LMFDB - Embedded newform 169.2.h.a.25.1

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			25.1
Character	$\chi$	$=$	169.25
Dual form			169.2.h.a.142.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.49582 - 0.946540i) q^{2} +(-0.730291 - 1.05801i) q^{3} +(3.83616 + 3.39854i) q^{4} +(-0.453685 - 0.0550874i) q^{5} +(0.821227 + 3.33185i) q^{6} +(-1.38308 - 2.63524i) q^{7} +(-3.87657 - 7.38618i) q^{8} +(0.477757 - 1.25974i) q^{9} +O(q^{10})$	\(q+(-2.49582 - 0.946540i) q^{2} +(-0.730291 - 1.05801i) q^{3} +(3.83616 + 3.39854i) q^{4} +(-0.453685 - 0.0550874i) q^{5} +(0.821227 + 3.33185i) q^{6} +(-1.38308 - 2.63524i) q^{7} +(-3.87657 - 7.38618i) q^{8} +(0.477757 - 1.25974i) q^{9} +(1.08017 + 0.566920i) q^{10} +(-5.12585 + 1.94398i) q^{11} +(0.794175 - 6.54062i) q^{12} +(-0.193413 + 3.60036i) q^{13} +(0.957560 + 7.88622i) q^{14} +(0.273039 + 0.520233i) q^{15} +(1.44838 + 11.9285i) q^{16} +(2.13492 - 1.12049i) q^{17} +(-2.38479 + 2.69187i) q^{18} +3.91431i q^{19} +(-1.55319 - 1.75319i) q^{20} +(-1.77805 + 3.38780i) q^{21} +14.6333 q^{22} -6.60766 q^{23} +(-4.98362 + 9.49550i) q^{24} +(-4.65191 - 1.14659i) q^{25} +(3.89061 - 8.80278i) q^{26} +(-5.42638 + 1.33748i) q^{27} +(3.65025 - 14.8097i) q^{28} +(-0.456382 + 1.20338i) q^{29} +(-0.189036 - 1.55685i) q^{30} +(-0.138189 - 0.560653i) q^{31} +(3.68333 - 14.9439i) q^{32} +(5.80011 + 4.00353i) q^{33} +(-6.38896 + 0.775760i) q^{34} +(0.482314 + 1.27176i) q^{35} +(6.11404 - 3.20889i) q^{36} +(-1.50320 - 6.09874i) q^{37} +(3.70505 - 9.76943i) q^{38} +(3.95046 - 2.42468i) q^{39} +(1.35186 + 3.56455i) q^{40} +(2.05226 - 1.41657i) q^{41} +(7.64439 - 6.77234i) q^{42} +(3.08976 + 0.761558i) q^{43} +(-26.2703 - 9.96302i) q^{44} +(-0.286147 + 0.545208i) q^{45} +(16.4915 + 6.25442i) q^{46} +(0.310500 + 0.350483i) q^{47} +(11.5627 - 10.2437i) q^{48} +(-1.05511 + 1.52859i) q^{49} +(10.5250 + 7.26492i) q^{50} +(-2.74460 - 1.44048i) q^{51} +(-12.9779 + 13.1542i) q^{52} +(3.58647 - 1.88233i) q^{53} +(14.8092 + 1.79817i) q^{54} +(2.43261 - 0.599585i) q^{55} +(-14.1027 + 20.4313i) q^{56} +(4.14138 - 2.85859i) q^{57} +(2.27810 - 2.57144i) q^{58} +(-11.0972 - 1.34745i) q^{59} +(-0.720611 + 2.92363i) q^{60} +(-7.63210 - 4.00564i) q^{61} +(-0.185787 + 1.53009i) q^{62} +(-3.98049 + 0.483319i) q^{63} +(-9.68602 + 14.0326i) q^{64} +(0.286083 - 1.62278i) q^{65} +(-10.6865 - 15.4821i) q^{66} +(-7.64095 - 8.62485i) q^{67} +(11.9979 + 2.95722i) q^{68} +(4.82552 + 6.99097i) q^{69} -3.63061i q^{70} +(12.9346 - 8.92811i) q^{71} +(-11.1567 + 1.35467i) q^{72} +(2.41889 - 0.917363i) q^{73} +(-2.02097 + 16.6442i) q^{74} +(2.18414 + 5.75911i) q^{75} +(-13.3030 + 15.0159i) q^{76} +(12.2123 + 10.8192i) q^{77} +(-12.1547 + 2.31229i) q^{78} +(0.0369776 - 0.0327593i) q^{79} -5.49158i q^{80} +(2.35251 + 2.08414i) q^{81} +(-6.46292 + 1.59297i) q^{82} +(12.2157 + 8.43190i) q^{83} +(-18.3345 + 6.95335i) q^{84} +(-1.03031 + 0.390743i) q^{85} +(-6.99065 - 4.82530i) q^{86} +(1.60648 - 0.395962i) q^{87} +(34.2293 + 30.3245i) q^{88} -9.44591i q^{89} +(1.23023 - 1.08989i) q^{90} +(9.75531 - 4.46989i) q^{91} +(-25.3481 - 22.4564i) q^{92} +(-0.492258 + 0.555645i) q^{93} +(-0.443208 - 1.16864i) q^{94} +(0.215629 - 1.77587i) q^{95} +(-18.5006 + 7.01637i) q^{96} +(-2.67205 + 0.324445i) q^{97} +(4.08025 - 2.81639i) q^{98} +7.38600i 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 $

$2$	−2.49582	−	0.946540i	−1.76481	−	0.669305i	−0.999676	−	0.0254358i	$-0.991903\pi$
$2$	−2.49582	−	0.946540i	−1.76481	−	0.669305i	−0.765136	−	0.643869i	$-0.777328\pi$
$3$	−0.730291	−	1.05801i	−0.421634	−	0.610842i	0.553396	−	0.832919i	$-0.313332\pi$
$3$	−0.730291	−	1.05801i	−0.421634	−	0.610842i	−0.975029	+	0.222077i	$0.928716\pi$
$4$	3.83616	+	3.39854i	1.91808	+	1.69927i
$5$	−0.453685	−	0.0550874i	−0.202894	−	0.0246358i	0.0184585	−	0.999830i	$-0.494124\pi$
$5$	−0.453685	−	0.0550874i	−0.202894	−	0.0246358i	−0.221353	+	0.975194i	$0.571047\pi$
$6$	0.821227	+	3.33185i	0.335265	+	1.36022i
$7$	−1.38308	−	2.63524i	−0.522755	−	0.996026i	−0.993508	−	0.113761i	$-0.963710\pi$
$7$	−1.38308	−	2.63524i	−0.522755	−	0.996026i	0.470753	−	0.882265i	$-0.343982\pi$
$8$	−3.87657	−	7.38618i	−1.37057	−	2.61141i
$9$	0.477757	−	1.25974i	0.159252	−	0.419914i
$10$	1.08017	+	0.566920i	0.341581	+	0.179276i
$11$	−5.12585	+	1.94398i	−1.54550	+	0.586132i	−0.972394	−	0.233347i	$-0.925032\pi$
$11$	−5.12585	+	1.94398i	−1.54550	+	0.586132i	−0.573109	+	0.819479i	$0.694263\pi$
$12$	0.794175	−	6.54062i	0.229259	−	1.88811i
$13$	−0.193413	+	3.60036i	−0.0536432	+	0.998560i
$13$	−0.193413	+	3.60036i	−0.0536432	+	0.998560i
$14$	0.957560	+	7.88622i	0.255919	+	2.10768i
$15$	0.273039	+	0.520233i	0.0704984	+	0.134324i
$16$	1.44838	+	11.9285i	0.362096	+	2.98213i
$17$	2.13492	−	1.12049i	0.517794	−	0.271759i	−0.185518	−	0.982641i	$-0.559396\pi$
$17$	2.13492	−	1.12049i	0.517794	−	0.271759i	0.703311	+	0.710882i	$0.251704\pi$
$18$	−2.38479	+	2.69187i	−0.562101	+	0.634480i
$19$			3.91431i			0.898005i	0.893530	+	0.449003i	$0.148221\pi$
$19$			3.91431i			0.898005i	−0.893530	+	0.449003i	$0.851779\pi$
$20$	−1.55319	−	1.75319i	−0.347305	−	0.392026i
$21$	−1.77805	+	3.38780i	−0.388003	+	0.739278i
$22$	14.6333			3.11982
$23$	−6.60766			−1.37779			−0.688897	−	0.724860i	$-0.741905\pi$
$23$	−6.60766			−1.37779			−0.688897	+	0.724860i	$0.741905\pi$
$24$	−4.98362	+	9.49550i	−1.01728	+	1.93826i
$25$	−4.65191	−	1.14659i	−0.930383	−	0.229319i
$26$	3.89061	−	8.80278i	0.763011	−	1.72637i
$27$	−5.42638	+	1.33748i	−1.04431	+	0.257399i
$28$	3.65025	−	14.8097i	0.689833	−	2.79876i
$29$	−0.456382	+	1.20338i	−0.0847481	+	0.223462i	−0.970691	−	0.240333i	$-0.922743\pi$
$29$	−0.456382	+	1.20338i	−0.0847481	+	0.223462i	0.885942	+	0.463795i	$0.153513\pi$
$30$	−0.189036	−	1.55685i	−0.0345131	−	0.284241i
$31$	−0.138189	−	0.560653i	−0.0248194	−	0.100696i	0.957226	−	0.289342i	$-0.0934364\pi$
$31$	−0.138189	−	0.560653i	−0.0248194	−	0.100696i	−0.982045	+	0.188646i	$0.939590\pi$
$32$	3.68333	−	14.9439i	0.651127	−	2.64173i
$33$	5.80011	+	4.00353i	1.00967	+	0.696925i
$34$	−6.38896	+	0.775760i	−1.09570	+	0.133042i
$35$	0.482314	+	1.27176i	0.0815260	+	0.214966i
$36$	6.11404	−	3.20889i	1.01901	−	0.534816i
$37$	−1.50320	−	6.09874i	−0.247125	−	1.00263i	−0.955075	−	0.296364i	$-0.904226\pi$
$37$	−1.50320	−	6.09874i	−0.247125	−	1.00263i	0.707950	−	0.706263i	$-0.249620\pi$
$38$	3.70505	−	9.76943i	0.601039	−	1.58481i
$39$	3.95046	−	2.42468i	0.632580	−	0.388259i
$40$	1.35186	+	3.56455i	0.213747	+	0.563605i
$41$	2.05226	−	1.41657i	0.320509	−	0.221232i	−0.396936	−	0.917846i	$-0.629927\pi$
$41$	2.05226	−	1.41657i	0.320509	−	0.221232i	0.717446	+	0.696615i	$0.245311\pi$
$42$	7.64439	−	6.77234i	1.17956	−	1.04499i
$43$	3.08976	+	0.761558i	0.471184	+	0.116137i	0.467756	−	0.883858i	$-0.345063\pi$
$43$	3.08976	+	0.761558i	0.471184	+	0.116137i	0.00342838	+	0.999994i	$0.498909\pi$
$44$	−26.2703	−	9.96302i	−3.96040	−	1.50198i
$45$	−0.286147	+	0.545208i	−0.0426563	+	0.0812747i
$46$	16.4915	+	6.25442i	2.43155	+	0.922164i
$47$	0.310500	+	0.350483i	0.0452912	+	0.0511231i	0.770720	−	0.637174i	$-0.219897\pi$
$47$	0.310500	+	0.350483i	0.0452912	+	0.0511231i	−0.725429	+	0.688297i	$0.758358\pi$
$48$	11.5627	−	10.2437i	1.66894	−	1.47855i
$49$	−1.05511	+	1.52859i	−0.150730	+	0.218371i
