LMFDB - Embedded newform 147.2.m.b.88.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(4,147)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("147.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.m (of order $21$, 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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			88.3
Character	$\chi$	$=$	147.88
Dual form			147.2.m.b.142.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0539669 - 0.00813420i) q^{2} +(0.826239 - 0.563320i) q^{3} +(-1.90830 - 0.588632i) q^{4} +(-0.234102 - 3.12387i) q^{5} +(-0.0491717 + 0.0236798i) q^{6} +(-2.39120 - 1.13233i) q^{7} +(0.196540 + 0.0946488i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})$	\(q+(-0.0539669 - 0.00813420i) q^{2} +(0.826239 - 0.563320i) q^{3} +(-1.90830 - 0.588632i) q^{4} +(-0.234102 - 3.12387i) q^{5} +(-0.0491717 + 0.0236798i) q^{6} +(-2.39120 - 1.13233i) q^{7} +(0.196540 + 0.0946488i) q^{8} +(0.365341 - 0.930874i) q^{9} +(-0.0127765 + 0.170490i) q^{10} +(1.33125 + 3.39197i) q^{11} +(-1.90830 + 0.588632i) q^{12} +(2.60561 - 3.26734i) q^{13} +(0.119835 + 0.0805589i) q^{14} +(-1.95317 - 2.44919i) q^{15} +(3.29020 + 2.24322i) q^{16} +(5.16661 + 4.79392i) q^{17} +(-0.0272882 + 0.0472646i) q^{18} +(-2.58312 - 4.47409i) q^{19} +(-1.39208 + 6.09909i) q^{20} +(-2.61357 + 0.411432i) q^{21} +(-0.0442525 - 0.193883i) q^{22} +(1.48110 - 1.37426i) q^{23} +(0.215707 - 0.0325126i) q^{24} +(-4.75963 + 0.717399i) q^{25} +(-0.167194 + 0.155133i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(3.89659 + 3.56837i) q^{28} +(0.417422 - 1.82884i) q^{29} +(0.0854840 + 0.148063i) q^{30} +(-1.02759 + 1.77984i) q^{31} +(-0.479136 - 0.444573i) q^{32} +(3.01070 + 2.05266i) q^{33} +(-0.239831 - 0.300739i) q^{34} +(-2.97748 + 7.73488i) q^{35} +(-1.24512 + 1.56133i) q^{36} +(2.73892 - 0.844846i) q^{37} +(0.103010 + 0.262464i) q^{38} +(0.312303 - 4.16740i) q^{39} +(0.249661 - 0.636125i) q^{40} +(1.59703 + 0.769087i) q^{41} +(0.144393 - 0.000944441i) q^{42} +(-10.7040 + 5.15476i) q^{43} +(-0.543801 - 7.25652i) q^{44} +(-2.99346 - 0.923360i) q^{45} +(-0.0911091 + 0.0621172i) q^{46} +(10.6509 + 1.60537i) q^{47} +3.98214 q^{48} +(4.43565 + 5.41526i) q^{49} +0.262698 q^{50} +(6.96936 + 1.05046i) q^{51} +(-6.89555 + 4.70131i) q^{52} +(-7.68111 - 2.36931i) q^{53} +(0.00407850 + 0.0544238i) q^{54} +(10.2844 - 4.95273i) q^{55} +(-0.362793 - 0.448873i) q^{56} +(-4.65461 - 2.24154i) q^{57} +(-0.0374031 + 0.0953017i) q^{58} +(-0.511123 + 6.82046i) q^{59} +(2.28555 + 5.82349i) q^{60} +(-1.15347 + 0.355797i) q^{61} +(0.0699333 - 0.0876936i) q^{62} +(-1.92766 + 1.81221i) q^{63} +(-4.94340 - 6.19883i) q^{64} +(-10.8167 - 7.37472i) q^{65} +(-0.145781 - 0.135265i) q^{66} +(4.30390 - 7.45457i) q^{67} +(-7.03759 - 12.1895i) q^{68} +(0.449595 - 1.96981i) q^{69} +(0.223602 - 0.393208i) q^{70} +(-0.152602 - 0.668593i) q^{71} +(0.159910 - 0.148375i) q^{72} +(8.72971 - 1.31579i) q^{73} +(-0.154683 + 0.0233148i) q^{74} +(-3.52847 + 3.27394i) q^{75} +(2.29576 + 10.0584i) q^{76} +(0.657558 - 9.61829i) q^{77} +(-0.0507525 + 0.222361i) q^{78} +(-2.75840 - 4.77769i) q^{79} +(6.23729 - 10.8033i) q^{80} +(-0.733052 - 0.680173i) q^{81} +(-0.0799306 - 0.0544957i) q^{82} +(2.62416 + 3.29059i) q^{83} +(5.22965 + 0.753294i) q^{84} +(13.7661 - 17.2621i) q^{85} +(0.619590 - 0.191118i) q^{86} +(-0.685335 - 1.74620i) q^{87} +(-0.0594017 + 0.792661i) q^{88} +(3.75598 - 9.57007i) q^{89} +(0.154037 + 0.0741803i) q^{90} +(-9.93025 + 4.86242i) q^{91} +(-3.63533 + 1.75068i) q^{92} +(0.153584 + 2.04943i) q^{93} +(-0.561740 - 0.173274i) q^{94} +(-13.3718 + 9.11672i) q^{95} +(-0.646317 - 0.0974166i) q^{96} -8.70015 q^{97} +(-0.195329 - 0.328325i) q^{98} +3.64386 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9} - 34 q^{10} - 11 q^{11} + 5 q^{12} - 2 q^{13} + 40 q^{14} - 3 q^{15} - 31 q^{16} - 9 q^{17} - 6 q^{18} - 29 q^{19} - 43 q^{20} - 11 q^{21} + 9 q^{22} - 4 q^{23} - 24 q^{24} + 55 q^{25} + 36 q^{26} - 10 q^{27} - 57 q^{28} + 4 q^{29} - 20 q^{30} - 39 q^{31} - 92 q^{32} - 18 q^{33} - 36 q^{34} - 33 q^{35} - 10 q^{36} - 24 q^{37} + 118 q^{38} - 6 q^{39} + 35 q^{41} + 38 q^{42} + 2 q^{43} + 40 q^{44} + 12 q^{45} - 40 q^{46} - 5 q^{47} + 76 q^{48} + 129 q^{49} - 176 q^{50} + 54 q^{51} - 6 q^{52} + 26 q^{53} + q^{54} + 2 q^{55} + 63 q^{56} - 12 q^{57} + 11 q^{58} - 41 q^{59} + 32 q^{60} + 6 q^{61} + 36 q^{62} - q^{63} + 74 q^{64} - 51 q^{65} - 15 q^{66} - 55 q^{67} - 22 q^{68} + 8 q^{69} - 68 q^{70} - 66 q^{71} - 24 q^{72} + 24 q^{73} + 28 q^{74} + 41 q^{75} + 3 q^{76} - 34 q^{77} - 30 q^{78} - 51 q^{79} - 5 q^{80} + 5 q^{81} - 41 q^{82} + 30 q^{83} - 30 q^{84} + 68 q^{85} + 110 q^{86} + 19 q^{87} + 129 q^{88} + 75 q^{89} - 16 q^{90} + 5 q^{91} - 4 q^{93} + 38 q^{94} + 36 q^{95} - 57 q^{96} - 168 q^{97} + 227 q^{98} + 36 q^{99}+O(q^{100}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9 - 34 * q^10 - 11 * q^11 + 5 * q^12 - 2 * q^13 + 40 * q^14 - 3 * q^15 - 31 * q^16 - 9 * q^17 - 6 * q^18 - 29 * q^19 - 43 * q^20 - 11 * q^21 + 9 * q^22 - 4 * q^23 - 24 * q^24 + 55 * q^25 + 36 * q^26 - 10 * q^27 - 57 * q^28 + 4 * q^29 - 20 * q^30 - 39 * q^31 - 92 * q^32 - 18 * q^33 - 36 * q^34 - 33 * q^35 - 10 * q^36 - 24 * q^37 + 118 * q^38 - 6 * q^39 + 35 * q^41 + 38 * q^42 + 2 * q^43 + 40 * q^44 + 12 * q^45 - 40 * q^46 - 5 * q^47 + 76 * q^48 + 129 * q^49 - 176 * q^50 + 54 * q^51 - 6 * q^52 + 26 * q^53 + q^54 + 2 * q^55 + 63 * q^56 - 12 * q^57 + 11 * q^58 - 41 * q^59 + 32 * q^60 + 6 * q^61 + 36 * q^62 - q^63 + 74 * q^64 - 51 * q^65 - 15 * q^66 - 55 * q^67 - 22 * q^68 + 8 * q^69 - 68 * q^70 - 66 * q^71 - 24 * q^72 + 24 * q^73 + 28 * q^74 + 41 * q^75 + 3 * q^76 - 34 * q^77 - 30 * q^78 - 51 * q^79 - 5 * q^80 + 5 * q^81 - 41 * q^82 + 30 * q^83 - 30 * q^84 + 68 * q^85 + 110 * q^86 + 19 * q^87 + 129 * q^88 + 75 * q^89 - 16 * q^90 + 5 * q^91 - 4 * q^93 + 38 * q^94 + 36 * q^95 - 57 * q^96 - 168 * q^97 + 227 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	−0.0539669	−	0.00813420i	−0.0381603	−	0.00575175i	0.129934	−	0.991523i	$-0.458523\pi$
$2$	−0.0539669	−	0.00813420i	−0.0381603	−	0.00575175i	−0.168095	+	0.985771i	$0.553761\pi$
$3$	0.826239	−	0.563320i	0.477029	−	0.325233i
$3$	0.826239	−	0.563320i	0.477029	−	0.325233i
$4$	−1.90830	−	0.588632i	−0.954150	−	0.294316i
$5$	−0.234102	−	3.12387i	−0.104694	−	1.39704i	−0.764025	−	0.645187i	$-0.776780\pi$
$5$	−0.234102	−	3.12387i	−0.104694	−	1.39704i	0.659331	−	0.751852i	$-0.270839\pi$
$6$	−0.0491717	+	0.0236798i	−0.0200743	+	0.00966725i
$7$	−2.39120	−	1.13233i	−0.903787	−	0.427982i
$7$	−2.39120	−	1.13233i	−0.903787	−	0.427982i
$8$	0.196540	+	0.0946488i	0.0694875	+	0.0334634i
$9$	0.365341	−	0.930874i	0.121780	−	0.310291i
$10$	−0.0127765	+	0.170490i	−0.00404027	+	0.0539137i
$11$	1.33125	+	3.39197i	0.401387	+	1.02272i	0.978535	+	0.206079i	$0.0660703\pi$
$11$	1.33125	+	3.39197i	0.401387	+	1.02272i	−0.577148	+	0.816640i	$0.695834\pi$
$12$	−1.90830	+	0.588632i	−0.550879	+	0.169924i
$13$	2.60561	−	3.26734i	0.722667	−	0.906196i	−0.275818	−	0.961210i	$-0.588949\pi$
$13$	2.60561	−	3.26734i	0.722667	−	0.906196i	0.998486	+	0.0550135i	$0.0175202\pi$
$14$	0.119835	+	0.0805589i	0.0320272	+	0.0215303i
$15$	−1.95317	−	2.44919i	−0.504305	−	0.632379i
$16$	3.29020	+	2.24322i	0.822549	+	0.560804i
$17$	5.16661	+	4.79392i	1.25309	+	1.16270i	0.979630	+	0.200811i	$0.0643577\pi$
$17$	5.16661	+	4.79392i	1.25309	+	1.16270i	0.273457	+	0.961884i	$0.411833\pi$
$18$	−0.0272882	+	0.0472646i	−0.00643190	+	0.0111404i
$19$	−2.58312	−	4.47409i	−0.592607	−	1.02643i	−0.993880	−	0.110467i	$-0.964765\pi$
$19$	−2.58312	−	4.47409i	−0.592607	−	1.02643i	0.401272	−	0.915959i	$-0.368568\pi$
$20$	−1.39208	+	6.09909i	−0.311278	+	1.36380i
$21$	−2.61357	+	0.411432i	−0.570327	+	0.0897818i
$22$	−0.0442525	−	0.193883i	−0.00943466	−	0.0413360i
$23$	1.48110	−	1.37426i	0.308832	−	0.286554i	−0.510495	−	0.859881i	$-0.670538\pi$
$23$	1.48110	−	1.37426i	0.308832	−	0.286554i	0.819327	+	0.573327i	$0.194347\pi$
$24$	0.215707	−	0.0325126i	0.0440310	−	0.00663660i
$25$	−4.75963	+	0.717399i	−0.951927	+	0.143480i
$26$	−0.167194	+	0.155133i	−0.0327895	+	0.0304242i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	3.89659	+	3.56837i	0.736387	+	0.674358i
$29$	0.417422	−	1.82884i	0.0775133	−	0.339608i	−0.921270	−	0.388924i	$-0.872847\pi$
$29$	0.417422	−	1.82884i	0.0775133	−	0.339608i	0.998783	+	0.0493158i	$0.0157041\pi$
$30$	0.0854840	+	0.148063i	0.0156072	+	0.0270324i
$31$	−1.02759	+	1.77984i	−0.184561	+	0.319668i	−0.943428	−	0.331576i	$-0.892419\pi$
$31$	−1.02759	+	1.77984i	−0.184561	+	0.319668i	0.758868	+	0.651245i	$0.225753\pi$
$32$	−0.479136	−	0.444573i	−0.0847000	−	0.0785901i
$33$	3.01070	+	2.05266i	0.524095	+	0.357322i
$34$	−0.239831	−	0.300739i	−0.0411307	−	0.0515763i
$35$	−2.97748	+	7.73488i	−0.503286	+	1.30743i
$36$	−1.24512	+	1.56133i	−0.207520	+	0.260222i
$37$	2.73892	−	0.844846i	0.450276	−	0.138892i	−0.0613193	−	0.998118i	$-0.519531\pi$
$37$	2.73892	−	0.844846i	0.450276	−	0.138892i	0.511596	+	0.859226i	$0.329055\pi$
$38$	0.103010	+	0.262464i	0.0167104	+	0.0425773i
$39$	0.312303	−	4.16740i	0.0500085	−	0.667317i
$40$	0.249661	−	0.636125i	0.0394748	−	0.100580i
$41$	1.59703	+	0.769087i	0.249413	+	0.120111i	0.554414	−	0.832241i	$-0.312942\pi$
$41$	1.59703	+	0.769087i	0.249413	+	0.120111i	−0.305001	+	0.952352i	$0.598657\pi$
$42$	0.144393		0.000944441i	0.0222803		0.000145730i
$43$	−10.7040	+	5.15476i	−1.63234	+	0.786094i	−0.632406	+	0.774637i	$0.717932\pi$
$43$	−10.7040	+	5.15476i	−1.63234	+	0.786094i	−0.999934	+	0.0114564i	$0.996353\pi$
$44$	−0.543801	−	7.25652i	−0.0819810	−	1.09396i
$45$	−2.99346	−	0.923360i	−0.446239	−	0.137646i
$46$	−0.0911091	+	0.0621172i	−0.0134333	+	0.00915868i
$47$	10.6509	+	1.60537i	1.55360	+	0.234168i	0.869022	−	0.494773i	$-0.164749\pi$
$47$	10.6509	+	1.60537i	1.55360	+	0.234168i	0.684577	+	0.728940i	$0.259987\pi$
$48$	3.98214			0.574772
$49$	4.43565	+	5.41526i	0.633664	+	0.773609i
$50$	0.262698			0.0371511
$51$	6.96936	+	1.05046i	0.975906	+	0.147094i
$52$	−6.89555	+	4.70131i	−0.956241	+	0.651954i
$53$	−7.68111	−	2.36931i	−1.05508	−	0.325450i	−0.281774	−	0.959481i	$-0.590923\pi$
