LMFDB - Embedded newform 169.2.g.a.27.4

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			27.4
Character	$\chi$	$=$	169.27
Dual form			169.2.g.a.144.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.553905 - 1.46053i) q^{2} +(-0.577862 + 0.837177i) q^{3} +(-0.329307 + 0.291741i) q^{4} +(0.268400 + 2.21047i) q^{5} +(1.54280 + 0.380266i) q^{6} +(3.47659 + 1.82465i) q^{7} +(-2.15772 - 1.13246i) q^{8} +(0.696873 + 1.83750i) q^{9} +O(q^{10})$	\(q+(-0.553905 - 1.46053i) q^{2} +(-0.577862 + 0.837177i) q^{3} +(-0.329307 + 0.291741i) q^{4} +(0.268400 + 2.21047i) q^{5} +(1.54280 + 0.380266i) q^{6} +(3.47659 + 1.82465i) q^{7} +(-2.15772 - 1.13246i) q^{8} +(0.696873 + 1.83750i) q^{9} +(3.07979 - 1.61640i) q^{10} +(0.440706 - 1.16205i) q^{11} +(-0.0539447 - 0.444274i) q^{12} +(1.75157 - 3.15151i) q^{13} +(0.739257 - 6.08833i) q^{14} +(-2.00565 - 1.05265i) q^{15} +(-0.564876 + 4.65218i) q^{16} +(-0.323252 - 0.169656i) q^{17} +(2.29772 - 2.03560i) q^{18} -0.0607791 q^{19} +(-0.733271 - 0.649621i) q^{20} +(-3.53654 + 1.85612i) q^{21} -1.94131 q^{22} +1.62786 q^{23} +(2.19494 - 1.15199i) q^{24} +(0.0405622 - 0.00999768i) q^{25} +(-5.57307 - 0.812585i) q^{26} +(-4.90407 - 1.20875i) q^{27} +(-1.67719 + 0.413391i) q^{28} +(0.378580 + 0.998234i) q^{29} +(-0.426480 + 3.51238i) q^{30} +(-5.11532 - 1.26081i) q^{31} +(2.37543 - 0.585492i) q^{32} +(0.718172 + 1.04045i) q^{33} +(-0.0687360 + 0.566092i) q^{34} +(-3.10023 + 8.17463i) q^{35} +(-0.765560 - 0.401797i) q^{36} +(-1.02730 - 0.253207i) q^{37} +(0.0336659 + 0.0887696i) q^{38} +(1.62620 + 3.28751i) q^{39} +(1.92414 - 5.07354i) q^{40} +(-5.47439 + 7.93102i) q^{41} +(4.66982 + 4.13710i) q^{42} +(8.94471 - 2.20467i) q^{43} +(0.193889 + 0.511243i) q^{44} +(-3.87471 + 2.03360i) q^{45} +(-0.901680 - 2.37753i) q^{46} +(-7.59014 - 6.72427i) q^{47} +(-3.56827 - 3.16122i) q^{48} +(4.78084 + 6.92624i) q^{49} +(-0.0370695 - 0.0537044i) q^{50} +(0.328827 - 0.172582i) q^{51} +(0.342617 + 1.54882i) q^{52} +(0.122643 + 0.0643680i) q^{53} +(0.950984 + 7.83206i) q^{54} +(2.68696 + 0.662276i) q^{55} +(-5.43517 - 7.87420i) q^{56} +(0.0351219 - 0.0508829i) q^{57} +(1.24825 - 1.10585i) q^{58} +(-1.20684 - 9.93920i) q^{59} +(0.967577 - 0.238486i) q^{60} +(-10.3882 + 5.45214i) q^{61} +(0.991950 + 8.16944i) q^{62} +(-0.930067 + 7.65979i) q^{63} +(3.15340 + 4.56849i) q^{64} +(7.43644 + 3.02594i) q^{65} +(1.12181 - 1.62522i) q^{66} +(-9.33975 - 8.27430i) q^{67} +(0.155945 - 0.0384370i) q^{68} +(-0.940678 + 1.36281i) q^{69} +13.6565 q^{70} +(6.75811 - 9.79081i) q^{71} +(0.577241 - 4.75401i) q^{72} +(5.29800 - 13.9697i) q^{73} +(0.199212 + 1.64066i) q^{74} +(-0.0150695 + 0.0397350i) q^{75} +(0.0200150 - 0.0177318i) q^{76} +(3.65249 - 3.23582i) q^{77} +(3.90074 - 4.19608i) q^{78} +(1.48316 + 1.31397i) q^{79} -10.4351 q^{80} +(-0.567134 + 0.502437i) q^{81} +(14.6158 + 3.60246i) q^{82} +(-4.07266 - 5.90026i) q^{83} +(0.623103 - 1.64299i) q^{84} +(0.288259 - 0.760075i) q^{85} +(-8.17450 - 11.8428i) q^{86} +(-1.05447 - 0.259902i) q^{87} +(-2.26690 + 2.00829i) q^{88} +5.81279 q^{89} +(5.11635 + 4.53269i) q^{90} +(11.8399 - 7.76047i) q^{91} +(-0.536066 + 0.474913i) q^{92} +(4.01147 - 3.55386i) q^{93} +(-5.61677 + 14.8102i) q^{94} +(-0.0163131 - 0.134351i) q^{95} +(-0.882512 + 2.32699i) q^{96} +(-1.42435 + 11.7306i) q^{97} +(7.46783 - 10.8190i) q^{98} +2.44238 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 $

$2$	−0.553905	−	1.46053i	−0.391670	−	1.03275i	−0.975330	−	0.220751i	$-0.929149\pi$
$2$	−0.553905	−	1.46053i	−0.391670	−	1.03275i	0.583660	−	0.811998i	$-0.301620\pi$
$3$	−0.577862	+	0.837177i	−0.333629	+	0.483344i	−0.953514	−	0.301348i	$-0.902564\pi$
$3$	−0.577862	+	0.837177i	−0.333629	+	0.483344i	0.619886	+	0.784692i	$0.287179\pi$
$4$	−0.329307	+	0.291741i	−0.164654	+	0.145870i
$5$	0.268400	+	2.21047i	0.120032	+	0.988553i	0.920923	+	0.389743i	$0.127436\pi$
$5$	0.268400	+	2.21047i	0.120032	+	0.988553i	−0.800891	+	0.598810i	$0.795641\pi$
$6$	1.54280	+	0.380266i	0.629846	+	0.155243i
$7$	3.47659	+	1.82465i	1.31403	+	0.689654i	0.968561	−	0.248777i	$-0.0800288\pi$
$7$	3.47659	+	1.82465i	1.31403	+	0.689654i	0.345465	+	0.938431i	$0.387721\pi$
$8$	−2.15772	−	1.13246i	−0.762871	−	0.400385i
$9$	0.696873	+	1.83750i	0.232291	+	0.612501i
$10$	3.07979	−	1.61640i	0.973914	−	0.511149i
$11$	0.440706	−	1.16205i	0.132878	−	0.350370i	−0.852019	−	0.523510i	$-0.824622\pi$
$11$	0.440706	−	1.16205i	0.132878	−	0.350370i	0.984897	+	0.173140i	$0.0553913\pi$
$12$	−0.0539447	−	0.444274i	−0.0155725	−	0.128251i
$13$	1.75157	−	3.15151i	0.485799	−	0.874071i
$13$	1.75157	−	3.15151i	0.485799	−	0.874071i
$14$	0.739257	−	6.08833i	0.197575	−	1.62718i
$15$	−2.00565	−	1.05265i	−0.517858	−	0.271793i
$16$	−0.564876	+	4.65218i	−0.141219	+	1.16304i
$17$	−0.323252	−	0.169656i	−0.0784002	−	0.0411476i	0.425067	−	0.905162i	$-0.360250\pi$
$17$	−0.323252	−	0.169656i	−0.0784002	−	0.0411476i	−0.503468	+	0.864014i	$0.667943\pi$
$18$	2.29772	−	2.03560i	0.541578	−	0.479797i
$19$	−0.0607791			−0.0139437			−0.00697184	−	0.999976i	$-0.502219\pi$
$19$	−0.0607791			−0.0139437			−0.00697184	+	0.999976i	$0.502219\pi$
$20$	−0.733271	−	0.649621i	−0.163964	−	0.145260i
$21$	−3.53654	+	1.85612i	−0.771737	+	0.405039i
$22$	−1.94131			−0.413889
$23$	1.62786			0.339432			0.169716	−	0.985493i	$-0.445715\pi$
$23$	1.62786			0.339432			0.169716	+	0.985493i	$0.445715\pi$
$24$	2.19494	−	1.15199i	0.448040	−	0.235149i
$25$	0.0405622	−	0.00999768i	0.00811244	−	0.00199954i
$26$	−5.57307	−	0.812585i	−1.09297	−	0.159361i
$27$	−4.90407	−	1.20875i	−0.943789	−	0.232623i
$28$	−1.67719	+	0.413391i	−0.316959	+	0.0781235i
$29$	0.378580	+	0.998234i	0.0703006	+	0.185367i	0.965562	−	0.260175i	$-0.0837802\pi$
$29$	0.378580	+	0.998234i	0.0703006	+	0.185367i	−0.895261	+	0.445542i	$0.853011\pi$
$30$	−0.426480	+	3.51238i	−0.0778643	+	0.641270i
$31$	−5.11532	−	1.26081i	−0.918739	−	0.226449i	−0.248533	−	0.968623i	$-0.579948\pi$
$31$	−5.11532	−	1.26081i	−0.918739	−	0.226449i	−0.670207	+	0.742175i	$0.733795\pi$
$32$	2.37543	−	0.585492i	0.419922	−	0.103501i
$33$	0.718172	+	1.04045i	0.125018	+	0.181119i
$34$	−0.0687360	+	0.566092i	−0.0117881	+	0.0970839i
$35$	−3.10023	+	8.17463i	−0.524034	+	1.38177i
$36$	−0.765560	−	0.401797i	−0.127593	−	0.0669662i
$37$	−1.02730	−	0.253207i	−0.168887	−	0.0416270i	0.153965	−	0.988076i	$-0.450796\pi$
$37$	−1.02730	−	0.253207i	−0.168887	−	0.0416270i	−0.322853	+	0.946449i	$0.604642\pi$
$38$	0.0336659	+	0.0887696i	0.00546132	+	0.0144003i
$39$	1.62620	+	3.28751i	0.260401	+	0.526423i
$40$	1.92414	−	5.07354i	0.304233	−	0.802197i
$41$	−5.47439	+	7.93102i	−0.854955	+	1.23862i	0.114518	+	0.993421i	$0.463468\pi$
$41$	−5.47439	+	7.93102i	−0.854955	+	1.23862i	−0.969474	+	0.245196i	$0.921148\pi$
$42$	4.66982	+	4.13710i	0.720570	+	0.638369i
$43$	8.94471	−	2.20467i	1.36405	−	0.336209i	0.511696	−	0.859167i	$-0.329017\pi$
$43$	8.94471	−	2.20467i	1.36405	−	0.336209i	0.852359	+	0.522957i	$0.175171\pi$
$44$	0.193889	+	0.511243i	0.0292298	+	0.0770727i
$45$	−3.87471	+	2.03360i	−0.577608	+	0.303152i
$46$	−0.901680	−	2.37753i	−0.132945	−	0.350548i
$47$	−7.59014	−	6.72427i	−1.10714	−	0.980836i	−0.107225	−	0.994235i	$-0.534196\pi$
$47$	−7.59014	−	6.72427i	−1.10714	−	0.980836i	−0.999910	+	0.0133986i	$0.995735\pi$
$48$	−3.56827	−	3.16122i	−0.515036	−	0.456282i
$49$	4.78084	+	6.92624i	0.682977	+	0.989463i