$50$	10.5250	+	7.26492i	1.48847	+	1.02741i
$51$	−2.74460	−	1.44048i	−0.384321	−	0.201707i
$52$	−12.9779	+	13.1542i	−1.79972	+	1.82417i
$53$	3.58647	−	1.88233i	0.492640	−	0.258557i	−0.200060	−	0.979784i	$-0.564114\pi$
$53$	3.58647	−	1.88233i	0.492640	−	0.258557i	0.692699	+	0.721226i	$0.256421\pi$
$54$	14.8092	+	1.79817i	2.01528	+	0.244700i
$55$	2.43261	−	0.599585i	0.328013	−	0.0808481i
$56$	−14.1027	+	20.4313i	−1.88456	+	2.73025i
$57$	4.14138	−	2.85859i	0.548539	−	0.378629i
$58$	2.27810	−	2.57144i	0.299129	−	0.337647i
$59$	−11.0972	−	1.34745i	−1.44474	−	0.175423i	−0.639690	−	0.768633i	$-0.720937\pi$
$59$	−11.0972	−	1.34745i	−1.44474	−	0.175423i	−0.805048	+	0.593210i	$0.797860\pi$
$60$	−0.720611	+	2.92363i	−0.0930305	+	0.377440i
$61$	−7.63210	−	4.00564i	−0.977191	−	0.512869i	−0.101028	−	0.994884i	$-0.532213\pi$
$61$	−7.63210	−	4.00564i	−0.977191	−	0.512869i	−0.876163	+	0.482014i	$0.839905\pi$
$62$	−0.185787	+	1.53009i	−0.0235949	+	0.194322i
$63$	−3.98049	+	0.483319i	−0.501495	+	0.0608925i
$64$	−9.68602	+	14.0326i	−1.21075	+	1.75408i
$65$	0.286083	−	1.62278i	0.0354842	−	0.201281i
$66$	−10.6865	−	15.4821i	−1.31542	−	1.90572i
$67$	−7.64095	−	8.62485i	−0.933491	−	1.05369i	−0.998442	−	0.0558051i	$-0.982227\pi$
$67$	−7.64095	−	8.62485i	−0.933491	−	1.05369i	0.0649506	−	0.997888i	$-0.479311\pi$
$68$	11.9979	+	2.95722i	1.45496	+	0.358616i
$69$	4.82552	+	6.99097i	0.580924	+	0.841613i
$70$		−	3.63061i		−	0.433941i
$71$	12.9346	−	8.92811i	1.53505	−	1.05957i	0.562529	−	0.826778i	$-0.309829\pi$
$71$	12.9346	−	8.92811i	1.53505	−	1.05957i	0.972526	−	0.232794i	$-0.0747869\pi$
$72$	−11.1567	+	1.35467i	−1.31483	+	0.159650i
$73$	2.41889	−	0.917363i	0.283109	−	0.107369i	−0.208963	−	0.977924i	$-0.567009\pi$
$73$	2.41889	−	0.917363i	0.283109	−	0.107369i	0.492072	+	0.870554i	$0.336240\pi$
$74$	−2.02097	+	16.6442i	−0.234933	+	1.93485i
$75$	2.18414	+	5.75911i	0.252203	+	0.665005i
$76$	−13.3030	+	15.0159i	−1.52596	+	1.72245i
$77$	12.2123	+	10.8192i	1.39172	+	1.23296i
$78$	−12.1547	+	2.31229i	−1.37625	+	0.261815i
$79$	0.0369776	−	0.0327593i	0.00416030	−	0.00368571i	−0.661040	−	0.750351i	$-0.729885\pi$
$79$	0.0369776	−	0.0327593i	0.00416030	−	0.00368571i	0.665200	+	0.746665i	$0.268346\pi$
$80$		−	5.49158i		−	0.613978i
$81$	2.35251	+	2.08414i	0.261390	+	0.231571i
$82$	−6.46292	+	1.59297i	−0.713710	+	0.175914i
$83$	12.2157	+	8.43190i	1.34085	+	0.925522i	0.999894	−	0.0145577i	$-0.00463403\pi$
$83$	12.2157	+	8.43190i	1.34085	+	0.925522i	0.340956	+	0.940079i	$0.389249\pi$
$84$	−18.3345	+	6.95335i	−2.00046	+	0.758673i
$85$	−1.03031	+	0.390743i	−0.111752	+	0.0423821i
$86$	−6.99065	−	4.82530i	−0.753821	−	0.520325i
$87$	1.60648	−	0.395962i	0.172233	−	0.0424516i
$88$	34.2293	+	30.3245i	3.64885	+	3.23260i
$89$		−	9.44591i		−	1.00126i	−0.865660	−	0.500632i	$-0.833101\pi$
$89$		−	9.44591i		−	1.00126i	0.865660	−	0.500632i	$-0.166899\pi$
$90$	1.23023	−	1.08989i	0.129678	−	0.114885i
$91$	9.75531	−	4.46989i	1.02263	−	0.468572i
$92$	−25.3481	−	22.4564i	−2.64272	−	2.34125i
$93$	−0.492258	+	0.555645i	−0.0510448	+	0.0576177i
$94$	−0.443208	−	1.16864i	−0.0457134	−	0.120536i
$95$	0.215629	−	1.77587i	0.0221231	−	0.182200i
$96$	−18.5006	+	7.01637i	−1.88821	+	0.716105i
$97$	−2.67205	+	0.324445i	−0.271305	+	0.0329424i	−0.255059	−	0.966926i	$-0.582095\pi$
$97$	−2.67205	+	0.324445i	−0.271305	+	0.0329424i	−0.0162467	+	0.999868i	$0.505172\pi$
$98$	4.08025	−	2.81639i	0.412167	−	0.284499i
$99$			7.38600i			0.742321i
$100$	−13.9488	−	20.2083i	−1.39488	−	2.02083i
$101$	8.94644	+	2.20510i	0.890204	+	0.219416i	0.657790	−	0.753201i	$-0.271491\pi$
$101$	8.94644	+	2.20510i	0.890204	+	0.219416i	0.232414	+	0.972617i	$0.425338\pi$
$102$	5.48656	+	6.19305i	0.543250	+	0.613203i
$103$	−10.9433	−	15.8541i	−1.07827	−	1.56215i	−0.798413	−	0.602110i	$-0.794327\pi$
$103$	−10.9433	−	15.8541i	−1.07827	−	1.56215i	−0.279862	−	0.960040i	$-0.590289\pi$
$104$	27.3427	−	12.5284i	2.68117	−	1.22852i
$105$	0.993302	−	1.43905i	0.0969363	−	0.140437i
$106$	−10.7329	+	1.30321i	−1.04247	+	0.126579i
$107$	0.903609	−	7.44189i	0.0873552	−	0.719435i	−0.881565	−	0.472062i	$-0.843510\pi$
$107$	0.903609	−	7.44189i	0.0873552	−	0.719435i	0.968920	−	0.247373i	$-0.0795671\pi$
$108$	−25.3620	−	13.3110i	−2.44046	−	1.28085i
$109$	−1.00394	+	4.07314i	−0.0961600	+	0.390136i	−0.999225	−	0.0393679i	$-0.987466\pi$
$109$	−1.00394	+	4.07314i	−0.0961600	+	0.390136i	0.903065	+	0.429504i	$0.141312\pi$
$110$	−6.63890	−	0.806108i	−0.632994	−	0.0768594i
$111$	−5.35474	+	6.04425i	−0.508250	+	0.573695i
$112$	29.4312	−	20.3149i	2.78099	−	1.91958i
$113$	−10.7712	+	15.6048i	−1.01327	+	1.46797i	−0.134389	+	0.990929i	$0.542907\pi$
$113$	−10.7712	+	15.6048i	−1.01327	+	1.46797i	−0.878880	+	0.477044i	$0.841708\pi$
$114$	−13.0419	+	3.21454i	−1.22149	+	0.301069i
$115$	2.99780	+	0.363999i	0.279546	+	0.0339431i
$116$	−5.84050	+	3.06533i	−0.542277	+	0.284609i
$117$	4.44312	+	1.96375i	0.410766	+	0.181548i
$118$	26.4213	+	13.8670i	2.43228	+	1.27656i
$119$	−5.90552	−	4.07629i	−0.541358	−	0.373672i
$120$	2.78408	−	4.03343i	0.254150	−	0.368200i
$121$	14.2617	−	12.6348i	1.29652	−	1.14861i
$122$	15.2569	+	17.2214i	1.38129	+	1.55916i
$123$	−2.99749	−	1.13680i	−0.270275	−	0.102502i
$124$	1.37529	−	2.62040i	0.123505	−	0.235319i
$125$	4.18394	+	1.58676i	0.374223	+	0.141924i
$126$	10.3921	+	2.56142i	0.925800	+	0.228189i
$127$	−12.8446	+	11.3793i	−1.13978	+	1.00975i	−0.139967	+	0.990156i	$0.544700\pi$
$127$	−12.8446	+	11.3793i	−1.13978	+	1.00975i	−0.999808	+	0.0195964i	$0.993762\pi$
$128$	12.1238	−	8.36842i	1.07160	−	0.739671i
$129$	−1.45069	−	3.82516i	−0.127726	−	0.336786i
$130$	−2.25003	+	3.77937i	−0.197341	+	0.331473i
$131$	2.05190	−	5.41041i	0.179275	−	0.472710i	−0.815013	−	0.579443i	$-0.803270\pi$
$131$	2.05190	−	5.41041i	0.179275	−	0.472710i	0.994288	+	0.106734i	$0.0340393\pi$
$132$	8.64401	+	35.0701i	0.752364	+	3.05246i
$133$	10.3151	−	5.41380i	0.894436	−	0.469436i
$134$	10.9067	+	28.7586i	0.942194	+	2.48436i
$135$	2.53555	−	0.307871i	0.218225	−	0.0264973i
$136$	−16.5523	−	11.4252i	−1.41935	−	0.979705i
$137$	−4.33811	+	17.6004i	−0.370630	+	1.50370i	0.429051	+	0.903280i	$0.358848\pi$
$137$	−4.33811	+	17.6004i	−0.370630	+	1.50370i	−0.799681	+	0.600425i	$0.794998\pi$
$138$	−5.42639	−	22.0157i	−0.461925	−	1.87410i
$139$	−0.369898	−	3.04638i	−0.0313743	−	0.258391i	−0.999953	−	0.00968396i	$-0.996917\pi$
$139$	−0.369898	−	3.04638i	−0.0313743	−	0.258391i	0.968579	−	0.248707i	$-0.0800056\pi$
$140$	−2.47189	+	6.51784i	−0.208913	+	0.550858i
$141$	0.144058	−	0.584466i	0.0121319	−	0.0492210i
$142$	−40.7333	+	10.0398i	−3.41826	+	0.842525i
$143$	−6.00762	−	18.8309i	−0.502382	−	1.57472i
$144$	15.7188	+	3.87434i	1.30990	+	0.322862i
$145$	0.273345	−	0.520816i	0.0227001	−	0.0432514i
$146$	−6.90543			−0.571497
$147$	2.38780			0.196943
$148$	14.9603	−	28.5045i	1.22973	−	2.34305i
$149$	2.73114	+	3.08282i	0.223743	+	0.252554i	0.849654	−	0.527341i	$-0.176811\pi$
$149$	2.73114	+	3.08282i	0.223743	+	0.252554i	−0.625910	+	0.779895i	$0.715272\pi$
$150$		−	16.4411i		−	1.34241i
$151$	8.86535	−	10.0069i	0.721452	−	0.814351i	−0.267348	−	0.963600i	$-0.586147\pi$
$151$	8.86535	−	10.0069i	0.721452	−	0.814351i	0.988800	+	0.149249i	$0.0476857\pi$
$152$	28.9118	−	15.1741i	2.34506	−	1.23078i
$153$	−0.391557	−	3.22476i	−0.0316555	−	0.260707i
