LMFDB - Embedded newform 169.2.g.a.27.6

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			27.6
Character	$\chi$	$=$	169.27
Dual form			169.2.g.a.144.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.168406 - 0.444051i) q^{2} +(0.0744765 - 0.107898i) q^{3} +(1.32820 - 1.17668i) q^{4} +(-0.265542 - 2.18694i) q^{5} +(-0.0604545 - 0.0149007i) q^{6} +(-3.17143 - 1.66450i) q^{7} +(-1.58721 - 0.833034i) q^{8} +(1.05772 + 2.78898i) q^{9} +O(q^{10})$	\(q+(-0.168406 - 0.444051i) q^{2} +(0.0744765 - 0.107898i) q^{3} +(1.32820 - 1.17668i) q^{4} +(-0.265542 - 2.18694i) q^{5} +(-0.0604545 - 0.0149007i) q^{6} +(-3.17143 - 1.66450i) q^{7} +(-1.58721 - 0.833034i) q^{8} +(1.05772 + 2.78898i) q^{9} +(-0.926393 + 0.486209i) q^{10} +(-0.381234 + 1.00523i) q^{11} +(-0.0280418 - 0.230945i) q^{12} +(3.25777 - 1.54497i) q^{13} +(-0.205032 + 1.68859i) q^{14} +(-0.255743 - 0.134224i) q^{15} +(0.325162 - 2.67795i) q^{16} +(1.74024 + 0.913350i) q^{17} +(1.06032 - 0.939363i) q^{18} +1.98577 q^{19} +(-2.92603 - 2.59223i) q^{20} +(-0.415793 + 0.218225i) q^{21} +0.510576 q^{22} -0.763058 q^{23} +(-0.208093 + 0.109215i) q^{24} +(0.142520 - 0.0351280i) q^{25} +(-1.23468 - 1.18643i) q^{26} +(0.761588 + 0.187715i) q^{27} +(-6.17088 + 1.52099i) q^{28} +(2.65960 + 7.01279i) q^{29} +(-0.0165337 + 0.136167i) q^{30} +(2.41733 + 0.595818i) q^{31} +(-4.72480 + 1.16456i) q^{32} +(0.0800692 + 0.116000i) q^{33} +(0.112506 - 0.926570i) q^{34} +(-2.79800 + 7.37772i) q^{35} +(4.68661 + 2.45972i) q^{36} +(6.15828 + 1.51788i) q^{37} +(-0.334416 - 0.881784i) q^{38} +(0.0759280 - 0.466570i) q^{39} +(-1.40032 + 3.69234i) q^{40} +(-3.55018 + 5.14332i) q^{41} +(0.166925 + 0.147883i) q^{42} +(-1.25241 + 0.308691i) q^{43} +(0.676483 + 1.78374i) q^{44} +(5.81845 - 3.05376i) q^{45} +(0.128504 + 0.338836i) q^{46} +(-2.85457 - 2.52893i) q^{47} +(-0.264728 - 0.234529i) q^{48} +(3.31098 + 4.79679i) q^{49} +(-0.0395999 - 0.0573703i) q^{50} +(0.228156 - 0.119745i) q^{51} +(2.50903 - 5.88540i) q^{52} +(-10.5639 - 5.54436i) q^{53} +(-0.0449014 - 0.369796i) q^{54} +(2.29961 + 0.566803i) q^{55} +(3.64716 + 5.28382i) q^{56} +(0.147893 - 0.214260i) q^{57} +(2.66614 - 2.36200i) q^{58} +(0.511731 + 4.21448i) q^{59} +(-0.497617 + 0.122652i) q^{60} +(-1.97010 + 1.03399i) q^{61} +(-0.142520 - 1.17376i) q^{62} +(1.28776 - 10.6056i) q^{63} +(-1.75203 - 2.53826i) q^{64} +(-4.24384 - 6.71429i) q^{65} +(0.0380259 - 0.0550900i) q^{66} +(6.26593 + 5.55113i) q^{67} +(3.38612 - 0.834602i) q^{68} +(-0.0568299 + 0.0823323i) q^{69} +3.74729 q^{70} +(-1.38696 + 2.00935i) q^{71} +(0.644486 - 5.30782i) q^{72} +(-3.31646 + 8.74480i) q^{73} +(-0.363077 - 2.99021i) q^{74} +(0.00682415 - 0.0179938i) q^{75} +(2.63750 - 2.33662i) q^{76} +(2.88226 - 2.55346i) q^{77} +(-0.219968 + 0.0448575i) q^{78} +(-10.7698 - 9.54119i) q^{79} -5.94285 q^{80} +(-6.62102 + 5.86572i) q^{81} +(2.88177 + 0.710292i) q^{82} +(-3.50606 - 5.07941i) q^{83} +(-0.295475 + 0.779103i) q^{84} +(1.53533 - 4.04834i) q^{85} +(0.347989 + 0.504148i) q^{86} +(0.954743 + 0.235323i) q^{87} +(1.44249 - 1.27793i) q^{88} +8.43464 q^{89} +(-2.33589 - 2.06942i) q^{90} +(-12.9034 - 0.522768i) q^{91} +(-1.01349 + 0.897877i) q^{92} +(0.244322 - 0.216450i) q^{93} +(-0.642247 + 1.69347i) q^{94} +(-0.527307 - 4.34276i) q^{95} +(-0.226233 + 0.596529i) q^{96} +(2.01704 - 16.6118i) q^{97} +(1.57243 - 2.27805i) q^{98} -3.20680 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{13}\right)$

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 $

$2$	−0.168406	−	0.444051i	−0.119081	−	0.313991i	0.862201	−	0.506566i	$-0.169085\pi$
$2$	−0.168406	−	0.444051i	−0.119081	−	0.313991i	−0.981282	+	0.192575i	$0.938316\pi$
$3$	0.0744765	−	0.107898i	0.0429990	−	0.0622948i	−0.800895	−	0.598805i	$-0.795642\pi$
$3$	0.0744765	−	0.107898i	0.0429990	−	0.0622948i	0.843894	+	0.536510i	$0.180258\pi$
$4$	1.32820	−	1.17668i	0.664100	−	0.588342i
$5$	−0.265542	−	2.18694i	−0.118754	−	0.978029i	−0.923284	−	0.384117i	$-0.874506\pi$
$5$	−0.265542	−	2.18694i	−0.118754	−	0.978029i	0.804530	−	0.593912i	$-0.202417\pi$
$6$	−0.0604545	−	0.0149007i	−0.0246804	−	0.00608318i
$7$	−3.17143	−	1.66450i	−1.19869	−	0.629120i	−0.257263	−	0.966341i	$-0.582821\pi$
$7$	−3.17143	−	1.66450i	−1.19869	−	0.629120i	−0.941426	+	0.337221i	$0.890513\pi$
$8$	−1.58721	−	0.833034i	−0.561165	−	0.294522i
$9$	1.05772	+	2.78898i	0.352573	+	0.929659i
$10$	−0.926393	+	0.486209i	−0.292951	+	0.153753i
$11$	−0.381234	+	1.00523i	−0.114946	+	0.303088i	−0.980127	−	0.198372i	$-0.936435\pi$
$11$	−0.381234	+	1.00523i	−0.114946	+	0.303088i	0.865181	+	0.501461i	$0.167204\pi$
$12$	−0.0280418	−	0.230945i	−0.00809498	−	0.0666682i
$13$	3.25777	−	1.54497i	0.903543	−	0.428498i
$13$	3.25777	−	1.54497i	0.903543	−	0.428498i
$14$	−0.205032	+	1.68859i	−0.0547971	+	0.451294i
$15$	−0.255743	−	0.134224i	−0.0660325	−	0.0346565i
$16$	0.325162	−	2.67795i	0.0812905	−	0.669487i
$17$	1.74024	+	0.913350i	0.422071	+	0.221520i	0.662367	−	0.749180i	$-0.269552\pi$
$17$	1.74024	+	0.913350i	0.422071	+	0.221520i	−0.240296	+	0.970700i	$0.577244\pi$
$18$	1.06032	−	0.939363i	0.249920	−	0.221410i
$19$	1.98577			0.455567			0.227784	−	0.973712i	$-0.426852\pi$
$19$	1.98577			0.455567			0.227784	+	0.973712i	$0.426852\pi$
$20$	−2.92603	−	2.59223i	−0.654280	−	0.579641i
$21$	−0.415793	+	0.218225i	−0.0907334	+	0.0476206i
$22$	0.510576			0.108855
$23$	−0.763058			−0.159109			−0.0795543	−	0.996831i	$-0.525350\pi$
$23$	−0.763058			−0.159109			−0.0795543	+	0.996831i	$0.525350\pi$
$24$	−0.208093	+	0.109215i	−0.0424767	+	0.0222935i
$25$	0.142520	−	0.0351280i	0.0285040	−	0.00702560i
$26$	−1.23468	−	1.18643i	−0.242140	−	0.232679i
$27$	0.761588	+	0.187715i	0.146568	+	0.0361257i
$28$	−6.17088	+	1.52099i	−1.16619	+	0.287439i
$29$	2.65960	+	7.01279i	0.493876	+	1.30224i	0.917979	+	0.396629i	$0.129820\pi$
$29$	2.65960	+	7.01279i	0.493876	+	1.30224i	−0.424103	+	0.905614i	$0.639411\pi$
$30$	−0.0165337	+	0.136167i	−0.00301862	+	0.0248606i
$31$	2.41733	+	0.595818i	0.434165	+	0.107012i	0.450340	−	0.892857i	$-0.351303\pi$
$31$	2.41733	+	0.595818i	0.434165	+	0.107012i	−0.0161750	+	0.999869i	$0.505149\pi$
$32$	−4.72480	+	1.16456i	−0.835235	+	0.205867i
$33$	0.0800692	+	0.116000i	0.0139383	+	0.0201931i
$34$	0.112506	−	0.926570i	0.0192946	−	0.158905i
$35$	−2.79800	+	7.37772i	−0.472949	+	1.24706i
$36$	4.68661	+	2.45972i	0.781101	+	0.409953i
$37$	6.15828	+	1.51788i	1.01242	+	0.249538i	0.710425	−	0.703773i	$-0.248503\pi$
$37$	6.15828	+	1.51788i	1.01242	+	0.249538i	0.301990	+	0.953311i	$0.402349\pi$
$38$	−0.334416	−	0.881784i	−0.0542495	−	0.143044i
$39$	0.0759280	−	0.466570i	0.0121582	−	0.0747111i
$40$	−1.40032	+	3.69234i	−0.221410	+	0.583811i
$41$	−3.55018	+	5.14332i	−0.554444	+	0.803251i	−0.995553	−	0.0942025i	$-0.969970\pi$
$41$	−3.55018	+	5.14332i	−0.554444	+	0.803251i	0.441109	+	0.897454i	$0.354585\pi$
$42$	0.166925	+	0.147883i	0.0257571	+	0.0228188i
$43$	−1.25241	+	0.308691i	−0.190991	+	0.0470750i	−0.333651	−	0.942697i	$-0.608281\pi$
$43$	−1.25241	+	0.308691i	−0.190991	+	0.0470750i	0.142660	+	0.989772i	$0.454434\pi$
$44$	0.676483	+	1.78374i	0.101984	+	0.268909i
$45$	5.81845	−	3.05376i	0.867364	−	0.455228i
$46$	0.128504	+	0.338836i	0.0189468	+	0.0499587i
$47$	−2.85457	−	2.52893i	−0.416383	−	0.368883i	0.428765	−	0.903416i	$-0.358949\pi$
$47$	−2.85457	−	2.52893i	−0.416383	−	0.368883i	−0.845147	+	0.534533i	$0.820487\pi$
$48$	−0.264728	−	0.234529i	−0.0382102	−	0.0338513i
