LMFDB - Embedded newform 169.2.g.a.14.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(14,169)]

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([18]))

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

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

chi := DirichletCharacter("169.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.g (of order $13$, 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:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			14.7
Character	$\chi$	$=$	169.14
Dual form			169.2.g.a.157.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0917982 + 0.132993i) q^{2} +(-0.752776 + 0.395087i) q^{3} +(0.699950 + 1.84562i) q^{4} +(1.16867 + 1.03535i) q^{5} +(0.0165598 - 0.136382i) q^{6} +(-2.31458 - 0.570492i) q^{7} +(-0.623512 - 0.153682i) q^{8} +(-1.29362 + 1.87413i) q^{9} +O(q^{10})$	\(q+(-0.0917982 + 0.132993i) q^{2} +(-0.752776 + 0.395087i) q^{3} +(0.699950 + 1.84562i) q^{4} +(1.16867 + 1.03535i) q^{5} +(0.0165598 - 0.136382i) q^{6} +(-2.31458 - 0.570492i) q^{7} +(-0.623512 - 0.153682i) q^{8} +(-1.29362 + 1.87413i) q^{9} +(-0.244976 + 0.0603811i) q^{10} +(-0.0306707 - 0.0444342i) q^{11} +(-1.25608 - 1.11279i) q^{12} +(3.36948 + 1.28319i) q^{13} +(0.288345 - 0.255451i) q^{14} +(-1.28880 - 0.317661i) q^{15} +(-2.87727 + 2.54904i) q^{16} +(4.46417 + 1.10032i) q^{17} +(-0.130493 - 0.344083i) q^{18} -1.36974 q^{19} +(-1.09285 + 2.88161i) q^{20} +(1.96775 - 0.485007i) q^{21} +0.00872495 q^{22} +4.45818 q^{23} +(0.530083 - 0.130654i) q^{24} +(-0.308847 - 2.54358i) q^{25} +(-0.479968 + 0.330322i) q^{26} +(0.540785 - 4.45376i) q^{27} +(-0.567178 - 4.67113i) q^{28} +(-0.470864 + 0.682164i) q^{29} +(0.160556 - 0.142240i) q^{30} +(0.799878 - 6.58759i) q^{31} +(-0.229686 - 1.89163i) q^{32} +(0.0406436 + 0.0213314i) q^{33} +(-0.556137 + 0.492694i) q^{34} +(-2.11431 - 3.06311i) q^{35} +(-4.36438 - 1.07572i) q^{36} +(0.430050 - 3.54178i) q^{37} +(0.125740 - 0.182165i) q^{38} +(-3.04344 + 0.365284i) q^{39} +(-0.569565 - 0.825157i) q^{40} +(1.52303 - 0.799348i) q^{41} +(-0.116134 + 0.306219i) q^{42} +(0.462084 + 3.80560i) q^{43} +(0.0605405 - 0.0877081i) q^{44} +(-3.45219 + 0.850888i) q^{45} +(-0.409253 + 0.592905i) q^{46} +(1.57797 - 4.16077i) q^{47} +(1.15885 - 3.05563i) q^{48} +(-1.16640 - 0.612171i) q^{49} +(0.366629 + 0.192422i) q^{50} +(-3.79524 + 0.935443i) q^{51} +(-0.00981156 + 7.11694i) q^{52} +(13.0840 + 3.22491i) q^{53} +(0.542675 + 0.480768i) q^{54} +(0.0101611 - 0.0836838i) q^{55} +(1.35549 + 0.711417i) q^{56} +(1.03111 - 0.541167i) q^{57} +(-0.0474983 - 0.125243i) q^{58} +(6.73868 + 5.96995i) q^{59} +(-0.315816 - 2.60098i) q^{60} +(-10.2084 + 2.51616i) q^{61} +(0.802674 + 0.711107i) q^{62} +(4.06335 - 3.59981i) q^{63} +(-6.53472 - 3.42969i) q^{64} +(2.60926 + 4.98822i) q^{65} +(-0.00656793 + 0.00344712i) q^{66} +(3.90570 - 10.2985i) q^{67} +(1.09393 + 9.00931i) q^{68} +(-3.35601 + 1.76137i) q^{69} +0.601462 q^{70} +(-7.61139 + 3.99477i) q^{71} +(1.09461 - 0.969736i) q^{72} +(1.95987 + 2.83936i) q^{73} +(0.431553 + 0.382323i) q^{74} +(1.23743 + 1.79273i) q^{75} +(-0.958749 - 2.52801i) q^{76} +(0.0456404 + 0.120344i) q^{77} +(0.230802 - 0.438288i) q^{78} +(-0.301779 + 0.795725i) q^{79} -6.00173 q^{80} +(-1.07002 - 2.82141i) q^{81} +(-0.0335040 + 0.275931i) q^{82} +(-5.58265 - 2.93000i) q^{83} +(2.27246 + 3.29223i) q^{84} +(4.07792 + 5.90789i) q^{85} +(-0.548536 - 0.287894i) q^{86} +(0.0849406 - 0.699549i) q^{87} +(0.0122948 + 0.0324188i) q^{88} +8.99614 q^{89} +(0.203743 - 0.537226i) q^{90} +(-7.06687 - 4.89231i) q^{91} +(3.12050 + 8.22808i) q^{92} +(2.00054 + 5.27500i) q^{93} +(0.408497 + 0.591809i) q^{94} +(-1.60077 - 1.41816i) q^{95} +(0.920263 + 1.33323i) q^{96} +(-11.2311 + 9.94984i) q^{97} +(0.188487 - 0.0989258i) q^{98} +0.122952 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) $ 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{13}\right)$

Coefficient data

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

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

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

$2$	−0.0917982	+	0.132993i	−0.0649111	+	0.0940400i	−0.854095	−	0.520117i	$-0.825888\pi$
$2$	−0.0917982	+	0.132993i	−0.0649111	+	0.0940400i	0.789184	+	0.614157i	$0.210504\pi$
$3$	−0.752776	+	0.395087i	−0.434615	+	0.228104i	−0.667818	−	0.744324i	$-0.732772\pi$
$3$	−0.752776	+	0.395087i	−0.434615	+	0.228104i	0.233203	+	0.972428i	$0.425079\pi$
$4$	0.699950	+	1.84562i	0.349975	+	0.922808i
$5$	1.16867	+	1.03535i	0.522645	+	0.463023i	0.882719	−	0.469901i	$-0.155710\pi$
$5$	1.16867	+	1.03535i	0.522645	+	0.463023i	−0.360075	+	0.932923i	$0.617249\pi$
$6$	0.0165598	−	0.136382i	0.00676050	−	0.0556777i
$7$	−2.31458	−	0.570492i	−0.874827	−	0.215626i	−0.223759	−	0.974645i	$-0.571833\pi$
$7$	−2.31458	−	0.570492i	−0.874827	−	0.215626i	−0.651068	+	0.759019i	$0.725679\pi$
$8$	−0.623512	−	0.153682i	−0.220445	−	0.0543348i
$9$	−1.29362	+	1.87413i	−0.431205	+	0.624709i
$10$	−0.244976	+	0.0603811i	−0.0774681	+	0.0190942i
$11$	−0.0306707	−	0.0444342i	−0.00924757	−	0.0133974i	0.818333	−	0.574745i	$-0.194899\pi$
$11$	−0.0306707	−	0.0444342i	−0.00924757	−	0.0133974i	−0.827580	+	0.561347i	$0.810283\pi$
$12$	−1.25608	−	1.11279i	−0.362600	−	0.321236i
$13$	3.36948	+	1.28319i	0.934526	+	0.355894i
$13$	3.36948	+	1.28319i	0.934526	+	0.355894i
$14$	0.288345	−	0.255451i	0.0770635	−	0.0682723i
$15$	−1.28880	−	0.317661i	−0.332767	−	0.0820196i
$16$	−2.87727	+	2.54904i	−0.719318	+	0.637261i
$17$	4.46417	+	1.10032i	1.08272	+	0.266867i	0.740024	−	0.672580i	$-0.234814\pi$
$17$	4.46417	+	1.10032i	1.08272	+	0.266867i	0.342696	+	0.939446i	$0.388660\pi$
$18$	−0.130493	−	0.344083i	−0.0307576	−	0.0811011i
$19$	−1.36974			−0.314240			−0.157120	−	0.987580i	$-0.550221\pi$
$19$	−1.36974			−0.314240			−0.157120	+	0.987580i	$0.550221\pi$
$20$	−1.09285	+	2.88161i	−0.244368	+	0.644347i
$21$	1.96775	−	0.485007i	0.429398	−	0.105837i
$22$	0.00872495			0.00186016
$23$	4.45818			0.929594			0.464797	−	0.885417i	$-0.346127\pi$
$23$	4.45818			0.929594			0.464797	+	0.885417i	$0.346127\pi$
$24$	0.530083	−	0.130654i	0.108203	−	0.0266696i
$25$	−0.308847	−	2.54358i	−0.0617693	−	0.508716i
$26$	−0.479968	+	0.330322i	−0.0941294	+	0.0647814i
$27$	0.540785	−	4.45376i	0.104074	−	0.857127i
$28$	−0.567178	−	4.67113i	−0.107187	−	0.882761i
$29$	−0.470864	+	0.682164i	−0.0874372	+	0.126675i	−0.864262	−	0.503043i	$-0.832214\pi$
$29$	−0.470864	+	0.682164i	−0.0874372	+	0.126675i	0.776824	+	0.629717i	$0.216829\pi$
$30$	0.160556	−	0.142240i	0.0293134	−	0.0259694i
$31$	0.799878	−	6.58759i	0.143662	−	1.18317i	−0.725352	−	0.688378i	$-0.758323\pi$
$31$	0.799878	−	6.58759i	0.143662	−	1.18317i	0.869014	−	0.494787i	$-0.164754\pi$
$32$	−0.229686	−	1.89163i	−0.0406031	−	0.334397i
$33$	0.0406436	+	0.0213314i	0.00707514	+	0.00371332i
$34$	−0.556137	+	0.492694i	−0.0953767	+	0.0844964i
$35$	−2.11431	−	3.06311i	−0.357384	−	0.517760i
$36$	−4.36438	−	1.07572i	−0.727397	−	0.179287i
$37$	0.430050	−	3.54178i	0.0706998	−	0.582265i	−0.913709	−	0.406369i	$-0.866795\pi$
$37$	0.430050	−	3.54178i	0.0706998	−	0.582265i	0.984409	−	0.175896i	$-0.0562822\pi$
$38$	0.125740	−	0.182165i	0.0203977	−	0.0295511i
$39$	−3.04344	+	0.365284i	−0.487340	+	0.0584922i
$40$	−0.569565	−	0.825157i	−0.0900561	−	0.130469i
$41$	1.52303	−	0.799348i	0.237857	−	0.124837i	−0.341584	−	0.939851i	$-0.610963\pi$
$41$	1.52303	−	0.799348i	0.237857	−	0.124837i	0.579441	+	0.815014i	$0.303271\pi$
$42$	−0.116134	+	0.306219i	−0.0179198	+	0.0472506i