$154$	−20.2390	−	38.5621i	−1.63090	−	3.10742i
$155$	0.0318092	+	0.261973i	0.00255498	+	0.0210421i
$156$	23.3950	+	4.12436i	1.87310	+	0.330213i
$157$	0.226237	−	1.86323i	0.0180557	−	0.148702i	−0.980893	−	0.194549i	$-0.937676\pi$
$157$	0.226237	−	1.86323i	0.0180557	−	0.148702i	0.998948	+	0.0458471i	$0.0145987\pi$
$158$	−0.123297	+	0.0467605i	−0.00980901	+	0.00372007i
$159$	−4.61068	−	2.41987i	−0.365651	−	0.191908i
$160$	−2.49429	+	6.57690i	−0.197191	+	0.519950i
$161$	9.13892	+	17.4128i	0.720248	+	1.37232i
$162$	−3.89872	−	7.42839i	−0.306313	−	0.583630i
$163$	1.07606	+	4.36576i	0.0842839	+	0.341953i	0.997911	−	0.0645994i	$-0.0205770\pi$
$163$	1.07606	+	4.36576i	0.0842839	+	0.341953i	−0.913627	+	0.406553i	$0.866731\pi$
$164$	12.6871	+	1.54049i	0.990696	+	0.120292i
$165$	−2.41088	−	2.13585i	−0.187687	−	0.166276i
$166$	−22.5071	−	32.6072i	−1.74689	−	2.53081i
$167$	−16.1199	−	6.11346i	−1.24739	−	0.473074i	−0.359509	−	0.933142i	$-0.617056\pi$
$167$	−16.1199	−	6.11346i	−1.24739	−	0.473074i	−0.887884	+	0.460068i	$0.847825\pi$
$168$	31.9156			2.46234
$169$	−12.9252	−	1.39271i	−0.994245	−	0.107132i
$170$	2.94131			0.225588
$171$	4.93102	+	1.87009i	0.377085	+	0.143009i
$172$	9.26465	+	13.4222i	0.706423	+	1.02343i
$173$	−13.3981	−	11.8697i	−1.01864	−	0.902436i	−0.0233837	−	0.999727i	$-0.507444\pi$
$173$	−13.3981	−	11.8697i	−1.01864	−	0.902436i	−0.995256	+	0.0972905i	$0.968982\pi$
$174$	−4.38428	−	0.532348i	−0.332371	−	0.0403572i
$175$	3.41242	+	13.8447i	0.257955	+	1.04656i
$176$	−30.6130	−	58.3282i	−2.30754	−	4.39665i
$177$	6.67860	+	12.7250i	0.501994	+	0.956470i
$178$	−8.94094	+	23.5753i	−0.670151	+	1.76704i
$179$	7.30421	+	3.83354i	0.545942	+	0.286532i	0.715060	−	0.699063i	$-0.246399\pi$
$179$	7.30421	+	3.83354i	0.545942	+	0.286532i	−0.169118	+	0.985596i	$0.554092\pi$
$180$	−2.95062	+	1.11902i	−0.219926	+	0.0834070i
$181$	0.339809	−	2.79858i	0.0252578	−	0.208017i	−0.974616	−	0.223882i	$-0.928127\pi$
$181$	0.339809	−	2.79858i	0.0252578	−	0.208017i	0.999874	+	0.0158648i	$0.00505014\pi$
$182$	−28.5784	+	1.92226i	−2.11837	+	0.142488i
$183$	1.33566	+	11.0001i	0.0987345	+	0.813152i
$184$	25.6150	+	48.8054i	1.88837	+	3.59798i
$185$	0.346018	+	2.84971i	0.0254398	+	0.209515i
$186$	1.75453	−	0.920848i	0.128648	−	0.0675198i
$187$	−8.76506	+	9.89371i	−0.640965	+	0.723500i
$188$			2.39976i			0.175020i
$189$	11.0297	+	12.4499i	0.802292	+	0.905600i
$190$	−2.21910	+	4.22814i	−0.160990	+	0.306742i
$191$	−8.57427			−0.620412			−0.310206	−	0.950669i	$-0.600398\pi$
$191$	−8.57427			−0.620412			−0.310206	+	0.950669i	$0.600398\pi$
$192$	21.9202			1.58196
$193$	1.91203	−	3.64306i	0.137631	−	0.262234i	−0.806879	−	0.590717i	$-0.798845\pi$
$193$	1.91203	−	3.64306i	0.137631	−	0.262234i	0.944510	+	0.328483i	$0.106537\pi$
$194$	6.97605	+	1.71944i	0.500851	+	0.123449i
$195$	−1.92583	+	0.882420i	−0.137912	+	0.0631914i
$196$	−9.24258	+	2.27809i	−0.660184	+	0.162721i
$197$	0.786065	−	3.18919i	0.0560048	−	0.227221i	−0.936270	−	0.351282i	$-0.885746\pi$
$197$	0.786065	−	3.18919i	0.0560048	−	0.227221i	0.992275	+	0.124061i	$0.0395920\pi$
$198$	6.99114	−	18.4341i	0.496839	−	1.31006i
$199$	−0.992879	−	8.17709i	−0.0703833	−	0.579659i	−0.984649	−	0.174544i	$-0.944155\pi$
$199$	−0.992879	−	8.17709i	−0.0703833	−	0.579659i	0.914266	−	0.405114i	$-0.132768\pi$
$200$	9.56450	+	38.8047i	0.676313	+	2.74391i
$201$	−3.54505	+	14.3828i	−0.250049	+	1.01449i
$202$	−20.2415	−	13.9717i	−1.42419	−	0.983045i
$203$	3.80241	−	0.461696i	0.266877	−	0.0324047i
$204$	−5.63321	−	14.8535i	−0.394403	−	1.03996i
$205$	−1.00912	+	0.529625i	−0.0704797	+	0.0369906i
$206$	12.3060	+	49.9273i	0.857397	+	3.47860i
$207$	−3.15686	+	8.32394i	−0.219417	+	0.578554i
$208$	−43.2271	+	2.90757i	−2.99726	+	0.201604i
$209$	−7.60935	−	20.0642i	−0.526349	−	1.38787i
$210$	−3.84122	+	2.65140i	−0.265069	+	0.182964i
$211$	0.283911	−	0.251523i	0.0195452	−	0.0173156i	−0.653294	−	0.757105i	$-0.726613\pi$
$211$	0.283911	−	0.251523i	0.0195452	−	0.0173156i	0.672839	+	0.739789i	$0.265075\pi$
$212$	20.1555	+	4.96787i	1.38428	+	0.341195i
$213$	−18.8920	−	7.16481i	−1.29446	−	0.490924i
$214$	−9.29929	+	17.7183i	−0.635687	+	1.21120i
$215$	−1.35983	−	0.515715i	−0.0927395	−	0.0351714i
$216$	30.9146	+	34.8954i	2.10347	+	2.37433i
$217$	−1.28633	+	1.13959i	−0.0873217	+	0.0773602i
$218$	6.36105	−	9.21557i	0.430825	−	0.624157i
$219$	−2.73707	−	1.88926i	−0.184954	−	0.127664i
$220$	11.3696	+	5.96724i	0.766539	+	0.402311i
$221$	3.62125	+	7.90319i	0.243592	+	0.531626i
$222$	19.0856	−	10.0169i	1.28094	−	0.672290i
$223$	27.8171	+	3.37761i	1.86277	+	0.226181i	0.973094	−	0.230410i	$-0.0740069\pi$
$223$	27.8171	+	3.37761i	1.86277	+	0.226181i	0.889676	+	0.456592i	$0.150930\pi$
$224$	−44.4750	+	10.9621i	−2.97161	+	0.732436i
$225$	−3.66689	+	5.31241i	−0.244460	+	0.354161i
$226$	41.6535	−	28.7513i	2.77075	−	1.91251i
$227$	2.25084	−	2.54068i	0.149394	−	0.168631i	−0.669050	−	0.743218i	$-0.733299\pi$
$227$	2.25084	−	2.54068i	0.149394	−	0.168631i	0.818444	+	0.574587i	$0.194837\pi$
$228$	25.6020	+	3.10865i	1.69554	+	0.205875i
$229$	−3.41030	+	13.8361i	−0.225359	+	0.914317i	0.743903	+	0.668287i	$0.232972\pi$
$229$	−3.41030	+	13.8361i	−0.225359	+	0.914317i	−0.969262	+	0.246030i	$0.920874\pi$
$230$	−7.13743	−	3.74601i	−0.470628	−	0.247005i
$231$	2.52823	−	20.8219i	0.166345	−	1.36998i
$232$	10.6576	−	1.29407i	0.699705	−	0.0849596i
$233$	−5.42573	+	7.86053i	−0.355452	+	0.514961i	−0.959395	−	0.282067i	$-0.908980\pi$
$233$	−5.42573	+	7.86053i	−0.355452	+	0.514961i	0.603943	+	0.797027i	$0.293595\pi$
$234$	−9.23046	−	9.10675i	−0.603414	−	0.595327i
$235$	−0.121562	−	0.176113i	−0.00792985	−	0.0114884i
$236$	−37.9915	−	42.8835i	−2.47303	−	2.79148i
$237$	−0.0616640	−	0.0151988i	−0.00400551	−	0.000987269i
$238$	10.8808	+	15.7635i	0.705294	+	1.02180i
$239$		−	10.2917i		−	0.665716i	−0.942977	−	0.332858i	$-0.891987\pi$
$239$		−	10.2917i		−	0.665716i	0.942977	−	0.332858i	$-0.108013\pi$
$240$	−5.81014	+	4.01045i	−0.375043	+	0.258874i
$241$	0.175972	−	0.0213669i	0.0113353	−	0.00137636i	−0.114867	−	0.993381i	$-0.536644\pi$
$241$	0.175972	−	0.0213669i	0.0113353	−	0.00137636i	0.126202	+	0.992005i	$0.459721\pi$
$242$	−47.5540	+	18.0348i	−3.05688	+	1.15932i
$243$	−1.53393	+	12.6331i	−0.0984019	+	0.810412i
$244$	−15.6647	−	41.3043i	−1.00283	−	2.64424i
$245$	0.562895	−	0.635377i	0.0359621	−	0.0405928i
$246$	6.40518	+	5.67450i	0.408380	+	0.361793i
$247$	−14.0929	−	0.757080i	−0.896712	−	0.0481718i
$248$	−3.60539	+	3.19410i	−0.228942	+	0.202825i
$249$		−	19.0821i		−	1.20928i
$250$	−8.94042	−	7.92053i	−0.565442	−	0.500938i
$251$	3.74625	−	0.923368i	0.236461	−	0.0582825i	−0.119304	−	0.992858i	$-0.538066\pi$
$251$	3.74625	−	0.923368i	0.236461	−	0.0582825i	0.355765	+	0.934575i	$0.384220\pi$
$252$	−16.9124	−	11.6738i	−1.06538	−	0.735379i
$253$	33.8699	−	12.8452i	2.12938	−	0.807569i
$254$	42.8288	−	16.2428i	2.68732	−	1.01917i
$255$	1.16583	+	0.804716i	0.0730073	+	0.0503933i
$256$	−5.06890	+	1.24937i	−0.316806	+	0.0780857i
$257$	−5.63611	−	4.99315i	−0.351571	−	0.311464i	0.468791	−	0.883309i	$-0.344690\pi$
$257$	−5.63611	−	4.99315i	−0.351571	−	0.311464i	−0.820362	+	0.571844i	$0.806228\pi$
$258$			10.9200i			0.679852i
$259$	−13.9926	+	12.3963i	−0.869456	+	0.770271i
$260$	6.61254	−	5.25297i	0.410092	−	0.325775i