$49$	3.31098	+	4.79679i	0.472997	+	0.685255i
$50$	−0.0395999	−	0.0573703i	−0.00560027	−	0.00811339i
$51$	0.228156	−	0.119745i	0.0319482	−	0.0167677i
$52$	2.50903	−	5.88540i	0.347940	−	0.816158i
$53$	−10.5639	−	5.54436i	−1.45106	−	0.761576i	−0.459132	−	0.888368i	$-0.651840\pi$
$53$	−10.5639	−	5.54436i	−1.45106	−	0.761576i	−0.991929	+	0.126792i	$0.959532\pi$
$54$	−0.0449014	−	0.369796i	−0.00611030	−	0.0503229i
$55$	2.29961	+	0.566803i	0.310080	+	0.0764277i
$56$	3.64716	+	5.28382i	0.487372	+	0.706080i
$57$	0.147893	−	0.214260i	0.0195889	−	0.0283795i
$58$	2.66614	−	2.36200i	0.350082	−	0.310145i
$59$	0.511731	+	4.21448i	0.0666216	+	0.548679i	0.987359	+	0.158497i	$0.0506648\pi$
$59$	0.511731	+	4.21448i	0.0666216	+	0.548679i	−0.920738	+	0.390182i	$0.872412\pi$
$60$	−0.497617	+	0.122652i	−0.0642421	+	0.0158342i
$61$	−1.97010	+	1.03399i	−0.252246	+	0.132389i	−0.586108	−	0.810233i	$-0.699340\pi$
$61$	−1.97010	+	1.03399i	−0.252246	+	0.132389i	0.333862	+	0.942622i	$0.391648\pi$
$62$	−0.142520	−	1.17376i	−0.0181000	−	0.149067i
$63$	1.28776	−	10.6056i	0.162242	−	1.33618i
$64$	−1.75203	−	2.53826i	−0.219004	−	0.317282i
$65$	−4.24384	−	6.71429i	−0.526383	−	0.832805i
$66$	0.0380259	−	0.0550900i	0.00468066	−	0.00678111i
$67$	6.26593	+	5.55113i	0.765506	+	0.678179i	0.952621	−	0.304159i	$-0.0983754\pi$
$67$	6.26593	+	5.55113i	0.765506	+	0.678179i	−0.187116	+	0.982338i	$0.559914\pi$
$68$	3.38612	−	0.834602i	0.410627	−	0.101210i
$69$	−0.0568299	+	0.0823323i	−0.00684151	+	0.00991164i
$70$	3.74729			0.447886
$71$	−1.38696	+	2.00935i	−0.164602	+	0.238466i	−0.896602	−	0.442838i	$-0.853972\pi$
$71$	−1.38696	+	2.00935i	−0.164602	+	0.238466i	0.732000	+	0.681305i	$0.238587\pi$
$72$	0.644486	−	5.30782i	0.0759534	−	0.625532i
$73$	−3.31646	+	8.74480i	−0.388163	+	1.02350i	0.588457	+	0.808528i	$0.299735\pi$
$73$	−3.31646	+	8.74480i	−0.388163	+	1.02350i	−0.976620	+	0.214973i	$0.931034\pi$
$74$	−0.363077	−	2.99021i	−0.0422069	−	0.347605i
$75$	0.00682415	−	0.0179938i	0.000787985	−	0.00207775i
$76$	2.63750	−	2.33662i	0.302542	−	0.268029i
$77$	2.88226	−	2.55346i	0.328464	−	0.290994i
$78$	−0.219968	+	0.0448575i	−0.0249064	+	0.00507911i
$79$	−10.7698	−	9.54119i	−1.21169	−	1.07347i	−0.995268	−	0.0971687i	$-0.969021\pi$
$79$	−10.7698	−	9.54119i	−1.21169	−	1.07347i	−0.216426	−	0.976299i	$-0.569440\pi$
$80$	−5.94285			−0.664431
$81$	−6.62102	+	5.86572i	−0.735669	+	0.651746i
$82$	2.88177	+	0.710292i	0.318238	+	0.0784386i
$83$	−3.50606	−	5.07941i	−0.384840	−	0.557537i	0.581912	−	0.813252i	$-0.302305\pi$
$83$	−3.50606	−	5.07941i	−0.384840	−	0.557537i	−0.966752	+	0.255714i	$0.917689\pi$
$84$	−0.295475	+	0.779103i	−0.0322389	+	0.0850071i
$85$	1.53533	−	4.04834i	0.166530	−	0.439104i
$86$	0.347989	+	0.504148i	0.0375246	+	0.0543637i
$87$	0.954743	+	0.235323i	0.102359	+	0.0252293i
$88$	1.44249	−	1.27793i	0.153770	−	0.136228i
$89$	8.43464			0.894070			0.447035	−	0.894517i	$-0.352480\pi$
$89$	8.43464			0.894070			0.447035	+	0.894517i	$0.352480\pi$
$90$	−2.33589	−	2.06942i	−0.246224	−	0.218136i
$91$	−12.9034	−	0.522768i	−1.35264	−	0.0548009i
$92$	−1.01349	+	0.897877i	−0.105664	+	0.0936102i
$93$	0.244322	−	0.216450i	0.0253350	−	0.0224448i
$94$	−0.642247	+	1.69347i	−0.0662427	+	0.174668i
$95$	−0.527307	−	4.34276i	−0.0541005	−	0.445558i
$96$	−0.226233	+	0.596529i	−0.0230899	+	0.0608829i
$97$	2.01704	−	16.6118i	0.204799	−	1.68667i	−0.421293	−	0.906924i	$-0.638424\pi$
$97$	2.01704	−	16.6118i	0.204799	−	1.68667i	0.626093	−	0.779749i	$-0.284653\pi$
$98$	1.57243	−	2.27805i	0.158839	−	0.230118i
$99$	−3.20680			−0.322296
$100$	0.147961	−	0.214358i	0.0147961	−	0.0214358i
$101$	11.5124	−	2.83755i	1.14553	−	0.282347i	0.379522	−	0.925183i	$-0.376088\pi$
$101$	11.5124	−	2.83755i	1.14553	−	0.282347i	0.766004	+	0.642836i	$0.222242\pi$
$102$	−0.0915959	−	0.0811469i	−0.00906934	−	0.00803474i
$103$	7.78492	−	11.2784i	0.767071	−	1.11129i	−0.223555	−	0.974691i	$-0.571766\pi$
$103$	7.78492	−	11.2784i	0.767071	−	1.11129i	0.990626	−	0.136603i	$-0.0436183\pi$
$104$	−6.45779	−	0.261631i	−0.633238	−	0.0256550i
$105$	0.587655	+	0.851365i	0.0573493	+	0.0830847i
$106$	−0.682951	+	5.62461i	−0.0663341	+	0.546310i
$107$	2.27277	+	18.7179i	0.219717	+	1.80953i	0.518357	+	0.855165i	$0.326544\pi$
$107$	2.27277	+	18.7179i	0.219717	+	1.80953i	−0.298640	+	0.954366i	$0.596533\pi$
$108$	1.23242	−	0.646825i	0.118590	−	0.0622408i
$109$	3.08436	−	0.760227i	0.295428	−	0.0728165i	−0.0888159	−	0.996048i	$-0.528308\pi$
$109$	3.08436	−	0.760227i	0.295428	−	0.0728165i	0.384244	+	0.923232i	$0.374462\pi$
$110$	−0.135580	−	1.11660i	−0.0129270	−	0.106463i
$111$	0.622423	−	0.551419i	0.0590778	−	0.0523384i
$112$	−5.48866	+	7.95170i	−0.518630	+	0.751365i
$113$	0.742292	+	1.07540i	0.0698290	+	0.101165i	0.856342	−	0.516408i	$-0.172731\pi$
$113$	0.742292	+	1.07540i	0.0698290	+	0.101165i	−0.786513	+	0.617573i	$0.788116\pi$
$114$	−0.120049	−	0.0295894i	−0.0112436	−	0.00277130i
$115$	0.202624	+	1.66876i	0.0188948	+	0.155613i
$116$	11.7843	+	6.18489i	1.09415	+	0.574253i
$117$	7.75470	+	7.45170i	0.716922	+	0.688909i
$118$	1.78527	−	0.936980i	0.164347	−	0.0862560i
$119$	−3.99879	−	5.79325i	−0.366569	−	0.531067i
$120$	0.294105	+	0.426085i	0.0268480	+	0.0388960i
$121$	7.36847	+	6.52789i	0.669861	+	0.593445i
$122$	0.790923	+	0.700696i	0.0716068	+	0.0634381i
$123$	0.290548	+	0.766112i	0.0261978	+	0.0690780i
$124$	3.91179	−	2.05306i	0.351289	−	0.184371i
$125$	−4.02064	−	10.6016i	−0.359617	−	0.948233i
$126$	−4.92630	+	1.21422i	−0.438870	+	0.108172i
$127$	−4.68137	−	4.14733i	−0.415404	−	0.368016i	0.429379	−	0.903124i	$-0.358732\pi$
$127$	−4.68137	−	4.14733i	−0.415404	−	0.368016i	−0.844783	+	0.535108i	$0.820271\pi$
$128$	−6.36070	+	9.21507i	−0.562212	+	0.814505i
$129$	−0.0599680	+	0.158123i	−0.00527989	+	0.0139219i
$130$	−2.26680	+	3.01521i	−0.198811	+	0.264451i
$131$	−6.03292	−	15.9075i	−0.527099	−	1.38984i	−0.889120	−	0.457675i	$-0.848682\pi$
$131$	−6.03292	−	15.9075i	−0.527099	−	1.38984i	0.362021	−	0.932170i	$-0.382087\pi$
$132$	0.242844	+	0.0598556i	0.0211368	+	0.00520976i
$133$	−6.29774	−	3.30531i	−0.546083	−	0.286607i
$134$	1.40976	−	3.71724i	0.121785	−	0.321121i
$135$	0.208286	−	1.71539i	0.0179264	−	0.147637i
$136$	−2.00128	−	2.89936i	−0.171609	−	0.248618i
$137$	−7.59396	+	1.87174i	−0.648796	+	0.159914i	−0.549961	−	0.835190i	$-0.685358\pi$
$137$	−7.59396	+	1.87174i	−0.648796	+	0.159914i	−0.0988344	+	0.995104i	$0.531511\pi$
$138$	0.0461302	+	0.0113701i	0.00392687	+	0.000967885i
$139$	−1.88273	+	15.5057i	−0.159691	+	1.31517i	0.663828	+	0.747885i	$0.268931\pi$
$139$	−1.88273	+	15.5057i	−0.159691	+	1.31517i	−0.823519	+	0.567288i	$0.807993\pi$
$140$	4.96494	+	13.0915i	0.419614	+	1.10643i
$141$	−0.485465	+	0.119656i	−0.0408835	+	0.0100769i
$142$	1.12583	+	0.277492i	0.0944774	+	0.0232866i
$143$	0.311082	+	3.86380i	0.0260140	+	0.323108i
$144$	7.81267	−	1.92565i	0.651056	−	0.160471i
$145$	14.6303	−	7.67858i	1.21498	−	0.637672i
$146$	4.44165			0.367593
$147$	0.764153			0.0630263
$148$	9.96550	−	5.23030i	0.819159	−	0.429928i
$149$	−11.0631	−	9.80103i	−0.906323	−	0.802932i	0.0746234	−	0.997212i	$-0.476225\pi$
$149$	−11.0631	−	9.80103i	−0.906323	−	0.802932i	−0.980946	+	0.194280i	$0.937763\pi$
$150$	−0.00913940			−0.000746229
$151$	−17.2525	+	15.2844i	−1.40399	+	1.24383i	−0.471873	+	0.881667i	$0.656422\pi$
$151$	−17.2525	+	15.2844i	−1.40399	+	1.24383i	−0.932116	+	0.362159i	$0.882040\pi$