$53$	−7.68111	−	2.36931i	−1.05508	−	0.325450i	−0.773308	+	0.634031i	$0.781399\pi$
$54$	0.00407850	+	0.0544238i	0.000555014	+	0.00740615i
$55$	10.2844	−	4.95273i	1.38675	−	0.667826i
$56$	−0.362793	−	0.448873i	−0.0484802	−	0.0599832i
$57$	−4.65461	−	2.24154i	−0.616519	−	0.296900i
$58$	−0.0374031	+	0.0953017i	−0.00491127	+	0.0125137i
$59$	−0.511123	+	6.82046i	−0.0665425	+	0.887948i	0.859647	+	0.510889i	$0.170684\pi$
$59$	−0.511123	+	6.82046i	−0.0665425	+	0.887948i	−0.926189	+	0.377059i	$0.876935\pi$
$60$	2.28555	+	5.82349i	0.295063	+	0.751809i
$61$	−1.15347	+	0.355797i	−0.147686	+	0.0455551i	−0.367717	−	0.929938i	$-0.619860\pi$
$61$	−1.15347	+	0.355797i	−0.147686	+	0.0455551i	0.220031	+	0.975493i	$0.429384\pi$
$62$	0.0699333	−	0.0876936i	0.00888154	−	0.0111371i
$63$	−1.92766	+	1.81221i	−0.242862	+	0.228318i
$64$	−4.94340	−	6.19883i	−0.617925	−	0.774854i
$65$	−10.8167	−	7.37472i	−1.34165	−	0.914722i
$66$	−0.145781	−	0.135265i	−0.0179444	−	0.0166500i
$67$	4.30390	−	7.45457i	0.525805	−	0.910721i	−0.473743	−	0.880663i	$-0.657098\pi$
$67$	4.30390	−	7.45457i	0.525805	−	0.910721i	0.999548	−	0.0300578i	$-0.00956914\pi$
$68$	−7.03759	−	12.1895i	−0.853433	−	1.47819i
$69$	0.449595	−	1.96981i	0.0541249	−	0.237137i
$70$	0.223602	−	0.393208i	0.0267256	−	0.0469973i
$71$	−0.152602	−	0.668593i	−0.0181105	−	0.0793474i	0.965065	−	0.262010i	$-0.0843854\pi$
$71$	−0.152602	−	0.668593i	−0.0181105	−	0.0793474i	−0.983176	+	0.182663i	$0.941528\pi$
$72$	0.159910	−	0.148375i	0.0188456	−	0.0174862i
$73$	8.72971	−	1.31579i	1.02173	−	0.154002i	0.383257	−	0.923642i	$-0.374802\pi$
$73$	8.72971	−	1.31579i	1.02173	−	0.154002i	0.638478	+	0.769640i	$0.279564\pi$
$74$	−0.154683	+	0.0233148i	−0.0179816	+	0.00271029i
$75$	−3.52847	+	3.27394i	−0.407433	+	0.378042i
$76$	2.29576	+	10.0584i	0.263342	+	1.15378i
$77$	0.657558	−	9.61829i	0.0749357	−	1.09611i
$78$	−0.0507525	+	0.222361i	−0.00574658	+	0.0251774i
$79$	−2.75840	−	4.77769i	−0.310344	−	0.537532i	0.668093	−	0.744078i	$-0.267111\pi$
$79$	−2.75840	−	4.77769i	−0.310344	−	0.537532i	−0.978437	+	0.206546i	$0.933778\pi$
$80$	6.23729	−	10.8033i	0.697350	−	1.20785i
$81$	−0.733052	−	0.680173i	−0.0814502	−	0.0755747i
$82$	−0.0799306	−	0.0544957i	−0.00882686	−	0.00601805i
$83$	2.62416	+	3.29059i	0.288039	+	0.361190i	0.904707	−	0.426034i	$-0.140089\pi$
$83$	2.62416	+	3.29059i	0.288039	+	0.361190i	−0.616668	+	0.787223i	$0.711518\pi$
$84$	5.22965	+	0.753294i	0.570601	+	0.0821911i
$85$	13.7661	−	17.2621i	1.49314	−	1.87234i
$86$	0.619590	−	0.191118i	0.0668121	−	0.0206088i
$87$	−0.685335	−	1.74620i	−0.0734756	−	0.187213i
$88$	−0.0594017	+	0.792661i	−0.00633224	+	0.0844979i
$89$	3.75598	−	9.57007i	0.398133	−	1.01443i	−0.581486	−	0.813557i	$-0.697528\pi$
$89$	3.75598	−	9.57007i	0.398133	−	1.01443i	0.979618	−	0.200869i	$-0.0643764\pi$
$90$	0.154037	+	0.0741803i	0.0162369	+	0.00781929i
$91$	−9.93025	+	4.86242i	−1.04097	+	0.509721i
$92$	−3.63533	+	1.75068i	−0.379009	+	0.182521i
$93$	0.153584	+	2.04943i	0.0159259	+	0.212516i
$94$	−0.561740	−	0.173274i	−0.0579390	−	0.0178718i
$95$	−13.3718	+	9.11672i	−1.37192	+	0.935356i
$96$	−0.646317	−	0.0974166i	−0.0659645	−	0.00994254i
$97$	−8.70015			−0.883366			−0.441683	−	0.897171i	$-0.645618\pi$
$97$	−8.70015			−0.883366			−0.441683	+	0.897171i	$0.645618\pi$
$98$	−0.195329	−	0.328325i	−0.0197312	−	0.0331659i
$99$	3.64386			0.366222
$100$	9.50509	+	1.43266i	0.950509	+	0.143266i
$101$	−0.607508	+	0.414192i	−0.0604493	+	0.0412136i	−0.593168	−	0.805079i	$-0.702123\pi$
$101$	−0.607508	+	0.414192i	−0.0604493	+	0.0412136i	0.532718	+	0.846293i	$0.321171\pi$
$102$	−0.367570	−	0.113380i	−0.0363949	−	0.0112263i
$103$	1.13894	+	15.1981i	0.112223	+	1.49752i	0.714728	+	0.699403i	$0.246550\pi$
$103$	1.13894	+	15.1981i	0.112223	+	1.49752i	−0.602505	+	0.798115i	$0.705830\pi$
$104$	0.821358	−	0.395545i	0.0805408	−	0.0387864i
$105$	1.89710	+	8.06813i	0.185138	+	0.787369i
$106$	0.395253	+	0.190344i	0.0383904	+	0.0184878i
$107$	−4.03115	+	10.2712i	−0.389706	+	0.992955i	0.592570	+	0.805519i	$0.298113\pi$
$107$	−4.03115	+	10.2712i	−0.389706	+	0.992955i	−0.982277	+	0.187437i	$0.939982\pi$
$108$	−0.149238	+	1.99144i	−0.0143604	+	0.191626i
$109$	4.59033	+	11.6960i	0.439674	+	1.12027i	0.963325	+	0.268338i	$0.0864745\pi$
$109$	4.59033	+	11.6960i	0.439674	+	1.12027i	−0.523651	+	0.851933i	$0.675430\pi$
$110$	−0.595306	+	0.183628i	−0.0567602	+	0.0175082i
$111$	1.78709	−	2.24094i	0.169623	−	0.212700i
$112$	−5.32744	−	9.08957i	−0.503396	−	0.858884i
$113$	9.04064	+	11.3366i	0.850472	+	1.06646i	0.997011	+	0.0772535i	$0.0246151\pi$
$113$	9.04064	+	11.3366i	0.850472	+	1.06646i	−0.146539	+	0.989205i	$0.546813\pi$
$114$	0.232962	+	0.158831i	0.0218189	+	0.0148759i
$115$	−4.63976	−	4.30507i	−0.432660	−	0.401450i
$116$	−1.87308	+	3.24428i	−0.173911	+	0.301223i
$117$	−2.08954	−	3.61919i	−0.193178	−	0.334594i
$118$	0.0830627	−	0.363921i	0.00764654	−	0.0335017i
$119$	−6.92608	−	17.3135i	−0.634913	−	1.58713i
$120$	−0.152063	−	0.666230i	−0.0138814	−	0.0608182i
$121$	−1.66968	+	1.54923i	−0.151789	+	0.140840i