$50$	−0.0370695	−	0.0537044i	−0.00524241	−	0.00759495i
$51$	0.328827	−	0.172582i	0.0460450	−	0.0241663i
$52$	0.342617	+	1.54882i	0.0475125	+	0.214783i
$53$	0.122643	+	0.0643680i	0.0168463	+	0.00884162i	0.473125	−	0.880995i	$-0.343126\pi$
$53$	0.122643	+	0.0643680i	0.0168463	+	0.00884162i	−0.456279	+	0.889837i	$0.650818\pi$
$54$	0.950984	+	7.83206i	0.129413	+	1.06581i
$55$	2.68696	+	0.662276i	0.362309	+	0.0893012i
$56$	−5.43517	−	7.87420i	−0.726305	−	1.05223i
$57$	0.0351219	−	0.0508829i	0.00465201	−	0.00673960i
$58$	1.24825	−	1.10585i	0.163903	−	0.145206i
$59$	−1.20684	−	9.93920i	−0.157117	−	1.29397i	−0.831472	−	0.555567i	$-0.812501\pi$
$59$	−1.20684	−	9.93920i	−0.157117	−	1.29397i	0.674355	−	0.738407i	$-0.264422\pi$
$60$	0.967577	−	0.238486i	0.124914	−	0.0307885i
$61$	−10.3882	+	5.45214i	−1.33007	+	0.698075i	−0.971859	−	0.235564i	$-0.924306\pi$
$61$	−10.3882	+	5.45214i	−1.33007	+	0.698075i	−0.358213	+	0.933640i	$0.616614\pi$
$62$	0.991950	+	8.16944i	0.125978	+	1.03752i
$63$	−0.930067	+	7.65979i	−0.117177	+	0.965043i
$64$	3.15340	+	4.56849i	0.394175	+	0.571061i
$65$	7.43644	+	3.02594i	0.922377	+	0.375321i
$66$	1.12181	−	1.62522i	0.138085	−	0.200051i
$67$	−9.33975	−	8.27430i	−1.14103	−	1.01087i	−0.999782	−	0.0208923i	$-0.993349\pi$
$67$	−9.33975	−	8.27430i	−1.14103	−	1.01087i	−0.141250	−	0.989974i	$-0.545112\pi$
$68$	0.155945	−	0.0384370i	0.0189111	−	0.00466117i
$69$	−0.940678	+	1.36281i	−0.113244	+	0.164063i
$70$	13.6565			1.63226
$71$	6.75811	−	9.79081i	0.802040	−	1.16196i	−0.181876	−	0.983321i	$-0.558217\pi$
$71$	6.75811	−	9.79081i	0.802040	−	1.16196i	0.983916	−	0.178634i	$-0.0571677\pi$
$72$	0.577241	−	4.75401i	0.0680285	−	0.560265i
$73$	5.29800	−	13.9697i	0.620084	−	1.63503i	−0.143748	−	0.989614i	$-0.545916\pi$
$73$	5.29800	−	13.9697i	0.620084	−	1.63503i	0.763833	−	0.645414i	$-0.223315\pi$
$74$	0.199212	+	1.64066i	0.0231579	+	0.190722i
$75$	−0.0150695	+	0.0397350i	−0.00174008	+	0.00458820i
$76$	0.0200150	−	0.0177318i	0.00229588	−	0.00203397i
$77$	3.65249	−	3.23582i	0.416240	−	0.368756i
$78$	3.90074	−	4.19608i	0.441672	−	0.475113i
$79$	1.48316	+	1.31397i	0.166869	+	0.147833i	0.742425	−	0.669930i	$-0.233676\pi$
$79$	1.48316	+	1.31397i	0.166869	+	0.147833i	−0.575556	+	0.817763i	$0.695214\pi$
$80$	−10.4351			−1.16668
$81$	−0.567134	+	0.502437i	−0.0630149	+	0.0558263i
$82$	14.6158	+	3.60246i	1.61404	+	0.397825i
$83$	−4.07266	−	5.90026i	−0.447032	−	0.647638i	0.533084	−	0.846062i	$-0.321033\pi$
$83$	−4.07266	−	5.90026i	−0.447032	−	0.647638i	−0.980116	+	0.198424i	$0.936418\pi$
$84$	0.623103	−	1.64299i	0.0679862	−	0.179265i
$85$	0.288259	−	0.760075i	0.0312660	−	0.0824418i
$86$	−8.17450	−	11.8428i	−0.881479	−	1.27704i
$87$	−1.05447	−	0.259902i	−0.113051	−	0.0278645i
$88$	−2.26690	+	2.00829i	−0.241652	+	0.214085i
$89$	5.81279			0.616155			0.308077	−	0.951361i	$-0.400314\pi$
$89$	5.81279			0.616155			0.308077	+	0.951361i	$0.400314\pi$
$90$	5.11635	+	4.53269i	0.539311	+	0.477788i
$91$	11.8399	−	7.76047i	1.24116	−	0.813518i
$92$	−0.536066	+	0.474913i	−0.0558888	+	0.0495131i
$93$	4.01147	−	3.55386i	0.415971	−	0.368518i
$94$	−5.61677	+	14.8102i	−0.579326	+	1.52756i
$95$	−0.0163131	−	0.134351i	−0.00167369	−	0.0137841i
$96$	−0.882512	+	2.32699i	−0.0900710	+	0.237498i
$97$	−1.42435	+	11.7306i	−0.144621	+	1.19106i	0.721928	+	0.691968i	$0.243256\pi$
$97$	−1.42435	+	11.7306i	−0.144621	+	1.19106i	−0.866549	+	0.499092i	$0.833667\pi$
$98$	7.46783	−	10.8190i	0.754365	−	1.09289i
$99$	2.44238			0.245469
$100$	−0.0104407	+	0.0151260i	−0.00104407	+	0.00151260i
$101$	−8.43507	+	2.07906i	−0.839321	+	0.206874i	−0.635468	−	0.772127i	$-0.719193\pi$
$101$	−8.43507	+	2.07906i	−0.839321	+	0.206874i	−0.203853	+	0.979001i	$0.565347\pi$
$102$	−0.434199	−	0.384667i	−0.0429921	−	0.0380877i
$103$	5.54653	−	8.03553i	0.546515	−	0.791764i	−0.448254	−	0.893906i	$-0.647954\pi$
$103$	5.54653	−	8.03553i	0.546515	−	0.791764i	0.994770	+	0.102142i	$0.0325695\pi$
$104$	−7.34837	+	4.81649i	−0.720567	+	0.472296i
$105$	−5.05211	−	7.31925i	−0.493036	−	0.714285i
$106$	0.0260787	−	0.214777i	0.00253298	−	0.0208610i
$107$	−1.44721	−	11.9189i	−0.139907	−	1.15224i	−0.878382	−	0.477959i	$-0.841377\pi$
$107$	−1.44721	−	11.9189i	−0.139907	−	1.15224i	0.738475	−	0.674281i	$-0.235546\pi$
$108$	1.96759	−	1.03267i	0.189331	−	0.0993687i
$109$	−6.95637	+	1.71459i	−0.666300	+	0.164228i	−0.557937	−	0.829883i	$-0.688407\pi$
$109$	−6.95637	+	1.71459i	−0.666300	+	0.164228i	−0.108363	+	0.994111i	$0.534561\pi$
$110$	−0.521048	−	4.29121i	−0.0496799	−	0.409151i
$111$	0.805618	−	0.713715i	0.0764659	−	0.0677429i
$112$	−10.4524	+	15.1430i	−0.987664	+	1.43088i
$113$	4.92823	+	7.13977i	0.463609	+	0.671653i	0.983152	−	0.182791i	$-0.0585132\pi$
$113$	4.92823	+	7.13977i	0.463609	+	0.671653i	−0.519543	+	0.854444i	$0.673898\pi$
$114$	−0.0937700	−	0.0231122i	−0.00878237	−	0.00216466i
$115$	0.436917	+	3.59834i	0.0407428	+	0.335547i
$116$	−0.415895	−	0.218278i	−0.0386149	−	0.0202666i
$117$	7.01153	+	1.02232i	0.648216	+	0.0945136i
$118$	−13.8480	+	7.26799i	−1.27481	+	0.669073i
$119$	−0.814251	−	1.17965i	−0.0746423	−	0.108138i
$120$	3.13557	+	4.54265i	0.286237	+	0.414685i
$121$	7.07749	+	6.27011i	0.643408	+	0.570010i
$122$	13.7171	+	12.1523i	1.24189	+	1.10021i
$123$	−3.47623	−	9.16606i	−0.313441	−	0.826476i
$124$	2.05234	−	1.07715i	0.184306	−	0.0967313i
$125$	3.98099	+	10.4970i	0.356071	+	0.938881i
$126$	11.7025	−	2.88441i	1.04254	−	0.256963i
$127$	7.66467	+	6.79031i	0.680130	+	0.602542i	0.930799	−	0.365530i	$-0.119112\pi$
$127$	7.66467	+	6.79031i	0.680130	+	0.602542i	−0.250670	+	0.968073i	$0.580651\pi$
$128$	7.70529	−	11.1630i	0.681058	−	0.986683i
$129$	−3.32310	+	8.76230i	−0.292583	+	0.771477i
$130$	0.300385	−	12.5372i	0.0263455	−	1.09959i
$131$	4.78317	+	12.6122i	0.417908	+	1.10193i	0.964395	+	0.264465i	$0.0851952\pi$
$131$	4.78317	+	12.6122i	0.417908	+	1.10193i	−0.546488	+	0.837467i	$0.684036\pi$
$132$	−0.540042	−	0.133108i	−0.0470046	−	0.0115856i
$133$	−0.211304	−	0.110901i	−0.0183224	−	0.00961632i
$134$	−6.91150	+	18.2241i	−0.597063	+	1.57433i
$135$	1.35564	−	11.1647i	0.116675	−	0.960908i
$136$	0.505360	+	0.732141i	0.0433343	+	0.0627806i
$137$	−16.9667	+	4.18190i	−1.44956	+	0.357284i	−0.884025	−	0.467441i	$-0.845176\pi$
$137$	−16.9667	+	4.18190i	−1.44956	+	0.357284i	−0.565534	+	0.824725i	$0.691330\pi$
$138$	2.51146	+	0.619020i	0.213790	+	0.0526945i
$139$	−0.472428	+	3.89079i	−0.0400708	+	0.330013i	0.958864	+	0.283866i	$0.0916172\pi$
$139$	−0.472428	+	3.89079i	−0.0400708	+	0.330013i	−0.998935	+	0.0461464i	$0.985306\pi$
$140$	−1.36395	−	3.59643i	−0.115274	−	0.303954i
$141$	10.0155	−	2.46859i	0.843454	−	0.207893i
$142$	−18.0431	−	4.44722i	−1.51414	−	0.373203i
$143$	−2.89027	−	3.42430i	−0.241697	−	0.286354i
$144$	−8.94204	+	2.20401i	−0.745170	+	0.183668i
$145$	−2.10496	+	1.10477i	−0.174807	+	0.0917459i
$146$	−23.3377			−1.93144
$147$	−8.56115			−0.706112
$148$	0.412169	−	0.216323i	0.0338801	−	0.0177816i
$149$	6.35051	+	5.62606i	0.520254	+	0.460905i	0.881917	−	0.471404i	$-0.156253\pi$
$149$	6.35051	+	5.62606i	0.520254	+	0.460905i	−0.361663	+	0.932309i	$0.617791\pi$
$150$	0.0663811			0.00542000
$151$	−11.8864	+	10.5305i	−0.967304	+	0.856957i	−0.989753	−	0.142791i	$-0.954392\pi$
$151$	−11.8864	+	10.5305i	−0.967304	+	0.856957i	0.0224487	+	0.999748i	$0.492854\pi$
$152$	0.131145	+	0.0688300i	0.0106372	+	0.00558285i
