) q^{62} +(17.0321 - 2.06807i) q^{63} +(-0.437224 + 0.633429i) q^{64} +(-4.26806 - 11.8658i) q^{65} +(-4.73377 - 6.85804i) q^{66} +(6.40769 + 7.23278i) q^{67} +(-0.497432 - 0.122606i) q^{68} +(-9.46722 - 13.7156i) q^{69} +8.20648i q^{70} +(2.32404 - 1.60417i) q^{71} +(-11.4569 + 1.39112i) q^{72} +(6.70968 - 2.54465i) q^{73} +(-0.127937 + 1.05365i) q^{74} +(-7.19478 - 18.9711i) q^{75} +(1.95937 - 2.21167i) q^{76} +(11.7535 + 10.4127i) q^{77} +(5.12053 - 4.38148i) q^{78} +(-0.665946 + 0.589977i) q^{79} +5.36483i q^{80} +(-0.0868336 - 0.0769278i) q^{81} +(2.34168 - 0.577172i) q^{82} +(2.63349 + 1.81776i) q^{83} +(14.3779 - 5.45281i) q^{84} +(1.07659 - 0.408298i) q^{85} +(-2.70207 - 1.86510i) q^{86} +(-18.4403 + 4.54513i) q^{87} +(-7.90612 - 7.00421i) q^{88} -2.61048i q^{89} +(8.49585 - 7.52667i) q^{90} +(-7.39260 + 10.3254i) q^{91} +(-6.91914 - 6.12982i) q^{92} +(-12.3612 + 13.9529i) q^{93} +(2.46912 + 6.51054i) q^{94} +(-0.800450 + 6.59230i) q^{95} +(-15.1108 + 5.73075i) q^{96} +(-10.4348 + 1.26701i) q^{97} +(2.96344 - 2.04552i) q^{98} -21.7180i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

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