$122$	0.0651430	−	0.00981873i	0.00589777	−	0.000888946i
$123$	1.75277	−	0.264187i	0.158042	−	0.0238209i
$124$	3.00862	−	2.79159i	0.270182	−	0.250692i
$125$	−0.130077	−	0.569905i	−0.0116345	−	0.0509739i
$126$	0.118771	−	0.0821196i	0.0105809	−	0.00731580i
$127$	−2.99945	+	13.1414i	−0.266158	+	1.16611i	0.648285	+	0.761398i	$0.275487\pi$
$127$	−2.99945	+	13.1414i	−0.266158	+	1.16611i	−0.914443	+	0.404716i	$0.867371\pi$
$128$	0.869975	+	1.50684i	0.0768957	+	0.133187i
$129$	−5.94026	+	10.2888i	−0.523010	+	0.905880i
$130$	0.523758	+	0.485976i	0.0459366	+	0.0426229i
$131$	2.41559	+	1.64692i	0.211051	+	0.143892i	0.664232	−	0.747526i	$-0.268759\pi$
$131$	2.41559	+	1.64692i	0.211051	+	0.143892i	−0.453181	+	0.891418i	$0.649711\pi$
$132$	−4.53705	−	5.68928i	−0.394900	−	0.495188i
$133$	1.11058	+	13.6234i	0.0962997	+	1.18130i
$134$	−0.292905	+	0.367291i	−0.0253031	+	0.0317291i
$135$	−2.99346	+	0.923360i	−0.257636	+	0.0794702i
$136$	0.561709	+	1.43121i	0.0481661	+	0.122725i
$137$	0.0345593	−	0.461162i	0.00295260	−	0.0393997i	−0.995533	−	0.0944154i	$-0.969902\pi$
$137$	0.0345593	−	0.461162i	0.00295260	−	0.0393997i	0.998485	+	0.0550156i	$0.0175209\pi$
$138$	−0.0402861	+	0.102647i	−0.00342938	+	0.00873791i
$139$	−5.29961	−	2.55216i	−0.449507	−	0.216471i	0.195413	−	0.980721i	$-0.437395\pi$
$139$	−5.29961	−	2.55216i	−0.449507	−	0.216471i	−0.644921	+	0.764250i	$0.723110\pi$
$140$	10.2349	−	13.0078i	0.865009	−	1.09936i
$141$	9.70456	−	4.67347i	0.817271	−	0.393577i
$142$	0.00279698	+	0.0373232i	0.000234718	+	0.00313209i
$143$	14.5514	+	4.48853i	1.21685	+	0.375349i
$144$	3.29020	−	2.24322i	0.274183	−	0.186935i
$145$	−5.81080	−	0.875837i	−0.482561	−	0.0727343i
$146$	−0.481818			−0.0398755
$147$	6.71543	+	1.97561i	0.553879	+	0.162946i
$148$	−5.72399			−0.470509
$149$	−1.86062	−	0.280443i	−0.152428	−	0.0229748i	0.0723851	−	0.997377i	$-0.476939\pi$
$149$	−1.86062	−	0.280443i	−0.152428	−	0.0229748i	−0.224813	+	0.974402i	$0.572177\pi$
$150$	0.217051	−	0.147983i	0.0177222	−	0.0120828i
$151$	3.07184	+	0.947539i	0.249983	+	0.0771096i	0.417214	−	0.908808i	$-0.363006\pi$
$151$	3.07184	+	0.947539i	0.249983	+	0.0771096i	−0.167231	+	0.985918i	$0.553483\pi$
$152$	−0.0842192	−	1.12383i	−0.00683108	−	0.0911544i
$153$	6.35010	−	3.05805i	0.513376	−	0.247229i
$154$	−0.113723	+	0.513721i	−0.00916410	+	0.0413968i
$155$	5.80055	+	2.79340i	0.465911	+	0.224371i
$156$	−3.04903	+	7.76881i	−0.244118	+	0.622002i
$157$	0.298629	−	3.98493i	0.0238332	−	0.318032i	−0.972527	−	0.232790i	$-0.925215\pi$
$157$	0.298629	−	3.98493i	0.0238332	−	0.318032i	0.996360	−	0.0852420i	$-0.0271663\pi$
$158$	0.110000	+	0.280274i	0.00875110	+	0.0222974i
$159$	−7.68111	+	2.36931i	−0.609152	+	0.187898i
$160$	−1.27662	+	1.60083i	−0.100926	+	0.126557i
$161$	−5.09774	+	1.60903i	−0.401758	+	0.126810i
$162$	0.0340279	+	0.0426696i	0.00267348	+	0.00335244i
$163$	1.49682	+	1.02051i	0.117240	+	0.0799329i	0.620520	−	0.784190i	$-0.286921\pi$
$163$	1.49682	+	1.02051i	0.117240	+	0.0799329i	−0.503281	+	0.864123i	$0.667874\pi$
$164$	−2.59489	−	2.40771i	−0.202627	−	0.188010i
$165$	5.70744	−	9.88557i	0.444323	−	0.769591i
$166$	−0.114851	−	0.198928i	−0.00891420	−	0.0154398i
$167$	−5.59461	+	24.5116i	−0.432924	+	1.89676i	0.00949617	+	0.999955i	$0.496977\pi$
$167$	−5.59461	+	24.5116i	−0.432924	+	1.89676i	−0.442420	+	0.896808i	$0.645880\pi$
$168$	−0.552612	−	0.166508i	−0.0426350	−	0.0128464i
$169$	−0.993494	−	4.35278i	−0.0764226	−	0.334829i
$170$	−0.883326	+	0.819606i	−0.0677480	+	0.0628609i
$171$	−5.10853	+	0.769987i	−0.390659	+	0.0588824i
$172$	23.4606	−	3.53612i	1.78886	−	0.269627i
$173$	−6.86649	+	6.37117i	−0.522050	+	0.484391i	−0.896616	−	0.442809i	$-0.853982\pi$
$173$	−6.86649	+	6.37117i	−0.522050	+	0.484391i	0.374566	+	0.927200i	$0.377792\pi$
$174$	0.0227814	+	0.0998119i	0.00172705	+	0.00756672i
$175$	12.1936	+	3.67405i	0.921746	+	0.277732i
$176$	−3.22886	+	14.1465i	−0.243384	+	1.06634i
$177$	3.41979	+	5.92325i	0.257047	+	0.445219i
$178$	−0.280543	+	0.485915i	−0.0210276	+	0.0364209i
$179$	−16.3239	−	15.1463i	−1.22010	−	1.13209i	−0.987183	−	0.159595i	$-0.948981\pi$
$179$	−16.3239	−	15.1463i	−1.22010	−	1.13209i	−0.232921	−	0.972496i	$-0.574828\pi$
$180$	5.16890	+	3.52409i	0.385267	+	0.262671i
$181$	−13.9902	−	17.5432i	−1.03988	−	1.30397i	−0.951421	−	0.307894i	$-0.900376\pi$
$181$	−13.9902	−	17.5432i	−1.03988	−	1.30397i	−0.0884630	−	0.996079i	$-0.528196\pi$
$182$	0.575457	−	0.181635i	0.0426557	−	0.0134637i
$183$	−0.752610	+	0.943743i	−0.0556345	+	0.0697635i
$184$	0.421169	−	0.129914i	0.0310490	−	0.00957735i
$185$	−3.28038	−	8.35827i	−0.241178	−	0.614513i
$186$	0.00838205	−	0.111851i	0.000614602	−	0.00820129i
$187$	−9.38277	+	23.9069i	−0.686136	+	1.74825i
$188$	−19.3802	−	9.33302i	−1.41345	−	0.680680i
$189$	−0.571851	+	2.58321i	−0.0415961	+	0.187901i
$190$	0.795790	−	0.383232i	0.0577327	−	0.0278026i
$191$	−0.110065	−	1.46872i	−0.00796404	−	0.106273i	0.991805	−	0.127760i	$-0.0407788\pi$
$191$	−0.110065	−	1.46872i	−0.00796404	−	0.106273i	−0.999769	+	0.0214876i	$0.993160\pi$