$43$	0.462084	+	3.80560i	0.0704671	+	0.580349i	0.984586	+	0.174902i	$0.0559609\pi$
$43$	0.462084	+	3.80560i	0.0704671	+	0.580349i	−0.914119	+	0.405447i	$0.867116\pi$
$44$	0.0605405	−	0.0877081i	0.00912683	−	0.0132225i
$45$	−3.45219	+	0.850888i	−0.514622	+	0.126843i
$46$	−0.409253	+	0.592905i	−0.0603410	+	0.0874191i
$47$	1.57797	−	4.16077i	0.230171	−	0.606910i	−0.769319	−	0.638865i	$-0.779404\pi$
$47$	1.57797	−	4.16077i	0.230171	−	0.606910i	0.999489	+	0.0319551i	$0.0101734\pi$
$48$	1.15885	−	3.05563i	0.167265	−	0.441043i
$49$	−1.16640	−	0.612171i	−0.166628	−	0.0874531i
$50$	0.366629	+	0.192422i	0.0518492	+	0.0272126i
$51$	−3.79524	+	0.935443i	−0.531440	+	0.130988i
$52$	−0.00981156	+	7.11694i	−0.00136062	+	0.986942i
$53$	13.0840	+	3.22491i	1.79722	+	0.442975i	0.989249	−	0.146244i	$-0.0467184\pi$
$53$	13.0840	+	3.22491i	1.79722	+	0.442975i	0.807973	+	0.589219i	$0.200565\pi$
$54$	0.542675	+	0.480768i	0.0738487	+	0.0654242i
$55$	0.0101611	−	0.0836838i	0.00137012	−	0.0112839i
$56$	1.35549	+	0.711417i	0.181135	+	0.0950671i
$57$	1.03111	−	0.541167i	0.136573	−	0.0716793i
$58$	−0.0474983	−	0.125243i	−0.00623684	−	0.0164452i
$59$	6.73868	+	5.96995i	0.877301	+	0.777221i	0.975971	−	0.217899i	$-0.0699203\pi$
$59$	6.73868	+	5.96995i	0.877301	+	0.777221i	−0.0986699	+	0.995120i	$0.531459\pi$
$60$	−0.315816	−	2.60098i	−0.0407716	−	0.335784i
$61$	−10.2084	+	2.51616i	−1.30706	+	0.322161i	−0.830518	−	0.556992i	$-0.811955\pi$
$61$	−10.2084	+	2.51616i	−1.30706	+	0.322161i	−0.476540	+	0.879153i	$0.658109\pi$
$62$	0.802674	+	0.711107i	0.101940	+	0.0903107i
$63$	4.06335	−	3.59981i	0.511933	−	0.453533i
$64$	−6.53472	−	3.42969i	−0.816841	−	0.428711i
$65$	2.60926	+	4.98822i	0.323638	+	0.618713i
$66$	−0.00656793	+	0.00344712i	−0.000808456	+	0.000424311i
$67$	3.90570	−	10.2985i	0.477157	−	1.25816i	−0.453168	−	0.891425i	$-0.649706\pi$
$67$	3.90570	−	10.2985i	0.477157	−	1.25816i	0.930325	−	0.366735i	$-0.119524\pi$
$68$	1.09393	+	9.00931i	0.132658	+	1.09254i
$69$	−3.35601	+	1.76137i	−0.404016	+	0.212044i
$70$	0.601462			0.0718884
$71$	−7.61139	+	3.99477i	−0.903306	+	0.474092i	−0.851374	−	0.524559i	$-0.824230\pi$
$71$	−7.61139	+	3.99477i	−0.903306	+	0.474092i	−0.0519320	+	0.998651i	$0.516538\pi$
$72$	1.09461	−	0.969736i	0.129000	−	0.114284i
$73$	1.95987	+	2.83936i	0.229385	+	0.332322i	0.920728	−	0.390205i	$-0.127596\pi$
$73$	1.95987	+	2.83936i	0.229385	+	0.332322i	−0.691343	+	0.722527i	$0.742980\pi$
$74$	0.431553	+	0.382323i	0.0501670	+	0.0444441i
$75$	1.23743	+	1.79273i	0.142886	+	0.207006i
$76$	−0.958749	−	2.52801i	−0.109976	−	0.289983i
$77$	0.0456404	+	0.120344i	0.00520120	+	0.0137144i
$78$	0.230802	−	0.438288i	0.0261332	−	0.0496263i
$79$	−0.301779	+	0.795725i	−0.0339528	+	0.0895261i	−0.950921	−	0.309435i	$-0.899860\pi$
$79$	−0.301779	+	0.795725i	−0.0339528	+	0.0895261i	0.916968	+	0.398961i	$0.130629\pi$
$80$	−6.00173			−0.671014
$81$	−1.07002	−	2.82141i	−0.118891	−	0.313490i
$82$	−0.0335040	+	0.275931i	−0.00369990	+	0.0304714i
$83$	−5.58265	−	2.93000i	−0.612776	−	0.321610i	0.129627	−	0.991563i	$-0.458622\pi$
$83$	−5.58265	−	2.93000i	−0.612776	−	0.321610i	−0.742403	+	0.669953i	$0.766314\pi$
$84$	2.27246	+	3.29223i	0.247946	+	0.359212i
$85$	4.07792	+	5.90789i	0.442313	+	0.640800i
$86$	−0.548536	−	0.287894i	−0.0591501	−	0.0310444i
$87$	0.0849406	−	0.699549i	0.00910659	−	0.0749995i
$88$	0.0122948	+	0.0324188i	0.00131063	+	0.00345586i
$89$	8.99614			0.953589			0.476794	−	0.879015i	$-0.341799\pi$
$89$	8.99614			0.953589			0.476794	+	0.879015i	$0.341799\pi$
$90$	0.203743	−	0.537226i	0.0214764	−	0.0566285i
$91$	−7.06687	−	4.89231i	−0.740809	−	0.512853i
$92$	3.12050	+	8.22808i	0.325335	+	0.857837i
$93$	2.00054	+	5.27500i	0.207447	+	0.546992i
$94$	0.408497	+	0.591809i	0.0421332	+	0.0610405i
$95$	−1.60077	−	1.41816i	−0.164236	−	0.145500i
$96$	0.920263	+	1.33323i	0.0939240	+	0.136072i
$97$	−11.2311	+	9.94984i	−1.14034	+	1.01025i	−0.140544	+	0.990074i	$0.544885\pi$
$97$	−11.2311	+	9.94984i	−1.14034	+	1.01025i	−0.999796	+	0.0201793i	$0.993576\pi$
$98$	0.188487	−	0.0989258i	0.0190401	−	0.00999301i
$99$	0.122952			0.0123571
$100$	4.47830	−	2.35039i	0.447830	−	0.235039i
$101$	2.30646	+	18.9954i	0.229502	+	1.89012i	0.418618	+	0.908163i	$0.362515\pi$
$101$	2.30646	+	18.9954i	0.229502	+	1.89012i	−0.189116	+	0.981955i	$0.560562\pi$
$102$	0.223989	−	0.590611i	0.0221783	−	0.0584792i
$103$	1.43496	−	0.753124i	0.141391	−	0.0742076i	−0.392544	−	0.919733i	$-0.628405\pi$
$103$	1.43496	−	0.753124i	0.141391	−	0.0742076i	0.533935	+	0.845526i	$0.320713\pi$
$104$	−1.90371	−	1.31792i	−0.186674	−	0.129232i
$105$	2.80180	+	1.47050i	0.273428	+	0.143506i
$106$	−1.62997	+	1.44403i	−0.158317	+	0.140257i
$107$	−4.03967	−	3.57883i	−0.390529	−	0.345979i	0.444897	−	0.895582i	$-0.353240\pi$
$107$	−4.03967	−	3.57883i	−0.390529	−	0.345979i	−0.835426	+	0.549603i	$0.814779\pi$
$108$	8.59846	−	2.11933i	0.827387	−	0.203933i
$109$	−0.747290	−	6.15449i	−0.0715774	−	0.589493i	−0.983731	−	0.179645i	$-0.942505\pi$
$109$	−0.747290	−	6.15449i	−0.0715774	−	0.589493i	0.912154	−	0.409848i	$-0.134418\pi$
$110$	0.0101966	+	0.00903337i	0.000972205	+	0.000861298i
$111$	1.07558	+	2.83608i	0.102090	+	0.269188i
$112$	8.11387	−	4.25849i	0.766689	−	0.402389i
$113$	−12.0464	−	6.32244i	−1.13323	−	0.594765i	−0.209500	−	0.977809i	$-0.567184\pi$
$113$	−12.0464	−	6.32244i	−1.13323	−	0.594765i	−0.923730	+	0.383044i	$0.874876\pi$
$114$	−0.0226826	+	0.186808i	−0.00212442	+	0.0174962i
$115$	5.21013	+	4.61577i	0.485847	+	0.430423i
$116$	−1.58859	−	0.391553i	−0.147497	−	0.0363548i
$117$	−6.76368	+	4.65488i	−0.625303	+	0.430344i
$118$	−1.41256	+	0.348164i	−0.130037	+	0.0320511i
$119$	−9.70493	−	5.09354i	−0.889650	−	0.466924i
$120$	0.754764	+	0.396131i	0.0689002	+	0.0361616i
$121$	3.89962	−	10.2825i	0.354511	−	0.934768i
$122$	0.602487	−	1.58863i	0.0545466	−	0.143828i
$123$	−0.830689	+	1.20346i	−0.0749007	+	0.108512i
$124$	12.7180	−	3.13471i	1.14211	−	0.281506i
$125$	6.70723	−	9.71710i	0.599913	−	0.869124i
$126$	0.105741	+	0.870851i	0.00942011	+	0.0775816i
$127$	−6.19832	+	16.3436i	−0.550012	+	1.45026i	0.315283	+	0.948998i	$0.397901\pi$
$127$	−6.19832	+	16.3436i	−0.550012	+	1.45026i	−0.865294	+	0.501264i	$0.832869\pi$
$128$	4.43052	−	2.32532i	0.391607	−	0.205531i
$129$	−1.85139	−	2.68220i	−0.163006	−	0.236155i
$130$	−0.902922	−	0.110898i	−0.0791915	−	0.00972639i
$131$	−5.90425	+	8.55378i	−0.515856	+	0.747347i	−0.991188	−	0.132460i	$-0.957713\pi$
$131$	−5.90425	+	8.55378i	−0.515856	+	0.747347i	0.475332	+	0.879806i	$0.342328\pi$
$132$	−0.0109211	+	0.0899434i	−0.000950560	+	0.00782856i
$133$	3.17036	+	0.781425i	0.274905	+	0.0677581i
$134$	1.01109	+	1.46481i	0.0873446	+	0.126540i
$135$	5.24320	−	4.64507i	0.451263	−	0.399784i
$136$	−2.61437	−	1.37212i	−0.224180	−	0.117659i
$137$	0.179566	+	1.47886i	0.0153414	+	0.126348i	0.998367	−	0.0571185i	$-0.0181913\pi$
$137$	0.179566	+	1.47886i	0.0153414	+	0.126348i	−0.983026	+	0.183466i	$0.941268\pi$
$138$	0.0738264	−	0.608015i	0.00628452	−	0.0517577i
$139$	−4.29649	+	3.80636i	−0.364424	+	0.322851i	−0.825386	−	0.564568i	$-0.809043\pi$
$139$	−4.29649	+	3.80636i	−0.364424	+	0.322851i	0.460963	+	0.887420i	$0.347504\pi$
$140$	4.17341	−	6.04623i	0.352718	−	0.511000i
$141$	0.456008	+	3.75556i	0.0384028	+	0.316275i
$142$	0.167438	−	1.37897i	0.0140510	−	0.115721i
$143$	−0.0463268	−	0.189077i	−0.00387405	−	0.0158114i
$144$	−1.05514	−	8.68986i	−0.0879283	−	0.724155i
$145$	−1.25656	+	0.309715i	−0.104352	+	0.0257204i
$146$	−0.557527			−0.0461412
$147$	1.11990			0.0923674