$152$	−3.15184	−	1.65421i	−0.255648	−	0.134175i
$153$	−0.706623	+	5.81956i	−0.0571271	+	0.470484i
$154$	−1.61926	−	0.849851i	−0.130483	−	0.0684830i
$155$	0.661114	−	5.44477i	0.0531020	−	0.437334i
$156$	−0.448158	−	0.709043i	−0.0358814	−	0.0567688i
$157$	2.46587	+	20.3083i	0.196798	+	1.62078i	0.671758	+	0.740770i	$0.265539\pi$
$157$	2.46587	+	20.3083i	0.196798	+	1.62078i	−0.474960	+	0.880007i	$0.657538\pi$
$158$	−2.42308	+	6.38913i	−0.192770	+	0.508292i
$159$	−1.38499	+	0.726896i	−0.109836	+	0.0576466i
$160$	3.80146	+	10.0236i	0.300532	+	0.792437i
$161$	2.41999	+	1.27011i	0.190722	+	0.100098i
$162$	3.71970	+	1.95225i	0.292247	+	0.153383i
$163$	−17.0162	−	4.19411i	−1.33281	−	0.328508i	−0.492357	−	0.870394i	$-0.663864\pi$
$163$	−17.0162	−	4.19411i	−1.33281	−	0.328508i	−0.840452	+	0.541886i	$0.817711\pi$
$164$	1.33671	+	11.0088i	0.104379	+	0.859642i
$165$	0.232424	−	0.205910i	0.0180942	−	0.0160300i
$166$	−1.66507	+	2.41227i	−0.129235	+	0.187229i
$167$	8.04047	+	21.2010i	0.622190	+	1.64058i	0.759848	+	0.650101i	$0.225273\pi$
$167$	8.04047	+	21.2010i	0.622190	+	1.64058i	−0.137658	+	0.990480i	$0.543957\pi$
$168$	0.841740			0.0649417
$169$	8.22612	−	10.0663i	0.632778	−	0.774333i
$170$	−2.05623			−0.157705
$171$	2.10039	+	5.53827i	0.160621	+	0.423522i
$172$	−1.30022	+	1.88369i	−0.0991409	+	0.143630i
$173$	11.8345	−	10.4845i	0.899763	−	0.797120i	−0.0801011	−	0.996787i	$-0.525524\pi$
$173$	11.8345	−	10.4845i	0.899763	−	0.797120i	0.979864	+	0.199666i	$0.0639858\pi$
$174$	−0.0562894	−	0.463585i	−0.00426728	−	0.0351443i
$175$	−0.510463	−	0.125818i	−0.0385874	−	0.00951093i
$176$	2.56799	+	1.34779i	0.193570	+	0.101593i
$177$	0.492845	+	0.258665i	0.0370445	+	0.0194425i
$178$	−1.42045	−	3.74541i	−0.106467	−	0.280730i
$179$	−15.6409	+	8.20898i	−1.16906	+	0.613568i	−0.933600	−	0.358317i	$-0.883351\pi$
$179$	−15.6409	+	8.20898i	−1.16906	+	0.613568i	−0.235457	+	0.971885i	$0.575659\pi$
$180$	4.13477	−	10.9025i	0.308187	−	0.812623i
$181$	1.14135	+	9.39987i	0.0848360	+	0.698687i	0.971627	+	0.236517i	$0.0760059\pi$
$181$	1.14135	+	9.39987i	0.0848360	+	0.698687i	−0.886791	+	0.462170i	$0.847071\pi$
$182$	1.94088	+	5.81780i	0.143867	+	0.431244i
$183$	−0.0351611	+	0.289578i	−0.00259919	+	0.0214062i
$184$	1.21114	+	0.635653i	0.0892861	+	0.0468609i
$185$	1.68423	−	13.8708i	0.123827	−	1.01980i
$186$	−0.137260	−	0.0720397i	−0.0100644	−	0.00528221i
$187$	−1.58157	+	1.40115i	−0.115656	+	0.102462i
$188$	−6.76720			−0.493549
$189$	−2.10287	−	1.86298i	−0.152962	−	0.135512i
$190$	−1.83961	+	0.965499i	−0.133459	+	0.0700447i
$191$	11.2892			0.816856			0.408428	−	0.912790i	$-0.366077\pi$
$191$	11.2892			0.816856			0.408428	+	0.912790i	$0.366077\pi$
$192$	−0.404358			−0.0291820
$193$	−2.56411	+	1.34575i	−0.184569	+	0.0968691i	−0.554477	−	0.832199i	$-0.687082\pi$
$193$	−2.56411	+	1.34575i	−0.184569	+	0.0968691i	0.369908	+	0.929068i	$0.379389\pi$
$194$	−7.71617	+	1.90186i	−0.553989	+	0.136546i
$195$	−1.04052	−	0.0421557i	−0.0745134	−	0.00301883i
$196$	10.0419	+	2.47512i	0.717282	+	0.176794i
$197$	−17.8861	+	4.40853i	−1.27433	+	0.314095i	−0.817743	−	0.575583i	$-0.804775\pi$
$197$	−17.8861	+	4.40853i	−1.27433	+	0.314095i	−0.456589	+	0.889678i	$0.650929\pi$
$198$	0.540046	+	1.42398i	0.0383794	+	0.101198i
$199$	0.887649	−	7.31045i	0.0629238	−	0.518224i	−0.926834	−	0.375470i	$-0.877481\pi$
$199$	0.887649	−	7.31045i	0.0629238	−	0.518224i	0.989758	−	0.142754i	$-0.0455957\pi$
$200$	−0.255472	−	0.0629683i	−0.0180646	−	0.00445253i
$201$	1.06562	−	0.262652i	0.0751631	−	0.0185260i
$202$	−3.19878	−	4.63423i	−0.225065	−	0.326063i
$203$	3.23802	−	26.6675i	0.227265	−	1.87169i
$204$	0.162134	−	0.427513i	0.0113517	−	0.0299319i
$205$	12.1908	+	6.39825i	0.851445	+	0.446873i
$206$	−6.31921	−	1.55755i	−0.440280	−	0.108519i
$207$	−0.807101	−	2.12815i	−0.0560974	−	0.147917i
$208$	−3.07806	−	9.22651i	−0.213425	−	0.639743i
$209$	−0.757043	+	1.99616i	−0.0523657	+	0.138077i
$210$	0.279085	−	0.404324i	0.0192587	−	0.0279010i
$211$	−10.9868	−	9.73349i	−0.756365	−	0.670081i	0.194075	−	0.980987i	$-0.437829\pi$
$211$	−10.9868	−	9.73349i	−0.756365	−	0.670081i	−0.950441	+	0.310905i	$0.899368\pi$
$212$	−20.5549	+	5.06633i	−1.41172	+	0.347957i
$213$	0.113509	+	0.299299i	0.00777753	+	0.0205077i
$214$	7.92897	−	4.16144i	0.542013	−	0.284470i
$215$	1.00766	+	2.65697i	0.0687217	+	0.181204i
$216$	−1.05243	−	0.932371i	−0.0716088	−	0.0634398i
$217$	−6.67466	−	5.91323i	−0.453105	−	0.401416i
$218$	−0.857005	−	1.24159i	−0.0580437	−	0.0840908i
$219$	0.696546	+	1.00912i	0.0470682	+	0.0681901i
$220$	3.72129	−	1.95309i	0.250890	−	0.131677i
$221$	7.08041	+	0.286855i	0.476280	+	0.0192960i
$222$	−0.349678	−	0.183525i	−0.0234689	−	0.0123174i
$223$	−1.02238	−	8.42006i	−0.0684637	−	0.563849i	−0.986067	−	0.166351i	$-0.946802\pi$
$223$	−1.02238	−	8.42006i	−0.0684637	−	0.563849i	0.917603	−	0.397498i	$-0.130122\pi$
$224$	16.9228	+	4.17110i	1.13070	+	0.278693i
$225$	0.248717	+	0.360329i	0.0165812	+	0.0240220i
$226$	0.352524	−	0.510719i	0.0234495	−	0.0339725i
$227$	−8.43418	+	7.47203i	−0.559796	+	0.495936i	−0.894913	−	0.446240i	$-0.852763\pi$
$227$	−8.43418	+	7.47203i	−0.559796	+	0.495936i	0.335117	+	0.942177i	$0.391224\pi$
$228$	−0.0556847	−	0.458605i	−0.00368781	−	0.0303718i
$229$	22.2808	−	5.49172i	1.47236	−	0.362903i	0.580142	−	0.814515i	$-0.302997\pi$
$229$	22.2808	−	5.49172i	1.47236	−	0.362903i	0.892215	+	0.451612i	$0.149151\pi$
$230$	0.706891	−	0.371005i	0.0466110	−	0.0244634i
$231$	−0.0608521	−	0.501162i	−0.00400377	−	0.0329740i
$232$	1.62054	−	13.3463i	0.106394	−	0.876230i
$233$	−6.81623	−	9.87501i	−0.446546	−	0.646934i	0.533478	−	0.845814i	$-0.320885\pi$
$233$	−6.81623	−	9.87501i	−0.446546	−	0.646934i	−0.980024	+	0.198880i	$0.936269\pi$
$234$	2.00299	−	4.69839i	0.130940	−	0.307144i
$235$	−4.77261	+	6.91432i	−0.311331	+	0.451041i
$236$	5.63879	+	4.99553i	0.367054	+	0.325181i
$237$	−1.83157	+	0.451441i	−0.118973	+	0.0293243i
$238$	−1.89908	+	2.75129i	−0.123099	+	0.178340i
$239$	23.9254			1.54760			0.773802	−	0.633427i	$-0.218352\pi$
$239$	23.9254			1.54760			0.773802	+	0.633427i	$0.218352\pi$
$240$	−0.442603	+	0.641221i	−0.0285699	+	0.0413907i
$241$	−2.53988	+	20.9178i	−0.163608	+	1.34743i	0.647290	+	0.762244i	$0.275902\pi$
$241$	−2.53988	+	20.9178i	−0.163608	+	1.34743i	−0.810898	+	0.585188i	$0.801021\pi$
$242$	1.65782	−	4.37131i	0.106569	−	0.280999i
$243$	0.423427	+	3.48724i	0.0271629	+	0.223706i
$244$	−1.40002	+	3.69154i	−0.0896268	+	0.236326i
$245$	9.61107	−	8.51467i	0.614029	−	0.543982i
$246$	0.291263	−	0.258036i	0.0185702	−	0.0164518i
$247$	6.46918	−	3.06796i	0.411624	−	0.195210i
$248$	−3.34048	−	2.95941i	−0.212121	−	0.187923i
$249$	−0.809176			−0.0512795
$250$	−4.03053	+	3.57074i	−0.254913	+	0.225833i
$251$	14.2221	+	3.50544i	0.897692	+	0.221261i	0.661055	−	0.750337i	$-0.270109\pi$
$251$	14.2221	+	3.50544i	0.897692	+	0.221261i	0.236636	+	0.971598i	$0.423955\pi$
$252$	−10.7691	−	15.6017i	−0.678387	−	0.982813i
$253$	0.290903	−	0.767049i	0.0182889	−	0.0482239i
$254$	−1.05325	+	2.77720i	−0.0660870	+	0.174257i
$255$	−0.322461	−	0.467165i	−0.0201933	−	0.0292550i
$256$	−0.826037	−	0.203600i	−0.0516273	−	0.0127250i
$257$	15.4079	−	13.6502i	0.961118	−	0.851476i	−0.0278490	−	0.999612i	$-0.508866\pi$
$257$	15.4079	−	13.6502i	0.961118	−	0.851476i	0.988967	+	0.148136i	$0.0473273\pi$
$258$	0.0803135			0.00500010
$259$	−17.0041	−	15.0643i	−1.05658	−	0.936049i
$260$	−13.5373	−	3.92427i	−0.839545	−	0.243373i