$192$	−7.57636	−	2.33700i	−0.546776	−	0.168658i
$193$	1.51841	−	1.03524i	0.109298	−	0.0745180i	−0.507438	−	0.861688i	$-0.669407\pi$
$193$	1.51841	−	1.03524i	0.109298	−	0.0745180i	0.616735	+	0.787171i	$0.288455\pi$
$194$	0.469520	+	0.0707687i	0.0337096	+	0.00508090i
$195$	−13.0915			−0.937504
$196$	−5.27694	−	12.9449i	−0.376924	−	0.924636i
$197$	19.6408			1.39935			0.699675	−	0.714461i	$-0.253328\pi$
$197$	19.6408			1.39935			0.699675	+	0.714461i	$0.253328\pi$
$198$	−0.196648	−	0.0296399i	−0.0139751	−	0.00210641i
$199$	13.8485	−	9.44177i	0.981696	−	0.669309i	0.0377082	−	0.999289i	$-0.487994\pi$
$199$	13.8485	−	9.44177i	0.981696	−	0.669309i	0.943988	+	0.329980i	$0.107042\pi$
$200$	−1.00336	−	0.309496i	−0.0709483	−	0.0218847i
$201$	−0.643262	−	8.58373i	−0.0453722	−	0.605450i
$202$	0.0361544	−	0.0174111i	0.00254382	−	0.00122504i
$203$	−3.06900	+	3.90047i	−0.215401	+	0.273759i
$204$	−12.6813	−	6.10699i	−0.887868	−	0.427575i
$205$	2.02866	−	5.16895i	0.141688	−	0.361015i
$206$	0.0621595	−	0.829461i	0.00433086	−	0.0577913i
$207$	−0.738158	−	1.88080i	−0.0513055	−	0.130724i
$208$	15.9023	−	4.90522i	1.10263	−	0.340116i
$209$	11.7372	−	14.7180i	0.811880	−	1.01806i
$210$	−0.0367529	−	0.450843i	−0.00253619	−	0.0311112i
$211$	−2.39653	−	3.00515i	−0.164984	−	0.206883i	0.692466	−	0.721450i	$-0.256524\pi$
$211$	−2.39653	−	3.00515i	−0.164984	−	0.206883i	−0.857450	+	0.514567i	$0.827953\pi$
$212$	13.2632	+	9.04270i	0.910921	+	0.621055i
$213$	−0.502717	−	0.466454i	−0.0344456	−	0.0319609i
$214$	0.301097	−	0.521515i	0.0205826	−	0.0356500i
$215$	18.6086	+	32.2311i	1.26910	+	2.19814i
$216$	0.0485414	−	0.212674i	0.00330283	−	0.0144706i
$217$	4.47254	−	3.09237i	0.303616	−	0.209924i
$218$	−0.152589	−	0.668534i	−0.0103346	−	0.0452788i
$219$	6.47161	−	6.00478i	0.437311	−	0.405765i
$220$	−22.5411	+	3.39753i	−1.51972	+	0.229061i
$221$	29.1255	−	4.38997i	1.95920	−	0.295301i
$222$	−0.114672	+	0.106400i	−0.00769626	+	0.00714109i
$223$	−1.49592	−	6.55404i	−0.100174	−	0.438891i	−0.999997	−	0.00263494i	$-0.999161\pi$
$223$	−1.49592	−	6.55404i	−0.100174	−	0.438891i	0.899822	−	0.436256i	$-0.143696\pi$
$224$	0.642303	+	1.60560i	0.0429157	+	0.107279i
$225$	−1.07108	+	4.69271i	−0.0714054	+	0.312848i
$226$	−0.395681	−	0.685340i	−0.0263203	−	0.0455881i
$227$	5.63741	−	9.76427i	0.374168	−	0.648078i	−0.616034	−	0.787719i	$-0.711262\pi$
$227$	5.63741	−	9.76427i	0.374168	−	0.648078i	0.990202	+	0.139642i	$0.0445951\pi$
$228$	7.56295	+	7.01739i	0.500869	+	0.464738i
$229$	−10.7687	−	7.34200i	−0.711618	−	0.485173i	0.152602	−	0.988288i	$-0.451235\pi$
$229$	−10.7687	−	7.34200i	−0.711618	−	0.485173i	−0.864220	+	0.503115i	$0.832187\pi$
$230$	0.215375	+	0.270072i	0.0142014	+	0.0178080i
$231$	−4.87488	−	8.31742i	−0.320743	−	0.547246i
$232$	0.255138	−	0.319933i	0.0167506	−	0.0210046i
$233$	−24.6884	+	7.61537i	−1.61739	+	0.498900i	−0.965717	−	0.259598i	$-0.916410\pi$
$233$	−24.6884	+	7.61537i	−1.61739	+	0.498900i	−0.651676	+	0.758498i	$0.725934\pi$
$234$	0.0833268	+	0.212313i	0.00544724	+	0.0138793i
$235$	2.52157	−	33.6480i	0.164489	−	2.19496i
$236$	4.99012	−	12.7146i	0.324829	−	0.827651i
$237$	−4.97047	−	2.39365i	−0.322866	−	0.155484i
$238$	0.232947	+	0.990695i	0.0150997	+	0.0642172i
$239$	−18.4947	+	8.90658i	−1.19632	+	0.576118i	−0.922625	−	0.385698i	$-0.873961\pi$
$239$	−18.4947	+	8.90658i	−1.19632	+	0.576118i	−0.273697	+	0.961816i	$0.588247\pi$
$240$	−0.932226	−	12.4397i	−0.0601750	−	0.802979i
$241$	−19.3317	−	5.96303i	−1.24526	−	0.384112i	−0.399035	−	0.916936i	$-0.630655\pi$
$241$	−19.3317	−	5.96303i	−1.24526	−	0.384112i	−0.846227	+	0.532823i	$0.821131\pi$
$242$	0.102709	−	0.0700259i	0.00660239	−	0.00450143i
$243$	−0.988831	−	0.149042i	−0.0634335	−	0.00956107i
$244$	2.41059			0.154322
$245$	15.8782	−	15.1241i	1.01442	−	0.966245i
$246$	−0.0967403			−0.00616794
$247$	−21.3490	−	3.21784i	−1.35840	−	0.204746i
$248$	−0.370422	+	0.252550i	−0.0235218	+	0.0160369i
$249$	4.02184	+	1.24057i	0.254874	+	0.0786181i
$250$	0.00238414	+	0.0318141i	0.000150786	+	0.00201210i
$251$	3.47979	−	1.67578i	0.219642	−	0.105774i	−0.320827	−	0.947138i	$-0.603961\pi$
$251$	3.47979	−	1.67578i	0.219642	−	0.105774i	0.540470	+	0.841364i	$0.318247\pi$
$252$	4.74528	−	2.32356i	0.298925	−	0.146371i
$253$	6.63319	+	3.19438i	0.417025	+	0.200829i
$254$	0.268766	−	0.684804i	0.0168639	−	0.0429684i
$255$	1.64997	−	22.0173i	0.103325	−	1.37878i
$256$	5.75859	+	14.6727i	0.359912	+	0.917041i
$257$	11.0689	−	3.41430i	0.690457	−	0.212978i	0.0703819	−	0.997520i	$-0.477578\pi$
$257$	11.0689	−	3.41430i	0.690457	−	0.212978i	0.620075	+	0.784542i	$0.287102\pi$
$258$	0.404268	−	0.506937i	0.0251687	−	0.0315605i
$259$	−7.50595	−	1.08118i	−0.466397	−	0.0671812i
$260$	16.3006	+	20.4403i	1.01092	+	1.26765i
$261$	−1.54992	−	1.05672i	−0.0959378	−	0.0654093i
$262$	−0.116965	−	0.108528i	−0.00722614	−	0.00670488i
$263$	−10.6702	+	18.4813i	−0.657952	+	1.13961i	0.323193	+	0.946333i	$0.395244\pi$
$263$	−10.6702	+	18.4813i	−0.657952	+	1.13961i	−0.981145	+	0.193273i	$0.938090\pi$
$264$	0.397442	+	0.688389i	0.0244608	+	0.0423674i