$148$	6.83778	−	1.68536i	0.562062	−	0.138536i
$149$	6.65099	−	17.5372i	0.544871	−	1.43671i	−0.326083	−	0.945341i	$-0.605729\pi$
$149$	6.65099	−	17.5372i	0.544871	−	1.43671i	0.870954	−	0.491365i	$-0.163502\pi$
$150$	−0.352013			−0.0287418
$151$	−4.77645	−	12.5945i	−0.388702	−	1.02492i	−0.976424	−	0.215861i	$-0.930744\pi$
$151$	−4.77645	−	12.5945i	−0.388702	−	1.02492i	0.587722	−	0.809063i	$-0.300025\pi$
$152$	0.854049	+	0.210504i	0.0692726	+	0.0170742i
$153$	−7.83706	+	6.94303i	−0.633589	+	0.561311i
$154$	−0.0201945	−	0.00497751i	−0.00162732	−	0.000401099i
$155$	7.75525	−	6.87056i	0.622917	−	0.551856i
$156$	−2.80443	−	5.36134i	−0.224534	−	0.429251i
$157$	−4.42663	−	3.92165i	−0.353283	−	0.312982i	0.467751	−	0.883860i	$-0.345064\pi$
$157$	−4.42663	−	3.92165i	−0.353283	−	0.312982i	−0.821035	+	0.570879i	$0.806603\pi$
$158$	−0.0781229	−	0.113181i	−0.00621512	−	0.00900416i
$159$	−11.1234	+	2.74168i	−0.882145	+	0.217429i
$160$	1.69008	−	2.44850i	0.133612	−	0.193571i
$161$	−10.3188	−	2.54335i	−0.813234	−	0.200444i
$162$	0.473453	+	0.116696i	0.0371980	+	0.00916847i
$163$	1.75888	−	14.4857i	0.137766	−	1.13461i	−0.745757	−	0.666219i	$-0.767912\pi$
$163$	1.75888	−	14.4857i	0.137766	−	1.13461i	0.883523	−	0.468388i	$-0.155165\pi$
$164$	2.54133	+	2.25143i	0.198445	+	0.175807i
$165$	0.0254134	+	0.0670097i	0.00197843	+	0.00521670i
$166$	0.902147	−	0.473483i	0.0700202	−	0.0367494i
$167$	−4.02279	+	5.82802i	−0.311293	+	0.450986i	−0.947136	−	0.320833i	$-0.896037\pi$
$167$	−4.02279	+	5.82802i	−0.311293	+	0.450986i	0.635843	+	0.771819i	$0.280653\pi$
$168$	−1.30145			−0.100409
$169$	9.70683	+	8.64739i	0.746680	+	0.665184i
$170$	−1.16005			−0.0889719
$171$	1.77192	−	2.56707i	0.135502	−	0.196308i
$172$	−6.70024	+	3.51656i	−0.510889	+	0.268135i
$173$	−0.658423	−	1.73612i	−0.0500589	−	0.131995i	0.907655	−	0.419718i	$-0.137871\pi$
$173$	−0.658423	−	1.73612i	−0.0500589	−	0.131995i	−0.957714	+	0.287723i	$0.907102\pi$
$174$	0.0852375	+	0.0755138i	0.00646184	+	0.00572469i
$175$	−0.736243	+	6.06350i	−0.0556547	+	0.458358i
$176$	0.201513	+	0.0496685i	0.0151896	+	0.00374390i
$177$	−7.43137	−	1.83167i	−0.558576	−	0.137677i
$178$	−0.825829	+	1.19642i	−0.0618985	+	0.0896755i
$179$	11.1583	−	2.75029i	0.834014	−	0.205566i	0.200887	−	0.979614i	$-0.435617\pi$
$179$	11.1583	−	2.75029i	0.834014	−	0.205566i	0.633126	+	0.774048i	$0.281771\pi$
$180$	−3.98677	−	5.77583i	−0.297156	−	0.430505i
$181$	−5.99868	−	5.31436i	−0.445878	−	0.395013i	0.410088	−	0.912046i	$-0.365498\pi$
$181$	−5.99868	−	5.31436i	−0.445878	−	0.395013i	−0.855966	+	0.517033i	$0.827037\pi$
$182$	1.29937	−	0.490737i	0.0963155	−	0.0363758i
$183$	6.69057	−	5.92733i	0.494581	−	0.438161i
$184$	−2.77973	−	0.685141i	−0.204924	−	0.0505093i
$185$	4.16957	−	3.69392i	0.306553	−	0.271582i
$186$	−0.885183	−	0.218178i	−0.0649048	−	0.0159976i
$187$	−0.0880275	−	0.232110i	−0.00643721	−	0.0169735i
$188$	8.78367			0.640615
$189$	−3.79252	+	10.0001i	−0.275865	+	0.727397i
$190$	0.335553	−	0.0827064i	0.0243436	−	0.00600015i
$191$	3.77412			0.273086			0.136543	−	0.990634i	$-0.456401\pi$
$191$	3.77412			0.273086			0.136543	+	0.990634i	$0.456401\pi$
$192$	6.27421			0.452802
$193$	13.9817	−	3.44618i	1.00643	−	0.248062i	0.298546	−	0.954395i	$-0.403498\pi$
$193$	13.9817	−	3.44618i	1.00643	−	0.248062i	0.707879	+	0.706334i	$0.249652\pi$
$194$	−0.292266	−	2.40703i	−0.0209835	−	0.172814i
$195$	−3.93497	−	2.72413i	−0.281789	−	0.195079i
$196$	0.313415	−	2.58121i	0.0223868	−	0.184372i
$197$	−2.20689	−	18.1754i	−0.157235	−	1.29494i	−0.831114	−	0.556102i	$-0.812296\pi$
$197$	−2.20689	−	18.1754i	−0.157235	−	1.29494i	0.673880	−	0.738841i	$-0.264627\pi$
$198$	−0.0112867	+	0.0163517i	−0.000802113	+	0.00116206i
$199$	−5.70791	+	5.05677i	−0.404623	+	0.358465i	−0.840753	−	0.541419i	$-0.817887\pi$
$199$	−5.70791	+	5.05677i	−0.404623	+	0.358465i	0.436130	+	0.899884i	$0.356349\pi$
$200$	−0.198333	+	1.63342i	−0.0140243	+	0.115500i
$201$	1.12868	+	9.29554i	0.0796112	+	0.655657i
$202$	−2.73798	−	1.43700i	−0.192644	−	0.101107i
$203$	1.47902	−	1.31030i	0.103807	−	0.0919647i
$204$	−4.38295	−	6.34979i	−0.306868	−	0.444575i
$205$	2.60752	+	0.642697i	0.182117	+	0.0448879i
$206$	−0.0315666	+	0.259974i	−0.00219935	+	0.0181133i
$207$	−5.76717	+	8.35519i	−0.400846	+	0.580726i
$208$	−12.9658	+	4.89686i	−0.899019	+	0.339536i
$209$	0.0420109	+	0.0608633i	0.00290596	+	0.00421000i
$210$	−0.452766	+	0.237630i	−0.0312438	+	0.0163980i
$211$	−0.331621	+	0.874412i	−0.0228297	+	0.0601970i	−0.945947	−	0.324323i	$-0.894864\pi$
$211$	−0.331621	+	0.874412i	−0.0228297	+	0.0601970i	0.923117	+	0.384520i	$0.125633\pi$
$212$	3.20618	+	26.4053i	0.220201	+	1.81352i
$213$	4.15139	−	6.01433i	0.284449	−	0.412095i
$214$	0.846792	−	0.208716i	0.0578855	−	0.0142675i
$215$	−3.40011	+	4.92591i	−0.231885	+	0.335944i
$216$	−1.02165	+	2.69387i	−0.0695144	+	0.183294i
$217$	−5.60954	+	14.7911i	−0.380800	+	1.00409i
$218$	0.887102	+	0.465587i	0.0600821	+	0.0315335i
$219$	−2.59714	−	1.36308i	−0.175498	−	0.0921086i
$220$	0.161560	−	0.0398211i	0.0108924	−	0.00268474i
$221$	13.6300	+	9.43589i	0.916855	+	0.634727i
$222$	−0.475914	−	0.117302i	−0.0319412	−	0.00787281i
$223$	13.0904	+	11.5971i	0.876599	+	0.776599i	0.975845	−	0.218464i	$-0.0701045\pi$
$223$	13.0904	+	11.5971i	0.876599	+	0.776599i	−0.0992456	+	0.995063i	$0.531643\pi$
$224$	−0.547536	+	4.50936i	−0.0365838	+	0.301295i
$225$	5.16652	+	2.71160i	0.344435	+	0.180773i
$226$	1.94668	−	1.02169i	0.129491	−	0.0679621i
$227$	−9.17337	−	24.1882i	−0.608858	−	1.60543i	−0.783915	−	0.620869i	$-0.786780\pi$
$227$	−9.17337	−	24.1882i	−0.608858	−	1.60543i	0.175056	−	0.984558i	$-0.443989\pi$
$228$	1.72051	+	1.52424i	0.113943	+	0.100945i
$229$	2.30280	+	18.9653i	0.152173	+	1.25326i	0.846025	+	0.533143i	$0.178989\pi$
$229$	2.30280	+	18.9653i	0.152173	+	1.25326i	−0.693852	+	0.720118i	$0.744088\pi$
$230$	−1.09215	+	0.269190i	−0.0720139	+	0.0177498i
$231$	−0.0819033	−	0.0725600i	−0.00538884	−	0.00477410i
$232$	0.398426	−	0.352974i	0.0261579	−	0.0231739i
$233$	12.1164	+	6.35919i	0.793773	+	0.416604i	0.812311	−	0.583224i	$-0.198209\pi$
$233$	12.1164	+	6.35919i	0.793773	+	0.416604i	−0.0185383	+	0.999828i	$0.505901\pi$
$234$	0.00182920	−	1.32683i	0.000119578	−	0.0867376i
$235$	6.15197	−	3.22881i	0.401311	−	0.210624i
$236$	−6.30150	+	16.6157i	−0.410192	+	1.08159i
$237$	−0.0872091	−	0.718232i	−0.00566484	−	0.0466542i
$238$	1.56830	−	0.823107i	0.101658	−	0.0533541i
$239$	−26.1366			−1.69063			−0.845317	−	0.534266i	$-0.820588\pi$
$239$	−26.1366			−1.69063			−0.845317	+	0.534266i	$0.820588\pi$
$240$	4.51796	−	2.37121i	0.291633	−	0.153061i
$241$	−9.26340	+	8.20666i	−0.596708	+	0.528637i	−0.906521	−	0.422160i	$-0.861272\pi$
$241$	−9.26340	+	8.20666i	−0.596708	+	0.528637i	0.309813	+	0.950798i	$0.399734\pi$
$242$	1.00951	+	1.46253i	0.0648939	+	0.0940151i
$243$	11.9947	+	10.6264i	0.769461	+	0.681683i
$244$	−11.7893	−	17.0797i	−0.754730	−	1.09341i
$245$	−0.729318	−	1.92305i	−0.0465944	−	0.122859i
$246$	−0.0837957	−	0.220951i	−0.00534262	−	0.0140873i
$247$	−4.61531	−	1.75764i	−0.293665	−	0.111836i
$248$	−1.51113	+	3.98452i	−0.0959567	+	0.253017i
$249$	5.36010			0.339682
$250$	0.676591	+	1.78402i	0.0427914	+	0.112832i
$251$	1.56616	−	12.8985i	0.0988552	−	0.814146i	−0.855980	−	0.517009i	$-0.827045\pi$
$251$	1.56616	−	12.8985i	0.0988552	−	0.814146i	0.954835	−	0.297136i	$-0.0960316\pi$
$252$	9.48800	+	4.97969i	0.597688	+	0.313691i
$253$	−0.136736	−	0.198096i	−0.00859649	−	0.0124542i
$254$	−1.60459	−	2.32465i	−0.100681	−	0.145861i