$261$	−16.7454	+	14.8351i	−1.03651	+	0.918272i
$262$	−6.04776	+	5.35785i	−0.373632	+	0.331009i
$263$	4.88935	−	12.8922i	0.301490	−	0.794965i	−0.695578	−	0.718451i	$-0.744852\pi$
$263$	4.88935	−	12.8922i	0.301490	−	0.794965i	0.997068	−	0.0765144i	$-0.0243791\pi$
$264$	−0.0304548	−	0.250818i	−0.00187436	−	0.0154368i
$265$	−9.32001	+	24.5748i	−0.572524	+	1.50962i
$266$	−0.407146	+	3.35315i	−0.0249637	+	0.205595i
$267$	0.628182	−	0.910079i	0.0384441	−	0.0556959i
$268$	14.8543			0.907374
$269$	2.11288	−	3.06104i	0.128825	−	0.186635i	−0.753264	−	0.657718i	$-0.771522\pi$
$269$	2.11288	−	3.06104i	0.128825	−	0.186635i	0.882088	+	0.471084i	$0.156137\pi$
$270$	−0.796798	+	0.196393i	−0.0484916	+	0.0119521i
$271$	−3.29939	−	2.92301i	−0.200424	−	0.177560i	0.556941	−	0.830552i	$-0.311975\pi$
$271$	−3.29939	−	2.92301i	−0.200424	−	0.177560i	−0.757365	+	0.652992i	$0.773513\pi$
$272$	3.01176	−	4.36329i	0.182615	−	0.264564i
$273$	−1.01741	+	1.35331i	−0.0615762	+	0.0819063i
$274$	2.11002	+	3.05689i	0.127471	+	0.184674i
$275$	−0.0190216	+	0.156657i	−0.00114705	+	0.00944679i
$276$	0.0213975	+	0.176225i	0.00128798	+	0.0106075i
$277$	−13.1041	+	6.87757i	−0.787350	+	0.413233i	−0.809941	−	0.586512i	$-0.800501\pi$
$277$	−13.1041	+	6.87757i	−0.787350	+	0.413233i	0.0225910	+	0.999745i	$0.492808\pi$
$278$	7.20237	−	1.77522i	0.431969	−	0.106471i
$279$	0.895133	+	7.37208i	0.0535902	+	0.441355i
$280$	10.5869	−	9.37919i	0.632689	−	0.560514i
$281$	10.4366	−	15.1201i	0.622598	−	0.901989i	−0.377110	−	0.926169i	$-0.623082\pi$
$281$	10.4366	−	15.1201i	0.622598	−	0.901989i	0.999708	+	0.0241796i	$0.00769737\pi$
$282$	0.134889	+	0.195420i	0.00803252	+	0.0116371i
$283$	−28.1777	−	6.94518i	−1.67499	−	0.412848i	−0.716413	−	0.697677i	$-0.754217\pi$
$283$	−28.1777	−	6.94518i	−1.67499	−	0.412848i	−0.958579	+	0.284828i	$0.908063\pi$
$284$	0.522216	+	4.30084i	0.0309878	+	0.255208i
$285$	−0.507846	−	0.266538i	−0.0300822	−	0.0157884i
$286$	1.66334	−	0.788825i	0.0983552	−	0.0466442i
$287$	19.8202	−	10.4024i	1.16995	−	0.614036i
$288$	−8.24545	−	11.9456i	−0.485868	−	0.703901i
$289$	−7.46286	−	10.8118i	−0.438992	−	0.635990i
$290$	−5.87352	−	5.20348i	−0.344905	−	0.305559i
$291$	−1.64216	−	1.45482i	−0.0962649	−	0.0852832i
$292$	5.88493	+	15.5173i	0.344389	+	0.908080i
$293$	4.66967	−	2.45083i	0.272805	−	0.143179i	−0.322774	−	0.946476i	$-0.604615\pi$
$293$	4.66967	−	2.45083i	0.272805	−	0.143179i	0.595578	+	0.803297i	$0.296923\pi$
$294$	−0.128688	−	0.339323i	−0.00750525	−	0.0197897i
$295$	9.08093	−	2.23825i	0.528712	−	0.130316i
$296$	−8.51006	−	7.53925i	−0.494637	−	0.438210i
$297$	−0.479039	+	0.694008i	−0.0277967	+	0.0402704i
$298$	−2.48907	+	6.56313i	−0.144188	+	0.380192i
$299$	−2.48587	+	1.17890i	−0.143761	+	0.0681777i
$300$	−0.0121092	−	0.0319293i	−0.000699123	−	0.00184344i
$301$	4.48575	+	1.10564i	0.258554	+	0.0637279i
$302$	9.69248	+	5.08700i	0.557739	+	0.292724i
$303$	0.551237	−	1.45349i	0.0316677	−	0.0835010i
$304$	0.645697	−	5.31779i	0.0370333	−	0.304996i
$305$	2.78442	+	4.03393i	0.159435	+	0.230982i
$306$	2.70318	−	0.666275i	0.154531	−	0.0380884i
$307$	10.4194	+	2.56815i	0.594666	+	0.146572i	0.525151	−	0.851009i	$-0.324009\pi$
$307$	10.4194	+	2.56815i	0.594666	+	0.146572i	0.0695148	+	0.997581i	$0.477855\pi$
$308$	0.823607	−	6.78301i	0.0469293	−	0.386498i
$309$	−0.637122	−	1.67995i	−0.0362446	−	0.0955691i
$310$	−2.52909	+	0.623365i	−0.143643	+	0.0354047i
$311$	10.0792	+	2.48431i	0.571541	+	0.140872i	0.514486	−	0.857499i	$-0.327983\pi$
$311$	10.0792	+	2.48431i	0.571541	+	0.140872i	0.0570552	+	0.998371i	$0.481829\pi$
$312$	−0.509183	+	0.677296i	−0.0288268	+	0.0383443i
$313$	0.457832	−	0.112845i	0.0258782	−	0.00637840i	−0.226355	−	0.974045i	$-0.572681\pi$
$313$	0.457832	−	0.112845i	0.0258782	−	0.00637840i	0.252234	+	0.967666i	$0.418835\pi$
$314$	8.60265	−	4.51502i	0.485475	−	0.254797i
$315$	−23.5358			−1.32609
$316$	−25.5314			−1.43625
$317$	−19.7338	+	10.3571i	−1.10836	+	0.581713i	−0.916631	−	0.399734i	$-0.869102\pi$
$317$	−19.7338	+	10.3571i	−1.10836	+	0.581713i	−0.191731	+	0.981447i	$0.561410\pi$
$318$	0.556019	+	0.492590i	0.0311800	+	0.0276231i
$319$	−8.06340			−0.451464
$320$	−5.08577	+	4.50560i	−0.284303	+	0.251871i
$321$	2.18889	+	1.14882i	0.122172	+	0.0641208i
$322$	0.156451	−	1.28849i	0.00871868	−	0.0718048i
$323$	3.45572	+	1.81370i	0.192282	+	0.100917i
$324$	−1.89196	+	15.5817i	−0.105109	+	0.865650i
$325$	0.410025	−	0.334628i	0.0227441	−	0.0185618i
$326$	1.00323	+	8.26236i	0.0555639	+	0.457610i
$327$	0.147686	−	0.389415i	0.00816703	−	0.0215347i
$328$	9.91944	−	5.20612i	0.547710	−	0.287460i
$329$	4.84369	+	12.7718i	0.267041	+	0.704130i
$330$	−0.130576	−	0.0685316i	−0.00718797	−	0.00377254i
$331$	18.3363	+	9.62364i	1.00785	+	0.528963i	0.886049	−	0.463591i	$-0.153439\pi$
$331$	18.3363	+	9.62364i	1.00785	+	0.528963i	0.121805	+	0.992554i	$0.461132\pi$
$332$	−10.6336	−	2.62095i	−0.583595	−	0.143843i
$333$	2.28040	+	18.7808i	0.124965	+	1.02918i
$334$	8.06025	−	7.14076i	0.441037	−	0.390725i
$335$	10.4761	−	15.1773i	0.572371	−	0.829223i
$336$	0.449195	+	1.18443i	0.0245056	+	0.0646160i
$337$	0.342026			0.0186313			0.00931566	−	0.999957i	$-0.497035\pi$
$337$	0.342026			0.0186313			0.00931566	+	0.999957i	$0.497035\pi$
$338$	−5.85529	−	1.95758i	−0.318486	−	0.106478i
$339$	0.171316			0.00930462
$340$	−2.72438	−	7.18360i	−0.147750	−	0.389586i
$341$	−1.52050	+	2.20283i	−0.0823398	+	0.119290i
$342$	2.10556	−	1.86536i	0.113855	−	0.100867i
$343$	0.505753	+	4.16525i	0.0273081	+	0.224903i
$344$	2.24499	+	0.553341i	0.121042	+	0.0298341i
$345$	0.195146	+	0.102421i	0.0105063	+	0.00551415i
$346$	−6.64865	−	3.48948i	−0.357434	−	0.187596i
$347$	1.67648	+	4.42052i	0.0899983	+	0.237306i	0.972456	−	0.233085i	$-0.0748821\pi$
$347$	1.67648	+	4.42052i	0.0899983	+	0.237306i	−0.882458	+	0.470391i	$0.844113\pi$
$348$	1.54499	−	0.810874i	0.0828202	−	0.0434674i
$349$	−12.3411	+	32.5408i	−0.660604	+	1.74187i	0.00988677	+	0.999951i	$0.496853\pi$
$349$	−12.3411	+	32.5408i	−0.660604	+	1.74187i	−0.670491	+	0.741918i	$0.733916\pi$
$350$	0.0300957	+	0.247860i	0.00160868	+	0.0132487i
$351$	2.77109	−	0.565102i	0.147910	−	0.0301629i
$352$	0.630603	−	5.19349i	0.0336113	−	0.276814i
$353$	−4.23494	−	2.22267i	−0.225403	−	0.118301i	0.348242	−	0.937405i	$-0.386779\pi$
$353$	−4.23494	−	2.22267i	−0.225403	−	0.118301i	−0.573645	+	0.819104i	$0.694471\pi$
$354$	0.0318623	−	0.262409i	0.00169346	−	0.0139469i
$355$	4.76263	+	2.49962i	0.252774	+	0.132666i
$356$	11.2029	−	9.92490i	0.593752	−	0.526019i
$357$	−0.922896			−0.0488448
$358$	6.27924	+	5.56292i	0.331868	+	0.294009i
$359$	7.07405	−	3.71275i	0.373354	−	0.195951i	−0.267601	−	0.963530i	$-0.586231\pi$
$359$	7.07405	−	3.71275i	0.373354	−	0.195951i	0.640955	+	0.767579i	$0.278539\pi$
$360$	−11.7790			−0.620808
$361$	−15.0567			−0.792459
$362$	3.98181	−	2.08982i	0.209279	−	0.109838i
$363$	1.25312	−	0.308867i	0.0657719	−	0.0162113i
$364$	−17.7534	+	14.4889i	−0.930533	+	0.759423i
$365$	20.0050	+	4.93079i	1.04711	+	0.258089i
$366$	0.134509	−	0.0331534i	0.00703089	−	0.00173296i
$367$	8.39723	+	22.1417i	0.438332	+	1.15579i	0.954213	+	0.299127i	$0.0966953\pi$
$367$	8.39723	+	22.1417i	0.438332	+	1.15579i	−0.515881	+	0.856660i	$0.672535\pi$
$368$	−0.248117	+	2.04343i	−0.0129340	+	0.106521i
$369$	−18.0997	−	4.46117i	−0.942232	−	0.232239i
$370$	−6.44300	+	1.58806i	−0.334955	+	0.0825591i
$371$	24.2741	+	35.1671i	1.26025	+	1.82578i