$265$	−5.60326	+	24.5495i	−0.344206	+	1.50806i
$266$	0.0508805	−	0.744244i	0.00311969	−	0.0456326i
$267$	−2.28768	−	10.0230i	−0.140004	−	0.613396i
$268$	−12.6011	+	11.6921i	−0.769736	+	0.714211i
$269$	11.9986	−	1.80849i	0.731565	−	0.110266i	0.227313	−	0.973822i	$-0.427006\pi$
$269$	11.9986	−	1.80849i	0.731565	−	0.110266i	0.504253	+	0.863556i	$0.331768\pi$
$270$	0.169058	−	0.0254815i	0.0102886	−	0.00155075i
$271$	10.4437	−	9.69036i	0.634411	−	0.588647i	−0.295990	−	0.955191i	$-0.595650\pi$
$271$	10.4437	−	9.69036i	0.634411	−	0.588647i	0.930401	+	0.366544i	$0.119459\pi$
$272$	6.24537	+	27.3628i	0.378681	+	1.65911i
$273$	−5.46566	+	9.61143i	−0.330797	+	0.581710i
$274$	−0.00561624	+	0.0246064i	−0.000339289	+	0.00148652i
$275$	−8.76967	−	15.1895i	−0.528831	−	0.915962i
$276$	−2.01745	+	3.49433i	−0.121437	+	0.210334i
$277$	−8.91877	−	8.27541i	−0.535877	−	0.497221i	0.365171	−	0.930940i	$-0.381011\pi$
$277$	−8.91877	−	8.27541i	−0.535877	−	0.497221i	−0.901048	+	0.433719i	$0.857201\pi$
$278$	0.265244	+	0.180840i	0.0159083	+	0.0108461i
$279$	1.28138	+	1.60680i	0.0767144	+	0.0961968i
$280$	−1.31729	+	1.23840i	−0.0787233	+	0.0740086i
$281$	−3.52867	+	4.42482i	−0.210503	+	0.263962i	−0.875863	−	0.482561i	$-0.839707\pi$
$281$	−3.52867	+	4.42482i	−0.210503	+	0.263962i	0.665360	+	0.746523i	$0.268278\pi$
$282$	−0.561740	+	0.173274i	−0.0334511	+	0.0103183i
$283$	3.80283	+	9.68946i	0.226055	+	0.575979i	0.998233	−	0.0594279i	$-0.0189277\pi$
$283$	3.80283	+	9.68946i	0.226055	+	0.575979i	−0.772178	+	0.635407i	$0.780832\pi$
$284$	−0.102345	+	1.36570i	−0.00607307	+	0.0810395i
$285$	−5.91265	+	15.0652i	−0.350235	+	0.892384i
$286$	−0.748786	−	0.360596i	−0.0442766	−	0.0213225i
$287$	−2.94794	−	3.64740i	−0.174011	−	0.215299i
$288$	−0.588889	+	0.283594i	−0.0347006	+	0.0167109i
$289$	2.44184	+	32.5841i	0.143638	+	1.91671i
$290$	0.306467	+	0.0945324i	0.0179963	+	0.00555113i
$291$	−7.18840	+	4.90097i	−0.421391	+	0.287300i
$292$	−17.4334	−	2.62766i	−1.02021	−	0.153772i
$293$	6.00082			0.350572			0.175286	−	0.984518i	$-0.443915\pi$
$293$	6.00082			0.350572			0.175286	+	0.984518i	$0.443915\pi$
$294$	−0.346341	−	0.161242i	−0.0201990	−	0.00940383i
$295$	21.4259			1.24746
$296$	0.618273	+	0.0931896i	0.0359364	+	0.00541653i
$297$	3.01070	−	2.05266i	0.174698	−	0.119107i
$298$	0.0981305	+	0.0302693i	0.00568455	+	0.00175345i
$299$	−0.630997	−	8.42007i	−0.0364915	−	0.486945i
$300$	8.66052	−	4.17069i	0.500016	−	0.240795i
$301$	31.4322	−	0.205591i	1.81172	−	0.0118501i
$302$	−0.158070	−	0.0761227i	−0.00909593	−	0.00438037i
$303$	−0.268624	+	0.684443i	−0.0154321	+	0.0393202i
$304$	1.53740	−	20.5151i	0.0881757	−	1.17662i
$305$	1.38149	+	3.51999i	0.0791041	+	0.201554i
$306$	−0.367570	+	0.113380i	−0.0210126	+	0.00648152i
$307$	4.71392	−	5.91107i	0.269038	−	0.337363i	−0.628899	−	0.777487i	$-0.716494\pi$
$307$	4.71392	−	5.91107i	0.269038	−	0.337363i	0.897937	+	0.440124i	$0.145066\pi$
$308$	−6.91646	+	17.9675i	−0.394102	+	1.02379i
$309$	9.50246	+	11.9157i	0.540576	+	0.677861i
$310$	−0.290315	−	0.197934i	−0.0164888	−	0.0112419i
$311$	−8.76082	−	8.12886i	−0.496781	−	0.460945i	0.391545	−	0.920159i	$-0.371941\pi$
$311$	−8.76082	−	8.12886i	−0.496781	−	0.460945i	−0.888326	+	0.459214i	$0.848131\pi$
$312$	0.455819	−	0.789502i	0.0258057	−	0.0446968i
$313$	4.77414	+	8.26905i	0.269850	+	0.467394i	0.968823	−	0.247754i	$-0.0796924\pi$
$313$	4.77414	+	8.26905i	0.269850	+	0.467394i	−0.698973	+	0.715148i	$0.746359\pi$
$314$	−0.0485303	+	0.212625i	−0.00273872	+	0.0119991i
$315$	6.11240	+	5.59753i	0.344395	+	0.315385i
$316$	2.45155	+	10.7409i	0.137911	+	0.604225i
$317$	−10.4140	+	9.66277i	−0.584908	+	0.542715i	−0.916153	−	0.400830i	$-0.868722\pi$
$317$	−10.4140	+	9.66277i	−0.584908	+	0.542715i	0.331245	+	0.943545i	$0.392531\pi$
$318$	0.433798	−	0.0653846i	0.0243262	−	0.00366658i
$319$	6.75908	−	1.01877i	0.378436	−	0.0570401i
$320$	−18.2071	+	16.8937i	−1.01781	+	0.944388i
$321$	2.45528	+	10.7573i	0.137041	+	0.600414i
$322$	0.288197	−	0.0453685i	0.0160606	−	0.00252829i
$323$	8.10244	−	35.4991i	0.450832	−	1.97522i
$324$	0.998511	+	1.72947i	0.0554728	+	0.0960817i
$325$	−10.0578	+	17.4206i	−0.557906	+	0.966321i
$326$	−0.0724776	−	0.0672494i	−0.00401416	−	0.00372460i
$327$	10.3813	+	7.07784i	0.574087	+	0.391406i
$328$	0.241087	+	0.302313i	0.0133118	+	0.0166925i
$329$	−23.6507	−	15.8992i	−1.30390	−	0.876550i
$330$	−0.388424	+	0.487068i	−0.0213820	+	0.0268122i
$331$	14.1630	−	4.36872i	0.778471	−	0.240126i	0.120041	−	0.992769i	$-0.461697\pi$
$331$	14.1630	−	4.36872i	0.778471	−	0.240126i	0.658429	+	0.752642i	$0.271221\pi$
$332$	−3.07073	−	7.82410i	−0.168528	−	0.429403i
$333$	0.214196	−	2.85825i	0.0117379	−	0.156631i
$334$	0.501306	−	1.27731i	0.0274302	−	0.0698911i
$335$	−24.2947	−	11.6997i	−1.32736	−	0.639223i
$336$	−9.52207	−	4.50910i	−0.519472	−	0.245992i
$337$	6.62944	−	3.19257i	0.361128	−	0.173910i	−0.244517	−	0.969645i	$-0.578629\pi$
$337$	6.62944	−	3.19257i	0.361128	−	0.173910i	0.605645	+	0.795735i	$0.292915\pi$
$338$	0.0182094	+	0.242987i	0.000990460	+	0.0132168i