$153$	0.0864774	−	0.712206i	0.00699129	−	0.0575784i
$154$	−6.74913	−	3.54222i	−0.543861	−	0.285440i
$155$	1.41404	−	11.6457i	0.113579	−	0.935404i
$156$	−1.49462	−	0.608172i	−0.119666	−	0.0486927i
$157$	−1.34440	−	11.0721i	−0.107295	−	0.883651i	−0.942614	−	0.333885i	$-0.891640\pi$
$157$	−1.34440	−	11.0721i	−0.107295	−	0.883651i	0.835319	−	0.549766i	$-0.185283\pi$
$158$	1.09756	−	2.89402i	0.0873168	−	0.230236i
$159$	−0.124758	+	0.0654781i	−0.00989396	+	0.00519275i
$160$	1.93178	+	5.09369i	0.152721	+	0.402691i
$161$	5.65940	+	2.97028i	0.446023	+	0.234091i
$162$	1.04796	+	0.550012i	0.0823356	+	0.0432131i
$163$	−14.3833	−	3.54516i	−1.12659	−	0.277679i	−0.368369	−	0.929680i	$-0.620084\pi$
$163$	−14.3833	−	3.54516i	−1.12659	−	0.277679i	−0.758218	+	0.652001i	$0.773930\pi$
$164$	−0.511046	−	4.20884i	−0.0399060	−	0.328655i
$165$	−2.10713	+	1.86676i	−0.164040	+	0.145327i
$166$	−6.36163	+	9.21641i	−0.493758	+	0.715332i
$167$	5.79120	+	15.2701i	0.448136	+	1.18164i	0.948767	+	0.315977i	$0.102332\pi$
$167$	5.79120	+	15.2701i	0.448136	+	1.18164i	−0.500631	+	0.865661i	$0.666899\pi$
$168$	9.73287			0.750907
$169$	−6.86399	−	11.0402i	−0.527999	−	0.849245i
$170$	−1.26978			−0.0973876
$171$	−0.0423553	−	0.111682i	−0.00323899	−	0.00854053i
$172$	−2.30236	+	3.33555i	−0.175554	+	0.254333i
$173$	5.88078	−	5.20991i	0.447107	−	0.396102i	−0.409303	−	0.912399i	$-0.634228\pi$
$173$	5.88078	−	5.20991i	0.447107	−	0.396102i	0.856410	+	0.516296i	$0.172690\pi$
$174$	0.204479	+	1.68404i	0.0155015	+	0.127666i
$175$	0.159260	+	0.0392541i	0.0120389	+	0.00296733i
$176$	5.15710	+	2.70666i	0.388731	+	0.204022i
$177$	9.01826	+	4.73315i	0.677854	+	0.355765i
$178$	−3.21973	−	8.48974i	−0.241329	−	0.636333i
$179$	15.1989	−	7.97701i	1.13602	−	0.596230i	0.211507	−	0.977377i	$-0.432163\pi$
$179$	15.1989	−	7.97701i	1.13602	−	0.596230i	0.924515	+	0.381147i	$0.124471\pi$
$180$	0.682685	−	1.80009i	0.0508843	−	0.134171i
$181$	−1.87511	−	15.4429i	−0.139376	−	1.14786i	−0.879672	−	0.475582i	$-0.842238\pi$
$181$	−1.87511	−	15.4429i	−0.139376	−	1.14786i	0.740296	−	0.672281i	$-0.234686\pi$
$182$	−17.8926	−	12.9939i	−1.32628	−	0.963174i
$183$	1.43853	−	11.8473i	0.106339	−	0.875781i
$184$	−3.51247	−	1.84349i	−0.258943	−	0.135904i
$185$	0.283980	−	2.33878i	0.0208786	−	0.171951i
$186$	−7.41248	−	3.89037i	−0.543509	−	0.285256i
$187$	−0.339607	+	0.300866i	−0.0248346	+	0.0220015i
$188$	4.46123			0.325369
$189$	−14.8439	−	13.1505i	−1.07973	−	0.956561i
$190$	−0.187187	+	0.0982431i	−0.0135799	+	0.00712731i
$191$	−0.984574			−0.0712413			−0.0356206	−	0.999365i	$-0.511341\pi$
$191$	−0.984574			−0.0712413			−0.0356206	+	0.999365i	$0.511341\pi$
$192$	−5.64687			−0.407527
$193$	4.65410	−	2.44266i	0.335009	−	0.175826i	−0.288827	−	0.957381i	$-0.593265\pi$
$193$	4.65410	−	2.44266i	0.335009	−	0.175826i	0.623837	+	0.781555i	$0.285573\pi$
$194$	17.9218	−	4.41732i	1.28671	−	0.317145i
$195$	−6.83048	+	4.47704i	−0.489141	+	0.320608i
$196$	−3.59503	−	0.886096i	−0.256788	−	0.0632926i
$197$	25.2983	−	6.23547i	1.80243	−	0.444259i	0.812162	−	0.583433i	$-0.198291\pi$
$197$	25.2983	−	6.23547i	1.80243	−	0.444259i	0.990268	+	0.139174i	$0.0444446\pi$
$198$	−1.35285	−	3.56717i	−0.0961427	−	0.253507i
$199$	−2.45620	+	20.2286i	−0.174116	+	1.43397i	0.599530	+	0.800352i	$0.295354\pi$
$199$	−2.45620	+	20.2286i	−0.174116	+	1.43397i	−0.773646	+	0.633618i	$0.781569\pi$
$200$	−0.0988440	−	0.0243629i	−0.00698932	−	0.00172271i
$201$	12.3241	−	3.03763i	0.869277	−	0.214258i
$202$	7.70875	+	11.1681i	0.542386	+	0.785781i
$203$	−0.505264	+	4.16122i	−0.0354626	+	0.292061i
$204$	−0.0579360	+	0.152765i	−0.00405633	+	0.0106957i
$205$	−19.0006	−	9.97229i	−1.32706	−	0.696495i
$206$	−14.8084	−	3.64993i	−1.03175	−	0.254303i
$207$	1.13441	+	2.99120i	0.0788471	+	0.207903i
$208$	13.6719	+	9.92883i	0.947978	+	0.688441i
$209$	−0.0267857	+	0.0706282i	−0.00185281	+	0.00488546i
$210$	−7.89157	+	11.4329i	−0.544570	+	0.788946i
$211$	−4.40832	−	3.90543i	−0.303481	−	0.268861i	0.497613	−	0.867399i	$-0.334210\pi$
$211$	−4.40832	−	3.90543i	−0.303481	−	0.268861i	−0.801094	+	0.598538i	$0.795748\pi$
$212$	−0.0591660	+	0.0145831i	−0.00406354	+	0.00100157i
$213$	4.29139	+	11.3155i	0.294041	+	0.775323i
$214$	−16.6062	+	8.71560i	−1.13518	+	0.595786i
$215$	7.27412	+	19.1803i	0.496091	+	1.30808i
$216$	9.21278	+	8.16181i	0.626850	+	0.555341i
$217$	−15.4833	−	13.7170i	−1.05108	−	0.931172i
$218$	6.35738	+	9.21025i	0.430576	+	0.623797i
$219$	8.63359	+	12.5079i	0.583404	+	0.845207i
$220$	−1.07805	+	0.565803i	−0.0726820	+	0.0381464i
$221$	−1.10087	+	0.721567i	−0.0740526	+	0.0485378i
$222$	−1.48864	−	0.781297i	−0.0999107	−	0.0524372i
$223$	0.604914	+	4.98192i	0.0405081	+	0.333614i	0.998848	+	0.0479841i	$0.0152797\pi$
$223$	0.604914	+	4.98192i	0.0405081	+	0.333614i	−0.958340	+	0.285630i	$0.907797\pi$
$224$	9.32672	+	2.29883i	0.623168	+	0.153597i
$225$	0.0466375	+	0.0675660i	0.00310916	+	0.00450440i
$226$	7.69806	−	11.1526i	0.512067	−	0.741858i
$227$	11.1975	−	9.92008i	0.743202	−	0.658419i	−0.204032	−	0.978964i	$-0.565405\pi$
$227$	11.1975	−	9.92008i	0.743202	−	0.658419i	0.947233	+	0.320545i	$0.103866\pi$
$228$	0.00327871	+	0.0270026i	0.000217138	+	0.00178829i
$229$	10.2125	−	2.51715i	0.674858	−	0.166338i	0.113030	−	0.993592i	$-0.463944\pi$
$229$	10.2125	−	2.51715i	0.674858	−	0.166338i	0.561828	+	0.827254i	$0.310098\pi$
$230$	5.01346	−	2.63127i	0.330578	−	0.173501i
$231$	0.598323	+	4.92764i	0.0393668	+	0.324215i
$232$	0.313589	−	2.58264i	0.0205881	−	0.169559i
$233$	14.8144	+	21.4623i	0.970521	+	1.40604i	0.913120	+	0.407691i	$0.133666\pi$
$233$	14.8144	+	21.4623i	0.970521	+	1.40604i	0.0574012	+	0.998351i	$0.481719\pi$
$234$	−2.39059	−	10.8068i	−0.156278	−	0.706462i
$235$	12.8266	−	18.5826i	0.836717	−	1.21219i
$236$	3.29709	+	2.92097i	0.214622	+	0.190139i
$237$	−1.95709	+	0.482379i	−0.127127	+	0.0313339i
$238$	−1.27189	+	1.84265i	−0.0824442	+	0.119441i
$239$	−4.12835			−0.267041			−0.133521	−	0.991046i	$-0.542628\pi$
$239$	−4.12835			−0.267041			−0.133521	+	0.991046i	$0.542628\pi$
$240$	6.03005	−	8.73604i	0.389238	−	0.563909i
$241$	−2.61208	+	21.5124i	−0.168259	+	1.38574i	0.626789	+	0.779189i	$0.284369\pi$
$241$	−2.61208	+	21.5124i	−0.168259	+	1.38574i	−0.795048	+	0.606547i	$0.792554\pi$
$242$	5.23741	−	13.8099i	0.336673	−	0.887734i
$243$	−1.91934	−	15.8072i	−0.123126	−	1.01403i
$244$	1.83029	−	4.82609i	0.117173	−	0.308959i
$245$	−14.0271	+	12.4269i	−0.896158	+	0.793926i
$246$	−11.4618	+	10.1543i	−0.730776	+	0.647411i
$247$	−0.106459	+	0.191546i	−0.00677383	+	0.0121878i
$248$	9.60964	+	8.51340i	0.610213	+	0.540601i
$249$	7.29300			0.462175
$250$	13.1261	−	11.6287i	0.830166	−	0.735463i
$251$	−15.3767	−	3.79002i	−0.970570	−	0.239224i	−0.278005	−	0.960580i	$-0.589673\pi$
$251$	−15.3767	−	3.79002i	−0.970570	−	0.239224i	−0.692565	+	0.721356i	$0.743519\pi$
$252$	−1.92840	−	2.79376i	−0.121478	−	0.175991i
$253$	0.717408	−	1.89165i	0.0451031	−	0.118927i
$254$	5.67193	−	14.9556i	0.355888	−	0.938401i
$255$	0.469744	+	0.680542i	0.0294165	+	0.0426172i
$256$	−9.79227	−	2.41358i	−0.612017	−	0.150849i
$257$	2.01791	−	1.78771i	0.125874	−	0.111514i	−0.597838	−	0.801617i	$-0.703973\pi$
$257$	2.01791	−	1.78771i	0.125874	−	0.111514i	0.723711	+	0.690103i	$0.242435\pi$
$258$	14.6383			0.911338
$259$	−3.10949	−	2.75477i	−0.193214	−	0.171173i
$260$	−3.33166	+	1.17305i	−0.206621	+	0.0727494i