$255$	−5.40389	−	2.83618i	−0.338405	−	0.177609i
$256$	1.68167	−	13.8498i	0.105105	−	0.865614i
$257$	−3.89528	−	10.2710i	−0.242981	−	0.640689i	0.756937	−	0.653488i	$-0.226695\pi$
$257$	−3.89528	−	10.2710i	−0.242981	−	0.640689i	−0.999918	+	0.0127994i	$0.995926\pi$
$258$	0.526668			0.0327889
$259$	−3.01594	+	7.95238i	−0.187401	+	0.494137i
$260$	−7.37999	+	8.30719i	−0.457688	+	0.515190i
$261$	−0.669345	−	1.76492i	−0.0414314	−	0.109246i
$262$	−0.595590	−	1.57044i	−0.0367957	−	0.0970223i
$263$	−5.50297	−	7.97243i	−0.339328	−	0.491601i	0.615756	−	0.787937i	$-0.288851\pi$
$263$	−5.50297	−	7.97243i	−0.339328	−	0.491601i	−0.955084	+	0.296336i	$0.904235\pi$
$264$	−0.0220635	−	0.0195466i	−0.00135792	−	0.00120301i
$265$	11.9519	+	17.3153i	0.734201	+	1.06367i
$266$	−0.394958	+	0.349902i	−0.0242164	+	0.0214539i
$267$	−6.77208	+	3.55426i	−0.414444	+	0.217517i
$268$	21.7408			1.32803
$269$	10.5935	−	5.55991i	0.645898	−	0.338994i	−0.109761	−	0.993958i	$-0.535009\pi$
$269$	10.5935	−	5.55991i	0.645898	−	0.338994i	0.755660	+	0.654964i	$0.227316\pi$
$270$	0.136444	+	1.12372i	0.00830371	+	0.0683872i
$271$	−10.7236	+	28.2758i	−0.651412	+	1.71763i	0.0440101	+	0.999031i	$0.485987\pi$
$271$	−10.7236	+	28.2758i	−0.651412	+	1.71763i	−0.695422	+	0.718601i	$0.744783\pi$
$272$	−15.6494	+	8.21344i	−0.948884	+	0.498013i
$273$	7.25266	+	0.890780i	0.438951	+	0.0539125i
$274$	−0.213162	−	0.111876i	−0.0128776	−	0.00675867i
$275$	−0.103550	+	0.0917369i	−0.00624427	+	0.00553194i
$276$	−5.59985	−	4.96103i	−0.337071	−	0.298619i
$277$	7.60689	−	1.87493i	0.457054	−	0.112654i	−0.00406554	−	0.999992i	$-0.501294\pi$
$277$	7.60689	−	1.87493i	0.457054	−	0.112654i	0.461119	+	0.887338i	$0.347448\pi$
$278$	−0.111808	−	0.920819i	−0.00670578	−	0.0552271i
$279$	11.3112	+	10.0209i	0.677186	+	0.599935i
$280$	0.847555	+	2.23482i	0.0506511	+	0.133556i
$281$	−11.3009	+	5.93117i	−0.674155	+	0.353824i	−0.766810	−	0.641874i	$-0.778157\pi$
$281$	−11.3009	+	5.93117i	−0.674155	+	0.353824i	0.0926545	+	0.995698i	$0.470465\pi$
$282$	−0.541323	−	0.284108i	−0.0322353	−	0.0169184i
$283$	2.05934	−	16.9602i	0.122415	−	1.00818i	−0.793991	−	0.607929i	$-0.792000\pi$
$283$	2.05934	−	16.9602i	0.122415	−	1.00818i	0.916406	−	0.400250i	$-0.131077\pi$
$284$	−12.7004	−	11.2516i	−0.753630	−	0.667658i
$285$	1.76532	+	0.435112i	0.104569	+	0.0257738i
$286$	0.0293986	+	0.0111958i	0.00173837	+	0.000662021i
$287$	−3.98119	+	0.981275i	−0.235002	+	0.0579228i
$288$	3.84229	+	2.01659i	0.226409	+	0.118829i
$289$	3.66535	+	1.92373i	0.215609	+	0.113160i
$290$	0.0741604	−	0.195545i	0.00435485	−	0.0114828i
$291$	4.52341	−	11.9273i	0.265167	−	0.699188i
$292$	−3.86856	+	5.60457i	−0.226390	+	0.327983i
$293$	12.3170	−	3.03587i	0.719568	−	0.177358i	0.137505	−	0.990501i	$-0.456092\pi$
$293$	12.3170	−	3.03587i	0.719568	−	0.177358i	0.582063	+	0.813144i	$0.302246\pi$
$294$	−0.102804	+	0.148938i	−0.00599568	+	0.00868624i
$295$	1.69430	+	13.9538i	0.0986458	+	0.812421i
$296$	−0.812449	+	2.14225i	−0.0472227	+	0.124516i
$297$	−0.214486	+	0.112571i	−0.0124457	+	0.00653202i
$298$	1.72177	+	2.49442i	0.0997397	+	0.144498i
$299$	15.0218	+	5.72070i	0.868730	+	0.330837i
$300$	−2.44254	+	3.53864i	−0.141020	+	0.204303i
$301$	1.10154	−	9.07196i	0.0634915	−	0.522899i
$302$	2.11344	+	0.520917i	0.121615	+	0.0299754i
$303$	−9.24111	−	13.3881i	−0.530888	−	0.769124i
$304$	3.94112	−	3.49152i	0.226038	−	0.200253i
$305$	−14.5354	−	7.62876i	−0.832294	−	0.436822i
$306$	−0.203944	−	1.67963i	−0.0116587	−	0.0960180i
$307$	−1.82176	+	15.0035i	−0.103973	+	0.856297i	0.843647	+	0.536898i	$0.180404\pi$
$307$	−1.82176	+	15.0035i	−0.103973	+	0.856297i	−0.947620	+	0.319399i	$0.896519\pi$
$308$	−0.190162	+	0.168469i	−0.0108355	+	0.00959942i
$309$	−0.782653	+	1.13387i	−0.0445236	+	0.0645035i
$310$	0.201815	+	1.66210i	0.0114623	+	0.0944008i
$311$	−0.0137720	+	0.113423i	−0.000780941	+	0.00643162i	−0.993094	−	0.117320i	$-0.962570\pi$
$311$	−0.0137720	+	0.113423i	−0.000780941	+	0.00643162i	0.992313	+	0.123752i	$0.0394927\pi$
$312$	1.95376	+	0.239963i	0.110610	+	0.0135852i
$313$	−2.09109	−	17.2217i	−0.118195	−	0.973425i	−0.924304	−	0.381658i	$-0.875353\pi$
$313$	−2.09109	−	17.2217i	−0.118195	−	0.973425i	0.806109	−	0.591768i	$-0.201570\pi$
$314$	0.927907	−	0.228708i	0.0523648	−	0.0129068i
$315$	8.47577			0.477556
$316$	−1.67983			−0.0944980
$317$	−22.5402	+	5.55566i	−1.26598	+	0.312037i	−0.814459	−	0.580221i	$-0.802966\pi$
$317$	−22.5402	+	5.55566i	−1.26598	+	0.312037i	−0.451526	+	0.892258i	$0.649120\pi$
$318$	0.656487	−	1.73101i	0.0368140	−	0.0970705i
$319$	0.0447532			0.00250570
$320$	−4.08600	−	10.7739i	−0.228414	−	0.602279i
$321$	4.45491	+	1.09804i	0.248649	+	0.0612865i
$322$	1.28549	−	1.13885i	0.0716377	−	0.0634655i
$323$	−6.11475	−	1.50715i	−0.340234	−	0.0838601i
$324$	4.45828	−	3.94969i	0.247682	−	0.219427i
$325$	2.22325	−	8.96686i	0.123324	−	0.497392i
$326$	1.76503	+	1.56368i	0.0977559	+	0.0866042i
$327$	2.99410	+	4.33771i	0.165574	+	0.239876i
$328$	−1.07247	+	0.264341i	−0.0592174	+	0.0145958i
$329$	−6.02601	+	8.73019i	−0.332225	+	0.481311i
$330$	−0.0112447	−	0.00277157i	−0.000619001	−	0.000152570i
$331$	9.88931	+	2.43750i	0.543566	+	0.133977i	0.501532	−	0.865139i	$-0.332770\pi$
$331$	9.88931	+	2.43750i	0.543566	+	0.133977i	0.0420339	+	0.999116i	$0.486616\pi$
$332$	1.50008	−	12.3543i	0.0823277	−	0.678030i
$333$	6.08143	+	5.38767i	0.333260	+	0.295243i
$334$	−0.405799	−	1.07000i	−0.0222043	−	0.0585480i
$335$	15.2270	−	7.99175i	0.831940	−	0.436636i
$336$	−4.42545	+	6.41138i	−0.241428	+	0.349769i
$337$	6.89120			0.375388			0.187694	−	0.982228i	$-0.439899\pi$
$337$	6.89120			0.375388			0.187694	+	0.982228i	$0.439899\pi$
$338$	−2.04111	+	0.497123i	−0.111022	+	0.0270399i
$339$	11.5662			0.628188
$340$	−8.04935	+	11.6615i	−0.436537	+	0.632433i
$341$	−0.317247	+	0.166504i	−0.0171799	+	0.00901671i
$342$	0.178742	+	0.471304i	0.00966526	+	0.0254852i
$343$	14.8408	+	13.1478i	0.801328	+	0.709915i
$344$	0.296737	−	2.44385i	0.0159990	−	0.131764i
$345$	−5.74570	−	1.41619i	−0.309338	−	0.0762450i
$346$	0.291333	+	0.0718071i	0.0156622	+	0.00386038i
$347$	18.8509	−	27.3102i	1.01197	−	1.46609i	0.131887	−	0.991265i	$-0.457896\pi$
$347$	18.8509	−	27.3102i	1.01197	−	1.46609i	0.880081	−	0.474824i	$-0.157488\pi$
$348$	1.35055	−	0.332881i	0.0723972	−	0.0178443i
$349$	−20.9098	−	30.2930i	−1.11927	−	1.62155i	−0.700876	−	0.713283i	$-0.747207\pi$
$349$	−20.9098	−	30.2930i	−1.11927	−	1.62155i	−0.418397	−	0.908264i	$-0.637408\pi$
$350$	−0.738816	−	0.654534i	−0.0394914	−	0.0349863i
$351$	7.53720	−	14.3129i	0.402306	−	0.763969i
$352$	−0.0770087	+	0.0682237i	−0.00410458	+	0.00363634i
$353$	−14.4637	−	3.56499i	−0.769828	−	0.189745i	−0.165207	−	0.986259i	$-0.552829\pi$
$353$	−14.4637	−	3.56499i	−0.769828	−	0.189745i	−0.604621	+	0.796513i	$0.706675\pi$
$354$	0.925785	−	0.820174i	0.0492049	−	0.0435917i
$355$	−13.0312	−	3.21190i	−0.691623	−	0.170470i
$356$	6.29684	+	16.6034i	0.333732	+	0.879979i
$357$	9.31803			0.493163
$358$	−0.658548	+	1.73645i	−0.0348054	+	0.0917742i
$359$	−24.0252	+	5.92169i	−1.26800	+	0.312535i	−0.815254	−	0.579103i	$-0.803403\pi$
$359$	−24.0252	+	5.92169i	−1.26800	+	0.312535i	−0.452749	+	0.891638i	$0.649557\pi$
$360$	2.28325			0.120338
$361$	−17.1238			−0.901253
$362$	1.25744	−	0.309931i	0.0660895	−	0.0162896i
$363$	1.12693	+	9.28108i	0.0591483	+	0.487130i
$364$	4.08286	−	16.4671i	0.214000	−	0.863110i
$365$	−0.649295	+	5.34742i	−0.0339856	+	0.279897i
$366$	0.174109	+	1.43392i	0.00910081	+	0.0749519i
