LMFDB - Embedded newform 169.2.h.a.12.12

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			12.12
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62113 - 1.11899i) q^{2} +(0.214934 + 0.112806i) q^{3} +(0.666728 - 1.75802i) q^{4} +(0.457146 + 0.516011i) q^{5} +(0.474664 - 0.0576347i) q^{6} +(-0.520249 - 2.11073i) q^{7} +(0.0564755 + 0.229130i) q^{8} +(-1.67072 - 2.42046i) q^{9} +O(q^{10})$	\(q+(1.62113 - 1.11899i) q^{2} +(0.214934 + 0.112806i) q^{3} +(0.666728 - 1.75802i) q^{4} +(0.457146 + 0.516011i) q^{5} +(0.474664 - 0.0576347i) q^{6} +(-0.520249 - 2.11073i) q^{7} +(0.0564755 + 0.229130i) q^{8} +(-1.67072 - 2.42046i) q^{9} +(1.31850 + 0.324982i) q^{10} +(3.20329 + 2.21107i) q^{11} +(0.341617 - 0.302646i) q^{12} +(-2.77912 + 2.29707i) q^{13} +(-3.20527 - 2.83962i) q^{14} +(0.0400470 + 0.162477i) q^{15} +(3.16265 + 2.80186i) q^{16} +(-3.95902 + 0.975810i) q^{17} +(-5.41692 - 2.05437i) q^{18} +1.37925i q^{19} +(1.21195 - 0.459631i) q^{20} +(0.126284 - 0.512355i) q^{21} +7.66712 q^{22} -6.84453 q^{23} +(-0.0137087 + 0.0556186i) q^{24} +(0.545398 - 4.49176i) q^{25} +(-1.93493 + 6.83364i) q^{26} +(-0.173829 - 1.43161i) q^{27} +(-4.05757 - 0.492678i) q^{28} +(4.25797 + 6.16874i) q^{29} +(0.246731 + 0.218584i) q^{30} +(-5.28453 + 0.641658i) q^{31} +(7.79377 + 0.946335i) q^{32} +(0.439074 + 0.836585i) q^{33} +(-5.32617 + 6.01200i) q^{34} +(0.851331 - 1.23337i) q^{35} +(-5.36912 + 1.32337i) q^{36} +(2.72839 - 0.331287i) q^{37} +(1.54336 + 2.23594i) q^{38} +(-0.856449 + 0.180216i) q^{39} +(-0.0924161 + 0.133888i) q^{40} +(5.43075 - 10.3474i) q^{41} +(-0.368595 - 0.971905i) q^{42} +(-0.238673 + 1.96565i) q^{43} +(6.02283 - 4.15726i) q^{44} +(0.485220 - 1.96861i) q^{45} +(-11.0959 + 7.65893i) q^{46} +(0.501321 - 0.190126i) q^{47} +(0.363693 + 0.958980i) q^{48} +(2.01366 - 1.05685i) q^{49} +(-4.14206 - 7.89203i) q^{50} +(-0.961004 - 0.236866i) q^{51} +(2.18537 + 6.41725i) q^{52} +(9.30260 - 2.29289i) q^{53} +(-1.88375 - 2.12632i) q^{54} +(0.323434 + 2.66372i) q^{55} +(0.454251 - 0.238409i) q^{56} +(-0.155587 + 0.296447i) q^{57} +(13.8055 + 5.23572i) q^{58} +(-6.13211 - 6.92173i) q^{59} +(0.312338 + 0.0379246i) q^{60} +(4.92368 + 1.21358i) q^{61} +(-7.84891 + 6.95353i) q^{62} +(-4.23975 + 4.78569i) q^{63} +(6.21112 - 3.25985i) q^{64} +(-2.45577 - 0.383960i) q^{65} +(1.64792 + 0.864897i) q^{66} +(-9.39667 + 3.56369i) q^{67} +(-0.924096 + 7.61062i) q^{68} +(-1.47112 - 0.772103i) q^{69} -2.95208i q^{70} +(3.06379 - 5.83757i) q^{71} +(0.460245 - 0.519510i) q^{72} +(-2.04047 - 1.40843i) q^{73} +(4.05238 - 3.59009i) q^{74} +(0.623922 - 0.903907i) q^{75} +(2.42474 + 0.919583i) q^{76} +(3.00048 - 7.91160i) q^{77} +(-1.18676 + 1.25051i) q^{78} +(-2.73404 - 7.20907i) q^{79} +2.91282i q^{80} +(-3.00463 + 7.92256i) q^{81} +(-2.77467 - 22.8515i) q^{82} +(-0.674514 - 1.28518i) q^{83} +(-0.816531 - 0.563611i) q^{84} +(-2.31338 - 1.59681i) q^{85} +(1.81261 + 3.45365i) q^{86} +(0.219312 + 1.80620i) q^{87} +(-0.325716 + 0.858843i) q^{88} -2.87983i q^{89} +(-1.41625 - 3.73434i) q^{90} +(6.29432 + 4.67092i) q^{91} +(-4.56343 + 12.0328i) q^{92} +(-1.20821 - 0.458212i) q^{93} +(0.599959 - 0.869190i) q^{94} +(-0.711707 + 0.630517i) q^{95} +(1.56839 + 1.08258i) q^{96} +(-11.2498 + 12.6983i) q^{97} +(2.08181 - 3.96655i) q^{98} -11.4475i 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{26}\right)$

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 $

$2$	1.62113	−	1.11899i	1.14631	−	0.791243i	0.165503	−	0.986209i	$-0.447075\pi$
$2$	1.62113	−	1.11899i	1.14631	−	0.791243i	0.980810	+	0.194966i	$0.0624598\pi$
$3$	0.214934	+	0.112806i	0.124092	+	0.0651286i	0.525627	−	0.850715i	$-0.323831\pi$
$3$	0.214934	+	0.112806i	0.124092	+	0.0651286i	−0.401535	+	0.915844i	$0.631523\pi$
$4$	0.666728	−	1.75802i	0.333364	−	0.879008i
$5$	0.457146	+	0.516011i	0.204442	+	0.230767i	0.841785	−	0.539813i	$-0.181505\pi$
$5$	0.457146	+	0.516011i	0.204442	+	0.230767i	−0.637343	+	0.770580i	$0.719967\pi$
$6$	0.474664	−	0.0576347i	0.193781	−	0.0235293i
$7$	−0.520249	−	2.11073i	−0.196636	−	0.797782i	−0.983538	−	0.180704i	$-0.942162\pi$
$7$	−0.520249	−	2.11073i	−0.196636	−	0.797782i	0.786902	−	0.617078i	$-0.211684\pi$
$8$	0.0564755	+	0.229130i	0.0199671	+	0.0810097i
$9$	−1.67072	−	2.42046i	−0.556908	−	0.806820i
$10$	1.31850	+	0.324982i	0.416947	+	0.102768i
$11$	3.20329	+	2.21107i	0.965830	+	0.666664i	0.942901	−	0.333073i	$-0.108086\pi$
$11$	3.20329	+	2.21107i	0.965830	+	0.666664i	0.0229286	+	0.999737i	$0.492701\pi$
$12$	0.341617	−	0.302646i	0.0986163	−	0.0873665i
$13$	−2.77912	+	2.29707i	−0.770788	+	0.637092i
$13$	−2.77912	+	2.29707i	−0.770788	+	0.637092i
$14$	−3.20527	−	2.83962i	−0.856645	−	0.758921i
$15$	0.0400470	+	0.162477i	0.0103401	+	0.0419514i
$16$	3.16265	+	2.80186i	0.790661	+	0.700465i
$17$	−3.95902	+	0.975810i	−0.960203	+	0.236669i	−0.688113	−	0.725603i	$-0.741561\pi$
$17$	−3.95902	+	0.975810i	−0.960203	+	0.236669i	−0.272090	+	0.962272i	$0.587715\pi$
$18$	−5.41692	−	2.05437i	−1.27678	−	0.484219i
$19$			1.37925i			0.316421i	0.987405	+	0.158211i	$0.0505725\pi$
$19$			1.37925i			0.316421i	−0.987405	+	0.158211i	$0.949427\pi$
$20$	1.21195	−	0.459631i	0.271000	−	0.102777i
$21$	0.126284	−	0.512355i	0.0275575	−	0.111805i
$22$	7.66712			1.63464
$23$	−6.84453			−1.42718			−0.713591	−	0.700562i	$-0.752933\pi$
$23$	−6.84453			−1.42718			−0.713591	+	0.700562i	$0.752933\pi$
$24$	−0.0137087	+	0.0556186i	−0.00279829	+	0.0113531i
$25$	0.545398	−	4.49176i	0.109080	−	0.898352i
$26$	−1.93493	+	6.83364i	−0.379470	+	1.34019i
$27$	−0.173829	−	1.43161i	−0.0334534	−	0.275514i
$28$	−4.05757	−	0.492678i	−0.766808	−	0.0931073i
$29$	4.25797	+	6.16874i	0.790686	+	1.14551i	0.986322	+	0.164829i	$0.0527074\pi$
$29$	4.25797	+	6.16874i	0.790686	+	1.14551i	−0.195636	+	0.980676i	$0.562677\pi$
$30$	0.246731	+	0.218584i	0.0450467	+	0.0399079i
$31$	−5.28453	+	0.641658i	−0.949129	+	0.115245i	−0.580436	−	0.814306i	$-0.697118\pi$
$31$	−5.28453	+	0.641658i	−0.949129	+	0.115245i	−0.368693	+	0.929551i	$0.620195\pi$
$32$	7.79377	+	0.946335i	1.37776	+	0.167290i
$33$	0.439074	+	0.836585i	0.0764330	+	0.145631i
$34$	−5.32617	+	6.01200i	−0.913431	+	1.03105i
$35$	0.851331	−	1.23337i	0.143901	−	0.208477i
$36$	−5.36912	+	1.32337i	−0.894854	+	0.220562i
$37$	2.72839	−	0.331287i	0.448545	−	0.0544632i	0.106852	−	0.994275i	$-0.465923\pi$
$37$	2.72839	−	0.331287i	0.448545	−	0.0544632i	0.341693	+	0.939812i	$0.389000\pi$
$38$	1.54336	+	2.23594i	0.250366	+	0.362718i
$39$	−0.856449	+	0.180216i	−0.137142	+	0.0288577i
$40$	−0.0924161	+	0.133888i	−0.0146123	+	0.0211695i
$41$	5.43075	−	10.3474i	0.848141	−	1.61600i	0.0618960	−	0.998083i	$-0.480285\pi$
$41$	5.43075	−	10.3474i	0.848141	−	1.61600i	0.786245	−	0.617915i	$-0.212022\pi$
$42$	−0.368595	−	0.971905i	−0.0568754	−	0.149968i
$43$	−0.238673	+	1.96565i	−0.0363973	+	0.299758i	0.963131	+	0.269034i	$0.0867045\pi$
$43$	−0.238673	+	1.96565i	−0.0363973	+	0.299758i	−0.999528	+	0.0307243i	$0.990219\pi$
$44$	6.02283	−	4.15726i	0.907976	−	0.626730i
$45$	0.485220	−	1.96861i	0.0723323	−	0.293464i
$46$	−11.0959	+	7.65893i	−1.63600	+	1.12925i
$47$	0.501321	−	0.190126i	0.0731251	−	0.0277327i	−0.317771	−	0.948167i	$-0.602934\pi$
$47$	0.501321	−	0.190126i	0.0731251	−	0.0277327i	0.390896	+	0.920435i	$0.372165\pi$
$48$	0.363693	+	0.958980i	0.0524946	+	0.138417i
$49$	2.01366	−	1.05685i	0.287666	−	0.150979i