$372$	0.0698150	−	0.574979i	0.00361974	−	0.0298112i
$373$	−2.53068	+	6.67286i	−0.131034	+	0.345508i	−0.984436	−	0.175746i	$-0.943766\pi$
$373$	−2.53068	+	6.67286i	−0.131034	+	0.345508i	0.853402	+	0.521254i	$0.174535\pi$
$374$	0.888525	+	0.466334i	0.0459446	+	0.0241136i
$375$	−1.44333	−	0.355749i	−0.0745332	−	0.0183708i
$376$	2.42413	+	6.39191i	0.125015	+	0.329638i
$377$	19.4989	+	18.7371i	1.00425	+	0.965007i
$378$	−0.473122	+	1.24752i	−0.0243348	+	0.0641656i
$379$	9.73075	−	14.0974i	0.499835	−	0.724136i	−0.489142	−	0.872204i	$-0.662690\pi$
$379$	9.73075	−	14.0974i	0.499835	−	0.724136i	0.988977	+	0.148068i	$0.0473054\pi$
$380$	−5.81042	−	5.14759i	−0.298068	−	0.264066i
$381$	−0.796140	+	0.196231i	−0.0407875	+	0.0100532i
$382$	−1.90117	−	5.01297i	−0.0972723	−	0.256486i
$383$	5.55285	−	2.91436i	0.283737	−	0.148917i	−0.316851	−	0.948475i	$-0.602625\pi$
$383$	5.55285	−	2.91436i	0.283737	−	0.148917i	0.600588	+	0.799559i	$0.294933\pi$
$384$	0.520563	+	1.37261i	0.0265649	+	0.0700458i
$385$	−6.34962	−	5.62527i	−0.323607	−	0.286690i
$386$	1.02939	+	0.911962i	0.0523947	+	0.0464177i
$387$	−2.18563	−	3.16643i	−0.111102	−	0.160959i
$388$	−16.8678	−	24.4372i	−0.856333	−	1.24061i
$389$	−26.7170	+	14.0222i	−1.35461	+	0.710953i	−0.976643	−	0.214867i	$-0.931068\pi$
$389$	−26.7170	+	14.0222i	−1.35461	+	0.710953i	−0.377964	+	0.925820i	$0.623376\pi$
$390$	0.156511	+	0.469145i	0.00792526	+	0.0237561i
$391$	−1.32791	−	0.696938i	−0.0671551	−	0.0352457i
$392$	−1.25935	−	10.3717i	−0.0636068	−	0.523849i
$393$	−2.16570	−	0.533796i	−0.109245	−	0.0269265i
$394$	4.96974	+	7.19992i	0.250372	+	0.362727i
$395$	−18.0062	+	26.0864i	−0.905988	+	1.31255i
$396$	−4.25928	+	3.77339i	−0.214037	+	0.189620i
$397$	0.928650	+	7.64812i	0.0466076	+	0.383848i	0.997283	+	0.0736616i	$0.0234685\pi$
$397$	0.928650	+	7.64812i	0.0466076	+	0.383848i	−0.950676	+	0.310187i	$0.899608\pi$
$398$	−3.39570	+	0.836964i	−0.170211	+	0.0419532i
$399$	−0.825669	+	0.433345i	−0.0413352	+	0.0216944i
$400$	−0.0477290	−	0.393083i	−0.00238645	−	0.0196542i
$401$	−0.112268	+	0.924611i	−0.00560640	+	0.0461729i	−0.995244	−	0.0974177i	$-0.968942\pi$
$401$	−0.112268	+	0.924611i	−0.00560640	+	0.0461729i	0.989637	+	0.143591i	$0.0458648\pi$
$402$	−0.296088	−	0.428957i	−0.0147675	−	0.0213945i
$403$	8.79562	−	1.79367i	0.438141	−	0.0893490i
$404$	11.9519	−	17.3153i	0.594628	−	0.861467i
$405$	14.5861	+	12.9222i	0.724790	+	0.642108i
$406$	−12.3870	+	3.05313i	−0.614758	+	0.151524i
$407$	−3.87356	+	5.61182i	−0.192005	+	0.278168i
$408$	−0.461884			−0.0228666
$409$	−1.74827	+	2.53281i	−0.0864464	+	0.125239i	−0.863821	−	0.503798i	$-0.831935\pi$
$409$	−1.74827	+	2.53281i	−0.0864464	+	0.125239i	0.777375	+	0.629038i	$0.216551\pi$
$410$	0.788133	−	6.49086i	0.0389231	−	0.320561i
$411$	−0.363615	+	0.958773i	−0.0179358	+	0.0472928i
$412$	−2.93117	−	24.1404i	−0.144408	−	1.18931i
$413$	5.39207	−	14.2177i	0.265326	−	0.699608i
$414$	−0.809086	+	0.716788i	−0.0397644	+	0.0352282i
$415$	−10.1773	+	9.01634i	−0.499586	+	0.442595i
$416$	−13.5931	+	11.0936i	−0.666457	+	0.543907i
$417$	1.53281	+	1.35795i	0.0750620	+	0.0664991i
$418$	1.01389			0.0495908
$419$	11.8447	−	10.4935i	0.578650	−	0.512639i	−0.322257	−	0.946652i	$-0.604441\pi$
$419$	11.8447	−	10.4935i	0.578650	−	0.512639i	0.900906	+	0.434013i	$0.142903\pi$
$420$	1.78231	+	0.439300i	0.0869679	+	0.0214357i
$421$	−12.8711	−	18.6470i	−0.627298	−	0.908798i	0.372517	−	0.928025i	$-0.378495\pi$
$421$	−12.8711	−	18.6470i	−0.627298	−	0.908798i	−0.999815	+	0.0192271i	$0.993879\pi$
$422$	−2.47191	+	6.51790i	−0.120331	+	0.317286i
$423$	4.03380	−	10.6362i	0.196130	−	0.517152i
$424$	12.1485	+	17.6002i	0.589984	+	0.854739i
$425$	0.280103	+	0.0690393i	0.0135870	+	0.00334890i
$426$	0.113788	−	0.100808i	0.00551307	−	0.00488415i
$427$	7.96913			0.385653
$428$	25.0438	+	22.1868i	1.21054	+	1.07244i
$429$	0.440064	+	0.254197i	0.0212465	+	0.0122728i
$430$	1.01014	−	0.894903i	0.0487131	−	0.0431560i
$431$	23.9389	−	21.2080i	1.15310	−	1.02156i	0.153657	−	0.988124i	$-0.450895\pi$
$431$	23.9389	−	21.2080i	1.15310	−	1.02156i	0.999441	−	0.0334313i	$-0.0106435\pi$
$432$	0.750329	−	1.97846i	0.0361002	−	0.0951885i
$433$	−4.69774	−	38.6893i	−0.225759	−	1.85929i	−0.461061	−	0.887368i	$-0.652531\pi$
$433$	−4.69774	−	38.6893i	−0.225759	−	1.85929i	0.235302	−	0.971922i	$-0.424392\pi$
$434$	−1.50172	+	3.95971i	−0.0720849	+	0.190072i
$435$	0.261112	−	2.15045i	0.0125194	−	0.103106i
$436$	3.20210	−	4.63905i	0.153353	−	0.222170i
$437$	−1.51526			−0.0724846
$438$	0.330798	−	0.479244i	0.0158062	−	0.0228992i
$439$	−10.5973	+	2.61201i	−0.505784	+	0.124664i	−0.483947	−	0.875097i	$-0.660797\pi$
$439$	−10.5973	+	2.61201i	−0.505784	+	0.124664i	−0.0218362	+	0.999762i	$0.506951\pi$
$440$	−3.17781	−	2.81529i	−0.151496	−	0.134214i
$441$	−9.87604	+	14.3079i	−0.470287	+	0.681329i
$442$	−1.06501	−	3.19237i	−0.0506572	−	0.151846i
$443$	14.3398	+	20.7748i	0.681303	+	0.987038i	0.999242	+	0.0389270i	$0.0123940\pi$
$443$	14.3398	+	20.7748i	0.681303	+	0.987038i	−0.317939	+	0.948111i	$0.602991\pi$
$444$	0.177858	−	1.46479i	0.00844075	−	0.0695158i
$445$	−2.23975	−	18.4460i	−0.106175	−	0.874426i
$446$	−3.56676	+	1.87198i	−0.168891	+	0.0886409i
$447$	−1.88145	+	0.463736i	−0.0889895	+	0.0219339i
$448$	1.33153	+	10.9662i	0.0629090	+	0.518102i
$449$	14.6220	−	12.9540i	0.690056	−	0.611336i	−0.243444	−	0.969915i	$-0.578277\pi$
$449$	14.6220	−	12.9540i	0.690056	−	0.611336i	0.933499	+	0.358579i	$0.116739\pi$
$450$	0.118119	−	0.171125i	0.00556818	−	0.00806690i
$451$	−3.81677	−	5.52955i	−0.179725	−	0.260376i
$452$	2.25131	+	0.554899i	0.105893	+	0.0261003i
$453$	0.364246	+	2.99984i	0.0171138	+	0.140945i
$454$	4.73833	+	2.48687i	0.222381	+	0.116715i
$455$	2.28314	+	28.3578i	0.107035	+	1.32943i
$456$	−0.413224	+	0.216877i	−0.0193510	+	0.0101562i
$457$	4.05160	+	5.86976i	0.189526	+	0.274576i	0.906215	−	0.422817i	$-0.138959\pi$
$457$	4.05160	+	5.86976i	0.189526	+	0.274576i	−0.716689	+	0.697393i	$0.754343\pi$
$458$	−6.19083	−	8.96897i	−0.289279	−	0.419092i
$459$	1.15390	+	1.02226i	0.0538594	+	0.0477152i
$460$	2.23273	+	1.97802i	0.104101	+	0.0922259i
$461$	−11.5511	−	30.4578i	−0.537990	−	1.41856i	−0.878237	−	0.478226i	$-0.841280\pi$
$461$	−11.5511	−	30.4578i	−0.537990	−	1.41856i	0.340247	−	0.940336i	$-0.389489\pi$
$462$	−0.212294	+	0.111420i	−0.00987679	+	0.00518374i
$463$	11.4714	+	30.2476i	0.533121	+	1.40572i	0.883197	+	0.469002i	$0.155386\pi$
$463$	11.4714	+	30.2476i	0.533121	+	1.40572i	−0.350077	+	0.936721i	$0.613844\pi$
$464$	19.6447	−	4.84199i	0.911983	−	0.224784i
$465$	−0.538241	−	0.476840i	−0.0249603	−	0.0221129i
$466$	−3.23711	+	4.68977i	−0.149956	+	0.217249i
$467$	3.33066	−	8.78224i	0.154125	−	0.406394i	−0.835608	−	0.549327i	$-0.814884\pi$
$467$	3.33066	−	8.78224i	0.154125	−	0.406394i	0.989732	+	0.142933i	$0.0456534\pi$
$468$	19.0681	+	0.772524i	0.881423	+	0.0357099i
$469$	−10.6321	−	28.0347i	−0.490947	−	1.29452i
$470$	3.87405	+	0.954867i	0.178697	+	0.0440447i
$471$	2.37487	+	1.24643i	0.109428	+	0.0574324i
$472$	2.69858	−	7.11557i	0.124212	−	0.327521i
$473$	0.167155	−	1.37664i	0.00768579	−	0.0632982i
$474$	0.508911	+	0.737284i	0.0233750	+	0.0338646i
$475$	0.283012	−	0.0697562i	0.0129855	−	0.00320063i
$476$	−12.1280	−	2.98929i	−0.555887	−	0.137014i
$477$	4.28945	−	35.3268i	0.196401	−	1.61750i
$478$	−4.02919	−	10.6241i	−0.184291	−	0.485935i
$479$	−25.9926	+	6.40660i	−1.18763	+	0.292725i	−0.783157	−	0.621824i	$-0.786392\pi$