$367$	12.3825	−	17.9391i	0.646359	−	0.936413i	−0.353640	−	0.935381i	$-0.615056\pi$
$367$	12.3825	−	17.9391i	0.646359	−	0.936413i	0.999999	−	0.00103132i	$-0.000328280\pi$
$368$	−12.8274	+	11.3641i	−0.668674	+	0.592394i
$369$	−0.472138	+	3.88840i	−0.0245785	+	0.202422i
$370$	0.108505	+	0.893617i	0.00564089	+	0.0464569i
$371$	−28.4441	−	14.9286i	−1.47674	−	0.775054i
$372$	−8.33534	+	7.38447i	−0.432167	+	0.382867i
$373$	9.72673	+	14.0916i	0.503631	+	0.729636i	0.989522	−	0.144384i	$-0.0461200\pi$
$373$	9.72673	+	14.0916i	0.503631	+	0.729636i	−0.485891	+	0.874020i	$0.661505\pi$
$374$	0.0389496	+	0.00960022i	0.00201404	+	0.000496416i
$375$	−1.20994	+	9.96474i	−0.0624809	+	0.514577i
$376$	−1.62332	+	2.35178i	−0.0837163	+	0.121284i
$377$	−2.46191	+	1.69433i	−0.126795	+	0.0872625i
$378$	−0.981787	−	1.42236i	−0.0504977	−	0.0731585i
$379$	23.6550	−	12.4151i	1.21508	−	0.637721i	0.269462	−	0.963011i	$-0.413154\pi$
$379$	23.6550	−	12.4151i	1.21508	−	0.637721i	0.945614	+	0.325289i	$0.105462\pi$
$380$	1.49692	−	3.94705i	0.0767903	−	0.202479i
$381$	−1.79121	−	14.7520i	−0.0917666	−	0.755766i
$382$	−0.346457	+	0.501930i	−0.0177263	+	0.0256810i
$383$	−9.24850	+	2.27955i	−0.472577	+	0.116480i	−0.468409	−	0.883512i	$-0.655173\pi$
$383$	−9.24850	+	2.27955i	−0.472577	+	0.116480i	−0.00416736	+	0.999991i	$0.501327\pi$
$384$	−2.41649	+	3.50089i	−0.123316	+	0.178654i
$385$	−0.0712595	+	0.187896i	−0.00363172	+	0.00957605i
$386$	−0.825179	+	2.17582i	−0.0420005	+	0.110746i
$387$	−7.72994	−	4.05699i	−0.392935	−	0.206228i
$388$	−26.2248	−	13.7638i	−1.33136	−	0.698752i
$389$	24.6682	−	6.08017i	1.25073	−	0.308277i	0.442298	−	0.896868i	$-0.354164\pi$
$389$	24.6682	−	6.08017i	1.25073	−	0.308277i	0.808431	+	0.588592i	$0.200317\pi$
$390$	0.723513	−	0.273252i	0.0366365	−	0.0138366i
$391$	19.9021	+	4.90542i	1.00649	+	0.248078i
$392$	0.633182	+	0.560950i	0.0319805	+	0.0283323i
$393$	1.06509	−	8.77177i	0.0537265	−	0.442477i
$394$	2.61978	+	1.37497i	0.131983	+	0.0692699i
$395$	−1.17653	+	0.617492i	−0.0591978	+	0.0310694i
$396$	0.0860599	+	0.226921i	0.00432467	+	0.0114032i
$397$	−16.5751	−	14.6842i	−0.831880	−	0.736981i	0.135373	−	0.990795i	$-0.456777\pi$
$397$	−16.5751	−	14.6842i	−0.831880	−	0.736981i	−0.967253	+	0.253813i	$0.918315\pi$
$398$	−0.148537	−	1.22331i	−0.00744549	−	0.0613191i
$399$	−2.69531	+	0.664333i	−0.134934	+	0.0332583i
$400$	7.37233	+	6.53132i	0.368617	+	0.326566i
$401$	15.4058	−	13.6484i	0.769331	−	0.681567i	−0.184192	−	0.982890i	$-0.558967\pi$
$401$	15.4058	−	13.6484i	0.769331	−	0.681567i	0.953522	+	0.301323i	$0.0974282\pi$
$402$	−1.33985	−	0.703208i	−0.0668257	−	0.0350728i
$403$	11.1483	−	21.1704i	0.555337	−	1.05457i
$404$	−33.4439	+	17.5527i	−1.66390	+	0.873280i
$405$	1.67065	−	4.40514i	0.0830152	−	0.218893i
$406$	0.0384885	+	0.316981i	0.00191015	+	0.0157315i
$407$	−0.170566	+	0.0895201i	−0.00845466	+	0.00443735i
$408$	2.51014			0.124270
$409$	14.5473	−	7.63501i	0.719317	−	0.377527i	−0.0650011	−	0.997885i	$-0.520705\pi$
$409$	14.5473	−	7.63501i	0.719317	−	0.377527i	0.784319	+	0.620358i	$0.213013\pi$
$410$	−0.324840	+	0.287783i	−0.0160427	+	0.0142126i
$411$	−0.719453	−	1.04231i	−0.0354880	−	0.0514132i
$412$	2.39438	+	2.12123i	0.117962	+	0.104506i
$413$	−12.1914	−	17.6623i	−0.599898	−	0.869103i
$414$	−0.581763	−	1.53398i	−0.0285921	−	0.0753912i
$415$	−3.49069	−	9.20421i	−0.171351	−	0.451817i
$416$	1.65341	−	6.66856i	0.0810650	−	0.326953i
$417$	1.73045	−	4.56283i	0.0847406	−	0.223443i
$418$	−0.0119509			−0.000584538
$419$	2.02728	+	5.34550i	0.0990392	+	0.261145i	0.975374	−	0.220558i	$-0.0707878\pi$
$419$	2.02728	+	5.34550i	0.0990392	+	0.261145i	−0.876335	+	0.481703i	$0.840019\pi$
$420$	−0.752855	+	6.20032i	−0.0367356	+	0.302545i
$421$	2.99518	+	1.57199i	0.145976	+	0.0766142i	0.536130	−	0.844136i	$-0.319886\pi$
$421$	2.99518	+	1.57199i	0.145976	+	0.0766142i	−0.390154	+	0.920750i	$0.627578\pi$
$422$	−0.0858482	−	0.124373i	−0.00417903	−	0.00605436i
$423$	5.75652	+	8.33975i	0.279891	+	0.405493i
$424$	−7.66241	−	4.02154i	−0.372119	−	0.195303i
$425$	1.42001	−	11.6948i	0.0688804	−	0.567282i
$426$	0.418771	+	1.10421i	0.0202895	+	0.0534991i
$427$	25.0637			1.21292
$428$	3.77758	−	9.96067i	0.182596	−	0.481467i
$429$	0.109576	+	0.124029i	0.00529036	+	0.00598819i
$430$	−0.342986	−	0.904379i	−0.0165402	−	0.0436130i
$431$	13.6341	+	35.9502i	0.656732	+	1.73166i	0.681345	+	0.731962i	$0.261395\pi$
$431$	13.6341	+	35.9502i	0.656732	+	1.73166i	−0.0246137	+	0.999697i	$0.507836\pi$
$432$	9.79684	+	14.1932i	0.471351	+	0.682870i
$433$	5.37160	+	4.75882i	0.258142	+	0.228694i	0.782261	−	0.622951i	$-0.214067\pi$
$433$	5.37160	+	4.75882i	0.258142	+	0.228694i	−0.524118	+	0.851646i	$0.675605\pi$
$434$	−1.45217	−	2.10383i	−0.0697063	−	0.100987i
$435$	0.823545	−	0.729598i	0.0394860	−	0.0349815i
$436$	10.8358	−	5.68704i	0.518938	−	0.272360i
$437$	−6.10654			−0.292115
$438$	0.419693	−	0.220272i	0.0200537	−	0.0105250i
$439$	2.72780	+	22.4655i	0.130191	+	1.07222i	0.900594	+	0.434662i	$0.143132\pi$
$439$	2.72780	+	22.4655i	0.130191	+	1.07222i	−0.770403	+	0.637558i	$0.779945\pi$
$440$	−0.0191962	+	0.0506163i	−0.000915145	+	0.00241304i
$441$	2.65616	−	1.39406i	0.126484	−	0.0663837i
$442$	−2.50612	+	0.946495i	−0.119204	+	0.0450202i
$443$	−13.0584	−	6.85359i	−0.620424	−	0.325624i	0.125058	−	0.992149i	$-0.460088\pi$
$443$	−13.0584	−	6.85359i	−0.620424	−	0.325624i	−0.745482	+	0.666526i	$0.767781\pi$
$444$	−4.48145	+	3.97022i	−0.212680	+	0.188418i
$445$	10.5135	+	9.31415i	0.498388	+	0.441533i
$446$	−2.74401	+	0.676337i	−0.129932	+	0.0320255i
$447$	1.92203	+	15.8293i	0.0909088	+	0.748702i
$448$	13.1685	+	11.6663i	0.622153	+	0.551180i
$449$	−4.79308	−	12.6383i	−0.226200	−	0.596439i	0.773083	−	0.634305i	$-0.218713\pi$
$449$	−4.79308	−	12.6383i	−0.226200	−	0.596439i	−0.999283	+	0.0378652i	$0.987944\pi$
$450$	−0.834901	+	0.438190i	−0.0393576	+	0.0206565i
$451$	−0.0822309	−	0.0431581i	−0.00387210	−	0.00203224i
$452$	3.23692	−	26.6584i	0.152252	−	1.25391i
$453$	8.57152	+	7.59370i	0.402725	+	0.356783i
$454$	4.05895	+	1.00044i	0.190496	+	0.0469531i
$455$	−3.19358	−	13.0342i	−0.149717	−	0.611051i
$456$	−0.726076	+	0.178962i	−0.0340016	+	0.00838064i
$457$	−10.9319	−	5.73751i	−0.511374	−	0.268390i	0.189239	−	0.981931i	$-0.439398\pi$
$457$	−10.9319	−	5.73751i	−0.511374	−	0.268390i	−0.700613	+	0.713541i	$0.747090\pi$
$458$	−2.73363	−	1.43472i	−0.127734	−	0.0670402i
$459$	7.31471	−	19.2873i	0.341422	−	0.900255i
$460$	−4.87211	+	12.8467i	−0.227164	+	0.598981i
$461$	−4.93906	+	7.15547i	−0.230035	+	0.333263i	−0.920956	−	0.389667i	$-0.872590\pi$
$461$	−4.93906	+	7.15547i	−0.230035	+	0.333263i	0.690921	+	0.722931i	$0.257205\pi$
$462$	0.0171685	−	0.00423166i	0.000798752	−	0.000196875i
$463$	−19.3652	+	28.0553i	−0.899976	+	1.30384i	0.0523095	+	0.998631i	$0.483342\pi$
$463$	−19.3652	+	28.0553i	−0.899976	+	1.30384i	−0.952285	+	0.305209i	$0.901274\pi$
$464$	−0.384061	−	3.16302i	−0.0178296	−	0.146840i
$465$	−3.12350	+	8.23599i	−0.144849	+	0.381935i
$466$	−1.95799	+	1.02763i	−0.0907022	+	0.0476042i
$467$	22.8017	+	33.0340i	1.05514	+	1.52863i	0.832731	+	0.553678i	$0.186776\pi$
$467$	22.8017	+	33.0340i	1.05514	+	1.52863i	0.222408	+	0.974954i	$0.428608\pi$
$468$	−13.3254	−	9.22498i	−0.615965	−	0.426425i
$469$	−14.9152	+	21.6084i	−0.688721	+	0.997785i
$470$	−0.135333	+	1.11457i	−0.00624244	+	0.0514111i
$471$	4.88165	+	1.20322i	0.224935	+	0.0554414i
$472$	−3.28418	−	4.75795i	−0.151166	−	0.219002i
$473$	0.154927	−	0.137253i	0.00712353	−	0.00631090i
$474$	0.103525	+	0.0543342i	0.00475507	+	0.00249565i