$339$	13.8559	+	4.27397i	0.752547	+	0.232130i
$340$	−36.4308	+	24.8381i	−1.97574	+	1.34704i
$341$	−7.40514	−	1.11614i	−0.401011	−	0.0604426i
$342$	0.281955			0.0152464
$343$	−4.47462	−	17.9716i	−0.241607	−	0.970374i
$344$	−2.59165			−0.139733
$345$	−6.25868	−	0.943344i	−0.336956	−	0.0507879i
$346$	0.422388	−	0.287979i	0.0227077	−	0.0154818i
$347$	32.1098	+	9.90457i	1.72375	+	0.531705i	0.989164	−	0.146815i	$-0.0469023\pi$
$347$	32.1098	+	9.90457i	1.72375	+	0.531705i	0.734582	+	0.678520i	$0.237378\pi$
$348$	0.279951	+	3.73569i	0.0150070	+	0.200254i
$349$	23.9198	−	11.5192i	1.28040	−	0.616607i	0.334906	−	0.942252i	$-0.391295\pi$
$349$	23.9198	−	11.5192i	1.28040	−	0.616607i	0.945492	+	0.325644i	$0.105581\pi$
$350$	−0.628163	−	0.297462i	−0.0335767	−	0.0159000i
$351$	−3.76522	−	1.81324i	−0.200973	−	0.0967833i
$352$	0.870129	−	2.21705i	0.0463780	−	0.118169i
$353$	−2.18700	+	29.1835i	−0.116402	+	1.55328i	0.567296	+	0.823514i	$0.307990\pi$
$353$	−2.18700	+	29.1835i	−0.116402	+	1.55328i	−0.683698	+	0.729765i	$0.739629\pi$
$354$	−0.136375	−	0.347477i	−0.00724823	−	0.0184682i
$355$	−2.05288	+	0.633228i	−0.108955	+	0.0336083i
$356$	−12.8008	+	16.0517i	−0.678440	+	0.850737i
$357$	−15.4756	−	10.4035i	−0.819058	−	0.550612i
$358$	0.757745	+	0.950183i	0.0400481	+	0.0502187i
$359$	−11.3209	−	7.71843i	−0.597492	−	0.407363i	0.226462	−	0.974020i	$-0.427284\pi$
$359$	−11.3209	−	7.71843i	−0.597492	−	0.407363i	−0.823954	+	0.566657i	$0.808236\pi$
$360$	−0.500941	−	0.464805i	−0.0264019	−	0.0244974i
$361$	−3.84497	+	6.65969i	−0.202367	+	0.350510i
$362$	0.612308	+	1.06055i	0.0321822	+	0.0557412i
$363$	−0.506838	+	2.22060i	−0.0266021	+	0.116551i
$364$	21.8121	−	3.43369i	1.14326	−	0.179974i
$365$	−6.15401	−	26.9625i	−0.322116	−	1.41128i
$366$	0.0482926	−	0.0448090i	0.00252430	−	0.00234220i
$367$	0.287706	−	0.0433647i	0.0150181	−	0.00226362i	−0.141529	−	0.989934i	$-0.545202\pi$
$367$	0.287706	−	0.0433647i	0.0150181	−	0.00226362i	0.156547	+	0.987671i	$0.449964\pi$
$368$	7.95590	−	1.19916i	0.414730	−	0.0625105i
$369$	1.29938	−	1.20565i	0.0676431	−	0.0627636i
$370$	0.109044	+	0.477753i	0.00566893	+	0.0248372i
$371$	15.6842	+	14.3631i	0.814283	+	0.745693i
$372$	0.913278	−	4.00133i	0.0473513	−	0.207460i
$373$	3.15175	+	5.45899i	0.163191	+	0.282656i	0.936012	−	0.351969i	$-0.114488\pi$
$373$	3.15175	+	5.45899i	0.163191	+	0.282656i	−0.772820	+	0.634625i	$0.781155\pi$
$374$	0.700822	−	1.21386i	0.0362387	−	0.0627672i
$375$	−0.428514	−	0.397603i	−0.0221284	−	0.0205321i
$376$	1.94139	+	1.32362i	0.100120	+	0.0682605i
$377$	−4.88781	−	6.12912i	−0.251735	−	0.315666i
$378$	0.0518734	−	0.134756i	0.00266808	−	0.00693112i
$379$	−4.92035	+	6.16993i	−0.252742	+	0.316928i	−0.891975	−	0.452085i	$-0.850680\pi$
$379$	−4.92035	+	6.16993i	−0.252742	+	0.316928i	0.639233	+	0.769013i	$0.279252\pi$
$380$	30.8837	−	9.52637i	1.58430	−	0.488693i
$381$	4.92457	+	12.5476i	0.252294	+	0.642833i
$382$	−0.00600697	+	0.0801574i	−0.000307343	+	0.00410121i
$383$	5.81307	−	14.8115i	0.297034	−	0.756831i	−0.701970	−	0.712207i	$-0.747696\pi$
$383$	5.81307	−	14.8115i	0.297034	−	0.756831i	0.999004	−	0.0446239i	$-0.0142090\pi$
$384$	1.56764	+	0.754936i	0.0799983	+	0.0385252i
$385$	−30.2003	+	0.197533i	−1.53915	+	0.0100672i
$386$	−0.0903648	+	0.0435174i	−0.00459945	+	0.00221498i
$387$	0.887832	+	11.8473i	0.0451310	+	0.602232i
$388$	16.6025	+	5.12119i	0.842863	+	0.259989i
$389$	−10.5802	+	7.21343i	−0.536436	+	0.365736i	−0.801030	−	0.598624i	$-0.795714\pi$
$389$	−10.5802	+	7.21343i	−0.536436	+	0.365736i	0.264594	+	0.964360i	$0.414762\pi$
$390$	0.706509	+	0.106489i	0.0357755	+	0.00539229i
$391$	14.2404			0.720168
$392$	0.359235	+	1.48415i	0.0181441	+	0.0749607i
$393$	2.92359			0.147476
$394$	−1.05995	−	0.159762i	−0.0533997	−	0.00804871i
$395$	−14.2792	+	9.73536i	−0.718462	+	0.489839i
$396$	−6.95357	−	2.14489i	−0.349430	−	0.107785i
$397$	−0.558026	−	7.44634i	−0.0280065	−	0.373721i	−0.993543	−	0.113454i	$-0.963809\pi$
$397$	−0.558026	−	7.44634i	−0.0280065	−	0.373721i	0.965537	−	0.260267i	$-0.0838105\pi$
$398$	−0.824163	+	0.396896i	−0.0413116	+	0.0198946i
$399$	8.59192	+	10.6305i	0.430134	+	0.532193i
$400$	−17.2694	−	8.31651i	−0.863471	−	0.415826i
$401$	10.3910	−	26.4759i	0.518903	−	1.32214i	−0.395919	−	0.918285i	$-0.629574\pi$
$401$	10.3910	−	26.4759i	0.518903	−	1.32214i	0.914822	−	0.403858i	$-0.132331\pi$
$402$	−0.0351069	+	0.468469i	−0.00175097	+	0.0233651i
$403$	3.13783	+	7.99505i	0.156306	+	0.398262i
$404$	1.40311	−	0.432803i	0.0698075	−	0.0215328i
$405$	−1.95317	+	2.44919i	−0.0970536	+	0.121701i
$406$	0.197351	−	0.185532i	0.00979439	−	0.00920781i
$407$	6.51189	+	8.16565i	0.322782	+	0.404756i
$408$	1.27034	+	0.866100i	0.0628910	+	0.0428783i
$409$	8.43267	+	7.82437i	0.416969	+	0.386890i	0.860569	−	0.509335i	$-0.170108\pi$
$409$	8.43267	+	7.82437i	0.416969	+	0.386890i	−0.443600	+	0.896225i	$0.646299\pi$
$410$	−0.151526	+	0.262451i	−0.00748333	+	0.0129615i
$411$	−0.231228	−	0.400498i	−0.0114056	−	0.0197551i
$412$	6.77268	−	29.6730i	0.333666	−	1.46189i
$413$	8.94522	−	15.7303i	0.440166	−	0.774037i