$261$	1.29791	+	1.14985i	0.0803386	+	0.0711738i
$262$	−10.2423	+	11.5612i	−0.632774	+	0.714254i
$263$	4.92003	+	12.9731i	0.303382	+	0.799953i	0.996838	+	0.0794546i	$0.0253179\pi$
$263$	4.92003	+	12.9731i	0.303382	+	0.799953i	−0.693456	+	0.720499i	$0.743913\pi$
$264$	7.08626	−	58.3606i	0.436129	−	3.59185i
$265$	−1.73082	+	0.656414i	−0.106324	+	0.0403232i
$266$	−30.8691	+	3.74819i	−1.89271	+	0.229816i
$267$	−9.99386	+	6.89826i	−0.611614	+	0.422167i
$268$		−	59.0545i		−	3.60733i
$269$	−9.90703	−	14.3528i	−0.604042	−	0.875106i	0.395008	−	0.918678i	$-0.370742\pi$
$269$	−9.90703	−	14.3528i	−0.604042	−	0.875106i	−0.999050	+	0.0435713i	$0.986126\pi$
$270$	−6.61968	−	1.63161i	−0.402861	−	0.0992963i
$271$	1.00843	+	1.13829i	0.0612580	+	0.0691459i	0.778341	−	0.627842i	$-0.216062\pi$
$271$	1.00843	+	1.13829i	0.0612580	+	0.0691459i	−0.717083	+	0.696988i	$0.754523\pi$
$272$	16.4580	+	23.8435i	0.997912	+	1.44572i
$273$	−11.8534	−	7.05688i	−0.717400	−	0.427102i
$274$	27.4867	−	39.8213i	1.66053	−	2.40569i
$275$	26.0740	−	3.16595i	1.57232	−	0.190914i
$276$	−5.24764	+	43.2182i	−0.315871	+	2.60143i
$277$	20.8902	+	10.9640i	1.25517	+	0.658765i	0.955419	−	0.295252i	$-0.0954037\pi$
$277$	20.8902	+	10.9640i	1.25517	+	0.658765i	0.299752	+	0.954017i	$0.403096\pi$
$278$	−1.96033	+	7.95335i	−0.117573	+	0.477011i
$279$	−0.772298	−	0.0937740i	−0.0462363	−	0.00561410i
$280$	7.52371	−	8.49252i	0.449628	−	0.507525i
$281$	−18.8614	+	13.0191i	−1.12518	+	0.776653i	−0.977196	−	0.212338i	$-0.931892\pi$
$281$	−18.8614	+	13.0191i	−1.12518	+	0.776653i	−0.147979	+	0.988990i	$0.547277\pi$
$282$	−0.912764	+	1.32237i	−0.0543543	+	0.0787458i
$283$	−13.5156	+	3.33128i	−0.803416	+	0.198024i	−0.619581	−	0.784933i	$-0.712697\pi$
$283$	−13.5156	+	3.33128i	−0.803416	+	0.198024i	−0.183835	+	0.982957i	$0.558851\pi$
$284$	79.9618	+	9.70912i	4.74486	+	0.576131i
$285$	−2.03635	+	1.06876i	−0.120623	+	0.0633079i
$286$	−2.83027	+	52.6850i	−0.167357	+	3.11533i
$287$	−6.57145	−	3.44896i	−0.387900	−	0.203586i
$288$	−17.0657	−	11.7796i	−1.00560	−	0.694118i
$289$	−6.35473	+	9.20641i	−0.373808	+	0.541554i
$290$	−1.17519	+	1.04113i	−0.0690097	+	0.0611373i
$291$	2.29464	+	2.59011i	0.134514	+	0.151835i
$292$	12.3969	+	4.70154i	0.725476	+	0.275137i
$293$	12.3575	−	23.5453i	0.721934	−	1.37553i	−0.196717	−	0.980460i	$-0.563028\pi$
$293$	12.3575	−	23.5453i	0.721934	−	1.37553i	0.918651	−	0.395070i	$-0.129280\pi$
$294$	−5.95953	−	2.26015i	−0.347567	−	0.131815i
$295$	4.96043	+	1.22264i	0.288807	+	0.0711846i
$296$	−39.2191	+	34.7451i	−2.27956	+	2.01952i
$297$	25.2148	−	17.4045i	1.46311	−	1.00991i
$298$	−3.89842	−	10.2793i	−0.225829	−	0.595463i
$299$	1.27801	−	23.7900i	0.0739092	−	1.37581i
$300$	−11.1939	+	29.5158i	−0.646278	+	1.70410i
$301$	−2.26650	−	9.19555i	−0.130639	−	0.530023i
$302$	−31.5983	+	16.5840i	−1.81828	+	0.954305i
$303$	−4.20049	−	11.0758i	−0.241312	−	0.636287i
$304$	−46.6920	+	5.66943i	−2.67797	+	0.325164i
$305$	3.24191	+	2.23773i	0.185631	+	0.128132i
$306$	−2.07511	+	8.41906i	−0.118626	+	0.481286i
$307$	4.03925	+	16.3879i	0.230532	+	0.935305i	0.966165	+	0.257925i	$0.0830386\pi$
$307$	4.03925	+	16.3879i	0.230532	+	0.935305i	−0.735633	+	0.677380i	$0.763115\pi$
$308$	10.0790	+	83.0081i	0.574305	+	4.72983i
$309$	−8.78199	+	23.1562i	−0.499590	+	1.31731i
$310$	0.168577	−	0.683945i	0.00957455	−	0.0388455i
$311$	22.4409	−	5.53118i	1.27251	−	0.313645i	0.455480	−	0.890246i	$-0.349468\pi$
$311$	22.4409	−	5.53118i	1.27251	−	0.313645i	0.817026	+	0.576601i	$0.195621\pi$
$312$	−33.2233	−	19.7794i	−1.88090	−	1.11979i
$313$	−1.95856	−	0.482741i	−0.110704	−	0.0272862i	0.183574	−	0.983006i	$-0.441233\pi$
$313$	−1.95856	−	0.482741i	−0.110704	−	0.0272862i	−0.294279	+	0.955720i	$0.595079\pi$
$314$	−2.32827	+	4.43615i	−0.131392	+	0.250346i
$315$	1.83251			0.103251
$316$	0.253186			0.0142428
$317$	5.30516	−	10.1081i	0.297968	−	0.567730i	−0.689737	−	0.724060i	$-0.742274\pi$
$317$	5.30516	−	10.1081i	0.297968	−	0.567730i	0.987705	+	0.156330i	$0.0499663\pi$
$318$	9.21693	+	10.4038i	0.516860	+	0.583414i
$319$		−	7.05556i		−	0.395035i
$320$	5.16742	−	5.83282i	0.288868	−	0.326064i
$321$	−8.53348	+	4.47872i	−0.476293	+	0.249978i
$322$	−6.32724	−	52.1095i	−0.352603	−	2.90395i
$323$	4.38595	+	8.35674i	0.244041	+	0.464981i
$324$	1.94157	+	15.9902i	0.107865	+	0.888346i
$325$	5.02789	−	16.5268i	0.278897	−	0.916742i
$326$	1.44671	−	11.9147i	0.0801257	−	0.659895i
$327$	5.04259	−	1.91240i	0.278856	−	0.105756i
$328$	−18.4188	−	9.66693i	−1.01701	−	0.533767i
$329$	0.494158	−	1.30299i	0.0272438	−	0.0718360i
$330$	3.99546	+	7.61271i	0.219943	+	0.419066i
$331$	6.16095	+	11.7387i	0.338637	+	0.645218i	0.993913	−	0.110172i	$-0.0351400\pi$
$331$	6.16095	+	11.7387i	0.338637	+	0.645218i	−0.655276	+	0.755389i	$0.727448\pi$
$332$	18.2053	+	73.8618i	0.999146	+	4.05369i
$333$	−8.40099	−	1.02007i	−0.460372	−	0.0558992i
$334$	34.4457	+	30.5162i	1.88478	+	1.66977i
$335$	2.99147	+	4.33389i	0.163441	+	0.236786i
$336$	−42.9867	−	16.3027i	−2.34512	−	0.889386i
$337$	10.8960			0.593541			0.296771	−	0.954949i	$-0.404090\pi$
$337$	10.8960			0.593541			0.296771	+	0.954949i	$0.404090\pi$
$338$	30.9407	+	15.7102i	1.68295	+	0.854521i
$339$	24.3761			1.32393
$340$	−5.28038	−	2.00258i	−0.286369	−	0.108605i
$341$	1.79823	+	2.60519i	0.0973798	+	0.141079i
$342$	−10.5368	−	9.33482i	−0.569767	−	0.504769i
$343$	−15.1935	−	1.84483i	−0.820374	−	0.0996114i
$344$	−6.35267	−	25.7738i	−0.342513	−	1.38963i
$345$	−1.80415	−	3.43752i	−0.0971323	−	0.185070i
$346$	22.2042	+	42.3065i	1.19370	+	2.27441i
$347$	1.69228	−	4.46217i	0.0908462	−	0.239542i	−0.881890	−	0.471455i	$-0.843729\pi$
$347$	1.69228	−	4.46217i	0.0908462	−	0.239542i	0.972737	+	0.231913i	$0.0744984\pi$
$348$	7.50841	+	3.94072i	0.402493	+	0.211245i
$349$	−28.7780	+	10.9140i	−1.54045	+	0.584216i	−0.971266	−	0.237995i	$-0.923510\pi$
$349$	−28.7780	+	10.9140i	−1.54045	+	0.584216i	−0.569184	+	0.822210i	$0.692741\pi$
$350$	4.58780	−	37.7839i	0.245228	−	2.01964i
$351$	−3.76588	−	19.7956i	−0.201008	−	1.05661i
$352$	10.1703	+	83.7604i	0.542081	+	4.46444i
$353$	1.16277	+	2.21546i	0.0618878	+	0.117917i	0.914435	−	0.404733i	$-0.132636\pi$
$353$	1.16277	+	2.21546i	0.0618878	+	0.117917i	−0.852547	+	0.522650i	$0.824943\pi$
$354$	−4.62386	−	38.0809i	−0.245755	−	2.02398i
$355$	−6.36006	+	3.33802i	−0.337557	+	0.177164i
$356$	32.1024	−	36.2361i	1.70142	−	1.92051i
$357$			9.22496i			0.488237i
$358$	−14.6014	−	16.4816i	−0.771707	−	0.871078i
$359$	−1.37723	+	2.62409i	−0.0726874	+	0.138494i	−0.919088	−	0.394053i	$-0.871073\pi$
$359$	−1.37723	+	2.62409i	−0.0726874	+	0.138494i	0.846400	+	0.532547i	$0.178765\pi$
$360$	5.13627			0.270705
$361$	3.67815			0.193587
$362$	−3.49707	+	6.66311i	−0.183802	+	0.350206i
$363$	−23.7829	−	5.86195i	−1.24828	−	0.307673i
$364$	52.6141	+	16.0066i	2.75773	+	0.838974i
$365$	−1.14795	+	0.282944i	−0.0600864	+	0.0148100i
$366$	7.07849	−	28.7186i	0.369999	−	1.50114i
$367$	7.41132	−	19.5421i	0.386868	−	1.02009i	−0.590218	−	0.807244i	$-0.700958\pi$
$367$	7.41132	−	19.5421i	0.386868	−	1.02009i	0.977086	−	0.212843i	$-0.0682724\pi$
$368$	−9.57044	−	78.8197i	−0.498894	−	4.10876i
$369$	−0.804034	−	3.26209i	−0.0418563	−	0.169818i
$370$	1.83377	−	7.43990i	0.0953332	−	0.386782i
$371$	−9.92075	−	6.84780i	−0.515060	−	0.355520i