$50$	−4.14206	−	7.89203i	−0.585775	−	1.11610i
$51$	−0.961004	−	0.236866i	−0.134568	−	0.0331679i
$52$	2.18537	+	6.41725i	0.303056	+	0.889912i
$53$	9.30260	−	2.29289i	1.27781	−	0.314952i	0.458702	−	0.888590i	$-0.348315\pi$
$53$	9.30260	−	2.29289i	1.27781	−	0.314952i	0.819109	+	0.573638i	$0.194468\pi$
$54$	−1.88375	−	2.12632i	−0.256346	−	0.289355i
$55$	0.323434	+	2.66372i	0.0436118	+	0.359176i
$56$	0.454251	−	0.238409i	0.0607018	−	0.0318588i
$57$	−0.155587	+	0.296447i	−0.0206081	+	0.0392654i
$58$	13.8055	+	5.23572i	1.81275	+	0.687484i
$59$	−6.13211	−	6.92173i	−0.798333	−	0.901132i	0.198544	−	0.980092i	$-0.436379\pi$
$59$	−6.13211	−	6.92173i	−0.798333	−	0.901132i	−0.996878	+	0.0789598i	$0.974840\pi$
$60$	0.312338	+	0.0379246i	0.0403226	+	0.00489605i
$61$	4.92368	+	1.21358i	0.630413	+	0.155383i	0.541560	−	0.840662i	$-0.317834\pi$
$61$	4.92368	+	1.21358i	0.630413	+	0.155383i	0.0888525	+	0.996045i	$0.471680\pi$
$62$	−7.84891	+	6.95353i	−0.996812	+	0.883099i
$63$	−4.23975	+	4.78569i	−0.534158	+	0.602940i
$64$	6.21112	−	3.25985i	0.776390	−	0.407481i
$65$	−2.45577	−	0.383960i	−0.304601	−	0.0476243i
$66$	1.64792	+	0.864897i	0.202845	+	0.106462i
$67$	−9.39667	+	3.56369i	−1.14799	+	0.435374i	−0.853916	−	0.520411i	$-0.825779\pi$
$67$	−9.39667	+	3.56369i	−1.14799	+	0.435374i	−0.294069	+	0.955784i	$0.595010\pi$
$68$	−0.924096	+	7.61062i	−0.112063	+	0.922923i
$69$	−1.47112	−	0.772103i	−0.177102	−	0.0929503i
$70$		−	2.95208i		−	0.352841i
$71$	3.06379	−	5.83757i	0.363605	−	0.692792i	−0.633085	−	0.774082i	$-0.718212\pi$
$71$	3.06379	−	5.83757i	0.363605	−	0.692792i	0.996690	+	0.0812904i	$0.0259041\pi$
$72$	0.460245	−	0.519510i	0.0542404	−	0.0612248i
$73$	−2.04047	−	1.40843i	−0.238818	−	0.164844i	0.442644	−	0.896697i	$-0.354040\pi$
$73$	−2.04047	−	1.40843i	−0.238818	−	0.164844i	−0.681463	+	0.731853i	$0.738656\pi$
$74$	4.05238	−	3.59009i	0.471079	−	0.417340i
$75$	0.623922	−	0.903907i	0.0720443	−	0.104374i
$76$	2.42474	+	0.919583i	0.278137	+	0.105483i
$77$	3.00048	−	7.91160i	0.341936	−	0.901611i
$78$	−1.18676	+	1.25051i	−0.134374	+	0.141592i
$79$	−2.73404	−	7.20907i	−0.307603	−	0.811083i	−0.996293	−	0.0860270i	$-0.972583\pi$
$79$	−2.73404	−	7.20907i	−0.307603	−	0.811083i	0.688689	−	0.725056i	$-0.258186\pi$
$80$			2.91282i			0.325663i
$81$	−3.00463	+	7.92256i	−0.333848	+	0.880284i
$82$	−2.77467	−	22.8515i	−0.306411	−	2.52352i
$83$	−0.674514	−	1.28518i	−0.0740376	−	0.141067i	0.845624	−	0.533780i	$-0.179229\pi$
$83$	−0.674514	−	1.28518i	−0.0740376	−	0.141067i	−0.919661	+	0.392713i	$0.871537\pi$
$84$	−0.816531	−	0.563611i	−0.0890908	−	0.0614950i
$85$	−2.31338	−	1.59681i	−0.250921	−	0.173198i
$86$	1.81261	+	3.45365i	0.195459	+	0.372416i
$87$	0.219312	+	1.80620i	0.0235127	+	0.193644i
$88$	−0.325716	+	0.858843i	−0.0347214	+	0.0915529i
$89$		−	2.87983i		−	0.305262i	−0.988283	−	0.152631i	$-0.951225\pi$
$89$		−	2.87983i		−	0.305262i	0.988283	−	0.152631i	$-0.0487746\pi$
$90$	−1.41625	−	3.73434i	−0.149286	−	0.393634i
$91$	6.29432	+	4.67092i	0.659824	+	0.489646i
$92$	−4.56343	+	12.0328i	−0.475771	+	1.25450i
$93$	−1.20821	−	0.458212i	−0.125285	−	0.0475144i
$94$	0.599959	−	0.869190i	0.0618810	−	0.0896501i
$95$	−0.711707	+	0.630517i	−0.0730196	+	0.0646897i
$96$	1.56839	+	1.08258i	0.160073	+	0.110491i
$97$	−11.2498	+	12.6983i	−1.14224	+	1.28932i	−0.190751	+	0.981638i	$0.561092\pi$
$97$	−11.2498	+	12.6983i	−1.14224	+	1.28932i	−0.951489	+	0.307684i	$0.900446\pi$
$98$	2.08181	−	3.96655i	0.210294	−	0.400682i
$99$		−	11.4475i		−	1.15052i
$100$	−7.53296	−	3.95360i	−0.753296	−	0.395360i
$101$	−0.652546	+	5.37420i	−0.0649307	+	0.534752i	0.923558	+	0.383459i	$0.125267\pi$
$101$	−0.652546	+	5.37420i	−0.0649307	+	0.534752i	−0.988489	+	0.151294i	$0.951656\pi$
$102$	−1.82296	+	0.691359i	−0.180500	+	0.0684548i
$103$	0.977542	+	0.513054i	0.0963201	+	0.0505527i	0.512195	−	0.858869i	$-0.328832\pi$
$103$	0.977542	+	0.513054i	0.0963201	+	0.0505527i	−0.415875	+	0.909422i	$0.636525\pi$
$104$	−0.683279	−	0.507051i	−0.0670010	−	0.0497205i
$105$	0.322111	−	0.169057i	0.0314348	−	0.0164983i
$106$	12.5150	−	14.1266i	1.21557	−	1.37209i
$107$	5.60738	−	4.96771i	0.542086	−	0.480247i	−0.347077	−	0.937837i	$-0.612826\pi$
$107$	5.60738	−	4.96771i	0.542086	−	0.480247i	0.889163	+	0.457590i	$0.151287\pi$
$108$	−2.63269	−	0.648900i	−0.253331	−	0.0624404i
$109$	−3.77091	−	0.457872i	−0.361188	−	0.0438562i	−0.0620687	−	0.998072i	$-0.519770\pi$
$109$	−3.77091	−	0.457872i	−0.361188	−	0.0438562i	−0.299119	+	0.954216i	$0.596693\pi$
$110$	3.50499	+	3.95632i	0.334188	+	0.377220i
$111$	0.623795	+	0.236574i	0.0592080	+	0.0224546i
$112$	4.26861	−	8.13316i	0.403346	−	0.768511i
$113$	17.9940	−	9.44398i	1.69273	−	0.888415i	0.709812	−	0.704392i	$-0.248780\pi$
$113$	17.9940	−	9.44398i	1.69273	−	0.888415i	0.982922	−	0.184023i	$-0.0589122\pi$
$114$	0.0794926	+	0.654680i	0.00744516	+	0.0613164i
$115$	−3.12895	−	3.53185i	−0.291776	−	0.329347i
$116$	13.6836	−	3.37272i	1.27049	−	0.313149i
$117$	10.2031	+	2.88898i	0.943276	+	0.267086i
$118$	−17.6863	−	4.35928i	−1.62815	−	0.401304i
$119$	4.11935	+	7.84876i	0.377620	+	0.719495i
$120$	−0.0349667	+	0.0183519i	−0.00319201	+	0.00167529i
$121$	1.47159	+	3.88027i	0.133781	+	0.352751i
$122$	9.33991	−	3.54216i	0.845596	−	0.320692i
$123$	2.33450	−	1.61139i	0.210495	−	0.145294i
$124$	−2.39530	+	9.71810i	−0.215104	+	0.872711i
$125$	5.40388	−	3.73003i	0.483338	−	0.333624i
$126$	−1.51807	+	12.5025i	−0.135241	+	1.11381i
$127$	4.53470	+	11.9570i	0.402390	+	1.06102i	0.971141	+	0.238506i	$0.0766575\pi$
$127$	4.53470	+	11.9570i	0.402390	+	1.06102i	−0.568751	+	0.822510i	$0.692573\pi$
$128$	−0.875777	+	1.66865i	−0.0774085	+	0.147489i
$129$	−0.273036	+	0.395560i	−0.0240395	+	0.0348272i
$130$	−4.41078	+	2.12553i	−0.386851	+	0.186421i
$131$	5.17969	+	7.50407i	0.452551	+	0.655634i	0.981152	−	0.193237i	$-0.0618985\pi$
$131$	5.17969	+	7.50407i	0.452551	+	0.655634i	−0.528601	+	0.848871i	$0.677283\pi$
$132$	1.76347	−	0.214124i	0.153491	−	0.0186371i
$133$	2.91122	−	0.717552i	0.252435	−	0.0622197i
$134$	−11.2455	+	16.2919i	−0.971465	+	1.40741i
$135$	0.659261	−	0.744152i	0.0567402	−	0.0640464i
$136$	−0.447175	−	0.852021i	−0.0383449	−	0.0730602i
$137$	2.90549	+	0.352790i	0.248233	+	0.0301409i	0.243707	−	0.969849i	$-0.421636\pi$
$137$	2.90549	+	0.352790i	0.248233	+	0.0301409i	0.00452548	+	0.999990i	$0.498559\pi$
$138$	−3.24885	+	0.394482i	−0.276561	+	0.0335805i
$139$	7.77123	+	6.88471i	0.659147	+	0.583954i	0.924957	−	0.380072i	$-0.124101\pi$
$139$	7.77123	+	6.88471i	0.659147	+	0.583954i	−0.265810	+	0.964026i	$0.585639\pi$
$140$	−1.60067	−	2.31897i	−0.135281	−	0.195989i
$141$	0.129198	+	0.0156875i	0.0108804	+	0.00132112i
$142$	−1.56535	−	12.8918i	−0.131361	−	1.08186i
$143$	−13.9813	+	1.21335i	−1.16918	+	0.101465i
$144$	1.49788	−	12.3362i	0.124824	−	1.02802i
$145$	−1.23662	+	5.01717i	−0.102696	+	0.416653i
$146$	−4.88388			−0.404193
$147$	0.552023			0.0455301
$148$	1.23669	−	5.01743i	0.101655	−	0.412431i
$149$	3.43627	−	1.30320i	0.281510	−	0.106763i	−0.209809	−	0.977742i	$-0.567284\pi$
$149$	3.43627	−	1.30320i	0.281510	−	0.106763i	0.491319	+	0.870980i	$0.336515\pi$
$150$		−	2.16351i		−	0.176650i
$151$	−0.704508	−	0.267184i	−0.0573320	−	0.0217432i	0.325772	−	0.945448i	$-0.394376\pi$
$151$	−0.704508	−	0.267184i	−0.0573320	−	0.0217432i	−0.383104	+	0.923705i	$0.625145\pi$
$152$	−0.316027	+	0.0778937i	−0.0256332	+	0.00631802i