$479$	−25.9926	+	6.40660i	−1.18763	+	0.292725i	−0.404475	+	0.914549i	$0.632546\pi$
$480$	1.36465	+	0.336355i	0.0622873	+	0.0153524i
$481$	22.4073	−	4.56947i	1.02169	−	0.208350i
$482$	9.71628	−	2.39485i	0.442565	−	0.109082i
$483$	0.317274	−	0.166518i	0.0144365	−	0.00757684i
$484$	17.4681			0.794003
$485$	−36.8646			−1.67394
$486$	1.47720	−	0.775296i	0.0670073	−	0.0351681i
$487$	2.38643	+	2.11419i	0.108139	+	0.0958032i	0.715460	−	0.698654i	$-0.246217\pi$
$487$	2.38643	+	2.11419i	0.108139	+	0.0958032i	−0.607321	+	0.794457i	$0.707756\pi$
$488$	3.98833			0.180543
$489$	−1.71984	+	1.52365i	−0.0777738	+	0.0689016i
$490$	−5.39951	−	2.83388i	−0.243925	−	0.128022i
$491$	1.73226	−	14.2665i	0.0781759	−	0.643836i	−0.899975	−	0.435941i	$-0.856416\pi$
$491$	1.73226	−	14.2665i	0.0781759	−	0.643836i	0.978151	−	0.207895i	$-0.0666613\pi$
$492$	1.28738	+	0.675668i	0.0580395	+	0.0304615i
$493$	−1.77678	+	14.6331i	−0.0800222	+	0.659042i
$494$	−2.45178	−	2.35598i	−0.110311	−	0.106001i
$495$	0.851542	+	7.01308i	0.0382740	+	0.315215i
$496$	2.38159	−	6.27975i	0.106937	−	0.281969i
$497$	7.74320	−	4.06395i	0.347330	−	0.182293i
$498$	0.136270	+	0.359316i	0.00610642	+	0.0161013i
$499$	−20.0313	−	10.5132i	−0.896723	−	0.470636i	−0.0476207	−	0.998865i	$-0.515164\pi$
$499$	−20.0313	−	10.5132i	−0.896723	−	0.470636i	−0.849102	+	0.528229i	$0.822856\pi$
$500$	−17.8149	−	9.34998i	−0.796707	−	0.418144i
$501$	2.88637	+	0.711425i	0.128953	+	0.0317841i
$502$	−0.838501	−	6.90568i	−0.0374241	−	0.308216i
$503$	−13.6612	+	12.1027i	−0.609121	+	0.539634i	−0.910308	−	0.413931i	$-0.864156\pi$
$503$	−13.6612	+	12.1027i	−0.609121	+	0.539634i	0.301187	+	0.953565i	$0.402617\pi$
$504$	−10.8788	+	15.7606i	−0.484580	+	0.702035i
$505$	−9.26258	−	24.4234i	−0.412179	−	1.08683i
$506$	−0.389599			−0.0173198
$507$	−0.473483	−	1.63729i	−0.0210281	−	0.0727144i
$508$	−11.0979			−0.492389
$509$	−0.158371	−	0.417590i	−0.00701967	−	0.0185094i	0.931461	−	0.363842i	$-0.118535\pi$
$509$	−0.158371	−	0.417590i	−0.00701967	−	0.0185094i	−0.938480	+	0.345333i	$0.887766\pi$
$510$	−0.153141	+	0.221863i	−0.00678118	+	0.00982424i
$511$	25.0736	−	22.2133i	1.10919	−	0.982658i
$512$	2.74803	+	22.6321i	0.121447	+	1.00021i
$513$	1.51234	+	0.372758i	0.0667714	+	0.0164577i
$514$	−8.65617	−	4.54311i	−0.381807	−	0.200388i
$515$	−26.7324	−	14.0302i	−1.17797	−	0.618246i
$516$	0.106411	+	0.280582i	0.00468447	+	0.0123519i
$517$	3.63042	−	1.90539i	0.159666	−	0.0837990i
$518$	−3.82572	+	10.0876i	−0.168092	+	0.443223i
$519$	−0.249858	−	2.05777i	−0.0109676	−	0.0903260i
$520$	1.14265	+	14.1923i	0.0501084	+	0.622372i
$521$	3.26178	−	26.8632i	0.142901	−	1.17690i	−0.728049	−	0.685526i	$-0.759572\pi$
$521$	3.26178	−	26.8632i	0.142901	−	1.17690i	0.870950	−	0.491372i	$-0.163504\pi$
$522$	9.40759	+	4.93748i	0.411759	+	0.216108i
$523$	0.895016	−	7.37112i	0.0391363	−	0.322316i	−0.959972	−	0.280096i	$-0.909634\pi$
$523$	0.895016	−	7.37112i	0.0391363	−	0.322316i	0.999108	−	0.0422205i	$-0.0134432\pi$
$524$	−26.7310	−	14.0295i	−1.16775	−	0.612883i
$525$	−0.0515929	+	0.0457074i	−0.00225170	+	0.00199483i
$526$	−6.54818			−0.285514
$527$	3.66255	+	3.24473i	0.159543	+	0.141343i
$528$	0.336678	−	0.176702i	0.0146520	−	0.00768999i
$529$	−22.4177			−0.974684
$530$	12.4820			0.542185
$531$	−11.2128	+	5.88494i	−0.486595	+	0.255385i
$532$	−12.2540	+	3.02033i	−0.531277	+	0.130948i
$533$	−3.61937	+	22.2407i	−0.156772	+	0.963350i
$534$	−0.509911	−	0.125682i	−0.0220660	−	0.00543879i
$535$	40.3315	−	9.94081i	1.74368	−	0.429779i
$536$	−5.32109	−	14.0306i	−0.229836	−	0.606028i
$537$	−0.279149	+	2.29900i	−0.0120462	+	0.0992091i
$538$	−1.71508	−	0.422729i	−0.0739423	−	0.0182251i
$539$	−6.08413	+	1.49960i	−0.262062	+	0.0645925i
$540$	−1.74183	−	2.52347i	−0.0749563	−	0.108593i
$541$	3.54016	−	29.1559i	0.152204	−	1.25351i	−0.693736	−	0.720230i	$-0.744036\pi$
$541$	3.54016	−	29.1559i	0.152204	−	1.25351i	0.845939	−	0.533279i	$-0.179040\pi$
$542$	−0.742325	+	1.95735i	−0.0318856	+	0.0840754i
$543$	1.09923	+	0.576920i	0.0471725	+	0.0247580i
$544$	−9.28596	−	2.28878i	−0.398132	−	0.0981307i
$545$	−2.48160	−	6.54344i	−0.106300	−	0.280290i
$546$	0.772278	+	0.223873i	0.0330505	+	0.00958088i
$547$	−2.02231	+	5.33239i	−0.0864676	+	0.227996i	−0.971275	−	0.237961i	$-0.923521\pi$
$547$	−2.02231	+	5.33239i	−0.0864676	+	0.227996i	0.884807	+	0.465958i	$0.154290\pi$
$548$	−7.88386	+	11.4217i	−0.336782	+	0.487912i
$549$	−4.96759	−	4.40090i	−0.212012	−	0.187826i
$550$	0.0727672	−	0.0179355i	0.00310280	−	0.000764773i
$551$	5.28136	+	13.9258i	0.224994	+	0.593259i
$552$	0.158787	−	0.0833377i	0.00675841	−	0.00354709i
$553$	18.2743	+	48.1855i	0.777104	+	2.04906i
$554$	5.26081	+	4.66067i	0.223510	+	0.198013i
$555$	−1.37120	−	1.21478i	−0.0582042	−	0.0515644i
$556$	15.7446	+	22.8100i	0.667720	+	0.967360i
$557$	−1.34919	−	1.95464i	−0.0571669	−	0.0828206i	0.793358	−	0.608755i	$-0.208331\pi$
$557$	−1.34919	−	1.95464i	−0.0571669	−	0.0828206i	−0.850525	+	0.525935i	$0.823716\pi$
$558$	3.12283	−	1.63899i	0.132200	−	0.0693840i
$559$	−3.60314	+	2.94059i	−0.152397	+	0.124374i
$560$	18.8474	+	9.89186i	0.796446	+	0.418007i
$561$	0.0333910	+	0.275000i	0.00140977	+	0.0116105i
$562$	−8.47169	−	2.08808i	−0.357357	−	0.0880805i
$563$	−19.8515	−	28.7599i	−0.836642	−	1.21209i	−0.975111	−	0.221718i	$-0.928833\pi$
$563$	−19.8515	−	28.7599i	−0.836642	−	1.21209i	0.138469	−	0.990367i	$-0.455782\pi$
$564$	−0.503998	+	0.730166i	−0.0212221	+	0.0307456i
$565$	2.15472	−	1.90891i	0.0906495	−	0.0803085i
$566$	1.66129	+	13.6820i	0.0698292	+	0.575095i
$567$	30.7616	−	7.58205i	1.29187	−	0.318416i
$568$	3.87526	−	2.03389i	0.162602	−	0.0853402i
$569$	−1.13999	−	9.38867i	−0.0477909	−	0.393594i	−0.996902	−	0.0786525i	$-0.974938\pi$
$569$	−1.13999	−	9.38867i	−0.0477909	−	0.393594i	0.949111	−	0.314941i	$-0.101985\pi$
$570$	−0.0328321	+	0.270396i	−0.00137518	+	0.0113257i
$571$	10.8434	+	15.7094i	0.453782	+	0.657417i	0.981380	−	0.192077i	$-0.0615224\pi$
$571$	10.8434	+	15.7094i	0.453782	+	0.657417i	−0.527597	+	0.849495i	$0.676907\pi$
$572$	4.95965	+	4.76586i	0.207374	+	0.199271i
$573$	0.840779	−	1.21808i	0.0351240	−	0.0508859i
$574$	−7.95705	−	7.04933i	−0.332121	−	0.294233i
$575$	−0.108751	+	0.0268047i	−0.00453523	+	0.00111783i
$576$	5.22598	−	7.57114i	0.217749	−	0.315464i
$577$	16.8185			0.700164			0.350082	−	0.936719i	$-0.386154\pi$
$577$	16.8185			0.700164			0.350082	+	0.936719i	$0.386154\pi$
$578$	−3.54421	+	5.13467i	−0.147420	+	0.213574i
$579$	−0.0457625	+	0.376888i	−0.00190183	+	0.0156629i
$580$	10.3967	−	27.4139i	0.431701	−	1.13830i
$581$	2.66458	+	21.9448i	0.110546	+	0.910425i
$582$	−0.369466	+	0.974202i	−0.0153149	+	0.0403820i
$583$	9.60066	−	8.50545i	0.397619	−	0.352260i
$584$	12.5486	−	11.1171i	0.519267	−	0.460030i
$585$	14.2372	−	18.9378i	0.588636	−	0.782981i
$586$	−1.87469	−	1.66083i	−0.0774429	−	0.0686084i
$587$	−18.0236			−0.743913			−0.371957	−	0.928250i	$-0.621313\pi$
$587$	−18.0236			−0.743913			−0.371957	+	0.928250i	$0.621313\pi$
$588$	1.01495	−	0.899166i	0.0418558	−	0.0370810i
$589$	4.80026	+	1.18316i	0.197791	+	0.0487512i
$590$	−2.52318	−	3.65546i	−0.103878	−	0.150493i
$591$	−0.856424	+	2.25820i	−0.0352286	+	0.0928901i
$592$	6.06724	−	15.9980i	0.249362	−	0.657514i
$593$	−1.91823	−	2.77903i	−0.0787722	−	0.114121i	0.781617	−	0.623758i	$-0.214395\pi$
$593$	−1.91823	−	2.77903i	−0.0787722	−	0.114121i	−0.860389	+	0.509637i	$0.829780\pi$