$372$	−3.77677	+	0.458582i	−0.195816	+	0.0237764i
$373$	−6.02908	−	15.8974i	−0.312174	−	0.823135i	−0.995651	−	0.0931632i	$-0.970302\pi$
$373$	−6.02908	−	15.8974i	−0.312174	−	0.823135i	0.683477	−	0.729972i	$-0.260467\pi$
$374$	31.2408	−	16.3964i	1.61542	−	0.847840i
$375$	−1.37669	−	5.58543i	−0.0710918	−	0.288431i
$376$	1.38505	−	3.65208i	0.0714286	−	0.188342i
$377$	−4.24434	−	1.87589i	−0.218594	−	0.0966133i
$378$	−15.7438	−	41.5129i	−0.809772	−	2.13519i
$379$	−25.8245	+	17.8254i	−1.32652	+	0.915628i	−0.999567	−	0.0294144i	$-0.990636\pi$
$379$	−25.8245	+	17.8254i	−1.32652	+	0.915628i	−0.326948	+	0.945042i	$0.606020\pi$
$380$	6.86255	−	6.07969i	0.352041	−	0.311881i
$381$	21.4197	+	5.27949i	1.09737	+	0.270476i
$382$	21.3998	+	8.11589i	1.09491	+	0.415245i
$383$	4.47328	−	8.52313i	0.228574	−	0.435512i	−0.743976	−	0.668207i	$-0.767062\pi$
$383$	4.47328	−	8.52313i	0.228574	−	0.435512i	0.972550	+	0.232695i	$0.0747544\pi$
$384$	−17.7077	−	6.71566i	−0.903644	−	0.342707i
$385$	−4.94454	−	5.58124i	−0.251997	−	0.284446i
$386$	−8.22039	+	7.28263i	−0.418407	+	0.370676i
$387$	2.43552	−	3.52846i	0.123805	−	0.179362i
$388$	−11.3531	−	7.83645i	−0.576364	−	0.397835i
$389$	−5.70274	−	2.99303i	−0.289140	−	0.151753i	0.313917	−	0.949450i	$-0.398359\pi$
$389$	−5.70274	−	2.99303i	−0.289140	−	0.151753i	−0.603057	+	0.797698i	$0.706051\pi$
$390$	5.64178	−	0.379482i	0.285683	−	0.0192158i
$391$	−14.1068	+	7.40383i	−0.713412	+	0.374428i
$392$	15.3807	+	1.86755i	0.776842	+	0.0943257i
$393$	−7.22274	+	1.78025i	−0.364339	+	0.0898015i
$394$	−4.98058	+	7.21561i	−0.250918	+	0.363517i
$395$	−0.0185808	+	0.0128254i	−0.000934902	+	0.000645316i
$396$	−25.1016	+	28.3339i	−1.26140	+	1.42383i
$397$	−7.92668	−	0.962474i	−0.397829	−	0.0483052i	−0.0808223	−	0.996729i	$-0.525755\pi$
$397$	−7.92668	−	0.962474i	−0.397829	−	0.0483052i	−0.317007	+	0.948423i	$0.602678\pi$
$398$	−5.26190	+	21.3484i	−0.263755	+	1.07010i
$399$	−13.2609	−	6.95986i	−0.663876	−	0.348429i
$400$	6.93941	−	57.1512i	0.346970	−	2.85756i
$401$	0.0941903	−	0.0114368i	0.00470364	−	0.000571125i	−0.118185	−	0.992992i	$-0.537707\pi$
$401$	0.0941903	−	0.0114368i	0.00470364	−	0.000571125i	0.122888	+	0.992421i	$0.460784\pi$
$402$	22.4618	−	32.5415i	1.12029	−	1.62302i
$403$	2.04528	−	0.389091i	0.101883	−	0.0193820i
$404$	26.8259	+	38.8640i	1.33464	+	1.93356i
$405$	−0.952490	−	1.07514i	−0.0473296	−	0.0534241i
$406$	−9.92715	−	2.44682i	−0.492676	−	0.121434i
$407$	19.5610	+	28.3390i	0.969604	+	1.40471i
$408$			25.8562i			1.28007i
$409$	−7.86527	+	5.42901i	−0.388913	+	0.268447i	−0.746436	−	0.665457i	$-0.768237\pi$
$409$	−7.86527	+	5.42901i	−0.388913	+	0.268447i	0.357523	+	0.933904i	$0.383621\pi$
$410$	3.01988	−	0.366680i	0.149141	−	0.0181090i
$411$	21.7895	−	8.26366i	1.07480	−	0.407616i
$412$	11.9006	−	98.0102i	0.586300	−	4.82861i
$413$	11.7975	+	31.1075i	0.580518	+	1.53070i
$414$	15.7579	−	17.7870i	0.774458	−	0.874183i
$415$	−5.07760	−	4.49836i	−0.249250	−	0.220816i
$416$	53.0909	+	16.1517i	2.60299	+	0.791900i
$417$	−2.95297	+	2.61610i	−0.144607	+	0.128111i
$418$			57.2792i			2.80162i
$419$	15.7021	+	13.9108i	0.767096	+	0.679588i	0.952997	−	0.302981i	$-0.0979818\pi$
$419$	15.7021	+	13.9108i	0.767096	+	0.679588i	−0.185901	+	0.982569i	$0.559520\pi$
$420$	8.70113	−	2.14464i	0.424572	−	0.104648i
$421$	13.1724	+	9.09223i	0.641982	+	0.443128i	0.844066	−	0.536240i	$-0.180156\pi$
$421$	13.1724	+	9.09223i	0.641982	+	0.443128i	−0.202083	+	0.979368i	$0.564771\pi$
$422$	−0.946668	+	0.359024i	−0.0460831	+	0.0174770i
$423$	0.589861	−	0.223705i	0.0286800	−	0.0108769i
$424$	−27.8064	−	19.1934i	−1.35040	−	0.932112i
$425$	−11.2162	+	2.76454i	−0.544066	+	0.134100i
$426$	40.3694	+	35.7641i	1.95590	+	1.73278i
$427$			25.6525i			1.24141i
$428$	28.7580	−	25.4774i	1.39007	−	1.23149i
$429$	−15.5360	+	20.1082i	−0.750083	+	0.970831i
$430$	2.90574	+	2.57426i	0.140127	+	0.124142i
$431$	1.78530	−	2.01518i	0.0859948	−	0.0970680i	−0.703938	−	0.710261i	$-0.748577\pi$
$431$	1.78530	−	2.01518i	0.0859948	−	0.0970680i	0.789933	+	0.613193i	$0.210115\pi$
$432$	−23.8137	−	62.7915i	−1.14574	−	3.02106i
$433$	3.98786	−	32.8430i	0.191644	−	1.57833i	−0.506414	−	0.862290i	$-0.669029\pi$
$433$	3.98786	−	32.8430i	0.191644	−	1.57833i	0.698058	−	0.716041i	$-0.254048\pi$
$434$	4.28911	−	1.62665i	0.205884	−	0.0780815i
$435$	−0.750649	+	0.0911453i	−0.0359909	+	0.00437008i
$436$	−17.6940	+	12.2133i	−0.847391	+	0.584912i
$437$		−	25.8645i		−	1.23727i
$438$	5.04297	+	7.30600i	0.240962	+	0.349094i
$439$	7.42428	+	1.82992i	0.354341	+	0.0873373i	0.412468	−	0.910972i	$-0.364667\pi$
$439$	7.42428	+	1.82992i	0.354341	+	0.0873373i	−0.0581271	+	0.998309i	$0.518513\pi$
$440$	−13.8588	−	15.6434i	−0.660694	−	0.745769i
$441$	1.42155	+	2.05946i	0.0676926	+	0.0980697i
$442$	−1.55731	−	23.1526i	−0.0740736	−	1.10126i
$443$	−10.3546	+	15.0012i	−0.491961	+	0.712729i	−0.987807	−	0.155682i	$-0.950243\pi$
$443$	−10.3546	+	15.0012i	−0.491961	+	0.712729i	0.495846	+	0.868410i	$0.334858\pi$
$444$	−41.0833	+	4.98842i	−1.94973	+	0.236740i
$445$	−0.520350	+	4.28547i	−0.0246670	+	0.203151i
$446$	−66.2294	−	34.7599i	−3.13605	−	1.64593i
$447$	1.26712	−	5.14092i	0.0599329	−	0.243157i
$448$	50.3758	+	6.11673i	2.38003	+	0.288988i
$449$	−11.2326	+	12.6789i	−0.530097	+	0.598356i	−0.951169	−	0.308671i	$-0.900116\pi$
$449$	−11.2326	+	12.6789i	−0.530097	+	0.598356i	0.421072	+	0.907027i	$0.361654\pi$
$450$	14.1803	−	9.78797i	0.668467	−	0.461409i
$451$	−7.76580	+	11.2507i	−0.365677	+	0.529775i
$452$	−94.3535	+	23.2561i	−4.43802	+	1.09387i
$453$	−17.0617	−	2.07166i	−0.801628	−	0.0973352i
$454$	−8.02256	+	4.21056i	−0.376517	+	0.197612i
$455$	−4.67207	+	1.49053i	−0.219030	+	0.0698771i
$456$	−37.1684	−	19.5075i	−1.74057	−	0.913520i
$457$	12.5212	+	8.64273i	0.585715	+	0.404290i	0.823739	−	0.566969i	$-0.191884\pi$
$457$	12.5212	+	8.64273i	0.585715	+	0.404290i	−0.238024	+	0.971259i	$0.576500\pi$
$458$	21.6079	−	31.3045i	1.00967	−	1.46276i
$459$	−10.0862	+	8.93562i	−0.470785	+	0.417079i
$460$	10.2630	+	11.5845i	0.478514	+	0.540131i
$461$	14.2695	+	5.41171i	0.664597	+	0.252048i	0.663754	−	0.747951i	$-0.268962\pi$
$461$	14.2695	+	5.41171i	0.664597	+	0.252048i	0.000843429		1.00000i	$0.499732\pi$
$462$	−26.0187	+	49.5746i	−1.21050	+	2.30642i
$463$	−4.54780	−	1.72475i	−0.211354	−	0.0801561i	0.246656	−	0.969103i	$-0.420668\pi$
$463$	−4.54780	−	1.72475i	−0.211354	−	0.0801561i	−0.458010	+	0.888947i	$0.651438\pi$
$464$	−15.0156	−	3.70101i	−0.697081	−	0.171815i
$465$	0.253939	−	0.224971i	0.0117762	−	0.0104328i
$466$	20.9820	−	14.4828i	0.971971	−	0.670903i
$467$	7.91217	+	20.8627i	0.366131	+	0.965409i	0.983848	+	0.179008i	$0.0572889\pi$
$467$	7.91217	+	20.8627i	0.366131	+	0.965409i	−0.617716	+	0.786401i	$0.711942\pi$
$468$	10.3706	+	22.6334i	0.479383	+	1.04623i
$469$	−12.1605	+	32.0646i	−0.561519	+	1.48060i
$470$	0.136699	+	0.554611i	0.00630547	+	0.0255823i
$471$	−2.13653	+	1.12134i	−0.0984463	+	0.0516686i
$472$	33.0667	+	87.1897i	1.52202	+	4.01323i
$473$	−17.3181	+	2.10280i	−0.796288	+	0.0966869i
$474$	0.139516	+	0.0963009i	0.00640818	+	0.00442325i
$475$	4.48813	−	18.2090i	0.205929	−	0.835488i
$476$	−8.80110	−	35.7075i	−0.403398	−	1.63665i
$477$	−0.657782	−	5.41732i	−0.0301177	−	0.248042i
$478$	−9.74152	+	25.6863i	−0.445567	+	1.17486i
$479$	5.27108	−	21.3856i	0.240842	−	0.977133i	−0.718644	−	0.695378i	$-0.755237\pi$