$153$	8.97633	+	7.95234i	0.725693	+	0.642908i
$154$	−3.98881	−	16.1832i	−0.321428	−	1.30408i
$155$	−2.74690	−	2.43354i	−0.220636	−	0.195467i
$156$	−0.254195	+	1.62581i	−0.0203519	+	0.130169i
$157$	−10.8701	+	9.63008i	−0.867529	+	0.768564i	−0.974190	−	0.225732i	$-0.927523\pi$
$157$	−10.8701	+	9.63008i	−0.867529	+	0.768564i	0.106660	+	0.994296i	$0.465984\pi$
$158$	−12.4991	−	8.62750i	−0.994374	−	0.686367i
$159$	2.25810	+	0.556570i	0.179079	+	0.0441389i
$160$	3.07457	+	4.45428i	0.243066	+	0.352142i
$161$	3.56086	+	14.4470i	0.280635	+	1.13858i
$162$	3.99433	+	16.2056i	0.313824	+	1.27324i
$163$	−19.1764	+	2.32844i	−1.50201	+	0.182378i	−0.829834	−	0.558010i	$-0.811565\pi$
$163$	−19.1764	+	2.32844i	−1.50201	+	0.182378i	−0.672180	+	0.740387i	$0.734642\pi$
$164$	−14.5701	−	16.4463i	−1.13774	−	1.28424i
$165$	−0.230966	+	0.609008i	−0.0179807	+	0.0474112i
$166$	−2.53157	−	1.32867i	−0.196488	−	0.103125i
$167$	−18.3745	+	12.6830i	−1.42186	+	0.981439i	−0.424762	+	0.905305i	$0.639642\pi$
$167$	−18.3745	+	12.6830i	−1.42186	+	0.981439i	−0.997098	+	0.0761340i	$0.975742\pi$
$168$	0.124528			0.00960753
$169$	2.44697	−	12.7676i	0.188228	−	0.982125i
$170$	−5.53710			−0.424676
$171$	3.33842	−	2.30434i	0.255295	−	0.176217i
$172$	3.29651	+	1.73014i	0.251357	+	0.131922i
$173$	−3.24139	+	8.54684i	−0.246438	+	0.649804i	−0.999971	−	0.00760593i	$-0.997579\pi$
$173$	−3.24139	+	8.54684i	−0.246438	+	0.649804i	0.753533	+	0.657410i	$0.228348\pi$
$174$	2.37664	+	2.68267i	0.180173	+	0.203373i
$175$	−9.76465	+	1.18564i	−0.738138	+	0.0896262i
$176$	3.93576	+	15.9680i	0.296669	+	1.20364i
$177$	−0.537187	−	2.17945i	−0.0403774	−	0.163818i
$178$	−3.22250	−	4.66859i	−0.241536	−	0.349926i
$179$	0.401341	+	0.0989216i	0.0299976	+	0.00739374i	0.254286	−	0.967129i	$-0.418160\pi$
$179$	0.401341	+	0.0989216i	0.0299976	+	0.00739374i	−0.224288	+	0.974523i	$0.572006\pi$
$180$	−3.13735	−	2.16555i	−0.233844	−	0.161411i
$181$	−14.1452	+	12.5316i	−1.05141	+	0.931465i	−0.997747	−	0.0670941i	$-0.978627\pi$
$181$	−14.1452	+	12.5316i	−1.05141	+	0.931465i	−0.0536601	+	0.998559i	$0.517089\pi$
$182$	15.4306	+	0.528919i	1.14379	+	0.0392061i
$183$	0.921366	+	0.816259i	0.0681094	+	0.0603396i
$184$	−0.386548	−	1.56829i	−0.0284967	−	0.115616i
$185$	1.41822	+	1.25643i	0.104270	+	0.0923748i
$186$	−2.47140	+	0.609144i	−0.181211	+	0.0446646i
$187$	−14.8395	−	5.62788i	−1.08517	−	0.411551i
$188$		−	1.00809i		−	0.0735227i
$189$	−2.93131	+	1.11170i	−0.213222	+	0.0808643i
$190$	−0.448230	+	1.81854i	−0.0325181	+	0.131931i
$191$	−2.67180			−0.193325			−0.0966625	−	0.995317i	$-0.530817\pi$
$191$	−2.67180			−0.193325			−0.0966625	+	0.995317i	$0.530817\pi$
$192$	1.70271			0.122883
$193$	2.65867	−	10.7866i	0.191375	−	0.776440i	−0.794264	−	0.607573i	$-0.792143\pi$
$193$	2.65867	−	10.7866i	0.191375	−	0.776440i	0.985639	−	0.168866i	$-0.0540107\pi$
$194$	−4.02806	+	33.1740i	−0.289198	+	2.38176i
$195$	−0.484516	−	0.359552i	−0.0346969	−	0.0257480i
$196$	−0.515397	−	4.24468i	−0.0368141	−	0.303191i
$197$	23.2337	+	2.82108i	1.65533	+	0.200994i	0.894221	−	0.447626i	$-0.147730\pi$
$197$	23.2337	+	2.82108i	1.65533	+	0.200994i	0.761113	+	0.648619i	$0.224653\pi$
$198$	−12.8096	−	18.5580i	−0.910341	−	1.31886i
$199$	0.918566	+	0.813779i	0.0651154	+	0.0576872i	0.695053	−	0.718959i	$-0.255381\pi$
$199$	0.918566	+	0.813779i	0.0651154	+	0.0576872i	−0.629937	+	0.776646i	$0.716919\pi$
$200$	1.06000	−	0.128707i	0.0749533	−	0.00910097i
$201$	−2.42167	−	0.294044i	−0.170811	−	0.0207402i
$202$	4.95579	+	9.44247i	0.348688	+	0.664370i
$203$	10.8053	−	12.1967i	0.758387	−	0.856042i
$204$	−1.05714	+	1.53154i	−0.0740148	+	0.107229i
$205$	7.82203	−	1.92796i	0.546314	−	0.134654i
$206$	2.15882	−	0.262129i	0.150412	−	0.0182634i
$207$	11.4353	+	16.5669i	0.794809	+	1.15148i
$208$	−15.2254	−	0.521884i	−1.05569	−	0.0361862i
$209$	−3.04962	+	4.41814i	−0.210947	+	0.305609i
$210$	0.333012	−	0.634501i	0.0229800	−	0.0437847i
$211$	3.69438	+	9.74128i	0.254332	+	0.670617i	0.999991	+	0.00428985i	$0.00136550\pi$
$211$	3.69438	+	9.74128i	0.254332	+	0.670617i	−0.745659	+	0.666328i	$0.767865\pi$
$212$	2.17137	−	17.8829i	0.149130	−	1.22820i
$213$	1.31702	−	0.909076i	0.0902410	−	0.0622889i
$214$	3.53151	−	14.3279i	0.241409	−	0.979435i
$215$	−1.12340	+	0.775430i	−0.0766155	+	0.0528839i
$216$	0.318208	−	0.120680i	0.0216513	−	0.00821126i
$217$	4.10364	+	10.8204i	0.278573	+	0.734537i
$218$	−6.62550	+	3.47733i	−0.448735	+	0.235515i
$219$	−0.279686	−	0.532896i	−0.0188994	−	0.0360098i
$220$	4.89850	+	1.20737i	0.330257	+	0.0814010i
$221$	8.76107	−	11.8060i	0.589333	−	0.794159i
$222$	1.27598	−	0.314500i	0.0856379	−	0.0211079i
$223$	14.2300	+	16.0624i	0.952914	+	1.07562i	0.997063	+	0.0765922i	$0.0244039\pi$
$223$	14.2300	+	16.0624i	0.952914	+	1.07562i	−0.0441489	+	0.999025i	$0.514058\pi$
$224$	−2.05724	−	16.9429i	−0.137455	−	1.13204i
$225$	−11.7833	+	6.18437i	−0.785556	+	0.412291i
$226$	18.6030	−	35.4450i	1.23745	−	2.35777i
$227$	−18.2503	−	6.92142i	−1.21131	−	0.459391i	−0.335501	−	0.942040i	$-0.608905\pi$
$227$	−18.2503	−	6.92142i	−1.21131	−	0.459391i	−0.875814	+	0.482649i	$0.839675\pi$
$228$	0.417424	+	0.471175i	0.0276446	+	0.0312043i
$229$	2.31245	+	0.280782i	0.152811	+	0.0185546i	0.196584	−	0.980487i	$-0.437015\pi$
$229$	2.31245	+	0.280782i	0.152811	+	0.0185546i	−0.0437738	+	0.999041i	$0.513938\pi$
$230$	−9.02452	−	2.22435i	−0.595059	−	0.146669i
$231$	1.53738	−	1.36200i	0.101152	−	0.0896130i
$232$	−1.17297	+	1.32401i	−0.0770094	+	0.0869257i
$233$	7.16160	−	3.75870i	0.469172	−	0.246241i	−0.213531	−	0.976936i	$-0.568496\pi$
$233$	7.16160	−	3.75870i	0.469172	−	0.246241i	0.682703	+	0.730696i	$0.260804\pi$
$234$	19.7733	−	6.73371i	1.29262	−	0.440196i
$235$	0.327284	+	0.171772i	0.0213496	+	0.0112051i
$236$	−16.2570	+	6.16545i	−1.05824	+	0.401337i
$237$	0.225588	−	1.85789i	0.0146535	−	0.120683i
$238$	15.4607	+	8.11438i	1.00217	+	0.525977i
$239$		−	11.7127i		−	0.757635i	−0.925471	−	0.378817i	$-0.876331\pi$
$239$		−	11.7127i		−	0.757635i	0.925471	−	0.378817i	$-0.123669\pi$
$240$	−0.328583	+	0.626063i	−0.0212100	+	0.0404122i
$241$	17.0634	−	19.2606i	1.09915	−	1.24068i	0.130711	−	0.991420i	$-0.458274\pi$
$241$	17.0634	−	19.2606i	1.09915	−	1.24068i	0.968436	−	0.249261i	$-0.0801877\pi$
$242$	6.72761	+	4.64373i	0.432467	+	0.298510i
$243$	−4.77785	+	4.23280i	−0.306499	+	0.271534i
$244$	5.41624	−	7.84678i	0.346739	−	0.502339i
$245$	1.46588	+	0.555936i	0.0936518	+	0.0355174i
$246$	1.98141	−	5.22456i	0.126330	−	0.333106i
$247$	−3.16823	−	3.83309i	−0.201589	−	0.243894i
$248$	−0.445469	−	1.17461i	−0.0282873	−	0.0745876i
$249$		−	0.352318i		−	0.0223272i
$250$	4.58655	−	12.0937i	0.290079	−	0.764875i
$251$	3.31360	+	27.2899i	0.209152	+	1.72253i	0.598233	+	0.801322i	$0.295870\pi$
$251$	3.31360	+	27.2899i	0.209152	+	1.72253i	−0.389081	+	0.921204i	$0.627207\pi$
$252$	5.58656	+	10.6443i	0.351920	+	0.670528i
$253$	−21.9250	−	15.1338i	−1.37841	−	0.951451i
$254$	20.7311	+	14.3097i	1.30079	+	0.897867i
$255$	−0.317093	−	0.604171i	−0.0198572	−	0.0378346i
$256$	2.13848	+	17.6120i	0.133655	+	1.10075i
$257$	9.59298	−	25.2946i	0.598394	−	1.57783i	−0.202665	−	0.979248i	$-0.564960\pi$
$257$	9.59298	−	25.2946i	0.598394	−	1.57783i	0.801058	−	0.598586i	$-0.204271\pi$
$258$			0.946779i			0.0589439i
$259$	−2.11870	−	5.58655i	−0.131650	−	0.347131i
$260$	−2.31234	+	4.06129i	−0.143405	+	0.251871i