$475$	0.423040	+	3.48404i	0.0194104	+	0.159859i
$476$	2.60776	−	21.4768i	0.119526	−	0.984387i
$477$	−22.9695	+	20.3492i	−1.05170	+	0.931727i
$478$	2.39929	−	3.47597i	0.109741	−	0.158987i
$479$	4.95812	+	40.8338i	0.226542	+	1.86574i	0.452712	+	0.891657i	$0.350457\pi$
$479$	4.95812	+	40.8338i	0.226542	+	1.86574i	−0.226169	+	0.974088i	$0.572620\pi$
$480$	−0.304879	+	2.51090i	−0.0139157	+	0.114606i
$481$	5.99383	−	11.3821i	0.273295	−	0.518981i
$482$	−0.241062	−	1.98532i	−0.0109801	−	0.0904289i
$483$	8.77258	−	2.16225i	0.399166	−	0.0983856i
$484$	21.7070			0.986681
$485$	−23.4270			−1.06376
$486$	−2.51432	+	0.619725i	−0.114052	+	0.0281113i
$487$	1.88885	−	4.98050i	0.0855921	−	0.225688i	−0.885386	−	0.464857i	$-0.846106\pi$
$487$	1.88885	−	4.98050i	0.0855921	−	0.225688i	0.970978	+	0.239169i	$0.0768750\pi$
$488$	6.75178			0.305639
$489$	4.39907	+	11.5994i	0.198933	+	0.524543i
$490$	0.322702	+	0.0795389i	0.0145782	+	0.00359320i
$491$	−8.77694	+	7.77569i	−0.396098	+	0.350912i	−0.837538	−	0.546378i	$-0.816006\pi$
$491$	−8.77694	+	7.77569i	−0.396098	+	0.350912i	0.441441	+	0.897290i	$0.354468\pi$
$492$	−2.80257	−	0.690770i	−0.126349	−	0.0311423i
$493$	−2.85261	+	2.52719i	−0.128475	+	0.113819i
$494$	0.657431	−	0.452455i	0.0295792	−	0.0203569i
$495$	0.143690	+	0.127298i	0.00645837	+	0.00572162i
$496$	14.4906	+	20.9932i	0.650646	+	0.942623i
$497$	19.8961	−	4.90395i	0.892463	−	0.219972i
$498$	−0.492047	+	0.712853i	−0.0220492	+	0.0319437i
$499$	−8.28649	−	2.04244i	−0.370954	−	0.0914320i	0.0494315	−	0.998778i	$-0.484259\pi$
$499$	−8.28649	−	2.04244i	−0.370954	−	0.0914320i	−0.420386	+	0.907346i	$0.638105\pi$
$500$	22.6287	+	5.57748i	1.01199	+	0.249433i
$501$	0.725684	−	5.97655i	0.0324212	−	0.267013i
$502$	1.57163	+	1.39235i	0.0701455	+	0.0621435i
$503$	0.972311	+	2.56377i	0.0433532	+	0.114313i	0.954944	−	0.296785i	$-0.0959145\pi$
$503$	0.972311	+	2.56377i	0.0433532	+	0.114313i	−0.911591	+	0.411098i	$0.865145\pi$
$504$	−3.08677	+	1.62006i	−0.137496	+	0.0721633i
$505$	−16.9714	+	24.5874i	−0.755219	+	1.09412i
$506$	0.0388974			0.00172920
$507$	−10.7235	−	2.67450i	−0.476249	−	0.118779i
$508$	−34.5025			−1.53080
$509$	−20.7979	+	30.1310i	−0.921852	+	1.33553i	0.0201050	+	0.999798i	$0.493600\pi$
$509$	−20.7979	+	30.1310i	−0.921852	+	1.33553i	−0.941957	+	0.335735i	$0.891015\pi$
$510$	0.873259	−	0.458322i	0.0386686	−	0.0202948i
$511$	−2.91643	−	7.69000i	−0.129015	−	0.340186i
$512$	9.17814	+	8.13112i	0.405620	+	0.359348i
$513$	−0.740734	+	6.10049i	−0.0327042	+	0.269343i
$514$	1.72355	+	0.424817i	0.0760225	+	0.0187379i
$515$	2.45674	+	0.605532i	0.108257	+	0.0266829i
$516$	3.65443	−	5.29436i	0.160877	−	0.233071i
$517$	−0.233278	+	0.0574978i	−0.0102596	+	0.00252875i
$518$	−0.780750	−	1.13111i	−0.0343042	−	0.0496982i
$519$	1.18156	+	1.04677i	0.0518649	+	0.0459483i
$520$	−0.860303	−	3.51121i	−0.0377268	−	0.153977i
$521$	−0.0806527	+	0.0714521i	−0.00353346	+	0.00313037i	−0.664888	−	0.746943i	$-0.731521\pi$
$521$	−0.0806527	+	0.0714521i	−0.00353346	+	0.00313037i	0.661354	+	0.750074i	$0.269982\pi$
$522$	0.296166	+	0.0729983i	0.0129628	+	0.00319505i
$523$	−4.35086	+	3.85452i	−0.190250	+	0.168546i	−0.752871	−	0.658168i	$-0.771331\pi$
$523$	−4.35086	+	3.85452i	−0.190250	+	0.168546i	0.562621	+	0.826715i	$0.309793\pi$
$524$	−19.9197	−	4.90975i	−0.870194	−	0.214484i
$525$	−1.84139	−	4.85534i	−0.0803648	−	0.211904i
$526$	1.56544			0.0682563
$527$	10.8192	−	28.5280i	0.471294	−	1.24270i
$528$	−0.171317	+	0.0422259i	−0.00745563	+	0.00183765i
$529$	−3.12466			−0.135855
$530$	−3.39998			−0.147686
$531$	−19.9057	+	4.90632i	−0.863834	+	0.212916i
$532$	0.776886	+	6.39823i	0.0336823	+	0.277399i
$533$	6.15754	−	0.739048i	0.266713	−	0.0320117i
$534$	0.148974	−	1.22691i	0.00644674	−	0.0530936i
$535$	−1.01569	−	8.36494i	−0.0439120	−	0.361648i
$536$	−4.01794	+	5.82099i	−0.173549	+	0.251429i
$537$	−7.31313	+	6.47887i	−0.315585	+	0.279584i
$538$	−0.233039	+	1.91925i	−0.0100470	+	0.0827447i
$539$	0.00857283	+	0.0706036i	0.000369258	+	0.00304111i
$540$	12.2430	+	6.42562i	0.526855	+	0.276515i
$541$	4.30692	−	3.81560i	0.185169	−	0.164045i	−0.565446	−	0.824785i	$-0.691296\pi$
$541$	4.30692	−	3.81560i	0.185169	−	0.164045i	0.750615	+	0.660740i	$0.229757\pi$
$542$	−2.77607	−	4.02183i	−0.119242	−	0.172752i
$543$	6.61530	+	1.63052i	0.283890	+	0.0699725i
$544$	1.05604	−	8.69731i	0.0452775	−	0.372894i
$545$	5.49872	−	7.96627i	0.235539	−	0.341237i
$546$	−0.784248	+	0.882779i	−0.0335627	+	0.0377794i
$547$	−19.8862	−	28.8101i	−0.850272	−	1.23183i	−0.970984	−	0.239144i	$-0.923133\pi$
$547$	−19.8862	−	28.8101i	−0.850272	−	1.23183i	0.120712	−	0.992688i	$-0.461482\pi$
$548$	−2.60372	+	1.36654i	−0.111226	+	0.0583757i
$549$	8.49022	−	22.3869i	0.362354	−	0.955448i
$550$	−0.00269467	−	0.0221926i	−0.000114901	−	0.000946296i
$551$	0.644961	−	0.934387i	0.0274762	−	0.0398062i
$552$	2.36320	−	0.582477i	0.100585	−	0.0247919i
$553$	1.15244	−	1.66960i	0.0490069	−	0.0709988i
$554$	−0.448947	+	1.18378i	−0.0190739	+	0.0502938i
$555$	−1.67933	+	4.42804i	−0.0712837	+	0.187960i
$556$	−10.0324	−	5.26541i	−0.425469	−	0.223303i
$557$	15.9711	+	8.38229i	0.676718	+	0.355169i	0.767814	−	0.640673i	$-0.221345\pi$
$557$	15.9711	+	8.38229i	0.676718	+	0.355169i	−0.0910956	+	0.995842i	$0.529037\pi$
$558$	−2.37106	+	0.584413i	−0.100375	+	0.0247402i
$559$	−3.32634	+	13.4159i	−0.140689	+	0.567430i
$560$	13.8915	+	3.42394i	0.587021	+	0.144688i
$561$	0.157969	+	0.139948i	0.00666944	+	0.00590861i
$562$	0.248600	−	2.04741i	0.0104866	−	0.0863647i
$563$	−0.881510	−	0.462652i	−0.0371512	−	0.0194985i	0.446045	−	0.895010i	$-0.352832\pi$
$563$	−0.881510	−	0.462652i	−0.0371512	−	0.0194985i	−0.483197	+	0.875512i	$0.660524\pi$
$564$	−6.61214	+	3.47032i	−0.278421	+	0.146127i
$565$	−7.53232	−	19.8611i	−0.316887	−	0.835562i
$566$	2.06654	+	1.83079i	0.0868631	+	0.0769540i
$567$	0.867050	+	7.14080i	0.0364127	+	0.299885i
$568$	5.35972	−	1.32105i	0.224889	−	0.0554301i
$569$	12.3906	+	10.9771i	0.519442	+	0.460185i	0.881645	−	0.471914i	$-0.156437\pi$
$569$	12.3906	+	10.9771i	0.519442	+	0.460185i	−0.362203	+	0.932099i	$0.617975\pi$
$570$	−0.219920	+	0.194832i	−0.00921143	+	0.00816062i
$571$	25.6257	+	13.4494i	1.07240	+	0.562841i	0.906026	−	0.423221i	$-0.139101\pi$
$571$	25.6257	+	13.4494i	1.07240	+	0.562841i	0.166377	+	0.986062i	$0.446793\pi$
$572$	0.316537	−	0.217846i	0.0132351	−	0.00910859i
$573$	−2.84107	+	1.49111i	−0.118687	+	0.0622918i
$574$	0.234964	−	0.619548i	0.00980720	−	0.0258594i
$575$	−1.37689	−	11.3397i	−0.0574204	−	0.472900i
$576$	14.8811	−	7.81020i	0.620046	−	0.325425i
$577$	−33.2380			−1.38372			−0.691859	−	0.722033i	$-0.743208\pi$
$577$	−33.2380			−1.38372			−0.691859	+	0.722033i	$0.743208\pi$
$578$	−0.592314	+	0.310871i	−0.0246370	+	0.0129305i
$579$	−9.16355	+	8.11820i	−0.380824	+	0.337381i
$580$	−1.45114	−	2.10235i	−0.0602555	−	0.0872952i
$581$	11.2499	+	9.96657i	0.466726	+	0.413483i
$582$	1.17100	+	1.69648i	0.0485394	+	0.0703214i
$583$	−0.257999	−	0.680287i	−0.0106852	−	0.0281746i
$584$	−0.785644	−	2.07157i	−0.0325102	−	0.0857223i
$585$	−12.7239	−	1.56277i	−0.526070	−	0.0646125i
$586$	−0.726931	+	1.91676i	−0.0300293	+	0.0791807i
$587$	32.8722			1.35678			0.678391	−	0.734701i	$-0.262678\pi$
$587$	32.8722			1.35678			0.678391	+	0.734701i	$0.262678\pi$
$588$	0.783871	+	2.06690i	0.0323263	+	0.0852374i
$589$	−1.09562	+	9.02328i	−0.0451444	+	0.371798i
$590$	−2.01128	−	1.05560i	−0.0828033	−	0.0434585i
$591$	8.84216	+	12.8101i	0.363718	+	0.526936i
$592$	7.79078	+	11.2869i	0.320199	+	0.463888i