$261$	−1.57044	+	1.39128i	−0.0972075	+	0.0861184i
$262$	15.7710	−	13.9719i	0.974337	−	0.863187i
$263$	0.169781	−	0.447675i	0.0104691	−	0.0276048i	−0.929680	−	0.368369i	$-0.879916\pi$
$263$	0.169781	−	0.447675i	0.0104691	−	0.0276048i	0.940149	+	0.340764i	$0.110686\pi$
$264$	−0.371346	−	3.05831i	−0.0228548	−	0.188226i
$265$	−0.109366	+	0.288375i	−0.00671831	+	0.0177147i
$266$	−0.0449314	+	0.370044i	−0.00275492	+	0.0226888i
$267$	−3.35899	+	4.86634i	−0.205567	+	0.297815i
$268$	5.48960			0.335331
$269$	0.369967	−	0.535989i	0.0225573	−	0.0326798i	−0.811543	−	0.584293i	$-0.801372\pi$
$269$	0.369967	−	0.535989i	0.0225573	−	0.0326798i	0.834100	+	0.551613i	$0.185987\pi$
$270$	−17.0573	+	4.20425i	−1.03807	+	0.255862i
$271$	17.5332	+	15.5331i	1.06507	+	0.943566i	0.998529	−	0.0542175i	$-0.0172664\pi$
$271$	17.5332	+	15.5331i	1.06507	+	0.943566i	0.0665372	+	0.997784i	$0.478805\pi$
$272$	0.971866	−	1.40799i	0.0589280	−	0.0853720i
$273$	−0.344935	+	14.3966i	−0.0208764	+	0.871320i
$274$	15.5057	+	22.4639i	0.936733	+	1.35709i
$275$	0.00625824	−	0.0515412i	0.000377386	−	0.00310805i
$276$	−0.0878144	−	0.723217i	−0.00528581	−	0.0435325i
$277$	2.86313	−	1.50269i	0.172029	−	0.0902878i	−0.376511	−	0.926412i	$-0.622876\pi$
$277$	2.86313	−	1.50269i	0.172029	−	0.0902878i	0.548540	+	0.836124i	$0.315184\pi$
$278$	5.94429	−	1.46514i	0.356515	−	0.0878730i
$279$	−1.24798	−	10.2781i	−0.0747147	−	0.615331i
$280$	15.9469	−	14.1277i	0.953009	−	0.844292i
$281$	−4.61637	+	6.68796i	−0.275389	+	0.398970i	−0.936136	−	0.351639i	$-0.885624\pi$
$281$	−4.61637	+	6.68796i	−0.275389	+	0.398970i	0.660746	+	0.750609i	$0.270240\pi$
$282$	−9.15305	−	13.2605i	−0.545056	−	0.789650i
$283$	−23.1258	−	5.69999i	−1.37468	−	0.338829i	−0.518314	−	0.855190i	$-0.673440\pi$
$283$	−23.1258	−	5.69999i	−1.37468	−	0.338829i	−0.856371	+	0.516361i	$0.827286\pi$
$284$	0.630884	+	5.19580i	0.0374361	+	0.308314i
$285$	0.121902	+	0.0639791i	0.00722085	+	0.00378979i
$286$	−3.40035	+	6.11805i	−0.201067	+	0.361768i
$287$	−33.5035	+	17.5840i	−1.97765	+	1.03795i
$288$	2.73122	+	3.95686i	0.160939	+	0.233160i
$289$	−9.58139	−	13.8810i	−0.563611	−	0.816532i
$290$	2.77949	+	2.46241i	0.163217	+	0.144598i
$291$	−8.99750	−	7.97109i	−0.527443	−	0.467273i
$292$	2.33086	+	6.14597i	0.136403	+	0.359665i
$293$	−14.2486	+	7.47825i	−0.832413	+	0.436884i	−0.826390	−	0.563098i	$-0.809609\pi$
$293$	−14.2486	+	7.47825i	−0.832413	+	0.436884i	−0.00602264	+	0.999982i	$0.501917\pi$
$294$	4.74207	+	12.5038i	0.276563	+	0.729236i
$295$	21.6464	−	5.33536i	1.26030	−	0.310637i
$296$	1.92989	+	1.70973i	0.112172	+	0.0993761i
$297$	−3.56588	+	5.16606i	−0.206913	+	0.299765i
$298$	4.69944	−	12.3914i	0.272231	−	0.717814i
$299$	2.85132	−	5.13021i	0.164896	−	0.296688i
$300$	−0.00662983	−	0.0174814i	−0.000382773	−	0.00100929i
$301$	35.1198	+	8.65625i	2.02427	+	0.498938i
$302$	21.9640	+	11.5276i	1.26388	+	0.663338i
$303$	3.13376	−	8.26306i	0.180030	−	0.474700i
$304$	0.0343327	−	0.282755i	0.00196911	−	0.0162171i
$305$	−14.8400	−	21.4995i	−0.849736	−	1.23105i
$306$	−1.08810	+	0.268192i	−0.0622023	+	0.0153315i
$307$	−27.4710	−	6.77099i	−1.56785	−	0.386441i	−0.642725	−	0.766097i	$-0.722196\pi$
$307$	−27.4710	−	6.77099i	−1.56785	−	0.386441i	−0.925128	+	0.379656i	$0.876042\pi$
$308$	−0.258770	+	2.13116i	−0.0147448	+	0.121434i
$309$	3.52204	+	9.28685i	0.200362	+	0.528310i
$310$	−17.7921	+	4.38535i	−1.01052	+	0.249071i
$311$	4.91854	+	1.21231i	0.278905	+	0.0687438i	0.376287	−	0.926503i	$-0.377201\pi$
$311$	4.91854	+	1.21231i	0.278905	+	0.0687438i	−0.0973821	+	0.995247i	$0.531047\pi$
$312$	0.214082	−	8.93515i	0.0121200	−	0.505853i
$313$	13.2582	−	3.26785i	0.749398	−	0.184710i	0.153922	−	0.988083i	$-0.450810\pi$
$313$	13.2582	−	3.26785i	0.749398	−	0.184710i	0.595476	+	0.803373i	$0.296963\pi$
$314$	−15.4265	+	8.09643i	−0.870565	+	0.456908i
$315$	−17.1814			−0.968061
$316$	−0.871755			−0.0490401
$317$	3.99472	−	2.09659i	0.224366	−	0.117756i	−0.348795	−	0.937199i	$-0.613409\pi$
$317$	3.99472	−	2.09659i	0.224366	−	0.117756i	0.573161	+	0.819443i	$0.305717\pi$
$318$	0.164737	+	0.145944i	0.00923797	+	0.00818413i
$319$	1.32684			0.0742886
$320$	−9.25215	+	8.19669i	−0.517211	+	0.458209i
$321$	10.8145	+	5.67588i	0.603605	+	0.316797i
$322$	1.20341	−	9.91095i	0.0670633	−	0.552316i
$323$	0.0196470	+	0.0103115i	0.00109319	+	0.000573749i
$324$	0.0401800	−	0.330912i	0.00223222	−	0.0183840i
$325$	0.0395399	−	0.145344i	0.00219328	−	0.00806221i
$326$	2.78917	+	22.9709i	0.154478	+	1.27224i
$327$	2.58440	−	6.81451i	0.142918	−	0.376843i
$328$	20.7938	−	10.9134i	1.14814	−	0.602593i
$329$	−14.1183	−	37.2269i	−0.778367	−	2.05238i
$330$	3.89360	+	2.04352i	0.214336	+	0.112492i
$331$	−4.82066	−	2.53008i	−0.264967	−	0.139066i	0.327008	−	0.945021i	$-0.393959\pi$
$331$	−4.82066	−	2.53008i	−0.264967	−	0.139066i	−0.591976	+	0.805956i	$0.701652\pi$
$332$	3.06250	+	0.754839i	0.168077	+	0.0414272i
$333$	−0.250630	−	2.06413i	−0.0137344	−	0.113113i
$334$	19.0947	−	16.9164i	1.04481	−	0.925624i
$335$	15.7833	−	22.8661i	0.862334	−	1.24931i
$336$	−6.63729	−	17.5011i	−0.362094	−	0.954763i
$337$	−22.4164			−1.22110			−0.610549	−	0.791978i	$-0.709051\pi$
$337$	−22.4164			−1.22110			−0.610549	+	0.791978i	$0.709051\pi$
$338$	−12.3225	+	16.1403i	−0.670255	+	0.877914i
$339$	−8.82509			−0.479313
$340$	0.126819	+	0.334395i	0.00687775	+	0.0181351i
$341$	−3.71948	+	5.38860i	−0.201421	+	0.291809i
$342$	−0.139654	+	0.123722i	−0.00755160	+	0.00669013i
$343$	0.670150	+	5.51918i	0.0361847	+	0.298008i
$344$	−21.7969	−	5.37246i	−1.17521	−	0.289663i
$345$	−3.26492	−	1.71356i	−0.175778	−	0.0922552i
$346$	−10.8666	−	5.70324i	−0.584193	−	0.306608i
$347$	11.9832	+	31.5972i	0.643294	+	1.69623i	0.715296	+	0.698821i	$0.246292\pi$
$347$	11.9832	+	31.5972i	0.643294	+	1.69623i	−0.0720027	+	0.997404i	$0.522939\pi$
$348$	0.423067	−	0.222043i	0.0226788	−	0.0119027i
$349$	11.3842	−	30.0177i	0.609383	−	1.60681i	−0.173635	−	0.984810i	$-0.555551\pi$
$349$	11.3842	−	30.0177i	0.609383	−	1.60681i	0.783017	−	0.622000i	$-0.213680\pi$
$350$	−0.0308833	−	0.254347i	−0.00165078	−	0.0135954i
$351$	−12.3992	+	13.3380i	−0.661821	+	0.711930i
$352$	0.366500	−	3.01840i	0.0195345	−	0.160881i
$353$	−5.26242	−	2.76193i	−0.280091	−	0.147003i	0.318829	−	0.947812i	$-0.396711\pi$
$353$	−5.26242	−	2.76193i	−0.280091	−	0.147003i	−0.598919	+	0.800810i	$0.704403\pi$
$354$	1.91763	−	15.7931i	0.101921	−	0.839395i
$355$	23.4562	+	12.3108i	1.24492	+	0.653387i
$356$	−1.91420	+	1.69583i	−0.101452	+	0.0898788i
$357$	1.45810			0.0771707
$358$	−20.0694	−	17.7799i	−1.06070	−	0.939699i
$359$	28.4995	−	14.9577i	1.50415	−	0.789437i	0.506787	−	0.862071i	$-0.330833\pi$
$359$	28.4995	−	14.9577i	1.50415	−	0.789437i	0.997359	+	0.0726345i	$0.0231407\pi$
$360$	10.6635			0.562018
$361$	−18.9963			−0.999806
$362$	−21.5162	+	11.2926i	−1.13086	+	0.593524i
$363$	−9.33900	+	2.30186i	−0.490170	+	0.120816i
$364$	−1.63492	+	6.00976i	−0.0856931	+	0.314997i
$365$	32.3016	+	7.96163i	1.69074	+	0.416731i
$366$	−18.1002	+	4.46129i	−0.946111	+	0.233195i
$367$	0.442217	+	1.16603i	0.0230835	+	0.0608662i	0.946063	−	0.323984i	$-0.105022\pi$
$367$	0.442217	+	1.16603i	0.0230835	+	0.0608662i	−0.922979	+	0.384850i	$0.874253\pi$
$368$	−0.919540	+	7.57309i	−0.0479343	+	0.394775i
$369$	−18.3882	−	4.53229i	−0.957253	−	0.235942i
$370$	−3.57315	+	0.880704i	−0.185759	+	0.0457856i
$371$	0.308929	+	0.447562i	0.0160388	+	0.0232362i