$261$	7.81729	−	20.6125i	0.483878	−	1.27588i
$262$	16.7939	+	6.36909i	1.03753	+	0.393484i
$263$	−5.49462	+	7.96033i	−0.338813	+	0.490855i	−0.954943	−	0.296789i	$-0.904084\pi$
$263$	−5.49462	+	7.96033i	−0.338813	+	0.490855i	0.616130	+	0.787644i	$0.288699\pi$
$264$	−0.166890	+	0.147852i	−0.0102714	+	0.00909964i
$265$	5.43580	+	3.75206i	0.333918	+	0.230487i
$266$	3.91655	−	4.42087i	0.240139	−	0.271061i
$267$	0.324862	−	0.618974i	0.0198813	−	0.0378806i
$268$			18.8955i			1.15423i
$269$	−20.9755	−	11.0088i	−1.27890	−	0.671217i	−0.317991	−	0.948094i	$-0.603008\pi$
$269$	−20.9755	−	11.0088i	−1.27890	−	0.671217i	−0.960905	+	0.276877i	$0.910701\pi$
$270$	0.236053	−	1.94407i	0.0143657	−	0.118313i
$271$	21.6059	−	8.19405i	1.31247	−	0.497753i	0.403637	−	0.914919i	$-0.367746\pi$
$271$	21.6059	−	8.19405i	1.31247	−	0.497753i	0.908830	+	0.417166i	$0.136977\pi$
$272$	−15.2551	−	8.00647i	−0.924974	−	0.485464i
$273$	0.825955	+	1.71398i	0.0499891	+	0.103735i
$274$	5.10495	−	2.67928i	0.308401	−	0.161861i
$275$	11.6787	−	13.1825i	0.704251	−	0.794935i
$276$	−2.33821	+	2.07147i	−0.140744	+	0.124688i
$277$	−11.1292	−	2.74310i	−0.668689	−	0.164817i	−0.109665	−	0.993969i	$-0.534978\pi$
$277$	−11.1292	−	2.74310i	−0.668689	−	0.164817i	−0.559024	+	0.829152i	$0.688824\pi$
$278$	20.3021	+	2.46512i	1.21764	+	0.147848i
$279$	10.3821	+	11.7190i	0.621559	+	0.701595i
$280$	0.330681	+	0.125411i	0.0197619	+	0.00749472i
$281$	−6.06070	+	11.5477i	−0.361551	+	0.688877i	−0.996492	−	0.0836826i	$-0.973332\pi$
$281$	−6.06070	+	11.5477i	−0.361551	+	0.688877i	0.634942	+	0.772560i	$0.281024\pi$
$282$	0.227001	−	0.119139i	0.0135177	−	0.00709465i
$283$	−2.08429	−	17.1657i	−0.123898	−	1.02039i	−0.913518	−	0.406798i	$-0.866645\pi$
$283$	−2.08429	−	17.1657i	−0.123898	−	1.02039i	0.789620	−	0.613596i	$-0.210278\pi$
$284$	−8.21982	−	9.27826i	−0.487757	−	0.550563i
$285$	−0.224096	+	0.0552347i	−0.0132743	+	0.00327182i
$286$	−21.3078	+	17.6119i	−1.25996	+	1.04141i
$287$	−24.6660	−	6.07962i	−1.45599	−	0.358869i
$288$	−10.7307	−	20.4456i	−0.632311	−	1.20477i
$289$	−0.331133	+	0.173792i	−0.0194784	+	0.0102231i
$290$	3.60942	+	9.51726i	0.211952	+	0.558873i
$291$	−3.85040	+	1.46027i	−0.225715	+	0.0856023i
$292$	−3.83648	+	2.64813i	−0.224513	+	0.154970i
$293$	4.21762	−	17.1115i	0.246396	−	0.999667i	−0.709205	−	0.705002i	$-0.750946\pi$
$293$	4.21762	−	17.1115i	0.246396	−	0.999667i	0.955601	−	0.294665i	$-0.0952079\pi$
$294$	0.894902	−	0.617706i	0.0521917	−	0.0360254i
$295$	0.768416	−	6.32847i	0.0447389	−	0.368458i
$296$	0.229995	+	0.606447i	0.0133682	+	0.0352490i
$297$	2.60857	−	4.97022i	0.151365	−	0.288401i
$298$	4.11237	−	5.95780i	0.238223	−	0.345126i
$299$	19.0217	−	15.7223i	1.10006	−	0.909246i
$300$	−1.17310	−	1.69952i	−0.0677288	−	0.0981221i
$301$	4.27312	−	0.518851i	0.246299	−	0.0299061i
$302$	−1.44108	+	0.355193i	−0.0829246	+	0.0204391i
$303$	−0.746496	+	1.08149i	−0.0428850	+	0.0621297i
$304$	−3.86446	+	4.36207i	−0.221642	+	0.250182i
$305$	1.62462	+	3.09545i	0.0930254	+	0.177245i
$306$	23.4504	+	2.84739i	1.34057	+	0.162774i
$307$	−11.0892	+	1.34647i	−0.632893	+	0.0768471i	−0.430695	−	0.902498i	$-0.641732\pi$
$307$	−11.0892	+	1.34647i	−0.632893	+	0.0768471i	−0.202198	+	0.979345i	$0.564808\pi$
$308$	−11.9082	−	10.5498i	−0.678534	−	0.601129i
$309$	0.152231	+	0.220545i	0.00866014	+	0.0125464i
$310$	−7.17619	−	0.871347i	−0.407580	−	0.0494892i
$311$	1.50830	+	12.4220i	0.0855278	+	0.704385i	0.970897	+	0.239497i	$0.0769824\pi$
$311$	1.50830	+	12.4220i	0.0855278	+	0.704385i	−0.885369	+	0.464888i	$0.846095\pi$
$312$	−0.0896614	−	0.186060i	−0.00507608	−	0.0105336i
$313$	−1.17589	+	9.68432i	−0.0664652	+	0.547390i	0.921001	+	0.389560i	$0.127373\pi$
$313$	−1.17589	+	9.68432i	−0.0664652	+	0.547390i	−0.987466	+	0.157830i	$0.949550\pi$
$314$	−6.84596	+	27.7751i	−0.386340	+	1.56744i
$315$	−4.40765			−0.248343
$316$	−14.4965			−0.815493
$317$	−5.09312	+	20.6636i	−0.286058	+	1.16058i	0.635424	+	0.772163i	$0.280825\pi$
$317$	−5.09312	+	20.6636i	−0.286058	+	1.16058i	−0.921482	+	0.388420i	$0.873021\pi$
$318$	4.28346	−	1.62450i	0.240205	−	0.0910976i
$319$			29.1750i			1.63349i
$320$	4.52150	+	1.71478i	0.252760	+	0.0958592i
$321$	1.76560	−	0.435182i	0.0985464	−	0.0242895i
$322$	21.9386	+	19.4359i	1.22259	+	1.08312i
$323$	−1.34588	−	5.46047i	−0.0748870	−	0.303829i
$324$	11.9247	+	10.5644i	0.662484	+	0.586910i
$325$	8.80215	+	13.7359i	0.488255	+	0.761933i
$326$	−28.4820	+	25.2329i	−1.57747	+	1.39752i
$327$	−0.758846	−	0.523794i	−0.0419643	−	0.0289659i
$328$	2.67761	+	0.659972i	0.147846	+	0.0364409i
$329$	−0.662116	−	0.959241i	−0.0365036	−	0.0528847i
$330$	0.307045	+	1.24573i	0.0169023	+	0.0685752i
$331$	−6.55964	−	26.6135i	−0.360550	−	1.46281i	−0.818848	−	0.574011i	$-0.805387\pi$
$331$	−6.55964	−	26.6135i	−0.360550	−	1.46281i	0.458297	−	0.888799i	$-0.348459\pi$
$332$	−2.70908	+	0.328942i	−0.148680	+	0.0180531i
$333$	−5.36025	−	6.05047i	−0.293740	−	0.331564i
$334$	−15.5954	+	41.1216i	−0.853340	+	2.25007i
$335$	−6.13455	−	3.21966i	−0.335166	−	0.175909i
$336$	1.83494	−	1.26657i	0.100104	−	0.0690969i
$337$	−10.1055			−0.550484			−0.275242	−	0.961375i	$-0.588758\pi$
$337$	−10.1055			−0.550484			−0.275242	+	0.961375i	$0.588758\pi$
$338$	−10.3199	−	23.4361i	−0.561331	−	1.27476i
$339$	4.93286			0.267916
$340$	−4.34961	+	3.00232i	−0.235891	+	0.162824i
$341$	−18.3466	−	9.62906i	−0.993527	−	0.521443i
$342$	2.83348	−	7.47128i	0.153217	−	0.404001i
$343$	−13.3693	−	15.0908i	−0.721873	−	0.814826i
$344$	−0.463868	+	0.0563238i	−0.0250101	+	0.00303678i
$345$	−0.274102	−	1.11208i	−0.0147572	−	0.0598722i
$346$	4.30908	+	17.4826i	0.231658	+	0.939872i
$347$	−18.2925	−	26.5012i	−0.981992	−	1.42266i	−0.904894	−	0.425637i	$-0.860050\pi$
$347$	−18.2925	−	26.5012i	−0.981992	−	1.42266i	−0.0770981	−	0.997024i	$-0.524565\pi$
$348$	3.32154	+	0.818687i	0.178053	+	0.0438862i
$349$	−1.99739	−	1.37870i	−0.106918	−	0.0738000i	0.513406	−	0.858146i	$-0.328383\pi$
$349$	−1.99739	−	1.37870i	−0.106918	−	0.0738000i	−0.620324	+	0.784346i	$0.712999\pi$
$350$	−14.5031	+	12.8486i	−0.775221	+	0.686786i
$351$	3.77160	+	3.57932i	0.201313	+	0.191050i
$352$	22.8733	+	20.2640i	1.21915	+	1.08008i
$353$	−0.434272	−	1.76191i	−0.0231140	−	0.0937771i	0.958252	−	0.285925i	$-0.0923008\pi$
$353$	−0.434272	−	1.76191i	−0.0231140	−	0.0937771i	−0.981366	+	0.192148i	$0.938455\pi$
$354$	−3.30963	−	2.93207i	−0.175905	−	0.155838i
$355$	4.41285	−	1.08767i	0.234209	−	0.0577275i
$356$	−5.06279	−	1.92006i	−0.268328	−	0.101763i
$357$			2.15165i			0.113877i
$358$	0.761318	−	0.288730i	0.0402369	−	0.0152598i
$359$	5.38548	−	21.8498i	0.284235	−	1.15319i	−0.639080	−	0.769141i	$-0.720685\pi$
$359$	5.38548	−	21.8498i	0.284235	−	1.15319i	0.923314	−	0.384045i	$-0.125469\pi$
$360$	0.478472			0.0252177
$361$	17.0977			0.899878
$362$	−8.90861	+	36.1437i	−0.468226	+	1.89967i
$363$	−0.121423	+	1.00000i	−0.00637303	+	0.0524866i
$364$	12.4082	−	7.95129i	0.650364	−	0.416761i
$365$	−0.206024	−	1.69676i	−0.0107838	−	0.0888125i
$366$	2.40704	+	0.292268i	0.125818	+	0.0152771i
$367$	14.2840	+	20.6939i	0.745617	+	1.08021i	0.993765	+	0.111491i	$0.0355626\pi$
$367$	14.2840	+	20.6939i	0.745617	+	1.08021i	−0.248148	+	0.968722i	$0.579822\pi$
$368$	−21.6468	−	19.1774i	−1.12842	−	0.999691i
$369$	−34.1188	+	4.14278i	−1.77616	+	0.215664i
$370$	3.70505	+	0.449875i	0.192617	+	0.0233879i
$371$	−9.67933	−	18.4424i	−0.502526	−	0.957483i