$479$	5.27108	−	21.3856i	0.240842	−	0.977133i	0.959486	−	0.281756i	$-0.0909167\pi$
$480$	8.77998	−	2.16407i	0.400749	−	0.0987759i
$481$	22.2484	−	4.23250i	1.01444	−	0.192985i
$482$	−0.459419	−	0.113237i	−0.0209260	−	0.00515779i
$483$	11.7488	−	22.3854i	0.534588	−	1.01857i
$484$	97.6500			4.43864
$485$	1.23014			0.0558578
$486$	15.7861	−	30.0780i	0.716074	−	1.36436i
$487$	−19.6748	−	22.2083i	−0.891552	−	1.00635i	−0.999925	−	0.0122437i	$-0.996103\pi$
$487$	−19.6748	−	22.2083i	−0.891552	−	1.00635i	0.108373	−	0.994110i	$-0.465436\pi$
$488$			71.9002i			3.25477i
$489$	3.83318	−	4.32676i	0.173342	−	0.195663i
$490$	−2.00630	+	1.05299i	−0.0906352	+	0.0475690i
$491$	−2.05997	−	16.9654i	−0.0929651	−	0.765636i	−0.962409	−	0.271605i	$-0.912446\pi$
$491$	−2.05997	−	16.9654i	−0.0929651	−	0.765636i	0.869444	−	0.494032i	$-0.164477\pi$
$492$	−7.63541	−	14.5481i	−0.344231	−	0.655877i
$493$	0.374040	+	3.08049i	0.0168459	+	0.138738i
$494$	34.4568	+	15.2291i	1.55029	+	0.685188i
$495$	0.406875	−	3.35092i	0.0182877	−	0.150613i
$496$	6.48761	−	2.46043i	0.291302	−	0.110476i
$497$	−41.4173	−	21.7375i	−1.85782	−	0.975058i
$498$	−18.0620	+	47.6255i	−0.809376	+	2.13415i
$499$	7.45853	+	14.2111i	0.333890	+	0.636174i	0.993294	−	0.115615i	$-0.0368837\pi$
$499$	7.45853	+	14.2111i	0.333890	+	0.636174i	−0.659404	+	0.751789i	$0.729191\pi$
$500$	10.6576	+	20.3064i	0.476622	+	0.908128i
$501$	5.30410	+	21.5196i	0.236970	+	0.961423i
$502$	−10.2240	−	1.24142i	−0.456318	−	0.0554071i
$503$	6.85346	+	6.07164i	0.305581	+	0.270721i	0.801951	−	0.597390i	$-0.203796\pi$
$503$	6.85346	+	6.07164i	0.305581	+	0.270721i	−0.496370	+	0.868111i	$0.665334\pi$
$504$	19.0005	+	27.5270i	0.846350	+	1.22615i
$505$	−3.93740	−	1.49326i	−0.175212	−	0.0664491i
$506$	−96.6917			−4.29847
$507$	7.96564	+	14.6920i	0.353766	+	0.652496i
$508$	−87.9472			−3.90203
$509$	−25.7665	−	9.77194i	−1.14208	−	0.433133i	−0.290249	−	0.956951i	$-0.593738\pi$
$509$	−25.7665	−	9.77194i	−1.14208	−	0.433133i	−0.851830	+	0.523818i	$0.824507\pi$
$510$	−2.14801	−	3.11193i	−0.0951156	−	0.137799i
$511$	−5.76298	−	5.10555i	−0.254939	−	0.225856i
$512$	−15.4145	−	1.87165i	−0.681229	−	0.0827162i
$513$	−5.23532	−	21.2405i	−0.231145	−	0.937793i
$514$	9.34049	+	17.7968i	0.411991	+	0.784984i
$515$	4.09145	+	7.79561i	0.180291	+	0.343515i
$516$	7.43488	−	19.6042i	0.327302	−	0.863025i
$517$	−2.27291	−	1.19292i	−0.0999625	−	0.0524644i
$518$	46.6566	−	17.6945i	2.04997	−	0.777452i
$519$	−2.77372	+	22.8436i	−0.121753	+	1.00272i
$520$	−13.0951	+	4.17774i	−0.574260	+	0.183206i
$521$	−5.48686	−	45.1884i	−0.240384	−	1.97974i	−0.195227	−	0.980758i	$-0.562544\pi$
$521$	−5.48686	−	45.1884i	−0.240384	−	1.97974i	−0.0451571	−	0.998980i	$-0.514379\pi$
$522$	−2.15097	−	4.09834i	−0.0941455	−	0.179379i
$523$	3.62389	+	29.8454i	0.158461	+	1.30505i	0.827351	+	0.561686i	$0.189847\pi$
$523$	3.62389	+	29.8454i	0.158461	+	1.30505i	−0.668889	+	0.743362i	$0.733230\pi$
$524$	26.2589	−	13.7817i	1.14713	−	0.602058i
$525$	12.1558	−	13.7210i	0.530522	−	0.598835i
$526$		−	37.0355i		−	1.61482i
$527$	−0.923228	−	1.04211i	−0.0402165	−	0.0453950i
$528$	−39.3554	+	74.9854i	−1.71272	+	3.26332i
$529$	20.6612			0.898314
$530$	4.94114			0.214630
$531$	−6.99922	+	13.3359i	−0.303740	+	0.578728i
$532$	57.9696	+	14.2882i	2.51330	+	0.619473i
$533$	4.70324	+	7.66286i	0.203720	+	0.331915i
$534$	31.4724	−	7.75724i	1.36194	−	0.335689i
$535$	−0.819908	+	3.32650i	−0.0354477	+	0.143817i
$536$	−34.0841	+	89.8723i	−1.47221	+	3.88189i
$537$	−1.27827	−	10.5275i	−0.0551615	−	0.454296i
$538$	11.1407	+	45.1995i	0.480308	+	1.94869i
$539$	2.43680	−	9.88647i	0.104960	−	0.425840i
$540$	10.7731	+	7.43612i	0.463600	+	0.320000i
$541$	−14.0875	+	1.71053i	−0.605670	+	0.0735416i	−0.417626	−	0.908619i	$-0.637138\pi$
$541$	−14.0875	+	1.71053i	−0.605670	+	0.0735416i	−0.188044	+	0.982161i	$0.560215\pi$
$542$	−1.43944	−	3.79548i	−0.0618291	−	0.163030i
$543$	−3.20908	+	1.68426i	−0.137715	+	0.0722784i
$544$	−8.88086	−	36.0311i	−0.380764	−	1.54482i
$545$	0.679852	−	1.79262i	0.0291216	−	0.0767875i
$546$	22.9043	+	28.8324i	0.980215	+	1.23391i
$547$	3.14710	+	8.29823i	0.134560	+	0.354807i	0.985313	−	0.170760i	$-0.0546224\pi$
$547$	3.14710	+	8.29823i	0.134560	+	0.354807i	−0.850752	+	0.525567i	$0.823853\pi$
$548$	−76.4575	+	52.7748i	−3.26610	+	2.25443i
$549$	−8.69235	+	7.70075i	−0.370981	+	0.328660i
$550$	−68.0727	−	16.7784i	−2.90263	−	0.715434i
$551$	−4.71041	−	1.78642i	−0.200670	−	0.0761042i
$552$	32.9301	−	62.7431i	1.40160	−	2.67052i
$553$	−0.137471	−	0.0521360i	−0.00584588	−	0.00221705i
$554$	−41.7603	−	47.1377i	−1.77423	−	2.00269i
$555$	2.76233	−	2.44721i	0.117254	−	0.103878i
$556$	8.93428	−	12.9435i	0.378898	−	0.548929i
$557$	−12.1351	−	8.37627i	−0.514182	−	0.354914i	0.282545	−	0.959254i	$-0.408821\pi$
$557$	−12.1351	−	8.37627i	−0.514182	−	0.354914i	−0.796726	+	0.604340i	$0.793437\pi$
$558$	1.83876	+	0.965055i	0.0778408	+	0.0408540i
$559$	−3.33948	+	10.9770i	−0.141245	+	0.464276i
$560$	−14.4716	+	7.59529i	−0.611538	+	0.320960i
$561$	16.8687	+	2.04823i	0.712196	+	0.0864762i
$562$	59.3977	−	14.6402i	2.50554	−	0.617561i
$563$	−23.7713	+	34.4387i	−1.00184	+	1.45142i	−0.112784	+	0.993620i	$0.535977\pi$
$563$	−23.7713	+	34.4387i	−1.00184	+	1.45142i	−0.889057	+	0.457797i	$0.848639\pi$
$564$	2.53897	−	1.75252i	0.106910	−	0.0737945i
$565$	5.74636	−	6.48629i	0.241751	−	0.272880i
$566$	36.8856	+	4.47872i	1.55042	+	0.188255i
$567$	2.23850	−	9.08196i	0.0940082	−	0.381406i
$568$	−116.086	−	60.9269i	−4.87088	−	2.55644i
$569$	1.18727	−	9.77804i	0.0497729	−	0.409917i	−0.946434	−	0.322898i	$-0.895343\pi$
$569$	1.18727	−	9.77804i	0.0497729	−	0.409917i	0.996207	−	0.0870187i	$-0.0277340\pi$
$570$	6.09400	−	0.739946i	0.255250	−	0.0309929i
$571$	8.31147	−	12.0412i	0.347824	−	0.503910i	−0.609555	−	0.792744i	$-0.708652\pi$
$571$	8.31147	−	12.0412i	0.347824	−	0.503910i	0.957379	+	0.288833i	$0.0932673\pi$
$572$	40.9515	−	92.6556i	1.71227	−	3.87413i
$573$	6.26171	+	9.07165i	0.261587	+	0.378974i
$574$	13.1366	+	14.8281i	0.548310	+	0.618914i
$575$	30.7383	+	7.57631i	1.28188	+	0.315954i
$576$	13.0499	+	18.9061i	0.543746	+	0.787752i
$577$			31.7349i			1.32114i	0.750764	+	0.660570i	$0.229686\pi$
$577$			31.7349i			1.32114i	−0.750764	+	0.660570i	$0.770314\pi$
$578$	24.5745	−	16.9626i	1.02216	−	0.705549i
$579$	−5.25073	+	0.637554i	−0.218213	+	0.0264958i
$580$	2.81861	−	1.06896i	0.117036	−	0.0443861i
$581$	5.32476	−	43.8533i	0.220908	−	1.81934i
$582$	−3.27536	−	8.63642i	−0.135768	−	0.357991i
$583$	−14.7245	+	16.6206i	−0.609828	+	0.688353i
$584$	−16.1528	−	14.3101i	−0.668407	−	0.592157i
$585$	−1.90760	−	1.13568i	−0.0788695	−	0.0469547i
$586$	−53.1287	+	47.0679i	−2.19473	+	1.94436i
$587$		−	14.9090i		−	0.615362i	−0.951490	−	0.307681i	$-0.900447\pi$
$587$		−	14.9090i		−	0.615362i	0.951490	−	0.307681i	$-0.0995529\pi$
$588$	9.16001	+	8.11506i	0.377752	+	0.334659i
$589$	2.19457	−	0.540914i	0.0904258	−	0.0222880i
$590$	−11.2231	−	7.74672i	−0.462046	−	0.318927i
$591$	−3.94825	+	1.49737i	−0.162409	+	0.0615937i
$592$	70.5717	−	26.7643i	2.90048	−	1.10001i
$593$	10.3100	+	7.11651i	0.423383	+	0.292240i	0.760642	−	0.649172i	$-0.224884\pi$
$593$	10.3100	+	7.11651i	0.423383	+	0.292240i	−0.337259	+	0.941412i	$0.609500\pi$