$372$	−0.284203	+	2.34062i	−0.0147352	+	0.121356i
$373$	−8.42743	+	22.2213i	−0.436356	+	1.15058i	0.518910	+	0.854829i	$0.326338\pi$
$373$	−8.42743	+	22.2213i	−0.436356	+	1.15058i	−0.955266	+	0.295747i	$0.904431\pi$
$374$	0.627533	+	0.329355i	0.0324490	+	0.0170305i
$375$	−11.0883	−	2.73303i	−0.572599	−	0.141133i
$376$	8.76244	+	23.1047i	0.451889	+	1.19153i
$377$	3.80905	+	0.555381i	0.196176	+	0.0286036i
$378$	−10.9846	+	28.9641i	−0.564988	+	1.48975i
$379$	1.70150	−	2.46505i	0.0874004	−	0.126621i	−0.776845	−	0.629692i	$-0.783181\pi$
$379$	1.70150	−	2.46505i	0.0874004	−	0.126621i	0.864245	+	0.503071i	$0.167796\pi$
$380$	0.0445676	+	0.0394834i	0.00228627	+	0.00202546i
$381$	−10.1138	+	2.49283i	−0.518146	+	0.127712i
$382$	0.545360	+	1.43800i	0.0279031	+	0.0735743i
$383$	−15.4843	+	8.12676i	−0.791208	+	0.415258i	−0.811366	−	0.584539i	$-0.801276\pi$
$383$	−15.4843	+	8.12676i	−0.791208	+	0.415258i	0.0201576	+	0.999797i	$0.493583\pi$
$384$	4.89285	+	12.9014i	0.249687	+	0.658371i
$385$	8.13302	+	7.20523i	0.414497	+	0.367212i
$386$	−6.14550	−	5.44443i	−0.312798	−	0.277114i
$387$	10.2844	+	14.8996i	0.522786	+	0.757387i
$388$	−2.95324	−	4.27851i	−0.149928	−	0.217208i
$389$	5.07010	−	2.66099i	0.257064	−	0.134918i	−0.331269	−	0.943536i	$-0.607477\pi$
$389$	5.07010	−	2.66099i	0.257064	−	0.134918i	0.588333	+	0.808619i	$0.299784\pi$
$390$	10.3223	+	7.49624i	0.522689	+	0.379587i
$391$	−0.526209	−	0.276176i	−0.0266116	−	0.0139668i
$392$	−2.47203	−	20.3590i	−0.124857	−	1.02829i
$393$	−13.3226	−	3.28374i	−0.672038	−	0.165643i
$394$	−23.1199	−	33.4950i	−1.16477	−	1.68745i
$395$	−2.50641	+	3.63116i	−0.126111	+	0.182704i
$396$	−0.804294	+	0.712543i	−0.0404173	+	0.0358066i
$397$	4.59532	+	37.8459i	0.230633	+	1.89943i	0.404301	+	0.914626i	$0.367515\pi$
$397$	4.59532	+	37.8459i	0.230633	+	1.89943i	−0.173668	+	0.984804i	$0.555562\pi$
$398$	30.9050	−	7.61739i	1.54913	−	0.381825i
$399$	0.214948	−	0.112813i	0.0107609	−	0.00564774i
$400$	0.0235983	+	0.194350i	0.00117992	+	0.00971749i
$401$	−2.85006	+	23.4723i	−0.142325	+	1.17215i	0.730077	+	0.683365i	$0.239484\pi$
$401$	−2.85006	+	23.4723i	−0.142325	+	1.17215i	−0.872402	+	0.488788i	$0.837439\pi$
$402$	−11.2629	−	16.3172i	−0.561744	−	0.813827i
$403$	−12.9333	+	13.9126i	−0.644255	+	0.693035i
$404$	2.17119	−	3.14550i	0.108020	−	0.156495i
$405$	−1.26284	−	1.11878i	−0.0627511	−	0.0555926i
$406$	6.35745	−	1.56697i	0.315515	−	0.0777674i
$407$	−0.746978	+	1.08218i	−0.0370263	+	0.0536419i
$408$	−0.904960			−0.0448022
$409$	−14.8290	+	21.4836i	−0.733249	+	1.06229i	0.262013	+	0.965064i	$0.415614\pi$
$409$	−14.8290	+	21.4836i	−0.733249	+	1.06229i	−0.995262	+	0.0972298i	$0.969002\pi$
$410$	−4.04027	+	33.2746i	−0.199535	+	1.64332i
$411$	6.30338	−	16.6207i	0.310923	−	0.819836i
$412$	0.517781	+	4.26431i	0.0255092	+	0.210087i
$413$	13.9399	−	36.7565i	0.685939	−	1.80867i
$414$	3.74037	−	3.31368i	0.183829	−	0.162858i
$415$	11.9493	−	10.5861i	0.586566	−	0.519652i
$416$	2.31556	−	8.51173i	0.113530	−	0.417322i
$417$	−2.98428	−	2.64385i	−0.146141	−	0.129470i
$418$	0.117991			0.00577114
$419$	−21.9327	+	19.4307i	−1.07148	+	0.949252i	−0.998842	−	0.0481061i	$-0.984681\pi$
$419$	−21.9327	+	19.4307i	−1.07148	+	0.949252i	−0.0726418	+	0.997358i	$0.523143\pi$
$420$	3.79902	+	0.936375i	0.185373	+	0.0456904i
$421$	4.44656	+	6.44196i	0.216712	+	0.313962i	0.916230	−	0.400654i	$-0.131217\pi$
$421$	4.44656	+	6.44196i	0.216712	+	0.313962i	−0.699517	+	0.714616i	$0.746602\pi$
$422$	−3.26220	+	8.60171i	−0.158801	+	0.418725i
$423$	7.06652	−	18.6329i	0.343586	−	0.905961i
$424$	−0.191735	−	0.277777i	−0.00931149	−	0.0134900i
$425$	−0.0148080	−	0.00364984i	−0.000718292	−	0.000177043i
$426$	14.1495	−	12.5354i	0.685547	−	0.607341i
$427$	−46.0637			−2.22918
$428$	3.95379	+	3.50276i	0.191114	+	0.169312i
$429$	4.53692	−	0.440897i	0.219045	−	0.0212867i
$430$	23.9842	−	21.2481i	1.15662	−	1.02467i
$431$	−5.27677	+	4.67481i	−0.254173	+	0.225178i	−0.780581	−	0.625054i	$-0.785077\pi$
$431$	−5.27677	+	4.67481i	−0.254173	+	0.225178i	0.526408	+	0.850232i	$0.323538\pi$
$432$	8.39349	−	22.1318i	0.403832	−	1.06482i
$433$	0.624684	+	5.14474i	0.0300204	+	0.247240i	0.999992	+	0.00402170i	$0.00128015\pi$
$433$	0.624684	+	5.14474i	0.0300204	+	0.247240i	−0.969972	+	0.243219i	$0.921797\pi$
$434$	−11.4578	+	30.2117i	−0.549992	+	1.45021i
$435$	0.291488	−	2.40062i	0.0139758	−	0.115101i
$436$	1.79057	−	2.59409i	0.0857527	−	0.124234i
$437$	−0.0989399			−0.00473294
$438$	13.4860	−	19.5378i	0.644384	−	0.933552i
$439$	2.43309	−	0.599704i	0.116125	−	0.0286223i	−0.180825	−	0.983515i	$-0.557877\pi$
$439$	2.43309	−	0.599704i	0.116125	−	0.0286223i	0.296950	+	0.954893i	$0.404031\pi$
$440$	−5.04771	−	4.47188i	−0.240640	−	0.213189i
$441$	−9.39536	+	13.6115i	−0.447398	+	0.648168i
$442$	1.66365	+	1.20817i	0.0791316	+	0.0574669i
$443$	9.17113	+	13.2867i	0.435733	+	0.631269i	0.977918	−	0.208991i	$-0.0670179\pi$
$443$	9.17113	+	13.2867i	0.435733	+	0.631269i	−0.542184	+	0.840260i	$0.682402\pi$
$444$	−0.0570760	+	0.470063i	−0.00270871	+	0.0223082i
$445$	1.56015	+	12.8490i	0.0739583	+	0.609102i
$446$	6.94116	−	3.64300i	0.328673	−	0.172501i
$447$	−8.37973	+	2.06542i	−0.396347	+	0.0976909i
$448$	2.62716	+	21.6366i	0.124122	+	1.02223i
$449$	20.0605	−	17.7720i	0.946712	−	0.838714i	−0.0403280	−	0.999186i	$-0.512840\pi$
$449$	20.0605	−	17.7720i	0.946712	−	0.838714i	0.987040	+	0.160473i	$0.0513018\pi$
$450$	0.0728493	−	0.105540i	0.00343415	−	0.00497522i
$451$	6.80362	+	9.85674i	0.320370	+	0.464136i
$452$	−3.70586	−	0.913413i	−0.174309	−	0.0429634i
$453$	−1.94715	−	16.0362i	−0.0914849	−	0.753446i
$454$	−20.6909	−	10.8594i	−0.971071	−	0.509657i
$455$	20.3321	+	24.0889i	0.953185	+	1.12930i
$456$	−0.133406	+	0.0700170i	−0.00624732	+	0.00327885i
$457$	−2.21492	−	3.20886i	−0.103609	−	0.150104i	0.767750	−	0.640750i	$-0.221376\pi$
$457$	−2.21492	−	3.20886i	−0.103609	−	0.150104i	−0.871359	+	0.490646i	$0.836761\pi$
$458$	−9.33309	−	13.5213i	−0.436107	−	0.631810i
$459$	1.38018	+	1.22273i	0.0644214	+	0.0570723i
$460$	−1.19366	−	1.05749i	−0.0556548	−	0.0493059i
$461$	8.62753	+	22.7489i	0.401824	+	1.05952i	0.971372	+	0.237564i	$0.0763491\pi$
$461$	8.62753	+	22.7489i	0.401824	+	1.05952i	−0.569548	+	0.821958i	$0.692882\pi$
$462$	6.86553	−	3.60331i	0.319413	−	0.167641i
$463$	3.72065	+	9.81055i	0.172913	+	0.455935i	0.993257	−	0.115936i	$-0.0369869\pi$
$463$	3.72065	+	9.81055i	0.172913	+	0.455935i	−0.820343	+	0.571871i	$0.806218\pi$
$464$	−4.85781	+	1.19734i	−0.225518	+	0.0555852i
$465$	8.93238	+	7.91340i	0.414229	+	0.366975i
$466$	23.1405	−	33.5249i	1.07196	−	1.55301i
$467$	−0.461511	+	1.21690i	−0.0213562	+	0.0563116i	−0.945270	−	0.326288i	$-0.894202\pi$
$467$	−0.461511	+	1.21690i	−0.0213562	+	0.0563116i	0.923914	+	0.382600i	$0.124971\pi$
$468$	−2.60720	+	1.70889i	−0.120518	+	0.0789935i
$469$	−17.3727	−	45.8081i	−0.802198	−	2.11522i
$470$	−34.2451	−	8.44066i	−1.57961	−	0.389338i
$471$	10.0462	+	5.27265i	0.462904	+	0.242951i
$472$	−8.65173	+	22.8128i	−0.398228	+	1.05004i
$473$	1.38006	−	11.3658i	0.0634550	−	0.522599i
$474$	1.78857	+	2.59119i	0.0821517	+	0.119017i
$475$	−0.00246533		0.000607650i	−0.000113117		2.78809e-5i
$476$	0.612290	+	0.150916i	0.0280643	+	0.00691722i
$477$	−0.0328098	+	0.270213i	−0.00150226	+	0.0123722i
$478$	2.28672	+	6.02957i	0.104592	+	0.275786i