$372$	−1.61109	+	1.81854i	−0.0835311	+	0.0942871i
$373$	−3.47676	+	5.03696i	−0.180020	+	0.260804i	−0.902597	−	0.430487i	$-0.858342\pi$
$373$	−3.47676	+	5.03696i	−0.180020	+	0.260804i	0.722577	+	0.691290i	$0.242957\pi$
$374$	−30.3543	+	7.48166i	−1.56958	+	0.386867i
$375$	1.58225	−	0.192119i	0.0817068	−	0.00992101i
$376$	0.0718759	+	0.104130i	0.00370672	+	0.00537010i
$377$	−26.0034	−	7.36279i	−1.33924	−	0.379203i
$378$	−3.50807	+	5.08231i	−0.180435	+	0.261406i
$379$	−9.83120	+	18.7318i	−0.504995	+	0.962188i	0.490861	+	0.871238i	$0.336682\pi$
$379$	−9.83120	+	18.7318i	−0.504995	+	0.962188i	−0.995856	+	0.0909494i	$0.971010\pi$
$380$	0.633945	+	1.67158i	0.0325207	+	0.0857500i
$381$	−0.374163	+	3.08151i	−0.0191690	+	0.157871i
$382$	−4.33135	+	2.98971i	−0.221611	+	0.152967i
$383$	−2.00020	+	8.11513i	−0.102205	+	0.414664i	−0.999650	−	0.0264640i	$-0.991575\pi$
$383$	−2.00020	+	8.11513i	−0.102205	+	0.414664i	0.897444	+	0.441128i	$0.145421\pi$
$384$	−0.376468	+	0.259857i	−0.0192116	+	0.0132608i
$385$	5.45413	−	2.06848i	0.277968	−	0.105419i
$386$	−7.76005	−	20.4616i	−0.394976	−	1.04147i
$387$	5.15653	−	2.70635i	0.262121	−	0.137572i
$388$	14.8234	+	28.2436i	0.752543	+	1.43385i
$389$	21.9538	+	5.41113i	1.11310	+	0.274355i	0.752649	−	0.658422i	$-0.228776\pi$
$389$	21.9538	+	5.41113i	1.11310	+	0.274355i	0.360454	+	0.932777i	$0.382622\pi$
$390$	−1.18780	−	0.0407143i	−0.0601464	−	0.00206165i
$391$	27.0976	−	6.67896i	1.37038	−	0.337769i
$392$	0.355879	+	0.401704i	0.0179746	+	0.0202891i
$393$	0.266786	+	2.19718i	0.0134576	+	0.110833i
$394$	40.8217	−	21.4249i	2.05657	−	1.07937i
$395$	2.47010	−	4.70639i	0.124284	−	0.236804i
$396$	−20.1250	−	7.63239i	−1.01132	−	0.383542i
$397$	−8.69631	−	9.81610i	−0.436455	−	0.492656i	0.488590	−	0.872514i	$-0.337511\pi$
$397$	−8.69631	−	9.81610i	−0.436455	−	0.492656i	−0.925045	+	0.379858i	$0.875973\pi$
$398$	2.39972	+	0.291379i	0.120287	+	0.0146055i
$399$	0.706665	+	0.174177i	0.0353775	+	0.00871977i
$400$	14.3102	−	12.6777i	0.715509	−	0.633886i
$401$	−7.80285	+	8.80760i	−0.389656	+	0.439830i	−0.910304	−	0.413941i	$-0.864152\pi$
$401$	−7.80285	+	8.80760i	−0.389656	+	0.439830i	0.520648	+	0.853771i	$0.325690\pi$
$402$	−4.25487	+	2.23313i	−0.212214	+	0.111378i
$403$	13.2124	−	13.9222i	0.658156	−	0.693512i
$404$	9.01285	+	4.73031i	0.448406	+	0.235342i
$405$	−5.46168	+	2.07134i	−0.271393	+	0.102926i
$406$	3.86893	−	31.8635i	0.192012	−	1.58136i
$407$	9.47234	+	4.97147i	0.469526	+	0.246427i
$408$		−	0.233572i		−	0.0115635i
$409$	−1.32410	+	2.52287i	−0.0654727	+	0.124748i	−0.915993	−	0.401195i	$-0.868595\pi$
$409$	−1.32410	+	2.52287i	−0.0654727	+	0.124748i	0.850520	+	0.525943i	$0.176287\pi$
$410$	10.5232	−	11.8782i	0.519703	−	0.586624i
$411$	0.584691	+	0.403583i	0.0288407	+	0.0199073i
$412$	1.55371	−	1.37647i	0.0765458	−	0.0678137i
$413$	−11.4197	+	16.5443i	−0.561926	+	0.814090i
$414$	37.0763	+	14.0612i	1.82220	+	0.691069i
$415$	0.354815	−	0.935571i	0.0174172	−	0.0459254i
$416$	−23.8336	+	15.2728i	−1.16854	+	0.748813i
$417$	0.893664	+	2.35640i	0.0437629	+	0.115393i
$418$			10.5749i			0.517234i
$419$	1.51853	−	4.00404i	0.0741851	−	0.195610i	−0.892794	−	0.450465i	$-0.851258\pi$
$419$	1.51853	−	4.00404i	0.0741851	−	0.195610i	0.966979	+	0.254855i	$0.0820276\pi$
$420$	−0.0824444	−	0.678991i	−0.00402288	−	0.0331314i
$421$	12.0267	+	22.9149i	0.586144	+	1.11681i	0.980254	+	0.197742i	$0.0633607\pi$
$421$	12.0267	+	22.9149i	0.586144	+	1.11681i	−0.394110	+	0.919063i	$0.628947\pi$
$422$	16.8894	+	11.6579i	0.822165	+	0.567499i
$423$	−1.29776	−	0.895779i	−0.0630992	−	0.0435543i
$424$	1.05074	+	2.00201i	0.0510284	+	0.0972264i
$425$	2.22386	+	18.3152i	0.107873	+	0.888416i
$426$	1.11783	−	2.94746i	0.0541588	−	0.142805i
$427$		−	11.0239i		−	0.533485i
$428$	−4.99472	−	13.1700i	−0.241429	−	0.636595i
$429$	−3.14193	−	1.31639i	−0.151694	−	0.0635557i
$430$	−0.953490	+	2.51415i	−0.0459814	+	0.121243i
$431$	−16.7482	−	6.35175i	−0.806732	−	0.305953i	−0.0834553	−	0.996512i	$-0.526596\pi$
$431$	−16.7482	−	6.35175i	−0.806732	−	0.305953i	−0.723277	+	0.690558i	$0.757365\pi$
$432$	3.46141	−	5.01472i	0.166537	−	0.241271i
$433$	11.8828	−	10.5273i	0.571053	−	0.505909i	−0.327454	−	0.944867i	$-0.606191\pi$
$433$	11.8828	−	10.5273i	0.571053	−	0.505909i	0.898508	+	0.438958i	$0.144652\pi$
$434$	18.7604	+	12.9494i	0.900529	+	0.621590i
$435$	−0.831759	+	0.938862i	−0.0398798	+	0.0450150i
$436$	−3.31912	+	6.32405i	−0.158957	+	0.302867i
$437$		−	9.44030i		−	0.451591i
$438$	−1.04971	−	0.550931i	−0.0501571	−	0.0263245i
$439$	−3.32093	+	27.3503i	−0.158499	+	1.30536i	0.668734	+	0.743501i	$0.266836\pi$
$439$	−3.32093	+	27.3503i	−0.158499	+	1.30536i	−0.827234	+	0.561858i	$0.810087\pi$
$440$	−0.592072	+	0.224543i	−0.0282259	+	0.0107047i
$441$	−5.92233	−	3.10828i	−0.282016	−	0.148013i
$442$	0.992072	−	28.9426i	0.0471881	−	1.37666i
$443$	30.5590	−	16.0386i	1.45190	−	0.762017i	0.459868	−	0.887987i	$-0.347897\pi$
$443$	30.5590	−	16.0386i	1.45190	−	0.762017i	0.992034	+	0.125971i	$0.0402045\pi$
$444$	0.831802	−	0.938911i	0.0394756	−	0.0445587i
$445$	1.48603	−	1.31650i	0.0704444	−	0.0624083i
$446$	41.0424	+	10.1160i	1.94341	+	0.479008i
$447$	0.885580	+	0.107529i	0.0418865	+	0.00508594i
$448$	−10.1120	−	11.4141i	−0.477747	−	0.539265i
$449$	−10.5493	−	4.00083i	−0.497853	−	0.188811i	0.0928808	−	0.995677i	$-0.470392\pi$
$449$	−10.5493	−	4.00083i	−0.497853	−	0.188811i	−0.590734	+	0.806866i	$0.701162\pi$
$450$	−12.1821	+	23.2111i	−0.574270	+	1.09418i
$451$	40.2752	−	21.1381i	1.89649	−	0.995353i
$452$	−4.60557	−	37.9303i	−0.216628	−	1.78409i
$453$	−0.121283	−	0.136900i	−0.00569835	−	0.00643211i
$454$	−37.3311	+	9.20129i	−1.75204	+	0.431838i
$455$	0.467176	+	5.38323i	0.0219016	+	0.252370i
$456$	−0.0767118	−	0.0189078i	−0.00359236	−	0.000885438i
$457$	2.30287	+	4.38775i	0.107724	+	0.205250i	0.933351	−	0.358966i	$-0.116871\pi$
$457$	2.30287	+	4.38775i	0.107724	+	0.205250i	−0.825627	+	0.564216i	$0.809178\pi$
$458$	4.06297	−	2.13241i	0.189850	−	0.0996410i
$459$	2.08517	+	5.49815i	0.0973275	+	0.256632i
$460$	−8.29520	+	3.14596i	−0.386766	+	0.146681i
$461$	18.8843	−	13.0349i	0.879529	−	0.607095i	−0.0403983	−	0.999184i	$-0.512863\pi$
$461$	18.8843	−	13.0349i	0.879529	−	0.607095i	0.919928	+	0.392088i	$0.128247\pi$
$462$	0.968236	−	3.92829i	0.0450464	−	0.182761i
$463$	−12.7404	+	8.79409i	−0.592098	+	0.408696i	−0.826086	−	0.563543i	$-0.809438\pi$
$463$	−12.7404	+	8.79409i	−0.592098	+	0.408696i	0.233988	+	0.972239i	$0.424822\pi$
$464$	−3.81748	+	31.4398i	−0.177222	+	1.45955i
$465$	−0.315884	−	0.832917i	−0.0146488	−	0.0386256i
$466$	7.40397	−	14.1071i	0.342982	−	0.653498i
$467$	10.2699	−	14.8785i	0.475233	−	0.688493i	−0.509911	−	0.860227i	$-0.670322\pi$
$467$	10.2699	−	14.8785i	0.475233	−	0.688493i	0.985143	+	0.171734i	$0.0549370\pi$
$468$	11.8816	−	16.0110i	0.549225	−	0.740110i
$469$	12.4106	+	17.9798i	0.573068	+	0.830232i
$470$	0.722780	−	0.0877614i	0.0333393	−	0.00404813i
$471$	−3.42269	+	0.843616i	−0.157709	+	0.0388718i
$472$	1.23966	−	1.79596i	0.0570601	−	0.0826658i
$473$	−5.11073	+	5.76882i	−0.234992	+	0.265251i
$474$	−1.71324	−	3.26431i	−0.0786919	−	0.149935i
$475$	6.19525	+	0.752240i	0.284258	+	0.0345151i
$476$	16.5447	−	2.00889i	0.758327	−	0.0920775i
$477$	−21.0919	−	18.6858i	−0.965732	−	0.855564i
$478$	−13.1064	−	18.9879i	−0.599473	−	0.868487i