$594$	0.388848	+	0.0958425i	0.0159546	+	0.00393246i
$595$	−11.6076	+	10.2835i	−0.475867	+	0.421581i
$596$	−26.2267			−1.07429
$597$	−0.722673	−	0.640232i	−0.0295770	−	0.0262030i
$598$	0.942128	+	0.905316i	0.0385265	+	0.0370211i
$599$	21.4409	−	18.9950i	0.876052	−	0.776115i	−0.0996943	−	0.995018i	$-0.531786\pi$
$599$	21.4409	−	18.9950i	0.876052	−	0.776115i	0.975746	+	0.218904i	$0.0702480\pi$
$600$	−0.0258208	+	0.0228753i	−0.00105413	+	0.000933878i
$601$	2.28098	−	6.01445i	0.0930431	−	0.245334i	−0.880413	−	0.474207i	$-0.842735\pi$
$601$	2.28098	−	6.01445i	0.0930431	−	0.245334i	0.973456	+	0.228873i	$0.0735040\pi$
$602$	−0.264469	−	2.17810i	−0.0107790	−	0.0887727i
$603$	−8.85438	+	23.3471i	−0.360578	+	0.950767i
$604$	−4.92991	+	40.6015i	−0.200595	+	1.65205i
$605$	12.3195	−	17.8478i	0.500857	−	0.725617i
$606$	−0.738257			−0.0299896
$607$	20.2630	−	29.3561i	0.822451	−	1.19153i	−0.156550	−	0.987670i	$-0.550037\pi$
$607$	20.2630	−	29.3561i	0.822451	−	1.19153i	0.979001	−	0.203856i	$-0.0653474\pi$
$608$	−9.38238	+	2.31255i	−0.380506	+	0.0937863i
$609$	−2.63621	−	2.33548i	−0.106825	−	0.0946383i
$610$	1.32236	−	1.91576i	0.0535407	−	0.0775670i
$611$	−13.2067	−	3.82844i	−0.534285	−	0.154882i
$612$	5.90925	+	8.56102i	0.238867	+	0.346059i
$613$	−2.74393	+	22.5983i	−0.110826	+	0.912736i	0.826176	+	0.563412i	$0.190512\pi$
$613$	−2.74393	+	22.5983i	−0.110826	+	0.912736i	−0.937002	+	0.349324i	$0.886411\pi$
$614$	−0.614302	−	5.05923i	−0.0247912	−	0.204174i
$615$	1.59829	−	0.838846i	0.0644492	−	0.0338256i
$616$	−6.70188	+	1.65186i	−0.270026	+	0.0665555i
$617$	0.0316395	+	0.260575i	0.00127376	+	0.0104904i	0.993332	−	0.115290i	$-0.0367797\pi$
$617$	0.0316395	+	0.260575i	0.00127376	+	0.0104904i	−0.992058	+	0.125780i	$0.959857\pi$
$618$	−0.638689	+	0.565829i	−0.0256918	+	0.0227610i
$619$	−7.07610	+	10.2515i	−0.284413	+	0.412043i	−0.938986	−	0.343956i	$-0.888233\pi$
$619$	−7.07610	+	10.2515i	−0.284413	+	0.412043i	0.654573	+	0.755999i	$0.272848\pi$
$620$	−5.52867	−	8.00967i	−0.222037	−	0.321676i
$621$	−0.581135	−	0.143237i	−0.0233202	−	0.00574790i
$622$	−0.594248	−	4.89407i	−0.0238272	−	0.196234i
$623$	−26.7499	−	14.0394i	−1.07171	−	0.562478i
$624$	−1.22476	−	0.355042i	−0.0490298	−	0.0142131i
$625$	−21.4675	+	11.2670i	−0.858699	+	0.450680i
$626$	−0.127211	−	0.184297i	−0.00508437	−	0.00736599i
$627$	0.158999	+	0.230350i	0.00634982	+	0.00919930i
$628$	27.1716	+	24.0719i	1.08426	+	0.960575i
$629$	9.33055	+	8.26614i	0.372033	+	0.329593i
$630$	3.96358	+	10.4511i	0.157913	+	0.416382i
$631$	16.9435	−	8.89265i	0.674511	−	0.354011i	−0.0924382	−	0.995718i	$-0.529466\pi$
$631$	16.9435	−	8.89265i	0.674511	−	0.354011i	0.766949	+	0.641708i	$0.221774\pi$
$632$	9.14580	+	24.1155i	0.363800	+	0.959263i
$633$	−1.86848	+	0.460540i	−0.0742656	+	0.0183048i
$634$	7.92239	+	7.01862i	0.314638	+	0.278745i
$635$	−7.82685	+	11.3392i	−0.310599	+	0.449981i
$636$	−0.984212	+	2.59515i	−0.0390265	+	0.102905i
$637$	18.1973	+	10.5114i	0.721004	+	0.416479i
$638$	1.35793	+	3.58056i	0.0537609	+	0.141756i
$639$	−7.07105	−	1.74286i	−0.279727	−	0.0689464i
$640$	21.8418	+	11.4635i	0.863374	+	0.453134i
$641$	−7.87524	+	20.7653i	−0.311053	+	0.820180i	0.684760	+	0.728769i	$0.259907\pi$
$641$	−7.87524	+	20.7653i	−0.311053	+	0.820180i	−0.995813	+	0.0914113i	$0.970862\pi$
$642$	0.141511	−	1.16545i	0.00558499	−	0.0459966i
$643$	23.7721	+	34.4398i	0.937480	+	1.35817i	0.933652	+	0.358182i	$0.116603\pi$
$643$	23.7721	+	34.4398i	0.937480	+	1.35817i	0.00382807	+	0.999993i	$0.498781\pi$
$644$	4.70874	−	1.16060i	0.185550	−	0.0457341i
$645$	0.361729	+	0.0891581i	0.0142430	+	0.00351060i
$646$	0.223411	−	1.83996i	0.00879000	−	0.0723921i
$647$	−7.77228	−	20.4938i	−0.305560	−	0.805695i	−0.996563	−	0.0828432i	$-0.973600\pi$
$647$	−7.77228	−	20.4938i	−0.305560	−	0.805695i	0.691003	−	0.722852i	$-0.257169\pi$
$648$	15.3953	−	3.79460i	0.604785	−	0.149066i
$649$	−4.43161	−	1.09229i	−0.173956	−	0.0428763i
$650$	−0.217643	−	0.125719i	−0.00853666	−	0.00493109i
$651$	−1.13513	+	0.279784i	−0.0444893	+	0.0109656i
$652$	−27.5360	+	14.4520i	−1.07839	+	0.565985i
$653$	−37.2733			−1.45862			−0.729308	−	0.684185i	$-0.760158\pi$
$653$	−37.2733			−1.45862			−0.729308	+	0.684185i	$0.760158\pi$
$654$	−0.197791			−0.00773425
$655$	−33.1867	+	17.4177i	−1.29671	+	0.680568i
$656$	12.6192	+	11.1796i	0.492695	+	0.436490i
$657$	−27.8969			−1.08836
$658$	4.85561	−	4.30169i	0.189291	−	0.167697i
$659$	35.8365	+	18.8085i	1.39599	+	0.732674i	0.983942	−	0.178487i	$-0.0571203\pi$
$659$	35.8365	+	18.8085i	1.39599	+	0.732674i	0.412051	+	0.911161i	$0.364813\pi$
$660$	0.0664152	−	0.546979i	0.00258521	−	0.0212911i
$661$	−1.84221	−	0.966866i	−0.0716537	−	0.0376067i	0.428516	−	0.903534i	$-0.359037\pi$
$661$	−1.84221	−	0.966866i	−0.0716537	−	0.0376067i	−0.500169	+	0.865928i	$0.666729\pi$
$662$	1.18544	−	9.76294i	0.0460732	−	0.379447i
$663$	0.558275	−	0.742597i	0.0216816	−	0.0288401i
$664$	1.33355	+	10.9828i	0.0517518	+	0.426214i
$665$	−5.55619	+	14.6505i	−0.215460	+	0.568121i
$666$	7.95560	−	4.17542i	0.308273	−	0.161794i
$667$	−2.02943	−	5.35117i	−0.0785798	−	0.207198i
$668$	35.6262	+	18.6981i	1.37842	+	0.723450i
$669$	−0.984650	−	0.516784i	−0.0380688	−	0.0199800i
$670$	−8.50373	−	2.09598i	−0.328528	−	0.0809748i
$671$	−0.288329	−	2.37460i	−0.0111308	−	0.0916705i
$672$	1.71040	−	1.51529i	0.0659802	−	0.0584534i
$673$	−1.83046	+	2.65188i	−0.0705590	+	0.102222i	−0.856675	−	0.515857i	$-0.827474\pi$
$673$	−1.83046	+	2.65188i	−0.0705590	+	0.102222i	0.786116	+	0.618079i	$0.212089\pi$
$674$	−0.0575993	−	0.151877i	−0.00221864	−	0.00585007i
$675$	0.115135			0.00443157
$676$	−0.918942	−	23.0496i	−0.0353439	−	0.886525i
$677$	−36.1864			−1.39076			−0.695379	−	0.718643i	$-0.744764\pi$
$677$	−36.1864			−1.39076			−0.695379	+	0.718643i	$0.744764\pi$
$678$	−0.0288507	−	0.0760731i	−0.00110801	−	0.00292157i
$679$	−34.0472	+	49.3259i	−1.30661	+	1.89295i
$680$	−5.80930	+	5.14659i	−0.222777	+	0.197363i
$681$	0.178068	+	1.46652i	0.00682358	+	0.0561972i
$682$	1.23423	+	0.304210i	0.0472611	+	0.0116488i
$683$	0.762649	+	0.400269i	0.0291819	+	0.0153159i	0.479251	−	0.877678i	$-0.340908\pi$
$683$	0.762649	+	0.400269i	0.0291819	+	0.0153159i	−0.450069	+	0.892994i	$0.648601\pi$
$684$	9.30653	+	4.88444i	0.355844	+	0.186761i
$685$	6.10991	+	16.1105i	0.233448	+	0.615551i
$686$	1.76441	−	0.926036i	0.0673656	−	0.0353562i
$687$	1.06685	−	2.81305i	0.0407029	−	0.107325i
$688$	0.419424	+	3.45427i	0.0159904	+	0.131693i
$689$	−42.9806	−	1.74131i	−1.63743	−	0.0663388i
$690$	0.0126161	−	0.103903i	0.000480288	−	0.00395553i
$691$	10.6293	+	5.57869i	0.404358	+	0.212223i	0.654626	−	0.755953i	$-0.272826\pi$
$691$	10.6293	+	5.57869i	0.404358	+	0.212223i	−0.250268	+	0.968177i	$0.580519\pi$
$692$	3.38172	−	27.8510i	0.128554	−	1.05874i
$693$	10.1702	+	5.33771i	0.386332	+	0.202763i
$694$	1.68061	−	1.48889i	0.0637949	−	0.0565174i
$695$	34.4099			1.30524
$696$	−1.31935	−	1.16884i	−0.0500098	−	0.0443048i
$697$	−10.8758	+	5.70807i	−0.411951	+	0.216208i
$698$	16.5281			0.625598
$699$	−1.57314			−0.0595017
$700$	−0.826045	+	0.433542i	−0.0312216	+	0.0163863i
$701$	3.77510	−	0.930479i	0.142584	−	0.0351437i	−0.167378	−	0.985893i	$-0.553530\pi$
$701$	3.77510	−	0.930479i	0.142584	−	0.0351437i	0.309961	+	0.950749i	$0.399684\pi$
$702$	−0.717603	−	1.13534i	−0.0270842	−	0.0428506i
$703$	12.2289	+	3.01416i	0.461223	+	0.113681i
$704$	3.21947	−	0.793527i	0.121338	−	0.0299072i