$479$	3.04219	−	0.749832i	0.139001	−	0.0342607i	−0.169201	−	0.985582i	$-0.554119\pi$
$479$	3.04219	−	0.749832i	0.139001	−	0.0342607i	0.308202	+	0.951321i	$0.400273\pi$
$480$	−5.38062	−	1.32620i	−0.245591	−	0.0605326i
$481$	−2.59738	+	2.79404i	−0.118430	+	0.127397i
$482$	32.8663	−	8.10081i	1.49702	−	0.368982i
$483$	−5.75700	+	3.02151i	−0.261953	+	0.137483i
$484$	−4.15991			−0.189087
$485$	−26.3124			−1.19479
$486$	−22.0237	+	11.5589i	−0.999014	+	0.524323i
$487$	26.6225	+	23.5855i	1.20638	+	1.06876i	0.995835	+	0.0911768i	$0.0290628\pi$
$487$	26.6225	+	23.5855i	1.20638	+	1.06876i	0.210547	+	0.977584i	$0.432476\pi$
$488$	28.5892			1.29417
$489$	11.2795	−	9.99275i	0.510076	−	0.451888i
$490$	25.9195	+	13.6036i	1.17092	+	0.614548i
$491$	2.43520	−	20.0557i	0.109899	−	0.905102i	−0.828605	−	0.559834i	$-0.810865\pi$
$491$	2.43520	−	20.0557i	0.109899	−	0.905102i	0.938504	−	0.345268i	$-0.112212\pi$
$492$	3.81886	+	2.00429i	0.172168	+	0.0903605i
$493$	0.0469793	−	0.386910i	0.00211584	−	0.0174255i
$494$	0.338726	+	0.0493882i	0.0152400	+	0.00222208i
$495$	0.655535	+	5.39882i	0.0294641	+	0.242659i
$496$	8.75506	−	23.0852i	0.393114	−	1.03656i
$497$	41.3600	−	21.7074i	1.85525	−	0.973709i
$498$	−4.03963	−	10.6516i	−0.181020	−	0.477310i
$499$	−9.63923	−	5.05906i	−0.431511	−	0.226474i	0.234961	−	0.972005i	$-0.424504\pi$
$499$	−9.63923	−	5.05906i	−0.431511	−	0.226474i	−0.666472	+	0.745530i	$0.732196\pi$
$500$	−4.37338	−	2.29533i	−0.195583	−	0.102650i
$501$	−16.1303	−	3.97576i	−0.720649	−	0.177624i
$502$	2.98181	+	24.5574i	0.133085	+	1.09605i
$503$	−14.8202	+	13.1296i	−0.660801	+	0.585419i	−0.925424	−	0.378933i	$-0.876291\pi$
$503$	−14.8202	+	13.1296i	−0.660801	+	0.585419i	0.264623	+	0.964352i	$0.414753\pi$
$504$	10.6812	−	15.4745i	0.475780	−	0.689287i
$505$	−6.85967	−	18.0875i	−0.305251	−	0.804882i
$506$	−3.16018			−0.140487
$507$	13.2090	+	0.633328i	0.586633	+	0.0281271i
$508$	−4.50504			−0.199879
$509$	7.21208	+	19.0167i	0.319670	+	0.842901i	0.994482	+	0.104911i	$0.0334556\pi$
$509$	7.21208	+	19.0167i	0.319670	+	0.842901i	−0.674812	+	0.737990i	$0.735775\pi$
$510$	0.733756	−	1.06303i	0.0324913	−	0.0470717i
$511$	43.9088	−	38.8998i	1.94241	−	1.72083i
$512$	−1.37105	−	11.2916i	−0.0605926	−	0.499025i
$513$	0.298065	+	0.0734665i	0.0131599	+	0.00324362i
$514$	−3.72873	−	1.95699i	−0.164467	−	0.0863190i
$515$	19.2510	+	10.1037i	0.848300	+	0.445222i
$516$	−1.46200	−	3.85497i	−0.0643609	−	0.169706i
$517$	−11.1589	+	5.85667i	−0.490770	+	0.257576i
$518$	−2.30105	+	6.06737i	−0.101102	+	0.266585i
$519$	0.963345	+	7.93386i	0.0422862	+	0.348258i
$520$	−12.6190	−	14.9506i	−0.553381	−	0.655628i
$521$	2.87749	−	23.6983i	0.126065	−	1.03824i	−0.783126	−	0.621863i	$-0.786376\pi$
$521$	2.87749	−	23.6983i	0.126065	−	1.03824i	0.909192	−	0.416378i	$-0.136701\pi$
$522$	2.90188	+	1.52302i	0.127012	+	0.0666610i
$523$	2.47589	−	20.3908i	0.108263	−	0.891627i	−0.832841	−	0.553512i	$-0.813287\pi$
$523$	2.47589	−	20.3908i	0.108263	−	0.891627i	0.941105	−	0.338116i	$-0.109789\pi$
$524$	−5.25462	−	2.75784i	−0.229549	−	0.120477i
$525$	−0.124893	+	0.110646i	−0.00545078	+	0.00482897i
$526$	−0.747884			−0.0326093
$527$	1.43964	+	1.27541i	0.0627115	+	0.0555575i
$528$	−5.24604	+	2.75334i	−0.228305	+	0.119824i
$529$	−20.3501			−0.884786
$530$	0.481758			0.0209262
$531$	17.4223	−	9.14393i	0.756064	−	0.396813i
$532$	0.101938	−	0.0251255i	0.00441958	−	0.00108933i
$533$	15.4059	+	31.1443i	0.667302	+	1.34901i
$534$	8.96798	+	2.21041i	0.388082	+	0.0956537i
$535$	25.9579	−	6.39804i	1.12226	−	0.276611i
$536$	10.7823	+	28.4306i	0.465724	+	1.22801i
$537$	−2.10470	+	17.3338i	−0.0908247	+	0.748009i
$538$	−0.987753	−	0.243459i	−0.0425851	−	0.0104963i
$539$	10.1556	−	2.50312i	0.437431	−	0.107817i
$540$	2.81079	+	4.07213i	0.120957	+	0.175236i
$541$	2.97025	−	24.4622i	0.127701	−	1.05171i	−0.778139	−	0.628092i	$-0.783836\pi$
$541$	2.97025	−	24.4622i	0.127701	−	1.05171i	0.905840	−	0.423620i	$-0.139241\pi$
$542$	12.9747	−	34.2116i	0.557313	−	1.46951i
$543$	14.0120	+	7.35407i	0.601313	+	0.315593i
$544$	−0.867197	−	0.213745i	−0.0371807	−	0.00916423i
$545$	−5.65715	−	14.9167i	−0.242326	−	0.638960i
$546$	21.2176	−	7.47054i	0.908031	−	0.319710i
$547$	−12.2832	+	32.3881i	−0.525191	+	1.38482i	0.365757	+	0.930710i	$0.380810\pi$
$547$	−12.2832	+	32.3881i	−0.525191	+	1.38482i	−0.890948	+	0.454105i	$0.849959\pi$
$548$	4.36721	−	6.32700i	0.186558	−	0.270276i
$549$	−17.2576	−	15.2889i	−0.736536	−	0.652514i
$550$	−0.0787438	+	0.0194086i	−0.00335765	+	0.000827586i
$551$	−0.0230098	−	0.0606718i	−0.000980249	−	0.00258470i
$552$	3.57305	−	1.87528i	0.152079	−	0.0798173i
$553$	2.75881	+	7.27439i	0.117317	+	0.309338i
$554$	−3.78062	−	3.34934i	−0.160623	−	0.142300i
$555$	1.79388	+	1.58923i	0.0761458	+	0.0674593i
$556$	−0.979529	−	1.41909i	−0.0415413	−	0.0601829i
$557$	−14.5773	−	21.1188i	−0.617659	−	0.894833i	0.381910	−	0.924200i	$-0.375266\pi$
$557$	−14.5773	−	21.1188i	−0.617659	−	0.894833i	−0.999569	+	0.0293662i	$0.990651\pi$
$558$	−14.3201	+	7.51578i	−0.606219	+	0.318168i
$559$	8.71926	−	32.0509i	0.368786	−	1.35561i
$560$	−36.2786	−	19.0405i	−1.53305	−	0.804607i
$561$	−0.0556320	−	0.458170i	−0.00234878	−	0.0193440i
$562$	12.3250	+	3.03783i	0.519898	+	0.128143i
$563$	2.39559	+	3.47062i	0.100962	+	0.146269i	0.870209	−	0.492683i	$-0.163984\pi$
$563$	2.39559	+	3.47062i	0.100962	+	0.146269i	−0.769247	+	0.638952i	$0.779368\pi$
$564$	−2.57798	+	3.73484i	−0.108552	+	0.157265i
$565$	−14.4595	+	12.8100i	−0.608317	+	0.538922i
$566$	4.48449	+	36.9331i	0.188497	+	1.55241i
$567$	−2.88846	+	0.711942i	−0.121304	+	0.0298988i
$568$	−25.6698	+	13.4726i	−1.07708	+	0.565297i
$569$	−0.876566	−	7.21917i	−0.0367476	−	0.302644i	−0.999482	−	0.0321937i	$-0.989751\pi$
$569$	−0.876566	−	7.21917i	−0.0367476	−	0.302644i	0.962734	−	0.270450i	$-0.0871724\pi$
$570$	0.0259211	−	0.213479i	0.00108571	−	0.00894167i
$571$	−6.40462	−	9.27870i	−0.268025	−	0.388302i	0.665742	−	0.746182i	$-0.268115\pi$
$571$	−6.40462	−	9.27870i	−0.268025	−	0.388302i	−0.933768	+	0.357880i	$0.883500\pi$
$572$	1.95080	+	0.284437i	0.0815668	+	0.0118929i
$573$	0.568948	−	0.824263i	0.0237681	−	0.0344341i
$574$	44.2397	+	39.1929i	1.84653	+	1.63588i
$575$	0.0660296	−	0.0162748i	0.00275362	−	0.000678707i
$576$	−6.19710	+	8.97805i	−0.258212	+	0.374085i
$577$	−16.4996			−0.686889			−0.343444	−	0.939173i	$-0.611594\pi$
$577$	−16.4996			−0.686889			−0.343444	+	0.939173i	$0.611594\pi$
$578$	−14.9665	+	21.6827i	−0.622523	+	0.901880i
$579$	−0.644486	+	5.30782i	−0.0267839	+	0.220586i
$580$	0.370872	−	0.977909i	0.0153996	−	0.0406055i
$581$	−3.39301	−	27.9440i	−0.140766	−	1.15931i
$582$	−6.65823	+	17.5563i	−0.275993	+	0.727733i
$583$	0.128848	−	0.114149i	0.00533634	−	0.00472759i
$584$	−27.2518	+	24.1430i	−1.12769	+	0.999043i
$585$	−0.377918	+	15.7732i	−0.0156250	+	0.652141i
$586$	18.8146	+	16.6682i	0.777222	+	0.688559i
$587$	−31.8981			−1.31657			−0.658287	−	0.752767i	$-0.728719\pi$
$587$	−31.8981			−1.31657			−0.658287	+	0.752767i	$0.728719\pi$
$588$	2.81925	−	2.49764i	0.116264	−	0.103001i
$589$	0.310905	+	0.0766312i	0.0128106	+	0.00315753i
$590$	−19.7825	−	28.6599i	−0.814432	−	1.17991i
$591$	−9.39873	+	24.7824i	−0.386612	+	1.01941i
$592$	1.75826	−	4.63616i	0.0722642	−	0.190545i
$593$	−0.309018	−	0.447690i	−0.0126899	−	0.0183844i	0.816588	−	0.577222i	$-0.195863\pi$
$593$	−0.309018	−	0.447690i	−0.0126899	−	0.0183844i	−0.829277	+	0.558837i	$0.811248\pi$