$479$	19.7502	+	2.39811i	0.902411	+	0.109573i	0.558572	−	0.829456i	$-0.311349\pi$
$479$	19.7502	+	2.39811i	0.902411	+	0.109573i	0.343839	+	0.939029i	$0.388273\pi$
$480$	0.158359	+	1.30421i	0.00722808	+	0.0595286i
$481$	−6.82153	+	7.18798i	−0.311035	+	0.327744i
$482$	6.10966	−	50.3176i	0.278287	−	2.29190i
$483$	−0.864355	+	3.50683i	−0.0393295	+	0.159566i
$484$	7.80272			0.354669
$485$	−11.6953			−0.531054
$486$	−3.00907	+	12.2083i	−0.136494	+	0.553779i
$487$	−33.3310	+	12.6408i	−1.51037	+	0.572809i	−0.964273	−	0.264911i	$-0.914658\pi$
$487$	−33.3310	+	12.6408i	−1.51037	+	0.572809i	−0.546100	+	0.837720i	$0.683888\pi$
$488$			1.19670i			0.0541721i
$489$	−4.38433	−	1.66276i	−0.198266	−	0.0751924i
$490$	2.99847	−	0.739057i	0.135457	−	0.0333872i
$491$	−17.1518	−	15.1951i	−0.774048	−	0.685747i	0.180576	−	0.983561i	$-0.442204\pi$
$491$	−17.1518	−	15.1951i	−0.774048	−	0.685747i	−0.954624	+	0.297814i	$0.903742\pi$
$492$	−1.27637	−	5.17846i	−0.0575434	−	0.233463i
$493$	−22.8769	−	20.2672i	−1.03032	−	0.912788i
$494$	−9.42529	−	2.66874i	−0.424064	−	0.120072i
$495$	5.90705	−	5.23319i	0.265502	−	0.235215i
$496$	−18.5109	−	12.7772i	−0.831165	−	0.573712i
$497$	−13.9155	−	3.42986i	−0.624194	−	0.153850i
$498$	−0.394239	−	0.571154i	−0.0176663	−	0.0255940i
$499$	6.89626	+	27.9792i	0.308719	+	1.25252i	0.896333	+	0.443381i	$0.146221\pi$
$499$	6.89626	+	27.9792i	0.308719	+	1.25252i	−0.587614	+	0.809141i	$0.699933\pi$
$500$	−2.95454	−	11.9870i	−0.132131	−	0.536076i
$501$	−5.38001	+	0.653252i	−0.240361	+	0.0291851i
$502$	35.9089	+	40.5327i	1.60269	+	1.80906i
$503$	−0.184885	+	0.487503i	−0.00824363	+	0.0217367i	−0.939075	−	0.343713i	$-0.888315\pi$
$503$	−0.184885	+	0.487503i	−0.00824363	+	0.0217367i	0.930831	+	0.365449i	$0.119085\pi$
$504$	−1.33599	−	0.701180i	−0.0595096	−	0.0312331i
$505$	−3.07145	+	2.12007i	−0.136678	+	0.0943419i
$506$	−52.4778			−2.33292
$507$	1.96620	−	2.46816i	0.0873221	−	0.109615i
$508$	24.0441			1.06678
$509$	−28.2028	+	19.4670i	−1.25007	+	0.862858i	−0.994582	−	0.103955i	$-0.966850\pi$
$509$	−28.2028	+	19.4670i	−1.25007	+	0.862858i	−0.255484	+	0.966813i	$0.582235\pi$
$510$	−1.19011	−	0.624617i	−0.0526989	−	0.0276585i
$511$	−1.91127	+	5.03961i	−0.0845497	+	0.222939i
$512$	20.6750	+	23.3373i	0.913716	+	1.03137i
$513$	1.97455	−	0.239753i	0.0871784	−	0.0105854i
$514$	−12.7528	−	51.7403i	−0.562504	−	2.28217i
$515$	0.182138	+	0.738962i	0.00802595	+	0.0325626i
$516$	0.513361	+	0.743732i	0.0225995	+	0.0327410i
$517$	2.02626	+	0.499428i	0.0891148	+	0.0219648i
$518$	−9.68597	−	6.68574i	−0.425577	−	0.293755i
$519$	−1.66082	+	1.47136i	−0.0729019	+	0.0645854i
$520$	−0.0507142	−	0.584376i	−0.00222397	−	0.0256266i
$521$	25.8689	+	22.9178i	1.13334	+	1.00405i	0.999916	+	0.0129887i	$0.00413454\pi$
$521$	25.8689	+	22.9178i	1.13334	+	1.00405i	0.133420	+	0.991060i	$0.457404\pi$
$522$	−10.3923	−	42.1630i	−0.454857	−	1.84543i
$523$	−10.5647	−	9.35951i	−0.461962	−	0.409263i	0.399778	−	0.916612i	$-0.369087\pi$
$523$	−10.5647	−	9.35951i	−0.461962	−	0.409263i	−0.861741	+	0.507349i	$0.830626\pi$
$524$	16.6457	−	4.10280i	0.727172	−	0.179232i
$525$	−2.23250	−	0.846676i	−0.0974343	−	0.0369520i
$526$			19.0531i			0.830756i
$527$	20.2954	−	7.69703i	0.884082	−	0.335288i
$528$	−0.955360	+	3.87605i	−0.0415767	+	0.168683i
$529$	23.8475			1.03685
$530$	13.0106			0.565146
$531$	−6.50870	+	26.4068i	−0.282453	+	1.14596i
$532$	0.679525	−	5.59639i	0.0294611	−	0.242634i
$533$	8.67605	+	41.2315i	0.375802	+	1.78594i
$534$	−0.165978	−	1.36695i	−0.00718259	−	0.0591539i
$535$	5.12678	+	0.622504i	0.221650	+	0.0269132i
$536$	−1.34723	−	1.95180i	−0.0581914	−	0.0843049i
$537$	0.0751027	+	0.0665352i	0.00324092	+	0.00287121i
$538$	−46.3227	+	5.62459i	−1.99711	+	0.242493i
$539$	8.78712	+	1.06695i	0.378488	+	0.0459568i
$540$	−0.868684	−	1.65514i	−0.0373822	−	0.0712258i
$541$	−5.10628	+	5.76380i	−0.219536	+	0.247805i	−0.847953	−	0.530072i	$-0.822165\pi$
$541$	−5.10628	+	5.76380i	−0.219536	+	0.247805i	0.628417	+	0.777877i	$0.283703\pi$
$542$	25.8570	−	37.4604i	1.11066	−	1.60906i
$543$	−4.45393	+	1.09779i	−0.191136	+	0.0471109i
$544$	−31.7791	+	3.85869i	−1.36252	+	0.165440i
$545$	−1.48759	−	2.15515i	−0.0637214	−	0.0923163i
$546$	3.25690	+	1.85435i	0.139382	+	0.0793588i
$547$	−20.2903	+	29.3955i	−0.867550	+	1.25686i	0.0976161	+	0.995224i	$0.468878\pi$
$547$	−20.2903	+	29.3955i	−0.867550	+	1.25686i	−0.965166	+	0.261639i	$0.915737\pi$
$548$	2.55738	−	4.87268i	0.109246	−	0.208151i
$549$	−5.28869	−	13.9451i	−0.225716	−	0.595163i
$550$	4.18164	−	34.4389i	0.178306	−	1.46848i
$551$	−8.50822	+	5.87280i	−0.362462	+	0.250190i
$552$	0.0938299	−	0.380683i	0.00399367	−	0.0162029i
$553$	−13.7940	+	9.52133i	−0.586582	+	0.404888i
$554$	−21.1114	+	8.00649i	−0.896937	+	0.340163i
$555$	0.163090	+	0.430034i	0.00692280	+	0.0182539i
$556$	17.2847	−	9.07173i	0.733036	−	0.384727i
$557$	11.4297	+	21.7774i	0.484291	+	0.922739i	0.997904	+	0.0647170i	$0.0206145\pi$
$557$	11.4297	+	21.7774i	0.484291	+	0.922739i	−0.513613	+	0.858022i	$0.671693\pi$
$558$	29.9441	+	7.38055i	1.26763	+	0.312444i
$559$	−3.85192	−	6.01101i	−0.162919	−	0.254239i
$560$	6.14818	−	1.51539i	0.259808	−	0.0640369i
$561$	−2.55465	−	2.88360i	−0.107857	−	0.121746i
$562$	3.09652	+	25.5022i	0.130619	+	1.07574i
$563$	32.4623	−	17.0375i	1.36812	−	0.718047i	0.388986	−	0.921244i	$-0.372825\pi$
$563$	32.4623	−	17.0375i	1.36812	−	0.718047i	0.979138	+	0.203197i	$0.0651330\pi$
$564$	0.113719	−	0.216673i	0.00478843	−	0.00912358i
$565$	13.0991	+	4.96782i	0.551082	+	0.208998i
$566$	−22.5871	−	25.4955i	−0.949405	−	1.07166i
$567$	18.2856	+	2.22027i	0.767921	+	0.0932425i
$568$	1.51059	+	0.372327i	0.0633830	+	0.0156225i
$569$	7.61885	−	6.74971i	0.319399	−	0.282963i	−0.488155	−	0.872757i	$-0.662330\pi$
$569$	7.61885	−	6.74971i	0.319399	−	0.282963i	0.807553	+	0.589795i	$0.200791\pi$
$570$	−0.301482	+	0.340303i	−0.0126277	+	0.0142537i
$571$	33.6850	−	17.6792i	1.40967	−	0.739853i	0.423550	−	0.905873i	$-0.360784\pi$
$571$	33.6850	−	17.6792i	1.40967	−	0.739853i	0.986123	+	0.166019i	$0.0530913\pi$
$572$	−7.18864	+	25.3883i	−0.300572	+	1.06154i
$573$	−0.574261	−	0.301395i	−0.0239901	−	0.0125910i
$574$	−46.7899	+	17.7451i	−1.95297	+	0.740664i
$575$	−3.73299	+	30.7440i	−0.155677	+	1.28211i
$576$	−18.2674	−	9.58747i	−0.761142	−	0.399478i
$577$		−	40.2841i		−	1.67705i	−0.544863	−	0.838525i	$-0.683418\pi$
$577$		−	40.2841i		−	1.67705i	0.544863	−	0.838525i	$-0.316582\pi$
$578$	−0.342339	+	0.652273i	−0.0142394	+	0.0271310i
$579$	1.78824	−	2.01850i	0.0743165	−	0.0838860i
$580$	7.99578	+	5.51909i	0.332007	+	0.229168i
$581$	−2.36175	+	2.09233i	−0.0979821	+	0.0868046i
$582$	−4.60799	+	6.67583i	−0.191007	+	0.276722i
$583$	34.8687	+	13.2240i	1.44411	+	0.547680i
$584$	0.207478	−	0.547074i	0.00858549	−	0.0226381i
$585$	3.17356	+	6.58559i	0.131210	+	0.272281i
$586$	−12.3103	−	32.4595i	−0.508533	−	1.34089i
$587$			11.4771i			0.473712i	0.971545	+	0.236856i	$0.0761169\pi$
$587$			11.4771i			0.473712i	−0.971545	+	0.236856i	$0.923883\pi$
$588$	0.368049	−	0.970465i	0.0151781	−	0.0400213i
$589$	−0.885006	−	7.28868i	−0.0364660	−	0.300325i
$590$	−5.83577	−	11.1191i	−0.240255	−	0.457768i
$591$	4.67548	+	3.22725i	0.192323	+	0.132751i
$592$	9.55715	+	6.59683i	0.392797	+	0.271128i
$593$	−4.58216	−	8.73059i	−0.188167	−	0.358522i	0.773037	−	0.634361i	$-0.218737\pi$
$593$	−4.58216	−	8.73059i	−0.188167	−	0.358522i	−0.961204	+	0.275839i	$0.911044\pi$