$705$	0.390593	+	1.02991i	0.0147106	+	0.0387886i
$706$	−0.273787	+	2.25484i	−0.0103041	+	0.0848621i
$707$	−41.2339	−	10.1632i	−1.55076	−	0.382228i
$708$	0.958964	−	0.236364i	0.0360401	−	0.00888309i
$709$	−1.27398	−	1.84568i	−0.0478455	−	0.0693161i	0.798331	−	0.602219i	$-0.205717\pi$
$709$	−1.27398	−	1.84568i	−0.0478455	−	0.0693161i	−0.846177	+	0.532903i	$0.821101\pi$
$710$	0.307902	−	2.53580i	0.0115554	−	0.0951670i
$711$	15.2188	−	40.1286i	0.570748	−	1.50494i
$712$	−13.3876	−	7.02634i	−0.501720	−	0.263323i
$713$	−1.84456	−	0.454644i	−0.0690794	−	0.0170265i
$714$	0.155421	+	0.409813i	0.00581650	+	0.0153369i
$715$	8.36730	−	1.70632i	0.312919	−	0.0638128i
$716$	−11.1149	+	29.3076i	−0.415383	+	1.09528i
$717$	1.78188	−	2.58150i	0.0665455	−	0.0964078i
$718$	−2.83996	−	2.51599i	−0.105986	−	0.0938958i
$719$	12.0544	−	2.97115i	0.449554	−	0.110805i	−0.00803714	−	0.999968i	$-0.502558\pi$
$719$	12.0544	−	2.97115i	0.449554	−	0.110805i	0.457592	+	0.889162i	$0.348712\pi$
$720$	−6.28587	−	16.5745i	−0.234261	−	0.617695i
$721$	−43.4622	+	22.8107i	−1.61862	+	0.849516i
$722$	2.53565	+	6.68595i	0.0943670	+	0.248825i
$723$	2.06782	+	1.83193i	0.0769031	+	0.0681302i
$724$	12.5766	+	11.1419i	0.467406	+	0.414086i
$725$	0.625392	+	0.906037i	0.0232265	+	0.0336494i
$726$	−0.348187	−	0.504436i	−0.0129224	−	0.0187214i
$727$	2.92844	−	1.53696i	0.108610	−	0.0570028i	−0.409543	−	0.912291i	$-0.634312\pi$
$727$	2.92844	−	1.53696i	0.108610	−	0.0570028i	0.518153	+	0.855288i	$0.326620\pi$
$728$	20.0450	+	11.5787i	0.742915	+	0.429135i
$729$	−23.0894	−	12.1182i	−0.855162	−	0.448823i
$730$	−1.17945	−	9.71361i	−0.0436533	−	0.359517i
$731$	−2.46144	−	0.606691i	−0.0910397	−	0.0224393i
$732$	0.294041	+	0.425991i	0.0108681	+	0.0157451i
$733$	3.23227	−	4.68275i	0.119387	−	0.172961i	−0.758734	−	0.651400i	$-0.774182\pi$
$733$	3.23227	−	4.68275i	0.119387	−	0.172961i	0.878121	+	0.478439i	$0.158797\pi$
$734$	8.41789	−	7.45760i	0.310710	−	0.275265i
$735$	−0.202915	−	1.67116i	−0.00748464	−	0.0616415i
$736$	3.60530	−	0.888626i	0.132893	−	0.0327552i
$737$	−7.96895	+	4.18243i	−0.293540	+	0.154062i
$738$	1.06711	+	8.78847i	0.0392810	+	0.323508i
$739$	−0.388749	+	3.20164i	−0.0143004	+	0.117774i	−0.998111	−	0.0614374i	$-0.980432\pi$
$739$	−0.388749	+	3.20164i	−0.0143004	+	0.117774i	0.983811	+	0.179211i	$0.0573546\pi$
$740$	−14.0846	−	20.4051i	−0.517760	−	0.750105i
$741$	0.150776	−	0.926502i	0.00553888	−	0.0340359i
$742$	11.5281	−	16.7013i	0.423209	−	0.613124i
$743$	−28.9437	−	25.6418i	−1.06184	−	0.940708i	−0.0634812	−	0.997983i	$-0.520220\pi$
$743$	−28.9437	−	25.6418i	−1.06184	−	0.940708i	−0.998358	+	0.0572752i	$0.981759\pi$
$744$	−0.568101	+	0.140024i	−0.0208276	+	0.00513354i
$745$	−18.4965	+	26.7969i	−0.677661	+	0.981761i
$746$	3.38927			0.124090
$747$	10.4579	−	15.1509i	0.382635	−	0.554343i
$748$	−0.451933	+	3.72200i	−0.0165243	+	0.136090i
$749$	23.9480	−	63.1457i	0.875040	−	2.30729i
$750$	0.0850952	+	0.700822i	0.00310724	+	0.0255904i
$751$	17.8804	−	47.1468i	0.652466	−	1.72041i	−0.0402376	−	0.999190i	$-0.512811\pi$
$751$	17.8804	−	47.1468i	0.652466	−	1.72041i	0.692704	−	0.721222i	$-0.256419\pi$
$752$	−7.70055	+	6.82209i	−0.280810	+	0.248776i
$753$	1.43744	−	1.27346i	0.0523833	−	0.0464076i
$754$	5.03646	−	11.8140i	0.183417	−	0.430239i
$755$	38.0073	+	33.6715i	1.38323	+	1.22543i
$756$	−4.98518			−0.181309
$757$	8.98475	−	7.95980i	0.326556	−	0.289304i	−0.483875	−	0.875137i	$-0.660771\pi$
$757$	8.98475	−	7.95980i	0.326556	−	0.289304i	0.810432	+	0.585833i	$0.199233\pi$
$758$	−7.89870	−	1.94685i	−0.286894	−	0.0707129i
$759$	−0.0610974	−	0.0885149i	−0.00221770	−	0.00321289i
$760$	−2.78072	+	7.33215i	−0.100867	+	0.265965i
$761$	−0.232988	+	0.614338i	−0.00844580	+	0.0222697i	−0.939173	−	0.343445i	$-0.888406\pi$
$761$	−0.232988	+	0.614338i	−0.00844580	+	0.0222697i	0.930727	+	0.365715i	$0.119175\pi$
$762$	0.221211	+	0.320480i	0.00801364	+	0.0116098i
$763$	−11.0472	−	2.72290i	−0.399937	−	0.0985756i
$764$	14.9943	−	13.2838i	0.542475	−	0.480591i
$765$	12.9147			0.466931
$766$	−2.22926	−	1.97495i	−0.0805464	−	0.0713579i
$767$

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)

\(f(q)\)	\(=\)	\(q+(-0.168406 - 0.444051i) q^{2} +(0.0744765 - 0.107898i) q^{3} +(1.32820 - 1.17668i) q^{4} +(-0.265542 - 2.18694i) q^{5} +(-0.0604545 - 0.0149007i) q^{6} +(-3.17143 - 1.66450i) q^{7} +(-1.58721 - 0.833034i) q^{8} +(1.05772 + 2.78898i) q^{9} +O(q^{10})\)	\(q+(-0.168406 - 0.444051i) q^{2} +(0.0744765 - 0.107898i) q^{3} +(1.32820 - 1.17668i) q^{4} +(-0.265542 - 2.18694i) q^{5} +(-0.0604545 - 0.0149007i) q^{6} +(-3.17143 - 1.66450i) q^{7} +(-1.58721 - 0.833034i) q^{8} +(1.05772 + 2.78898i) q^{9} +(-0.926393 + 0.486209i) q^{10} +(-0.381234 + 1.00523i) q^{11} +(-0.0280418 - 0.230945i) q^{12} +(3.25777 - 1.54497i) q^{13} +(-0.205032 + 1.68859i) q^{14} +(-0.255743 - 0.134224i) q^{15} +(0.325162 - 2.67795i) q^{16} +(1.74024 + 0.913350i) q^{17} +(1.06032 - 0.939363i) q^{18} +1.98577 q^{19} +(-2.92603 - 2.59223i) q^{20} +(-0.415793 + 0.218225i) q^{21} +0.510576 q^{22} -0.763058 q^{23} +(-0.208093 + 0.109215i) q^{24} +(0.142520 - 0.0351280i) q^{25} +(-1.23468 - 1.18643i) q^{26} +(0.761588 + 0.187715i) q^{27} +(-6.17088 + 1.52099i) q^{28} +(2.65960 + 7.01279i) q^{29} +(-0.0165337 + 0.136167i) q^{30} +(2.41733 + 0.595818i) q^{31} +(-4.72480 + 1.16456i) q^{32} +(0.0800692 + 0.116000i) q^{33} +(0.112506 - 0.926570i) q^{34} +(-2.79800 + 7.37772i) q^{35} +(4.68661 + 2.45972i) q^{36} +(6.15828 + 1.51788i) q^{37} +(-0.334416 - 0.881784i) q^{38} +(0.0759280 - 0.466570i) q^{39} +(-1.40032 + 3.69234i) q^{40} +(-3.55018 + 5.14332i) q^{41} +(0.166925 + 0.147883i) q^{42} +(-1.25241 + 0.308691i) q^{43} +(0.676483 + 1.78374i) q^{44} +(5.81845 - 3.05376i) q^{45} +(0.128504 + 0.338836i) q^{46} +(-2.85457 - 2.52893i) q^{47} +(-0.264728 - 0.234529i) q^{48} +(3.31098 + 4.79679i) q^{49} +(-0.0395999 - 0.0573703i) q^{50} +(0.228156 - 0.119745i) q^{51} +(2.50903 - 5.88540i) q^{52} +(-10.5639 - 5.54436i) q^{53} +(-0.0449014 - 0.369796i) q^{54} +(2.29961 + 0.566803i) q^{55} +(3.64716 + 5.28382i) q^{56} +(0.147893 - 0.214260i) q^{57} +(2.66614 - 2.36200i) q^{58} +(0.511731 + 4.21448i) q^{59} +(-0.497617 + 0.122652i) q^{60} +(-1.97010 + 1.03399i) q^{61} +(-0.142520 - 1.17376i) q^{62} +(1.28776 - 10.6056i) q^{63} +(-1.75203 - 2.53826i) q^{64} +(-4.24384 - 6.71429i) q^{65} +(0.0380259 - 0.0550900i) q^{66} +(6.26593 + 5.55113i) q^{67} +(3.38612 - 0.834602i) q^{68} +(-0.0568299 + 0.0823323i) q^{69} +3.74729 q^{70} +(-1.38696 + 2.00935i) q^{71} +(0.644486 - 5.30782i) q^{72} +(-3.31646 + 8.74480i) q^{73} +(-0.363077 - 2.99021i) q^{74} +(0.00682415 - 0.0179938i) q^{75} +(2.63750 - 2.33662i) q^{76} +(2.88226 - 2.55346i) q^{77} +(-0.219968 + 0.0448575i) q^{78} +(-10.7698 - 9.54119i) q^{79} -5.94285 q^{80} +(-6.62102 + 5.86572i) q^{81} +(2.88177 + 0.710292i) q^{82} +(-3.50606 - 5.07941i) q^{83} +(-0.295475 + 0.779103i) q^{84} +(1.53533 - 4.04834i) q^{85} +(0.347989 + 0.504148i) q^{86} +(0.954743 + 0.235323i) q^{87} +(1.44249 - 1.27793i) q^{88} +8.43464 q^{89} +(-2.33589 - 2.06942i) q^{90} +(-12.9034 - 0.522768i) q^{91} +(-1.01349 + 0.897877i) q^{92} +(0.244322 - 0.216450i) q^{93} +(-0.642247 + 1.69347i) q^{94} +(-0.527307 - 4.34276i) q^{95} +(-0.226233 + 0.596529i) q^{96} +(2.01704 - 16.6118i) q^{97} +(1.57243 - 2.27805i) q^{98} -3.20680 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