$594$	9.52033	+	2.34655i	0.390624	+	0.0962801i
$595$	2.38903	−	2.11650i	0.0979407	−	0.0867679i
$596$	−3.73262			−0.152894
$597$	−15.5156	−	13.7456i	−0.635012	−	0.562571i
$598$	−9.07217	−	1.32277i	−0.370989	−	0.0540923i
$599$	9.02044	−	7.99141i	0.368565	−	0.326520i	−0.458429	−	0.888731i	$-0.651588\pi$
$599$	9.02044	−	7.99141i	0.368565	−	0.326520i	0.826994	+	0.562211i	$0.190049\pi$
$600$	0.0775142	−	0.0686716i	0.00316450	−	0.00280350i
$601$	6.10862	−	16.1071i	0.249176	−	0.657023i	−0.750818	−	0.660509i	$-0.770341\pi$
$601$	6.10862	−	16.1071i	0.249176	−	0.657023i	0.999994	+	0.00348637i	$0.00110975\pi$
$602$	−6.81034	−	56.0882i	−0.277569	−	2.28598i
$603$	8.69543	−	22.9280i	0.354105	−	0.933699i
$604$	0.842124	−	6.93551i	0.0342655	−	0.282202i
$605$	−11.9603	+	17.3275i	−0.486255	+	0.704462i
$606$	−13.8042			−0.560758
$607$	−5.79554	+	8.39629i	−0.235234	+	0.340795i	−0.922767	−	0.385358i	$-0.874078\pi$
$607$	−5.79554	+	8.39629i	−0.235234	+	0.340795i	0.687534	+	0.726153i	$0.258693\pi$
$608$	−0.144377	+	0.0355857i	−0.00585525	+	0.00144319i
$609$	−3.19171	−	2.82761i	−0.129335	−	0.114580i
$610$	−23.1806	+	33.5829i	−0.938554	+	1.35973i
$611$	−34.4863	+	12.1423i	−1.39517	+	0.491225i
$612$	0.179302	+	0.259764i	0.00724785	+	0.0105003i
$613$	−2.51597	+	20.7209i	−0.101619	+	0.836907i	0.849395	+	0.527758i	$0.176967\pi$
$613$	−2.51597	+	20.7209i	−0.101619	+	0.836907i	−0.951014	+	0.309149i	$0.899956\pi$
$614$	5.32710	+	43.8726i	0.214984	+	1.77055i
$615$	19.3283	−	10.1443i	0.779392	−	0.409057i
$616$	−11.5455	+	2.84571i	−0.465182	+	0.114657i
$617$	−3.90444	−	32.1559i	−0.157187	−	1.29455i	−0.831260	−	0.555885i	$-0.812380\pi$
$617$	−3.90444	−	32.1559i	−0.157187	−	1.29455i	0.674073	−	0.738665i	$-0.264543\pi$
$618$	11.6128	−	10.2881i	0.467136	−	0.413847i
$619$	−4.27091	+	6.18748i	−0.171662	+	0.248696i	−0.899367	−	0.437195i	$-0.855972\pi$
$619$	−4.27091	+	6.18748i	−0.171662	+	0.248696i	0.727704	+	0.685891i	$0.240587\pi$
$620$	2.93187	+	4.24754i	0.117747	+	0.170585i
$621$	−7.98314	−	1.96767i	−0.320353	−	0.0789598i
$622$	−0.953789	−	7.85516i	−0.0382435	−	0.314963i
$623$	20.2087	+	10.6063i	0.809644	+	0.424934i
$624$	−16.2127	+	5.70834i	−0.649027	+	0.228517i
$625$	−21.9499	+	11.5202i	−0.877996	+	0.460808i
$626$	−12.1166	−	17.5539i	−0.484276	−	0.701594i
$627$	−0.0436499	−	0.0632377i	−0.00174321	−	0.00252547i
$628$	3.67291	+	3.25391i	0.146565	+	0.129845i
$629$	0.289120	+	0.256138i	0.0115280	+	0.0102129i
$630$	9.51685	+	25.0939i	0.379160	+	0.999764i
$631$	20.3864	−	10.6996i	0.811570	−	0.425945i	−0.00726534	−	0.999974i	$-0.502313\pi$
$631$	20.3864	−	10.6996i	0.811570	−	0.425945i	0.818835	+	0.574029i	$0.194620\pi$
$632$	−1.71224	−	4.51481i	−0.0681093	−	0.179589i
$633$	5.81694	−	1.43375i	0.231202	−	0.0569863i
$634$	−5.27483	−	4.67309i	−0.209490	−	0.185592i
$635$	−12.9526	+	18.7651i	−0.514008	+	0.744669i
$636$	0.0219811	−	0.0579594i	0.000871608	−	0.00229824i
$637$	30.2021	−	2.93503i	1.19665	−	0.116290i
$638$	−0.734942	−	1.93788i	−0.0290966	−	0.0767215i
$639$	22.7002	+	5.59509i	0.898006	+	0.221339i
$640$	26.7437	+	14.0362i	1.05714	+	0.554828i
$641$	12.0387	−	31.7433i	0.475498	−	1.25379i	−0.455980	−	0.889990i	$-0.650711\pi$
$641$	12.0387	−	31.7433i	0.475498	−	1.25379i	0.931479	−	0.363796i	$-0.118519\pi$
$642$	2.29958	−	18.9387i	0.0907571	−	0.747452i
$643$	13.4083	+	19.4253i	0.528772	+	0.766058i	0.992803	−	0.119761i	$-0.0382128\pi$
$643$	13.4083	+	19.4253i	0.528772	+	0.766058i	−0.464031	+	0.885819i	$0.653597\pi$
$644$	−2.73023	+	0.672942i	−0.107586	+	0.0265176i
$645$	−20.2607	−	4.99382i	−0.797766	−	0.196632i
$646$	0.00417771	−	0.0344066i	0.000164370	−	0.00135371i
$647$	6.74758	+	17.7919i	0.265275	+	0.699472i	0.999782	+	0.0208714i	$0.00664404\pi$
$647$	6.74758	+	17.7919i	0.265275	+	0.699472i	−0.734507	+	0.678601i	$0.762587\pi$
$648$	1.79271	−	0.441863i	0.0704243	−	0.0173580i
$649$	−12.0817	−	2.97787i	−0.474247	−	0.116891i
$650$	−0.234180	+	0.0227575i	−0.00918528	+	0.000892623i
$651$	20.4308	−	5.03574i	0.800746	−	0.197366i
$652$	5.77079	−	3.02875i	0.226002	−	0.118615i
$653$	29.8739			1.16906			0.584529	−	0.811373i	$-0.301279\pi$
$653$	29.8739			1.16906			0.584529	+	0.811373i	$0.301279\pi$
$654$	−11.3843			−0.445161
$655$	−26.5951	+	13.9582i	−1.03916	+	0.545391i
$656$	−33.8041	−	29.9478i	−1.31983	−	1.16927i
$657$	29.3614			1.14550
$658$	−46.5507	+	41.2403i	−1.81473	+	1.60771i
$659$	37.0891	+	19.4659i	1.44479	+	0.758282i	0.991130	−	0.132895i	$-0.0424273\pi$
$659$	37.0891	+	19.4659i	1.44479	+	0.758282i	0.453656	+	0.891177i	$0.350120\pi$
$660$	0.149285	−	1.22947i	0.00581091	−	0.0478572i
$661$	−4.92209	−	2.58331i	−0.191447	−	0.100479i	0.366276	−	0.930506i	$-0.380633\pi$
$661$	−4.92209	−	2.58331i	−0.191447	−	0.100479i	−0.557723	+	0.830027i	$0.688325\pi$
$662$	−1.02506	+	8.44212i	−0.0398400	+	0.328112i
$663$	0.0320720	−	1.33859i	0.00124557	−	0.0519865i
$664$	2.10585	+	17.3433i	0.0817230	+	0.673049i
$665$	0.188429	−	0.496847i	0.00730697	−	0.0192669i
$666$	−2.87589	+	1.50938i	−0.111438	+	0.0584873i
$667$	0.616275	+	1.62498i	0.0238623	+	0.0629197i
$668$	−6.36200	−	3.33904i	−0.246153	−	0.129191i
$669$	−4.52030	−	2.37244i	−0.174765	−	0.0917238i
$670$	−42.1390	−	10.3863i	−1.62797	−	0.401259i
$671$	1.75751	+	14.4744i	0.0678478	+	0.558777i
$672$	−7.31408	+	6.47971i	−0.282147	+	0.249960i
$673$	21.3167	−	30.8825i	0.821697	−	1.19043i	−0.157499	−	0.987519i	$-0.550343\pi$
$673$	21.3167	−	30.8825i	0.821697	−	1.19043i	0.979196	−	0.202915i	$-0.0650414\pi$
$674$	12.4165	+	32.7397i	0.478267	+	1.26109i
$675$	−0.211004			−0.00812157
$676$	5.48123	+	1.63311i	0.210817	+	0.0628119i
$677$	−4.98384			−0.191545			−0.0957723	−	0.995403i	$-0.530532\pi$
$677$	−4.98384			−0.191545			−0.0957723	+	0.995403i	$0.530532\pi$
$678$	4.88826	+	12.8893i	0.187732	+	0.495010i
$679$	−26.3561	+	38.1834i	−1.01146	+	1.46535i
$680$	−1.48274	+	1.31359i	−0.0568604	+	0.0503739i
$681$	1.83428	+	15.1067i	0.0702899	+	0.578890i
$682$	9.93044	+	2.44763i	0.380256	+	0.0937247i
$683$	−2.38235	−	1.25035i	−0.0911579	−	0.0478434i	0.418528	−	0.908204i	$-0.362546\pi$
$683$	−2.38235	−	1.25035i	−0.0911579	−	0.0478434i	−0.509686	+	0.860360i	$0.670238\pi$
$684$	0.0465301	+	0.0244209i	0.00177912	+	0.000933755i
$685$	−13.7978	−	36.3819i	−0.527188	−	1.39008i
$686$	7.68972	−	4.03587i	0.293595	−	0.154090i
$687$	−3.79409	+	10.0042i	−0.144754	+	0.381684i
$688$	5.20387	+	42.8577i	0.198396	+	1.63393i
$689$	0.417674	−	0.273765i	0.0159121	−	0.0104296i
$690$	−0.694250	+	5.71766i	−0.0264296	+	0.217668i
$691$	−1.95629	−	1.02674i	−0.0744208	−	0.0390590i	0.427102	−	0.904203i	$-0.359534\pi$
$691$	−1.95629	−	1.02674i	−0.0744208	−	0.0390590i	−0.501523	+	0.865144i	$0.667227\pi$
$692$	−0.416638	+	3.43133i	−0.0158382	+	0.130439i
$693$	8.49115	+	4.45650i	0.322552	+	0.169288i
$694$	39.5110	−	35.0037i	1.49982	−	1.32872i
$695$	−8.72729			−0.331045
$696$	1.98092	+	1.75494i	0.0750864	+	0.0665208i
$697$	3.11515	−	1.63496i	0.117995	−	0.0619284i
$698$	−50.1474			−1.89811
$699$	−26.5284			−1.00340
$700$	−0.0638976	+	0.0335360i	−0.00241510	+	0.00126754i
$701$	−30.5938	+	7.54070i	−1.15551	+	0.284808i	−0.770092	−	0.637933i	$-0.779790\pi$
$701$	−30.5938	+	7.54070i	−1.15551	+	0.284808i	−0.385421	+	0.922741i	$0.625944\pi$
$702$	26.3485	+	10.7214i	0.994460	+	0.404653i
$703$	0.0624385	+	0.0153897i	0.00235491	+	0.000580434i
$704$	6.69853	−	1.65104i	0.252460	−	0.0622259i