$594$	−1.33277	−	10.9763i	−0.0546842	−	0.450365i
$595$	−2.16690	+	5.71366i	−0.0888344	+	0.234237i
$596$		−	6.90990i		−	0.283040i
$597$	0.105632	+	0.278528i	0.00432322	+	0.0113994i
$598$	13.2437	−	46.7730i	0.541573	−	1.91269i
$599$	−4.88753	+	12.8874i	−0.199699	+	0.526564i	−0.997033	−	0.0769750i	$-0.975474\pi$
$599$	−4.88753	+	12.8874i	−0.199699	+	0.526564i	0.797334	+	0.603539i	$0.206243\pi$
$600$	0.242349	+	0.0919107i	0.00989384	+	0.00375224i
$601$	4.08808	−	5.92261i	0.166756	−	0.241588i	−0.730693	−	0.682707i	$-0.760803\pi$
$601$	4.08808	−	5.92261i	0.166756	−	0.241588i	0.897449	+	0.441118i	$0.145418\pi$
$602$	6.34671	−	5.62269i	0.258673	−	0.229164i
$603$	24.3250	+	16.7903i	0.990590	+	0.683755i
$604$	−0.939429	+	1.06040i	−0.0382248	+	0.0431469i
$605$	−1.32953	+	2.53320i	−0.0540530	+	0.102989i
$606$			2.58855i			0.105153i
$607$	−30.4988	−	16.0070i	−1.23791	−	0.649705i	−0.286631	−	0.958041i	$-0.592536\pi$
$607$	−30.4988	−	16.0070i	−1.23791	−	0.649705i	−0.951277	+	0.308336i	$0.900228\pi$
$608$	−1.30523	+	10.7496i	−0.0529341	+	0.435952i
$609$	3.69830	−	1.40258i	0.149863	−	0.0568354i
$610$	6.09749	+	3.20021i	0.246880	+	0.129573i
$611$	−0.956496	+	1.67995i	−0.0386957	+	0.0679634i
$612$	19.9651	−	10.4785i	0.807042	−	0.423568i
$613$	21.3923	−	24.1469i	0.864025	−	0.975283i	−0.135855	−	0.990729i	$-0.543378\pi$
$613$	21.3923	−	24.1469i	0.864025	−	0.975283i	0.999881	+	0.0154456i	$0.00491667\pi$
$614$	−16.4703	+	14.5914i	−0.664689	+	0.588863i
$615$	1.89870	+	0.467989i	0.0765632	+	0.0188711i
$616$	1.98224	+	0.240688i	0.0798667	+	0.00969758i
$617$	−2.47528	−	2.79401i	−0.0996508	−	0.112483i	0.696569	−	0.717489i	$-0.254709\pi$
$617$	−2.47528	−	2.79401i	−0.0996508	−	0.112483i	−0.796220	+	0.605007i	$0.793170\pi$
$618$	0.493574	+	0.187188i	0.0198545	+	0.00752980i
$619$	−6.94133	+	13.2256i	−0.278995	+	0.531582i	−0.984121	−	0.177501i	$-0.943199\pi$
$619$	−6.94133	+	13.2256i	−0.278995	+	0.531582i	0.705125	+	0.709083i	$0.250891\pi$
$620$	−6.10964	+	3.20659i	−0.245369	+	0.128780i
$621$	1.18978	+	9.79870i	0.0477441	+	0.393208i
$622$	16.3452	+	18.4499i	0.655381	+	0.739772i
$623$	−6.07856	+	1.49823i	−0.243532	+	0.0600253i
$624$	−3.21359	−	1.82969i	−0.128646	−	0.0732462i
$625$	−17.5713	−	4.33092i	−0.702850	−	0.173237i
$626$	8.93035	+	17.0154i	0.356929	+	0.680071i
$627$	−1.15386	+	0.605592i	−0.0460807	+	0.0241850i
$628$	9.68243	+	25.5305i	0.386371	+	1.01878i
$629$	−10.4785	+	3.97396i	−0.417804	+	0.158452i
$630$	−7.14538	+	4.93210i	−0.284679	+	0.196500i
$631$	1.39686	−	5.66727i	0.0556080	−	0.225610i	−0.936563	−	0.350500i	$-0.886012\pi$
$631$	1.39686	−	5.66727i	0.0556080	−	0.225610i	0.992171	+	0.124890i	$0.0398577\pi$
$632$	1.49741	−	1.03359i	0.0595637	−	0.0411139i
$633$	−0.304827	+	2.51048i	−0.0121158	+	0.0997826i
$634$	14.8657	+	39.1976i	0.590391	+	1.55673i
$635$	−4.09694	+	7.80606i	−0.162582	+	0.309774i
$636$	2.48399	−	3.59869i	0.0984968	−	0.142697i
$637$	−3.16854	+	7.56262i	−0.125542	+	0.299642i
$638$	32.6464	+	47.2965i	1.29248	+	1.87249i
$639$	−19.2483	+	2.33717i	−0.761452	+	0.0924571i
$640$	−1.26140	+	0.310907i	−0.0498612	+	0.0122897i
$641$	−2.43651	+	3.52989i	−0.0962364	+	0.139422i	−0.868144	−	0.496312i	$-0.834687\pi$
$641$	−2.43651	+	3.52989i	−0.0962364	+	0.139422i	0.771908	+	0.635734i	$0.219303\pi$
$642$	2.37531	−	2.68117i	0.0937461	−	0.105818i
$643$	−2.86678	−	5.46219i	−0.113055	−	0.215408i	0.822354	−	0.568976i	$-0.192660\pi$
$643$	−2.86678	−	5.46219i	−0.113055	−	0.215408i	−0.935409	+	0.353569i	$0.884968\pi$
$644$	27.7721	+	3.37214i	1.09437	+	0.132881i
$645$	−0.328931	+	0.0399394i	−0.0129516	+	0.00157261i
$646$	−8.29205	−	7.34611i	−0.326246	−	0.289029i
$647$	−16.4635	−	23.8515i	−0.647246	−	0.937698i	−0.999998	−	0.00198097i	$-0.999369\pi$
$647$	−16.4635	−	23.8515i	−0.647246	−	0.937698i	0.352752	−	0.935717i	$-0.385246\pi$
$648$	−1.98498	−	0.241021i	−0.0779775	−	0.00946819i
$649$	−4.33852	−	35.7309i	−0.170302	−	1.40256i
$650$	29.6398	+	12.4183i	1.16257	+	0.487085i
$651$	−0.338595	+	2.78858i	−0.0132706	+	0.109293i
$652$	−8.69202	+	35.2649i	−0.340406	+	1.38108i
$653$	1.31978			0.0516470			0.0258235	−	0.999667i	$-0.491779\pi$
$653$	1.31978			0.0516470			0.0258235	+	0.999667i	$0.491779\pi$
$654$	−1.81631			−0.0710233
$655$	−1.50431	+	6.10323i	−0.0587783	+	0.238473i
$656$	46.1676	−	17.5091i	1.80254	−	0.683614i
$657$			7.29197i			0.284487i
$658$	−2.14675	−	0.814157i	−0.0836892	−	0.0317391i
$659$	34.3952	−	8.47767i	1.33985	−	0.330243i	0.496699	−	0.867923i	$-0.334545\pi$
$659$	34.3952	−	8.47767i	1.33985	−	0.330243i	0.843149	+	0.537680i	$0.180699\pi$
$660$	0.916655	+	0.812085i	0.0356807	+	0.0316104i
$661$	−5.93095	−	24.0628i	−0.230687	−	0.935935i	−0.966069	−	0.258282i	$-0.916844\pi$
$661$	−5.93095	−	24.0628i	−0.230687	−	0.935935i	0.735382	−	0.677653i	$-0.237003\pi$
$662$	−40.4142	−	35.8038i	−1.57074	−	1.39156i
$663$	3.21484	−	1.54921i	0.124854	−	0.0601664i
$664$	0.256380	−	0.227133i	0.00994946	−	0.00881446i
$665$	1.70112	+	1.17420i	0.0659665	+	0.0455334i
$666$	−15.4601	−	3.81057i	−0.599066	−	0.147656i
$667$	−29.1438	−	42.2221i	−1.12845	−	1.63485i
$668$	10.0461	+	40.7587i	0.388696	+	1.57700i
$669$	1.24658	+	5.05758i	0.0481957	+	0.195537i
$670$	−13.5477	+	1.64498i	−0.523392	+	0.0635513i
$671$	13.0887	+	14.7741i	0.505283	+	0.570347i
$672$	1.46909	−	3.87367i	0.0566714	−	0.149430i
$673$	−30.0871	−	15.7909i	−1.15977	−	0.608696i	−0.228689	−	0.973499i	$-0.573444\pi$
$673$	−30.0871	−	15.7909i	−1.15977	−	0.608696i	−0.931085	+	0.364803i	$0.881136\pi$
$674$	−16.3824	+	11.3080i	−0.631027	+	0.435567i
$675$	−6.52526			−0.251157
$676$	−20.8142	−	12.8143i	−0.800548	−	0.492859i
$677$	1.49123			0.0573127			0.0286564	−	0.999589i	$-0.490877\pi$
$677$	1.49123			0.0573127			0.0286564	+	0.999589i	$0.490877\pi$
$678$	7.99681	−	5.51980i	0.307116	−	0.211987i
$679$	32.6555	+	17.1389i	1.25320	+	0.657731i
$680$	0.235228	−	0.620245i	0.00902057	−	0.0237853i
$681$	−3.14183	−	3.54639i	−0.120395	−	0.135898i
$682$	−40.5171	+	4.91967i	−1.55148	+	0.188384i
$683$	2.37094	+	9.61930i	0.0907217	+	0.368072i	0.998702	−	0.0509413i	$-0.0162221\pi$
$683$	2.37094	+	9.61930i	0.0907217	+	0.368072i	−0.907980	+	0.419014i	$0.862376\pi$
$684$	−1.82526	−	7.40536i	−0.0697904	−	0.283151i
$685$	1.14619	+	1.66054i	0.0437936	+	0.0634460i
$686$	−38.5598	−	9.50413i	−1.47222	−	0.362869i
$687$	0.465349	+	0.321207i	0.0177542	+	0.0122548i
$688$	−6.26231	+	5.54792i	−0.238748	+	0.211512i
$689$	−20.5861	+	27.7409i	−0.784268	+	1.05684i
$690$	−1.68876	−	1.49611i	−0.0642898	−	0.0569558i
$691$	−2.14754	−	8.71291i	−0.0816962	−	0.331455i	0.915845	−	0.401531i	$-0.131522\pi$
$691$	−2.14754	−	8.71291i	−0.0816962	−	0.331455i	−0.997542	+	0.0700764i	$0.977676\pi$
$692$	12.8644	+	11.3968i	0.489030	+	0.433243i
$693$	−24.1627	+	5.95557i	−0.917865	+	0.226233i
$694$	−59.3090	−	22.4930i	−2.25134	−	0.853821i
$695$			7.15736i			0.271494i
$696$	−0.401468	+	0.152257i	−0.0152176	+	0.00577128i
$697$	−11.4033	+	46.2651i	−0.431931	+	1.75241i
$698$	−4.78078			−0.180955
$699$	1.96327			0.0742578
$700$	−4.42598	+	17.9569i	−0.167286	+	0.678707i
$701$	−3.09636	+	25.5008i	−0.116948	+	0.963153i	0.809602	+	0.586980i	$0.199683\pi$
$701$	−3.09636	+	25.5008i	−0.116948	+	0.963153i	−0.926549	+	0.376173i	$0.877240\pi$
$702$	10.1195	+	1.58218i	0.381934	+	0.0597154i
$703$	0.456927	+	3.76313i	0.0172333	+	0.141929i
$704$	27.1038	+	3.29100i	1.02151	+	0.124034i