$594$	−79.4056	+	19.5717i	−3.25805	+	0.803038i
$595$	2.45470	+	2.17467i	0.100633	+	0.0891528i
$596$			21.1081i			0.864621i
$597$	−7.92635	+	7.02213i	−0.324404	+	0.287397i
$598$	−25.7078	+	58.1658i	−1.05127	+	2.37858i
$599$	13.0416	+	11.5539i	0.532867	+	0.472079i	0.886124	−	0.463447i	$-0.153388\pi$
$599$	13.0416	+	11.5539i	0.532867	+	0.472079i	−0.353258	+	0.935526i	$0.614926\pi$
$600$	34.0709	−	38.4580i	1.39094	−	1.57004i
$601$	−1.89569	−	4.99852i	−0.0773268	−	0.203894i	0.890778	−	0.454438i	$-0.150160\pi$
$601$	−1.89569	−	4.99852i	−0.0773268	−	0.203894i	−0.968105	+	0.250544i	$0.919391\pi$
$602$	−3.04718	+	25.0958i	−0.124194	+	1.02283i
$603$	−14.5156	+	5.50504i	−0.591121	+	0.224183i
$604$	68.0179	−	8.25886i	2.76761	−	0.336048i
$605$	−7.16634	+	4.94657i	−0.291353	+	0.201106i
$606$			31.6191i			1.28444i
$607$	13.5377	+	19.6128i	0.549480	+	0.796060i	0.995070	−	0.0991778i	$-0.0316213\pi$
$607$	13.5377	+	19.6128i	0.549480	+	0.796060i	−0.445589	+	0.895237i	$0.647006\pi$
$608$	58.4950	+	14.4177i	2.37228	+	0.584715i
$609$	−3.26534	−	3.68581i	−0.132318	−	0.149357i
$610$	−5.97313	−	8.65358i	−0.241845	−	0.350373i
$611$	−1.32192	+	1.05013i	−0.0534791	+	0.0424835i
$612$	9.45743	−	13.7015i	0.382294	−	0.553848i
$613$	18.2193	−	2.21223i	0.735872	−	0.0893511i	0.255984	−	0.966681i	$-0.417600\pi$
$613$	18.2193	−	2.21223i	0.735872	−	0.0893511i	0.479888	+	0.877330i	$0.340677\pi$
$614$	5.43054	−	44.7245i	0.219159	−	1.80493i
$615$	1.29730	+	0.680873i	0.0523120	+	0.0274555i
$616$	32.5704	−	132.143i	1.31230	−	5.32421i
$617$	−0.0650685	−	0.00790075i	−0.00261956	−	0.000318072i	0.119227	−	0.992867i	$-0.461958\pi$
$617$	−0.0650685	−	0.00790075i	−0.00261956	−	0.000318072i	−0.121846	+	0.992549i	$0.538882\pi$
$618$	43.8365	−	49.4812i	1.76336	−	1.99043i
$619$	15.2797	−	10.5468i	0.614144	−	0.423913i	−0.219969	−	0.975507i	$-0.570596\pi$
$619$	15.2797	−	10.5468i	0.614144	−	0.423913i	0.834113	+	0.551594i	$0.185980\pi$
$620$	−0.768300	+	1.11307i	−0.0308557	+	0.0447022i
$621$	35.8557	−	8.83763i	1.43884	−	0.354642i
$622$	−61.2439	−	7.43636i	−2.45566	−	0.298171i
$623$	−24.8922	+	13.0644i	−0.997286	+	0.523416i
$624$	34.6446	+	43.6113i	1.38689	+	1.74585i
$625$	19.4009	+	10.1824i	0.776037	+	0.407295i
$626$	4.43128	+	3.05869i	0.177110	+	0.122250i
$627$	−15.6711	+	22.7034i	−0.625842	+	0.906688i
$628$	7.20016	−	6.37878i	0.287317	−	0.254541i
$629$	−10.0428	−	11.3360i	−0.400433	−	0.451995i
$630$	−4.57363	−	1.73455i	−0.182218	−	0.0691061i
$631$	−0.352379	+	0.671402i	−0.0140280	+	0.0267281i	−0.892369	−	0.451306i	$-0.850958\pi$
$631$	−0.352379	+	0.671402i	−0.0140280	+	0.0267281i	0.878341	+	0.478034i	$0.158651\pi$
$632$	−0.385312	−	0.146130i	−0.0153269	−	0.00581272i
$633$	−0.473451	−	0.116695i	−0.0188180	−	0.00463822i
$634$	−22.8085	+	20.2066i	−0.905841	+	0.802506i
$635$	6.45427	−	4.45506i	0.256130	−	0.176794i
$636$	−9.46329	−	24.9526i	−0.375244	−	0.989437i
$637$	−5.29942	−	4.09443i	−0.209971	−	0.162227i
$638$	−6.67837	+	17.6094i	−0.264399	+	0.697163i
$639$	−5.06751	−	20.5597i	−0.200468	−	0.813330i
$640$	−5.96136	+	3.12876i	−0.235644	+	0.123675i
$641$	−6.03947	−	15.9248i	−0.238545	−	0.628990i	0.761266	−	0.648439i	$-0.224578\pi$
$641$	−6.03947	−	15.9248i	−0.238545	−	0.628990i	−0.999811	+	0.0194490i	$0.993809\pi$
$642$	25.5373	−	3.10079i	1.00788	−	0.122379i
$643$	26.9743	+	18.6190i	1.06376	+	0.734261i	0.965369	−	0.260887i	$-0.0840150\pi$
$643$	26.9743	+	18.6190i	1.06376	+	0.734261i	0.0983912	+	0.995148i	$0.468630\pi$
$644$	−24.1196	+	97.8572i	−0.950447	+	3.85612i
$645$	0.447439	+	1.81533i	0.0176179	+	0.0714786i
$646$	−3.03657	−	25.0084i	−0.119472	−	0.983942i
$647$	9.41125	−	24.8154i	0.369995	−	0.975596i	−0.612692	−	0.790322i	$-0.709913\pi$
$647$	9.41125	−	24.8154i	0.369995	−	0.975596i	0.982687	−	0.185274i	$-0.0593173\pi$
$648$	6.27419	−	25.4554i	0.246473	−	0.999982i
$649$	59.5022	−	14.6660i	2.33567	−	0.575690i
$650$	−28.1920	+	36.4888i	−1.10578	+	1.43121i
$651$	2.14509	+	0.528717i	0.0840726	+	0.0207220i
$652$	−10.7093	+	20.4048i	−0.419408	+	0.799115i
$653$	−7.60195			−0.297487			−0.148744	−	0.988876i	$-0.547523\pi$
$653$	−7.60195			−0.297487			−0.148744	+	0.988876i	$0.547523\pi$
$654$	−14.3956			−0.562911
$655$	−1.22896	+	2.34159i	−0.0480195	+	0.0914934i
$656$	19.8701	+	22.4287i	0.775797	+	0.875693i
$657$		−	3.48545i		−	0.135980i
$658$	−2.46666	+	2.78428i	−0.0961604	+	0.108543i
$659$	−13.1679	+	6.91105i	−0.512949	+	0.269216i	−0.701276	−	0.712890i	$-0.747386\pi$
$659$	−13.1679	+	6.91105i	−0.512949	+	0.269216i	0.188327	+	0.982106i	$0.439694\pi$
$660$	−1.98974	−	16.3870i	−0.0774505	−	0.637862i
$661$	−14.0054	−	26.6851i	−0.544748	−	1.03793i	−0.989805	−	0.142428i	$-0.954509\pi$
$661$	−14.0054	−	26.6851i	−0.544748	−	1.03793i	0.445058	−	0.895502i	$-0.353183\pi$
$662$	−4.26547	−	35.1293i	−0.165782	−	1.36534i
$663$	5.71708	−	9.60294i	0.222033	−	0.372947i
$664$	14.9245	−	122.914i	0.579183	−	4.77000i
$665$	−4.97806	+	1.88793i	−0.193041	+	0.0732108i
$666$	20.0018	+	10.4978i	0.775056	+	0.406781i
$667$	3.01562	−	7.95154i	0.116765	−	0.307885i
$668$	−41.0616	−	78.2363i	−1.58872	−	3.02705i
$669$	−16.7410	−	31.8974i	−0.647245	−	1.23322i
$670$	−3.36397	−	13.6482i	−0.129961	−	0.527274i
$671$	46.9079	+	5.69565i	1.81086	+	0.219878i
$672$	44.0776	+	39.0494i	1.70033	+	1.50636i
$673$	4.43476	+	6.42485i	0.170947	+	0.247660i	0.899088	−	0.437768i	$-0.144231\pi$
$673$	4.43476	+	6.42485i	0.170947	+	0.247660i	−0.728141	+	0.685428i	$0.759615\pi$
$674$	−27.1944	−	10.3135i	−1.04749	−	0.397260i
$675$	26.7766			1.03063
$676$	−44.8499	−	49.2695i	−1.72500	−	1.89498i
$677$	−5.03499			−0.193511			−0.0967553	−	0.995308i	$-0.530846\pi$
$677$	−5.03499			−0.193511			−0.0967553	+	0.995308i	$0.530846\pi$
$678$	−60.8383	−	23.0729i	−2.33648	−	0.886111i
$679$	4.55064	+	6.59274i	0.174638	+	0.253006i
$680$	6.88015	+	6.09528i	0.263842	+	0.233743i
$681$	−4.33183	−	0.525980i	−0.165996	−	0.0201556i
$682$	−2.02215	−	8.20419i	−0.0774322	−	0.314155i
$683$	0.683929	+	1.30312i	0.0261698	+	0.0498624i	0.898190	−	0.439608i	$-0.144883\pi$
$683$	0.683929	+	1.30312i	0.0261698	+	0.0498624i	−0.872020	+	0.489470i	$0.837190\pi$
$684$	12.5606	+	23.9323i	0.480267	+	0.915073i
$685$	2.93770	−	7.74607i	0.112244	−	0.295962i
$686$	36.1742	+	18.9857i	1.38114	+	0.724876i
$687$	17.1292	−	6.49627i	0.653522	−	0.247848i
$688$	−4.60910	+	37.9593i	−0.175720	+	1.44719i
$689$	6.08338	+	13.2767i	0.231758	+	0.505800i
$690$	1.24909	+	10.2871i	0.0475519	+	0.391625i
$691$	−12.6598	−	24.1213i	−0.481602	−	0.917616i	−0.998117	−	0.0613378i	$-0.980463\pi$
$691$	−12.6598	−	24.1213i	−0.481602	−	0.917616i	0.516515	−	0.856278i	$-0.327229\pi$
$692$	−11.0577	−	91.0682i	−0.420350	−	3.46189i
$693$	19.4638	−	10.2154i	0.739370	−	0.388052i
$694$	−8.44725	+	9.53497i	−0.320653	+	0.361943i
$695$			1.40248i			0.0531990i
$696$	−9.15227	−	10.3308i	−0.346916	−	0.391587i
$697$	2.79415	−	5.32381i	0.105836	−	0.201654i
$698$	82.1553			3.10962
$699$	12.2789			0.464430
$700$	−33.9613	+	64.7079i	−1.28362	+	2.44573i
$701$	15.0336	+	3.70546i	0.567813	+	0.139953i	0.512763	−	0.858530i	$-0.328622\pi$
$701$	15.0336	+	3.70546i	0.567813	+	0.139953i	0.0550501	+	0.998484i	$0.482468\pi$
$702$	−9.33836	+	52.9708i	−0.352454	+	1.99926i
$703$	23.8724	−	5.88401i	0.900364	−	0.221920i
$704$	22.3700	−	90.7586i	0.843100	−	3.42059i