$705$	8.14489	+	21.4763i	0.306754	+	0.808845i
$706$	−1.11900	+	9.21576i	−0.0421140	+	0.346840i
$707$	−33.1188	−	8.16306i	−1.24556	−	0.307003i
$708$	−4.35063	+	1.07233i	−0.163507	+	0.0403008i
$709$	1.23024	+	1.78231i	0.0462026	+	0.0669360i	0.845404	−	0.534127i	$-0.179360\pi$
$709$	1.23024	+	1.78231i	0.0462026	+	0.0669360i	−0.799202	+	0.601063i	$0.794744\pi$
$710$	4.98770	−	41.0774i	0.187185	−	1.54161i
$711$	−1.38085	+	3.64099i	−0.0517857	+	0.136548i
$712$	−12.5424	−	6.58276i	−0.470047	−	0.246699i
$713$	−8.32703	−	2.05243i	−0.311850	−	0.0768641i
$714$	−0.807647	−	2.12959i	−0.0302254	−	0.0796979i
$715$	6.79357	−	7.30794i	0.254065	−	0.273302i
$716$	−2.67790	+	7.06104i	−0.100078	+	0.263883i
$717$	2.38562	−	3.45616i	0.0890925	−	0.129073i
$718$	−37.6321	−	33.3391i	−1.40442	−	1.24421i
$719$	17.8863	−	4.40858i	0.667047	−	0.164412i	0.108770	−	0.994067i	$-0.465309\pi$
$719$	17.8863	−	4.40858i	0.667047	−	0.164412i	0.558277	+	0.829655i	$0.311463\pi$
$720$	−7.27195	−	19.1746i	−0.271010	−	0.714594i
$721$	33.9450	−	17.8157i	1.26418	−	0.663492i
$722$	10.5221	+	27.7446i	0.391594	+	1.03255i
$723$	−16.5003	−	14.6180i	−0.613652	−	0.543648i
$724$	5.12282	+	4.53842i	0.190388	+	0.168669i
$725$	0.0253361	+	0.0367056i	0.000940957	+	0.00136321i
$726$	8.53484	+	12.3648i	0.316758	+	0.458903i
$727$	17.1162	−	8.98328i	0.634805	−	0.333171i	−0.116437	−	0.993198i	$-0.537147\pi$
$727$	17.1162	−	8.98328i	0.634805	−	0.333171i	0.751242	+	0.660027i	$0.229455\pi$
$728$	−34.3357	+	3.33673i	−1.27256	+	0.123668i
$729$	12.3298	+	6.47119i	0.456660	+	0.239674i
$730$	−6.26384	−	51.5873i	−0.231835	−	1.90933i
$731$	−3.26543	−	0.804856i	−0.120776	−	0.0297687i
$732$	2.98264	+	4.32109i	0.110241	+	0.159712i
$733$	−26.1141	+	37.8327i	−0.964545	+	1.39738i	−0.0473793	+	0.998877i	$0.515087\pi$
$733$	−26.1141	+	37.8327i	−0.964545	+	1.39738i	−0.917165	+	0.398507i	$0.869528\pi$
$734$	1.45807	−	1.29174i	0.0538184	−	0.0476789i
$735$	−2.29781	−	18.9242i	−0.0847561	−	0.698029i
$736$	3.86688	−	0.953099i	0.142535	−	0.0351317i
$737$	−13.7312	+	7.20670i	−0.505796	+	0.265462i
$738$	3.56579	+	29.3670i	0.131259	+	1.08101i
$739$	4.57256	−	37.6584i	0.168204	−	1.38529i	−0.627034	−	0.778992i	$-0.715731\pi$
$739$	4.57256	−	37.6584i	0.168204	−	1.38529i	0.795239	−	0.606296i	$-0.207345\pi$
$740$	0.588802	+	0.853027i	0.0216448	+	0.0313579i
$741$	−0.0988392	−	0.199812i	−0.00363095	−	0.00734028i
$742$	0.482558	−	0.699106i	0.0177153	−	0.0256650i
$743$	−2.91635	−	2.58366i	−0.106990	−	0.0947852i	0.607932	−	0.793989i	$-0.291999\pi$
$743$	−2.91635	−	2.58366i	−0.106990	−	0.0947852i	−0.714922	+	0.699204i	$0.753538\pi$
$744$	−12.6803	+	3.12540i	−0.464881	+	0.114583i
$745$	−10.7318	+	15.5477i	−0.393182	+	0.569622i
$746$	37.1228			1.35916
$747$	8.00363	−	11.5953i	0.292837	−	0.424248i
$748$	0.0240603	−	0.198155i	0.000879733	−	0.00724525i
$749$	16.7164	−	44.0776i	0.610805	−	1.61056i
$750$	2.15022	+	17.7086i	0.0785148	+	0.646628i
$751$	−5.87294	+	15.4857i	−0.214306	+	0.565080i	−0.998459	−	0.0554879i	$-0.982329\pi$
$751$	−5.87294	+	15.4857i	−0.214306	+	0.565080i	0.784153	+	0.620568i	$0.213098\pi$
$752$	35.5700	−	31.5123i	1.29710	−	1.14913i
$753$	12.0585	−	10.6829i	0.439437	−	0.389307i
$754$	−1.29870	−	5.87085i	−0.0472959	−	0.213804i
$755$	−26.4676	−	23.4482i	−0.963255	−	0.853369i
$756$	8.72475			0.317316
$757$	7.19434	−	6.37363i	0.261483	−	0.231653i	−0.522187	−	0.852831i	$-0.674884\pi$
$757$	7.19434	−	6.37363i	0.261483	−	0.231653i	0.783670	+	0.621177i	$0.213345\pi$
$758$	−4.54275	−	1.11969i	−0.165000	−	0.0406689i
$759$	1.16908	+	1.69371i	0.0424350	+	0.0614778i
$760$	−0.116948	+	0.308365i	−0.00424213	+	0.0111856i
$761$	16.5186	−	43.5561i	0.598800	−	1.57891i	−0.201617	−	0.979464i	$-0.564620\pi$
$761$	16.5186	−	43.5561i	0.598800	−	1.57891i	0.800418	−	0.599443i	$-0.204611\pi$
$762$	9.24294	+	13.3907i	0.334836	+	0.485094i
$763$	−27.3130	−	6.73204i	−0.988796	−	0.243716i
$764$	0.324227	−	0.287240i	0.0117301	−	0.0103920i
$765$	1.59752			0.0577585
$766$	20.4462	+	18.1137i	0.738750	+	0.654475i
$767$	−33.4373	−	13.6059i	−1.20735

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)

\(f(q)\)	\(=\)	\(q+(-0.553905 - 1.46053i) q^{2} +(-0.577862 + 0.837177i) q^{3} +(-0.329307 + 0.291741i) q^{4} +(0.268400 + 2.21047i) q^{5} +(1.54280 + 0.380266i) q^{6} +(3.47659 + 1.82465i) q^{7} +(-2.15772 - 1.13246i) q^{8} +(0.696873 + 1.83750i) q^{9} +O(q^{10})\)	\(q+(-0.553905 - 1.46053i) q^{2} +(-0.577862 + 0.837177i) q^{3} +(-0.329307 + 0.291741i) q^{4} +(0.268400 + 2.21047i) q^{5} +(1.54280 + 0.380266i) q^{6} +(3.47659 + 1.82465i) q^{7} +(-2.15772 - 1.13246i) q^{8} +(0.696873 + 1.83750i) q^{9} +(3.07979 - 1.61640i) q^{10} +(0.440706 - 1.16205i) q^{11} +(-0.0539447 - 0.444274i) q^{12} +(1.75157 - 3.15151i) q^{13} +(0.739257 - 6.08833i) q^{14} +(-2.00565 - 1.05265i) q^{15} +(-0.564876 + 4.65218i) q^{16} +(-0.323252 - 0.169656i) q^{17} +(2.29772 - 2.03560i) q^{18} -0.0607791 q^{19} +(-0.733271 - 0.649621i) q^{20} +(-3.53654 + 1.85612i) q^{21} -1.94131 q^{22} +1.62786 q^{23} +(2.19494 - 1.15199i) q^{24} +(0.0405622 - 0.00999768i) q^{25} +(-5.57307 - 0.812585i) q^{26} +(-4.90407 - 1.20875i) q^{27} +(-1.67719 + 0.413391i) q^{28} +(0.378580 + 0.998234i) q^{29} +(-0.426480 + 3.51238i) q^{30} +(-5.11532 - 1.26081i) q^{31} +(2.37543 - 0.585492i) q^{32} +(0.718172 + 1.04045i) q^{33} +(-0.0687360 + 0.566092i) q^{34} +(-3.10023 + 8.17463i) q^{35} +(-0.765560 - 0.401797i) q^{36} +(-1.02730 - 0.253207i) q^{37} +(0.0336659 + 0.0887696i) q^{38} +(1.62620 + 3.28751i) q^{39} +(1.92414 - 5.07354i) q^{40} +(-5.47439 + 7.93102i) q^{41} +(4.66982 + 4.13710i) q^{42} +(8.94471 - 2.20467i) q^{43} +(0.193889 + 0.511243i) q^{44} +(-3.87471 + 2.03360i) q^{45} +(-0.901680 - 2.37753i) q^{46} +(-7.59014 - 6.72427i) q^{47} +(-3.56827 - 3.16122i) q^{48} +(4.78084 + 6.92624i) q^{49} +(-0.0370695 - 0.0537044i) q^{50} +(0.328827 - 0.172582i) q^{51} +(0.342617 + 1.54882i) q^{52} +(0.122643 + 0.0643680i) q^{53} +(0.950984 + 7.83206i) q^{54} +(2.68696 + 0.662276i) q^{55} +(-5.43517 - 7.87420i) q^{56} +(0.0351219 - 0.0508829i) q^{57} +(1.24825 - 1.10585i) q^{58} +(-1.20684 - 9.93920i) q^{59} +(0.967577 - 0.238486i) q^{60} +(-10.3882 + 5.45214i) q^{61} +(0.991950 + 8.16944i) q^{62} +(-0.930067 + 7.65979i) q^{63} +(3.15340 + 4.56849i) q^{64} +(7.43644 + 3.02594i) q^{65} +(1.12181 - 1.62522i) q^{66} +(-9.33975 - 8.27430i) q^{67} +(0.155945 - 0.0384370i) q^{68} +(-0.940678 + 1.36281i) q^{69} +13.6565 q^{70} +(6.75811 - 9.79081i) q^{71} +(0.577241 - 4.75401i) q^{72} +(5.29800 - 13.9697i) q^{73} +(0.199212 + 1.64066i) q^{74} +(-0.0150695 + 0.0397350i) q^{75} +(0.0200150 - 0.0177318i) q^{76} +(3.65249 - 3.23582i) q^{77} +(3.90074 - 4.19608i) q^{78} +(1.48316 + 1.31397i) q^{79} -10.4351 q^{80} +(-0.567134 + 0.502437i) q^{81} +(14.6158 + 3.60246i) q^{82} +(-4.07266 - 5.90026i) q^{83} +(0.623103 - 1.64299i) q^{84} +(0.288259 - 0.760075i) q^{85} +(-8.17450 - 11.8428i) q^{86} +(-1.05447 - 0.259902i) q^{87} +(-2.26690 + 2.00829i) q^{88} +5.81279 q^{89} +(5.11635 + 4.53269i) q^{90} +(11.8399 - 7.76047i) q^{91} +(-0.536066 + 0.474913i) q^{92} +(4.01147 - 3.55386i) q^{93} +(-5.61677 + 14.8102i) q^{94} +(-0.0163131 - 0.134351i) q^{95} +(-0.882512 + 2.32699i) q^{96} +(-1.42435 + 11.7306i) q^{97} +(7.46783 - 10.8190i) q^{98} +2.44238 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