$593$	8.74561	+	4.59005i	0.359139	+	0.188491i	0.634636	−	0.772811i	$-0.281150\pi$
$593$	8.74561	+	4.59005i	0.359139	+	0.188491i	−0.275497	+	0.961302i	$0.588842\pi$
$594$	0.00471832	−	0.0388588i	0.000193595	−	0.00159440i
$595$	−6.06825	−	16.0007i	−0.248774	−	0.655963i
$596$	37.0223			1.51649
$597$	2.29891	−	6.06174i	0.0940883	−	0.248090i
$598$	−2.13978	+	1.47263i	−0.0875022	+	0.0602204i
$599$	9.08801	+	23.9631i	0.371326	+	0.979106i	0.982277	+	0.187437i	$0.0600181\pi$
$599$	9.08801	+	23.9631i	0.371326	+	0.979106i	−0.610951	+	0.791669i	$0.709213\pi$
$600$	−0.496043	−	1.30796i	−0.0202509	−	0.0533971i
$601$	−18.6973	−	27.0878i	−0.762681	−	1.10493i	−0.991326	−	0.131424i	$-0.958045\pi$
$601$	−18.6973	−	27.0878i	−0.762681	−	1.10493i	0.228646	−	0.973510i	$-0.426570\pi$
$602$	1.10539	+	0.979286i	0.0450522	+	0.0399127i
$603$	14.2482	+	20.6421i	0.580231	+	0.840610i
$604$	19.9013	−	17.6310i	0.809771	−	0.717395i
$605$	15.2033	−	7.97931i	0.618102	−	0.324405i
$606$	2.62883			0.106789
$607$	−0.314006	+	0.164803i	−0.0127451	+	0.00668915i	−0.471084	−	0.882089i	$-0.656137\pi$
$607$	−0.314006	+	0.164803i	−0.0127451	+	0.00668915i	0.458339	+	0.888778i	$0.348445\pi$
$608$	0.314610	+	2.59105i	0.0127591	+	0.105081i
$609$	−0.595688	+	1.57070i	−0.0241385	+	0.0636480i
$610$	2.34889	−	1.23279i	0.0951039	−	0.0499144i
$611$	10.6560	−	11.9948i	0.431096	−	0.485257i
$612$	−18.2997	−	9.60443i	−0.739722	−	0.388236i
$613$	−15.6969	+	13.9062i	−0.633991	+	0.561667i	−0.917715	−	0.397239i	$-0.869968\pi$
$613$	−15.6969	+	13.9062i	−0.633991	+	0.561667i	0.283724	+	0.958906i	$0.408430\pi$
$614$	−1.82813	−	1.61958i	−0.0737772	−	0.0653609i
$615$	−2.21680	+	0.546393i	−0.0893901	+	0.0220327i
$616$	−0.00996266	−	0.0820499i	−0.000401407	−	0.00330588i
$617$	−7.36656	−	6.52621i	−0.296567	−	0.262735i	0.501697	−	0.865044i	$-0.332709\pi$
$617$	−7.36656	−	6.52621i	−0.296567	−	0.262735i	−0.798264	+	0.602308i	$0.794248\pi$
$618$	−0.0789500	−	0.208174i	−0.00317584	−	0.00837399i
$619$	−0.528419	+	0.277336i	−0.0212390	+	0.0111471i	−0.475309	−	0.879819i	$-0.657664\pi$
$619$	−0.528419	+	0.277336i	−0.0212390	+	0.0111471i	0.454070	+	0.890966i	$0.349972\pi$
$620$	18.1087	+	9.50417i	0.727263	+	0.381697i
$621$	2.41091	−	19.8557i	0.0967466	−	0.796780i
$622$	−0.0138202	−	0.0122436i	−0.000554138	−	0.000490924i
$623$	−20.8222	−	5.13222i	−0.834225	−	0.205618i
$624$	7.82569	−	8.80888i	0.313278	−	0.352637i
$625$	5.46008	−	1.34579i	0.218403	−	0.0538316i
$626$	2.48231	+	1.30282i	0.0992131	+	0.0520711i
$627$	−0.0556711	−	0.0292185i	−0.00222329	−	0.00116687i
$628$	4.13944	−	10.9148i	0.165182	−	0.435548i
$629$	5.81691	−	15.3379i	0.231935	−	0.611563i
$630$	−0.778061	+	1.12722i	−0.0309987	+	0.0449093i
$631$	−31.0808	+	7.66073i	−1.23731	+	0.304969i	−0.803100	−	0.595844i	$-0.796818\pi$
$631$	−31.0808	+	7.66073i	−1.23731	+	0.304969i	−0.434207	+	0.900813i	$0.642972\pi$
$632$	0.310451	−	0.449766i	0.0123491	−	0.0178907i
$633$	−0.0958330	−	0.789256i	−0.00380902	−	0.0313701i
$634$	1.33029	−	3.50768i	0.0528325	−	0.139308i
$635$	−24.1652	+	12.6828i	−0.958965	+	0.503304i
$636$	−12.8459	−	18.6105i	−0.509374	−	0.737955i
$637$	−3.14462	−	3.55941i	−0.124594	−	0.141029i
$638$	−0.00410826	+	0.00595184i	−0.000162648	+	0.000235636i
$639$	2.35952	−	19.4324i	0.0933413	−	0.768734i
$640$	7.58533	+	1.86962i	0.299837	+	0.0739031i
$641$	−24.9487	−	36.1445i	−0.985416	−	1.42762i	−0.902313	−	0.431080i	$-0.858133\pi$
$641$	−24.9487	−	36.1445i	−0.985416	−	1.42762i	−0.0831025	−	0.996541i	$-0.526483\pi$
$642$	−0.554984	+	0.491673i	−0.0219035	+	0.0194048i
$643$	28.0447	+	14.7190i	1.10597	+	0.580460i	0.915939	−	0.401317i	$-0.131447\pi$
$643$	28.0447	+	14.7190i	1.10597	+	0.580460i	0.190036	+	0.981777i	$0.439140\pi$
$644$	−2.52858	−	20.8247i	−0.0996400	−	0.820609i
$645$	0.613356	−	5.05144i	0.0241509	−	0.198900i
$646$	0.761763	−	0.674863i	0.0299712	−	0.0265521i
$647$	24.3594	−	35.2906i	0.957666	−	1.38742i	0.0360350	−	0.999351i	$-0.488527\pi$
$647$	24.3594	−	35.2906i	0.957666	−	1.38742i	0.921631	−	0.388068i	$-0.126857\pi$
$648$	0.233571	+	1.92363i	0.00917552	+	0.0755672i
$649$	0.0585898	−	0.482531i	0.00229985	−	0.0189410i
$650$	0.988437	+	1.11882i	0.0387697	+	0.0438837i
$651$	−1.62107	−	13.3507i	−0.0635346	−	0.523254i
$652$	27.9661	−	6.89304i	1.09524	−	0.269952i
$653$	−38.3288			−1.49992			−0.749962	−	0.661481i	$-0.769928\pi$
$653$	−38.3288			−1.49992			−0.749962	+	0.661481i	$0.769928\pi$
$654$	−0.851736			−0.0333055
$655$	−15.7563	+	3.88357i	−0.615648	+	0.151744i
$656$	−2.34460	+	6.18221i	−0.0915414	+	0.241375i
$657$	−7.85664			−0.306517
$658$	−0.607874	−	1.60283i	−0.0236974	−	0.0624849i
$659$	11.7717	+	2.90146i	0.458560	+	0.113025i	0.461828	−	0.886970i	$-0.347194\pi$
$659$	11.7717	+	2.90146i	0.458560	+	0.113025i	−0.00326737	+	0.999995i	$0.501040\pi$
$660$	−0.105886	+	0.0938068i	−0.00412161	+	0.00365143i
$661$	−29.5750	−	7.28959i	−1.15034	−	0.283532i	−0.382361	−	0.924013i	$-0.624889\pi$
$661$	−29.5750	−	7.28959i	−1.15034	−	0.283532i	−0.767974	+	0.640481i	$0.778735\pi$
$662$	−1.23199	+	1.09145i	−0.0478827	+	0.0424203i
$663$	−13.9884	−	1.71807i	−0.543263	−	0.0667242i
$664$	3.03056	+	2.68485i	0.117609	+	0.104192i
$665$	2.89606	+	4.19566i	0.112304	+	0.162701i
$666$	−1.27479	+	0.314206i	−0.0493969	+	0.0121753i
$667$	−2.09919	+	3.04121i	−0.0812811	+	0.117756i
$668$	−13.5720	−	3.34521i	−0.525118	−	0.129430i
$669$	−14.4360	−	3.55816i	−0.558129	−	0.137566i
$670$	−0.334968	+	2.75871i	−0.0129409	+	0.106578i
$671$	0.424904	+	0.376432i	0.0164032	+	0.0145320i
$672$	−1.36942	−	3.61087i	−0.0528266	−	0.139292i
$673$	0.512077	−	0.268759i	0.0197391	−	0.0103599i	−0.454825	−	0.890581i	$-0.650298\pi$
$673$	0.512077	−	0.268759i	0.0197391	−	0.0103599i	0.474564	+	0.880221i	$0.342606\pi$
$674$	−0.632600	+	0.916480i	−0.0243668	+	0.0353015i
$675$	−11.4955			−0.442463
$676$	−9.16547	+	23.9678i	−0.352518	+	0.921839i
$677$	−8.03573			−0.308838			−0.154419	−	0.988005i	$-0.549351\pi$
$677$	−8.03573			−0.308838			−0.154419	+	0.988005i	$0.549351\pi$
$678$	−1.06175	+	1.53821i	−0.0407764	+	0.0590748i
$679$	31.6714	−	16.6224i	1.21544	−	0.637911i
$680$	−1.63470	−	4.31034i	−0.0626878	−	0.165294i
$681$	16.4619	+	14.5840i	0.630823	+	0.558861i
$682$	0.00697889	−	0.0574764i	0.000267236	−	0.00220088i
$683$	−35.7488	−	8.81129i	−1.36789	−	0.337155i	−0.514081	−	0.857742i	$-0.671867\pi$
$683$	−35.7488	−	8.81129i	−1.36789	−	0.337155i	−0.853809	+	0.520587i	$0.825713\pi$
$684$	5.97807	+	1.47346i	0.228577	+	0.0563392i
$685$	−1.32129	+	1.91421i	−0.0504838	+	0.0731384i
$686$	−3.11092	+	0.766773i	−0.118776	+	0.0292755i
$687$	−9.22643	−	13.3668i	−0.352010	−	0.509975i
$688$	−11.0302	−	9.77189i	−0.420522	−	0.372550i
$689$	39.9480	+	27.6555i	1.52190	+	1.05359i
$690$	0.715787	−	0.634132i	0.0272496	−	0.0241410i
$691$	−20.1472	−	4.96585i	−0.766437	−	0.188910i	−0.163332	−	0.986571i	$-0.552224\pi$
$691$	−20.1472	−	4.96585i	−0.766437	−	0.188910i	−0.603105	+	0.797661i	$0.706070\pi$
$692$	2.74334	−	2.43039i	0.104286	−	0.0923896i
$693$	−0.284581	−	0.0701428i	−0.0108103	−	0.00266451i
$694$	1.90158	+	5.01406i	0.0721830	+	0.190331i
$695$	−8.96210			−0.339952
$696$	−0.160470	+	0.423123i	−0.00608258	+	0.0160385i
$697$	7.67860	−	1.89261i	0.290848	−	0.0716876i
$698$	5.94823			0.225144
$699$	−11.6334			−0.440015
$700$	−11.7062	+	2.88533i	−0.442454	+	0.109055i
$701$	2.39886	+	19.7564i	0.0906038	+	0.746190i	0.965232	+	0.261395i	$0.0841825\pi$
$701$	2.39886	+	19.7564i	0.0906038	+	0.746190i	−0.874628	+	0.484795i	$0.838894\pi$
$702$	1.21162	+	2.31630i	0.0457295	+	0.0874229i