$705$	−0.0975537	+	0.257228i	−0.00367409	+	0.00968777i
$706$	−0.805029	−	6.63001i	−0.0302977	−	0.249524i
$707$	−6.56267	−	26.6258i	−0.246815	−	1.00137i
$708$	−17.6263	+	71.5127i	−0.662437	+	2.68761i
$709$	−19.8337	−	13.6902i	−0.744871	−	0.514147i	0.134132	−	0.990963i	$-0.457175\pi$
$709$	−19.8337	−	13.6902i	−0.744871	−	0.514147i	−0.879003	+	0.476816i	$0.841791\pi$
$710$	19.0332	−	2.31104i	0.714301	−	0.0867319i
$711$	−0.0236019	−	0.0622331i	−0.000885141	−	0.00233392i
$712$	−69.7692	+	36.6177i	−2.61471	+	1.37231i
$713$	0.913104	+	3.70461i	0.0341960	+	0.138739i
$714$	8.73180	−	23.0239i	0.326779	−	0.861646i
$715$	1.68822	+	8.87425i	0.0631360	+	0.331878i
$716$	14.9917	+	39.5298i	0.560265	+	1.47730i
$717$	−10.8887	+	7.51594i	−0.406647	+	0.280688i
$718$	5.92113	−	5.24566i	0.220975	−	0.195766i
$719$	−7.88978	−	1.94466i	−0.294239	−	0.0725235i	0.0894328	−	0.995993i	$-0.471495\pi$
$719$	−7.88978	−	1.94466i	−0.294239	−	0.0725235i	−0.383672	+	0.923469i	$0.625341\pi$
$720$	−6.91797	−	2.62364i	−0.257818	−	0.0977773i
$721$	−26.6439	+	50.7656i	−0.992269	+	1.89061i
$722$	−9.18001	−	3.48152i	−0.341645	−	0.129569i
$723$	−0.151117	−	0.170576i	−0.00562010	−	0.00634378i
$724$	10.8147	−	9.58096i	0.401924	−	0.356073i
$725$	3.50284	−	5.07474i	0.130092	−	0.188471i
$726$	53.8092	+	37.1418i	1.99705	+	1.37846i
$727$	14.1873	+	7.44606i	0.526177	+	0.276159i	0.706825	−	0.707389i	$-0.250127\pi$
$727$	14.1873	+	7.44606i	0.526177	+	0.276159i	−0.180647	+	0.983548i	$0.557819\pi$
$728$	−70.8325	−	54.7266i	−2.62523	−	2.02830i
$729$	22.8349	−	11.9847i	0.845736	−	0.443877i
$730$	3.13289	+	0.380402i	0.115953	+	0.0140793i
$731$	7.44971	−	1.83619i	0.275537	−	0.0679139i
$732$	−32.2606	+	46.7375i	−1.19239	+	1.72747i
$733$	−22.9858	+	15.8660i	−0.849000	+	0.586022i	−0.911164	−	0.412043i	$-0.864815\pi$
$733$	−22.9858	+	15.8660i	−0.849000	+	0.586022i	0.0621641	+	0.998066i	$0.480200\pi$
$734$	−36.9947	+	41.7584i	−1.36550	+	1.54133i
$735$	−1.08331	−	0.131538i	−0.0399586	−	0.00485185i
$736$	−24.3382	+	98.7440i	−0.897119	+	3.63975i
$737$	55.9329	+	29.3559i	2.06032	+	1.08134i
$738$	−1.08098	+	8.90265i	−0.0397914	+	0.327711i
$739$	−7.29417	+	0.885672i	−0.268320	+	0.0325800i	−0.253591	−	0.967312i	$-0.581612\pi$
$739$	−7.29417	+	0.885672i	−0.268320	+	0.0325800i	−0.0147293	+	0.999892i	$0.504689\pi$
$740$	−8.35750	+	12.1079i	−0.307228	+	0.445096i
$741$	9.49094	+	15.4633i	0.348659	+	0.568060i
$742$	18.2787	+	26.4813i	0.671032	+	0.972158i
$743$	15.3024	+	17.2728i	0.561389	+	0.633677i	0.958840	−	0.283946i	$-0.0916437\pi$
$743$	15.3024	+	17.2728i	0.561389	+	0.633677i	−0.397451	+	0.917623i	$0.630105\pi$
$744$	6.01236	+	1.48191i	0.220424	+	0.0543296i
$745$	−1.06925	−	1.54908i	−0.0391744	−	0.0567539i
$746$			45.3838i			1.66162i
$747$	16.4582	−	11.3602i	0.602172	−	0.415650i
$748$	−67.2484	+	8.16544i	−2.45885	+	0.298558i
$749$	−20.8609	+	7.91150i	−0.762241	+	0.289080i
$750$	−1.85088	+	15.2433i	−0.0675844	+	0.556608i
$751$	2.41004	+	6.35477i	0.0879438	+	0.231889i	0.971772	−	0.235924i	$-0.0758115\pi$
$751$	2.41004	+	6.35477i	0.0879438	+	0.231889i	−0.883828	+	0.467812i	$0.845042\pi$
$752$	−3.73101	+	4.21145i	−0.136056	+	0.153576i
$753$	−3.71278	−	3.28924i	−0.135301	−	0.119867i
$754$	8.81750	+	8.69932i	0.321114	+	0.316811i
$755$	−4.57333	+	4.05162i	−0.166441	+	0.147454i
$756$			85.2449i			3.10033i
$757$	−36.9408	−	32.7267i	−1.34263	−	1.18947i	−0.964612	−	0.263674i	$-0.915066\pi$
$757$	−36.9408	−	32.7267i	−1.34263	−	1.18947i	−0.378023	−	0.925796i	$-0.623396\pi$
$758$	81.3258	−	20.0450i	2.95389	−	0.728067i
$759$	−38.3252	−	26.4540i	−1.39112	−	0.960218i
$760$	−13.9528	+	5.29159i	−0.506120	+	0.191946i
$761$	10.8732	−	4.12366i	0.394153	−	0.149482i	−0.149562	−	0.988752i	$-0.547786\pi$
$761$	10.8732	−	4.12366i	0.394153	−	0.149482i	0.543715	+	0.839270i	$0.317017\pi$
$762$	−48.4626	−	33.4513i	−1.75561	−	1.21181i
$763$	12.1222	−	2.98786i	0.438854	−	0.108168i
$764$	−32.8923	−	29.1400i	−1.19000	−	1.05425i
$765$			1.48460i			0.0536758i
$766$	−19.2320	+	17.0381i	−0.694881	+	0.615610i
$767$	6.99765	−	39.6934i

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)

\(f(q)\)	\(=\)	\(q+(-2.49582 - 0.946540i) q^{2} +(-0.730291 - 1.05801i) q^{3} +(3.83616 + 3.39854i) q^{4} +(-0.453685 - 0.0550874i) q^{5} +(0.821227 + 3.33185i) q^{6} +(-1.38308 - 2.63524i) q^{7} +(-3.87657 - 7.38618i) q^{8} +(0.477757 - 1.25974i) q^{9} +O(q^{10})\)	\(q+(-2.49582 - 0.946540i) q^{2} +(-0.730291 - 1.05801i) q^{3} +(3.83616 + 3.39854i) q^{4} +(-0.453685 - 0.0550874i) q^{5} +(0.821227 + 3.33185i) q^{6} +(-1.38308 - 2.63524i) q^{7} +(-3.87657 - 7.38618i) q^{8} +(0.477757 - 1.25974i) q^{9} +(1.08017 + 0.566920i) q^{10} +(-5.12585 + 1.94398i) q^{11} +(0.794175 - 6.54062i) q^{12} +(-0.193413 + 3.60036i) q^{13} +(0.957560 + 7.88622i) q^{14} +(0.273039 + 0.520233i) q^{15} +(1.44838 + 11.9285i) q^{16} +(2.13492 - 1.12049i) q^{17} +(-2.38479 + 2.69187i) q^{18} +3.91431i q^{19} +(-1.55319 - 1.75319i) q^{20} +(-1.77805 + 3.38780i) q^{21} +14.6333 q^{22} -6.60766 q^{23} +(-4.98362 + 9.49550i) q^{24} +(-4.65191 - 1.14659i) q^{25} +(3.89061 - 8.80278i) q^{26} +(-5.42638 + 1.33748i) q^{27} +(3.65025 - 14.8097i) q^{28} +(-0.456382 + 1.20338i) q^{29} +(-0.189036 - 1.55685i) q^{30} +(-0.138189 - 0.560653i) q^{31} +(3.68333 - 14.9439i) q^{32} +(5.80011 + 4.00353i) q^{33} +(-6.38896 + 0.775760i) q^{34} +(0.482314 + 1.27176i) q^{35} +(6.11404 - 3.20889i) q^{36} +(-1.50320 - 6.09874i) q^{37} +(3.70505 - 9.76943i) q^{38} +(3.95046 - 2.42468i) q^{39} +(1.35186 + 3.56455i) q^{40} +(2.05226 - 1.41657i) q^{41} +(7.64439 - 6.77234i) q^{42} +(3.08976 + 0.761558i) q^{43} +(-26.2703 - 9.96302i) q^{44} +(-0.286147 + 0.545208i) q^{45} +(16.4915 + 6.25442i) q^{46} +(0.310500 + 0.350483i) q^{47} +(11.5627 - 10.2437i) q^{48} +(-1.05511 + 1.52859i) q^{49} +(10.5250 + 7.26492i) q^{50} +(-2.74460 - 1.44048i) q^{51} +(-12.9779 + 13.1542i) q^{52} +(3.58647 - 1.88233i) q^{53} +(14.8092 + 1.79817i) q^{54} +(2.43261 - 0.599585i) q^{55} +(-14.1027 + 20.4313i) q^{56} +(4.14138 - 2.85859i) q^{57} +(2.27810 - 2.57144i) q^{58} +(-11.0972 - 1.34745i) q^{59} +(-0.720611 + 2.92363i) q^{60} +(-7.63210 - 4.00564i) q^{61} +(-0.185787 + 1.53009i) q^{62} +(-3.98049 + 0.483319i) q^{63} +(-9.68602 + 14.0326i) q^{64} +(0.286083 - 1.62278i) q^{65} +(-10.6865 - 15.4821i) q^{66} +(-7.64095 - 8.62485i) q^{67} +(11.9979 + 2.95722i) q^{68} +(4.82552 + 6.99097i) q^{69} -3.63061i q^{70} +(12.9346 - 8.92811i) q^{71} +(-11.1567 + 1.35467i) q^{72} +(2.41889 - 0.917363i) q^{73} +(-2.02097 + 16.6442i) q^{74} +(2.18414 + 5.75911i) q^{75} +(-13.3030 + 15.0159i) q^{76} +(12.2123 + 10.8192i) q^{77} +(-12.1547 + 2.31229i) q^{78} +(0.0369776 - 0.0327593i) q^{79} -5.49158i q^{80} +(2.35251 + 2.08414i) q^{81} +(-6.46292 + 1.59297i) q^{82} +(12.2157 + 8.43190i) q^{83} +(-18.3345 + 6.95335i) q^{84} +(-1.03031 + 0.390743i) q^{85} +(-6.99065 - 4.82530i) q^{86} +(1.60648 - 0.395962i) q^{87} +(34.2293 + 30.3245i) q^{88} -9.44591i q^{89} +(1.23023 - 1.08989i) q^{90} +(9.75531 - 4.46989i) q^{91} +(-25.3481 - 22.4564i) q^{92} +(-0.492258 + 0.555645i) q^{93} +(-0.443208 - 1.16864i) q^{94} +(0.215629 - 1.77587i) q^{95} +(-18.5006 + 7.01637i) q^{96} +(-2.67205 + 0.324445i) q^{97} +(4.08025 - 2.81639i) q^{98} +7.38600i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more