$705$	0.0509674	+	0.0738391i	0.00191954	+	0.00278094i
$706$	−2.67557	−	2.37035i	−0.100696	−	0.0892092i
$707$	11.6830	−	1.41857i	0.439383	−	0.0533508i
$708$	−4.18967	−	0.508718i	−0.157457	−	0.0191188i
$709$	5.00072	+	9.52808i	0.187806	+	0.357835i	0.961094	−	0.276220i	$-0.0890818\pi$
$709$	5.00072	+	9.52808i	0.187806	+	0.357835i	−0.773288	+	0.634054i	$0.781390\pi$
$710$	5.93672	−	6.70117i	0.222801	−	0.251490i
$711$	−12.8814	+	18.6620i	−0.483092	+	0.699879i
$712$	0.659857	−	0.162640i	0.0247292	−	0.00609519i
$713$	36.1701	−	4.39184i	1.35458	−	0.164476i
$714$	2.40767	+	3.48811i	0.0901048	+	0.130539i
$715$	−7.01760	−	6.65983i	−0.262443	−	0.249064i
$716$	0.441491	−	0.639609i	0.0164993	−	0.0239033i
$717$	1.32127	−	2.51747i	0.0493437	−	0.0940165i
$718$	−15.7190	−	41.4476i	−0.586628	−	1.54681i
$719$	0.212595	−	1.75087i	0.00792844	−	0.0652966i	−0.988208	−	0.153120i	$-0.951068\pi$
$719$	0.212595	−	1.75087i	0.00792844	−	0.0652966i	0.996136	+	0.0878232i	$0.0279911\pi$
$720$	7.05036	−	4.86651i	0.262751	−	0.181364i
$721$	0.574354	−	2.33024i	0.0213901	−	0.0867828i
$722$	27.7176	−	19.1321i	1.03154	−	0.712022i
$723$	5.84020	−	2.21490i	0.217199	−	0.0823729i
$724$	12.5997	+	33.2227i	0.468264	+	1.23471i
$725$	30.0308	−	15.7614i	1.11532	−	0.585363i
$726$	0.922150	+	1.75701i	0.0342242	+	0.0652087i
$727$	25.1108	+	6.18925i	0.931308	+	0.229547i	0.675652	−	0.737221i	$-0.263862\pi$
$727$	25.1108	+	6.18925i	0.931308	+	0.229547i	0.255656	+	0.966768i	$0.417709\pi$
$728$	−0.714774	+	1.70601i	−0.0264913	+	0.0632290i
$729$	23.1765	−	5.71249i	0.858388	−	0.211574i
$730$	−2.23264	−	2.52013i	−0.0826339	−	0.0932744i
$731$	−0.973189	−	8.01493i	−0.0359947	−	0.296443i
$732$	2.04930	−	1.07555i	0.0757442	−	0.0397536i
$733$	8.80957	−	16.7852i	0.325389	−	0.619977i	−0.666727	−	0.745302i	$-0.732305\pi$
$733$	8.80957	−	16.7852i	0.325389	−	0.619977i	0.992116	+	0.125325i	$0.0399975\pi$
$734$	46.3124	+	17.5640i	1.70942	+	0.648298i
$735$	0.252355	+	0.284850i	0.00930825	+	0.0105068i
$736$	−53.3447	−	6.47722i	−1.96631	−	0.238753i
$737$	−37.9799	−	9.36120i	−1.39901	−	0.344824i
$738$	−50.6754	+	44.8945i	−1.86539	+	1.65259i
$739$	24.2224	−	27.3415i	0.891036	−	1.00577i	−0.108895	−	0.994053i	$-0.534731\pi$
$739$	24.2224	−	27.3415i	0.891036	−	1.00577i	0.999931	−	0.0117184i	$-0.00373017\pi$
$740$	3.15440	−	1.65555i	0.115958	−	0.0608594i
$741$	−0.248563	−	1.18126i	−0.00913120	−	0.0433945i
$742$	−36.3283	−	19.0666i	−1.33365	−	0.699956i
$743$	−40.6684	+	15.4235i	−1.49198	+	0.565833i	−0.959772	−	0.280781i	$-0.909406\pi$
$743$	−40.6684	+	15.4235i	−1.49198	+	0.565833i	−0.532207	+	0.846614i	$0.678637\pi$
$744$	0.0367562	−	0.302714i	0.00134755	−	0.0110980i
$745$	2.24334	+	1.17740i	0.0821897	+	0.0431365i
$746$			12.0560i			0.441402i
$747$	−1.98380	+	3.77981i	−0.0725834	+	0.138296i
$748$	−19.7878	+	22.3358i	−0.723513	+	0.816678i
$749$	−13.4027	−	9.25124i	−0.489725	−	0.338033i
$750$	2.35005	−	2.08196i	0.0858117	−	0.0760225i
$751$	27.8237	−	40.3095i	1.01530	−	1.47092i	0.138321	−	0.990387i	$-0.455829\pi$
$751$	27.8237	−	40.3095i	1.01530	−	1.47092i	0.876979	−	0.480529i	$-0.159555\pi$
$752$	2.11821	+	0.803329i	0.0772430	+	0.0292944i
$753$	−2.36626	+	6.23932i	−0.0862314	+	0.227374i
$754$	−50.3938	+	17.1614i	−1.83523	+	0.624981i
$755$	−0.184193	−	0.485676i	−0.00670345	−	0.0176756i
$756$			5.89450i			0.214381i
$757$	−4.91150	+	12.9506i	−0.178512	+	0.470697i	−0.994168	−	0.107840i	$-0.965607\pi$
$757$	−4.91150	+	12.9506i	−0.178512	+	0.470697i	0.815657	+	0.578536i	$0.196376\pi$
$758$	5.02295	+	41.3677i	0.182442	+	1.50254i
$759$	−3.00525	−	5.72603i	−0.109084	−	0.207842i
$760$	−0.184665	−	0.127465i	−0.00669849	−	0.00462363i
$761$	−27.1955	−	18.7717i	−0.985837	−	0.680474i	−0.0380160	−	0.999277i	$-0.512104\pi$
$761$	−27.1955	−	18.7717i	−0.985837	−	0.680474i	−0.947821	+	0.318803i	$0.896719\pi$
$762$	2.84160	+	5.41422i	0.102940	+	0.196137i
$763$	0.995368	+	8.19760i	0.0360348	+	0.296773i
$764$	−1.78137	+	4.69707i	−0.0644475	+	0.169934i
$765$			8.26726i			0.298903i
$766$	5.83813	+	15.3939i	0.210940	+	0.556204i
$767$	32.9415

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)

\(f(q)\)	\(=\)	\(q+(1.62113 - 1.11899i) q^{2} +(0.214934 + 0.112806i) q^{3} +(0.666728 - 1.75802i) q^{4} +(0.457146 + 0.516011i) q^{5} +(0.474664 - 0.0576347i) q^{6} +(-0.520249 - 2.11073i) q^{7} +(0.0564755 + 0.229130i) q^{8} +(-1.67072 - 2.42046i) q^{9} +O(q^{10})\)	\(q+(1.62113 - 1.11899i) q^{2} +(0.214934 + 0.112806i) q^{3} +(0.666728 - 1.75802i) q^{4} +(0.457146 + 0.516011i) q^{5} +(0.474664 - 0.0576347i) q^{6} +(-0.520249 - 2.11073i) q^{7} +(0.0564755 + 0.229130i) q^{8} +(-1.67072 - 2.42046i) q^{9} +(1.31850 + 0.324982i) q^{10} +(3.20329 + 2.21107i) q^{11} +(0.341617 - 0.302646i) q^{12} +(-2.77912 + 2.29707i) q^{13} +(-3.20527 - 2.83962i) q^{14} +(0.0400470 + 0.162477i) q^{15} +(3.16265 + 2.80186i) q^{16} +(-3.95902 + 0.975810i) q^{17} +(-5.41692 - 2.05437i) q^{18} +1.37925i q^{19} +(1.21195 - 0.459631i) q^{20} +(0.126284 - 0.512355i) q^{21} +7.66712 q^{22} -6.84453 q^{23} +(-0.0137087 + 0.0556186i) q^{24} +(0.545398 - 4.49176i) q^{25} +(-1.93493 + 6.83364i) q^{26} +(-0.173829 - 1.43161i) q^{27} +(-4.05757 - 0.492678i) q^{28} +(4.25797 + 6.16874i) q^{29} +(0.246731 + 0.218584i) q^{30} +(-5.28453 + 0.641658i) q^{31} +(7.79377 + 0.946335i) q^{32} +(0.439074 + 0.836585i) q^{33} +(-5.32617 + 6.01200i) q^{34} +(0.851331 - 1.23337i) q^{35} +(-5.36912 + 1.32337i) q^{36} +(2.72839 - 0.331287i) q^{37} +(1.54336 + 2.23594i) q^{38} +(-0.856449 + 0.180216i) q^{39} +(-0.0924161 + 0.133888i) q^{40} +(5.43075 - 10.3474i) q^{41} +(-0.368595 - 0.971905i) q^{42} +(-0.238673 + 1.96565i) q^{43} +(6.02283 - 4.15726i) q^{44} +(0.485220 - 1.96861i) q^{45} +(-11.0959 + 7.65893i) q^{46} +(0.501321 - 0.190126i) q^{47} +(0.363693 + 0.958980i) q^{48} +(2.01366 - 1.05685i) q^{49} +(-4.14206 - 7.89203i) q^{50} +(-0.961004 - 0.236866i) q^{51} +(2.18537 + 6.41725i) q^{52} +(9.30260 - 2.29289i) q^{53} +(-1.88375 - 2.12632i) q^{54} +(0.323434 + 2.66372i) q^{55} +(0.454251 - 0.238409i) q^{56} +(-0.155587 + 0.296447i) q^{57} +(13.8055 + 5.23572i) q^{58} +(-6.13211 - 6.92173i) q^{59} +(0.312338 + 0.0379246i) q^{60} +(4.92368 + 1.21358i) q^{61} +(-7.84891 + 6.95353i) q^{62} +(-4.23975 + 4.78569i) q^{63} +(6.21112 - 3.25985i) q^{64} +(-2.45577 - 0.383960i) q^{65} +(1.64792 + 0.864897i) q^{66} +(-9.39667 + 3.56369i) q^{67} +(-0.924096 + 7.61062i) q^{68} +(-1.47112 - 0.772103i) q^{69} -2.95208i q^{70} +(3.06379 - 5.83757i) q^{71} +(0.460245 - 0.519510i) q^{72} +(-2.04047 - 1.40843i) q^{73} +(4.05238 - 3.59009i) q^{74} +(0.623922 - 0.903907i) q^{75} +(2.42474 + 0.919583i) q^{76} +(3.00048 - 7.91160i) q^{77} +(-1.18676 + 1.25051i) q^{78} +(-2.73404 - 7.20907i) q^{79} +2.91282i q^{80} +(-3.00463 + 7.92256i) q^{81} +(-2.77467 - 22.8515i) q^{82} +(-0.674514 - 1.28518i) q^{83} +(-0.816531 - 0.563611i) q^{84} +(-2.31338 - 1.59681i) q^{85} +(1.81261 + 3.45365i) q^{86} +(0.219312 + 1.80620i) q^{87} +(-0.325716 + 0.858843i) q^{88} -2.87983i q^{89} +(-1.41625 - 3.73434i) q^{90} +(6.29432 + 4.67092i) q^{91} +(-4.56343 + 12.0328i) q^{92} +(-1.20821 - 0.458212i) q^{93} +(0.599959 - 0.869190i) q^{94} +(-0.711707 + 0.630517i) q^{95} +(1.56839 + 1.08258i) q^{96} +(-11.2498 + 12.6983i) q^{97} +(2.08181 - 3.96655i) q^{98} -11.4475i 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