$703$	−0.589057	+	4.85132i	−0.0222167	+	0.182971i
$704$	0.0480293	+	0.395556i	0.00181017	+	0.0149081i
$705$	−3.35540	+	4.86113i	−0.126372	+	0.183081i
$706$	1.80186	−	1.59631i	0.0678141	−	0.0600780i
$707$	5.49825	−	45.2822i	0.206783	−	1.70301i
$708$	−1.82103	−	14.9975i	−0.0684385	−	0.563642i
$709$	13.0465	+	6.84735i	0.489973	+	0.257158i	0.691568	−	0.722311i	$-0.256920\pi$
$709$	13.0465	+	6.84735i	0.489973	+	0.257158i	−0.201595	+	0.979469i	$0.564612\pi$
$710$	1.62340	−	1.43821i	0.0609250	−	0.0539749i
$711$	−1.10090	−	1.59493i	−0.0412871	−	0.0598147i
$712$	−5.60920	−	1.38254i	−0.210214	−	0.0518130i
$713$	3.56600	−	29.3686i	0.133548	−	1.09986i
$714$	−0.855379	+	1.23923i	−0.0320118	+	0.0463770i
$715$	0.141620	−	0.268933i	0.00529629	−	0.0100575i
$716$	12.8862	+	18.6690i	0.481582	+	0.697692i
$717$	19.6750	−	10.3262i	0.734775	−	0.385640i
$718$	1.41793	−	3.73878i	0.0529168	−	0.139530i
$719$	3.16038	+	26.0281i	0.117862	+	0.970685i	0.924907	+	0.380194i	$0.124143\pi$
$719$	3.16038	+	26.0281i	0.117862	+	0.970685i	−0.807044	+	0.590491i	$0.798934\pi$
$720$	7.76394	−	11.2480i	0.289345	−	0.419188i
$721$	−3.75097	+	0.924531i	−0.139693	+	0.0344313i
$722$	1.57194	−	2.27734i	0.0585014	−	0.0847539i
$723$	3.73092	−	9.83763i	0.138754	−	0.365865i
$724$	5.60950	−	14.7910i	0.208475	−	0.549704i
$725$	1.88056	+	0.986996i	0.0698424	+	0.0366561i
$726$	−1.33776	−	0.702113i	−0.0496491	−	0.0260579i
$727$	−6.37892	+	1.57226i	−0.236581	+	0.0583120i	−0.355824	−	0.934553i	$-0.615800\pi$
$727$	−6.37892	+	1.57226i	−0.236581	+	0.0583120i	0.119242	+	0.992865i	$0.461953\pi$
$728$	3.65442	+	4.13646i	0.135442	+	0.153308i
$729$	−4.43824	−	1.09393i	−0.164379	−	0.0405158i
$730$	−0.651564	−	0.577235i	−0.0241155	−	0.0213644i
$731$	−2.12456	+	17.4973i	−0.0785795	+	0.647161i
$732$	15.6226	+	8.19939i	0.577429	+	0.303058i
$733$	−5.32890	+	2.79682i	−0.196827	+	0.103303i	−0.560258	−	0.828318i	$-0.689298\pi$
$733$	−5.32890	+	2.79682i	−0.196827	+	0.103303i	0.363430	+	0.931621i	$0.381606\pi$
$734$	1.24908	+	3.29355i	0.0461044	+	0.121567i
$735$	1.30879	+	1.15948i	0.0482753	+	0.0427682i
$736$	−1.02398	−	8.43324i	−0.0377444	−	0.310853i
$737$	−0.577396	+	0.142315i	−0.0212686	+	0.00524225i
$738$	−0.473788	−	0.419739i	−0.0174404	−	0.0154508i
$739$	−1.66361	+	1.47383i	−0.0611968	+	0.0542156i	−0.693167	−	0.720777i	$-0.743785\pi$
$739$	−1.66361	+	1.47383i	−0.0611968	+	0.0542156i	0.631970	+	0.774993i	$0.282247\pi$
$740$	9.73604	+	5.10987i	0.357904	+	0.187842i
$741$	4.16872	−	0.500343i	0.153142	−	0.0183806i
$742$	4.59651	−	2.41243i	0.168743	−	0.0885632i
$743$	−18.1112	+	47.7554i	−0.664437	+	1.75198i	−0.00526085	+	0.999986i	$0.501675\pi$
$743$	−18.1112	+	47.7554i	−0.664437	+	1.75198i	−0.659176	+	0.751989i	$0.729095\pi$
$744$	−0.436691	−	3.59648i	−0.0160099	−	0.131853i
$745$	25.9300	−	13.6091i	0.950001	−	0.498599i
$746$	−2.76698			−0.101306
$747$	12.7130	−	6.67230i	0.465145	−	0.244127i
$748$	0.366770	−	0.324930i	0.0134104	−	0.0118806i
$749$	7.30842	+	10.5881i	0.267044	+	0.386880i
$750$	−1.21417	−	1.07566i	−0.0443351	−	0.0392775i
$751$	18.4541	+	26.7354i	0.673399	+	0.975587i	0.999542	+	0.0302668i	$0.00963569\pi$
$751$	18.4541	+	26.7354i	0.673399	+	0.975587i	−0.326142	+	0.945321i	$0.605749\pi$
$752$	6.06572	+	15.9940i	0.221194	+	0.583240i
$753$	3.91706	+	10.3284i	0.142746	+	0.376390i
$754$	0.000665809	−	0.482953i	2.42473e−5	−	0.0175881i
$755$	7.45760	−	19.6641i	0.271410	−	0.715649i
$756$	−21.1108			−0.767793
$757$	0.452018	+	1.19187i	0.0164289	+	0.0433194i	0.942980	−	0.332850i	$-0.108010\pi$
$757$	0.452018	+	1.19187i	0.0164289	+	0.0433194i	−0.926551	+	0.376169i	$0.877241\pi$
$758$	−0.520370	+	4.28563i	−0.0189007	+	0.155661i
$759$	0.181196	+	0.0950992i	0.00657701	+	0.00345188i
$760$	0.780155	+	1.13025i	0.0282992	+	0.0409985i
$761$	−2.99820	−	4.34364i	−0.108685	−	0.157457i	0.764867	−	0.644188i	$-0.222805\pi$
$761$	−2.99820	−	4.34364i	−0.108685	−	0.157457i	−0.873552	+	0.486731i	$0.838189\pi$
$762$	2.12633	+	1.11599i	0.0770289	+	0.0404279i
$763$	−1.78142	+	14.6713i	−0.0644919	+	0.531138i
$764$	2.64169	+	6.96557i	0.0955731	+	0.252005i
$765$	−16.3474			−0.591041
$766$	0.545833	−	1.43924i	0.0197217	−	0.0520019i

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.g (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0917982 + 0.132993i) q^{2} +(-0.752776 + 0.395087i) q^{3} +(0.699950 + 1.84562i) q^{4} +(1.16867 + 1.03535i) q^{5} +(0.0165598 - 0.136382i) q^{6} +(-2.31458 - 0.570492i) q^{7} +(-0.623512 - 0.153682i) q^{8} +(-1.29362 + 1.87413i) q^{9} +O(q^{10})\)	\(q+(-0.0917982 + 0.132993i) q^{2} +(-0.752776 + 0.395087i) q^{3} +(0.699950 + 1.84562i) q^{4} +(1.16867 + 1.03535i) q^{5} +(0.0165598 - 0.136382i) q^{6} +(-2.31458 - 0.570492i) q^{7} +(-0.623512 - 0.153682i) q^{8} +(-1.29362 + 1.87413i) q^{9} +(-0.244976 + 0.0603811i) q^{10} +(-0.0306707 - 0.0444342i) q^{11} +(-1.25608 - 1.11279i) q^{12} +(3.36948 + 1.28319i) q^{13} +(0.288345 - 0.255451i) q^{14} +(-1.28880 - 0.317661i) q^{15} +(-2.87727 + 2.54904i) q^{16} +(4.46417 + 1.10032i) q^{17} +(-0.130493 - 0.344083i) q^{18} -1.36974 q^{19} +(-1.09285 + 2.88161i) q^{20} +(1.96775 - 0.485007i) q^{21} +0.00872495 q^{22} +4.45818 q^{23} +(0.530083 - 0.130654i) q^{24} +(-0.308847 - 2.54358i) q^{25} +(-0.479968 + 0.330322i) q^{26} +(0.540785 - 4.45376i) q^{27} +(-0.567178 - 4.67113i) q^{28} +(-0.470864 + 0.682164i) q^{29} +(0.160556 - 0.142240i) q^{30} +(0.799878 - 6.58759i) q^{31} +(-0.229686 - 1.89163i) q^{32} +(0.0406436 + 0.0213314i) q^{33} +(-0.556137 + 0.492694i) q^{34} +(-2.11431 - 3.06311i) q^{35} +(-4.36438 - 1.07572i) q^{36} +(0.430050 - 3.54178i) q^{37} +(0.125740 - 0.182165i) q^{38} +(-3.04344 + 0.365284i) q^{39} +(-0.569565 - 0.825157i) q^{40} +(1.52303 - 0.799348i) q^{41} +(-0.116134 + 0.306219i) q^{42} +(0.462084 + 3.80560i) q^{43} +(0.0605405 - 0.0877081i) q^{44} +(-3.45219 + 0.850888i) q^{45} +(-0.409253 + 0.592905i) q^{46} +(1.57797 - 4.16077i) q^{47} +(1.15885 - 3.05563i) q^{48} +(-1.16640 - 0.612171i) q^{49} +(0.366629 + 0.192422i) q^{50} +(-3.79524 + 0.935443i) q^{51} +(-0.00981156 + 7.11694i) q^{52} +(13.0840 + 3.22491i) q^{53} +(0.542675 + 0.480768i) q^{54} +(0.0101611 - 0.0836838i) q^{55} +(1.35549 + 0.711417i) q^{56} +(1.03111 - 0.541167i) q^{57} +(-0.0474983 - 0.125243i) q^{58} +(6.73868 + 5.96995i) q^{59} +(-0.315816 - 2.60098i) q^{60} +(-10.2084 + 2.51616i) q^{61} +(0.802674 + 0.711107i) q^{62} +(4.06335 - 3.59981i) q^{63} +(-6.53472 - 3.42969i) q^{64} +(2.60926 + 4.98822i) q^{65} +(-0.00656793 + 0.00344712i) q^{66} +(3.90570 - 10.2985i) q^{67} +(1.09393 + 9.00931i) q^{68} +(-3.35601 + 1.76137i) q^{69} +0.601462 q^{70} +(-7.61139 + 3.99477i) q^{71} +(1.09461 - 0.969736i) q^{72} +(1.95987 + 2.83936i) q^{73} +(0.431553 + 0.382323i) q^{74} +(1.23743 + 1.79273i) q^{75} +(-0.958749 - 2.52801i) q^{76} +(0.0456404 + 0.120344i) q^{77} +(0.230802 - 0.438288i) q^{78} +(-0.301779 + 0.795725i) q^{79} -6.00173 q^{80} +(-1.07002 - 2.82141i) q^{81} +(-0.0335040 + 0.275931i) q^{82} +(-5.58265 - 2.93000i) q^{83} +(2.27246 + 3.29223i) q^{84} +(4.07792 + 5.90789i) q^{85} +(-0.548536 - 0.287894i) q^{86} +(0.0849406 - 0.699549i) q^{87} +(0.0122948 + 0.0324188i) q^{88} +8.99614 q^{89} +(0.203743 - 0.537226i) q^{90} +(-7.06687 - 4.89231i) q^{91} +(3.12050 + 8.22808i) q^{92} +(2.00054 + 5.27500i) q^{93} +(0.408497 + 0.591809i) q^{94} +(-1.60077 - 1.41816i) q^{95} +(0.920263 + 1.33323i) q^{96} +(-11.2311 + 9.94984i) q^{97} +(0.188487 - 0.0989258i) q^{98} +0.122952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more