$414$	0.0245373	+	0.107505i	0.00120594	+	0.00528359i
$415$	9.66508	−	8.96788i	0.474440	−	0.440216i
$416$	−2.70101	+	0.407112i	−0.132428	+	0.0199603i
$417$	−5.81643	+	0.876686i	−0.284832	+	0.0429315i
$418$	−0.753139	+	0.698811i	−0.0368373	+	0.0341800i
$419$	−1.31115	−	5.74451i	−0.0640538	−	0.280638i	0.932750	−	0.360523i	$-0.117402\pi$
$419$	−1.31115	−	5.74451i	−0.0640538	−	0.280638i	−0.996804	+	0.0798851i	$0.974545\pi$
$420$	1.12892	−	16.5131i	0.0550859	−	0.805757i
$421$	−8.60684	+	37.7090i	−0.419472	+	1.83783i	0.115970	+	0.993253i	$0.463002\pi$
$421$	−8.60684	+	37.7090i	−0.419472	+	1.83783i	−0.535441	+	0.844572i	$0.679855\pi$
$422$	0.104889	+	0.181673i	0.00510591	+	0.00884369i
$423$	5.38563	−	9.32818i	0.261858	−	0.453551i
$424$	−1.28540	−	1.19267i	−0.0624243	−	0.0579213i
$425$	−28.0303	−	19.1108i	−1.35967	−	0.927008i
$426$	0.0233359	+	0.0292622i	0.00113063	+	0.00141776i
$427$	3.16104	+	0.455326i	0.152974	+	0.0220348i
$428$	13.7386	−	17.2277i	0.664081	−	0.832731i
$429$	14.5514	−	4.48853i	0.702550	−	0.216708i
$430$	−0.742076	−	1.89078i	−0.0357861	−	0.0911815i
$431$	0.749471	−	10.0010i	0.0361008	−	0.481731i	−0.949627	−	0.313383i	$-0.898538\pi$
$431$	0.749471	−	10.0010i	0.0361008	−	0.481731i	0.985728	−	0.168348i	$-0.0538433\pi$
$432$	1.45484	−	3.70687i	0.0699959	−	0.178347i
$433$	−26.6742	−	12.8456i	−1.28188	−	0.617321i	−0.336007	−	0.941860i	$-0.609077\pi$
$433$	−26.6742	−	12.8456i	−1.28188	−	0.617321i	−0.945872	+	0.324539i	$0.894791\pi$
$434$	−0.266523	+	0.130505i	−0.0127935	+	0.00626444i
$435$	−5.29449	+	2.54969i	−0.253851	+	0.122248i
$436$	−1.87510	−	25.0214i	−0.0898009	−	1.19831i
$437$	−9.97444	−	3.07671i	−0.477142	−	0.147179i
$438$	−0.398097	+	0.271418i	−0.0190218	+	0.0129688i
$439$	−1.00175	−	0.150989i	−0.0478108	−	0.00720632i	0.125093	−	0.992145i	$-0.460077\pi$
$439$	−1.00175	−	0.150989i	−0.0478108	−	0.00720632i	−0.172904	+	0.984939i	$0.555315\pi$
$440$	2.49008			0.118710
$441$	6.66145	−	2.15061i	0.317212	−	0.102410i
$442$	−1.60752			−0.0764621
$443$	6.84830	+	1.03222i	0.325373	+	0.0490420i	0.309698	−	0.950835i	$-0.399772\pi$
$443$	6.84830	+	1.03222i	0.325373	+	0.0490420i	0.0156750	+	0.999877i	$0.495010\pi$
$444$	−4.72938	+	3.22444i	−0.224447	+	0.153025i
$445$	−30.7750	−	9.49282i	−1.45887	−	0.450003i
$446$	0.0274181	+	0.365869i	0.00129829	+	0.0173244i
$447$	−1.69529	+	0.816410i	−0.0801846	+	0.0386149i
$448$	4.80151	+	20.4202i	0.226850	+	0.964764i
$449$	−31.6879	−	15.2601i	−1.49544	−	0.720168i	−0.505658	−	0.862734i	$-0.668750\pi$
$449$	−31.6879	−	15.2601i	−1.49544	−	0.720168i	−0.989785	+	0.142566i	$0.954465\pi$
$450$	0.0959744	−	0.244539i	0.00452428	−	0.0115277i
$451$	−0.482680	+	6.44091i	−0.0227285	+	0.303291i
$452$	−10.5792	−	26.9553i	−0.497602	−	1.26787i
$453$	3.07184	−	0.947539i	0.144328	−	0.0445192i
$454$	−0.383658	+	0.481092i	−0.0180059	+	0.0225787i
$455$	17.5143	+	29.8826i	0.821083	+	1.40092i
$456$	−0.702660	−	0.881107i	−0.0329050	−	0.0412616i
$457$	15.5212	+	10.5822i	0.726052	+	0.495014i	0.869060	−	0.494708i	$-0.164725\pi$
$457$	15.5212	+	10.5822i	0.726052	+	0.495014i	−0.143007	+	0.989722i	$0.545677\pi$
$458$	0.521434	+	0.483820i	0.0243650	+	0.0226074i
$459$	3.52404	−	6.10382i	0.164488	−	0.284902i
$460$	6.31995	+	10.9465i	0.294669	+	0.510382i
$461$	4.22617	−	18.5161i	0.196833	−	0.862380i	−0.775975	−	0.630764i	$-0.782742\pi$
$461$	4.22617	−	18.5161i	0.196833	−	0.862380i	0.972807	−	0.231616i	$-0.0744013\pi$
$462$	0.195426	+	0.488519i	0.00909206	+	0.0227279i
$463$	−6.31681	−	27.6757i	−0.293567	−	1.28620i	−0.879522	−	0.475858i	$-0.842138\pi$
$463$	−6.31681	−	27.6757i	−0.293567	−	1.28620i	0.585955	−	0.810343i	$-0.300719\pi$
$464$	5.47590	−	5.08089i	0.254212	−	0.235874i
$465$	6.36621	−	0.959552i	0.295226	−	0.0444982i
$466$	1.39430	−	0.210157i	0.0645898	−	0.00973535i
$467$	6.37029	−	5.91077i	0.294782	−	0.273518i	−0.518891	−	0.854840i	$-0.673655\pi$
$467$	6.37029	−	5.91077i	0.294782	−	0.273518i	0.813673	+	0.581323i	$0.197465\pi$
$468$	1.85710	+	8.13647i	0.0858443	+	0.376108i
$469$	−18.7325	+	12.9519i	−0.864988	+	0.598063i
$470$	−0.409781	+	1.79537i	−0.0189018	+	0.0828142i
$471$	−1.99805	−	3.46072i	−0.0920653	−	0.159462i
$472$	−0.746005	+	1.29212i	−0.0343376	+	0.0594745i
$473$	−31.7345	−	29.4453i	−1.45915	−	1.35390i
$474$	0.248770	+	0.169609i	0.0114264	+	0.00779038i
$475$	15.5044	+	19.4419i	0.711390	+	0.892055i
$476$	3.02573	+	37.1163i	0.138684	+	1.70122i
$477$	−5.01175	+	6.28454i	−0.229472	+	0.287749i
$478$	1.07055	−	0.330221i	0.0489658	−	0.0151039i
$479$	2.32224	+	5.91697i	0.106106	+	0.270353i	0.974060	−	0.226292i	$-0.0726603\pi$
$479$	2.32224	+	5.91697i	0.106106	+	0.270353i	−0.867954	+	0.496645i	$0.834565\pi$
$480$	−0.153013	+	2.04182i	−0.00698406	+	0.0931959i
$481$	4.37618	−	11.1503i	0.199537	−	0.508411i
$482$	0.994765	+	0.479054i	0.0453103	+	0.0218203i
$483$	−3.30555	+	4.20110i	−0.150408	+	0.191157i
$484$	4.09818	−	1.97358i	0.186281	−	0.0897081i
$485$	2.03672	+	27.1782i	0.0924828	+	1.23410i
$486$	0.0521518	+	0.0160867i	0.00236565	+	0.000729707i
$487$	7.86202	−	5.36024i	0.356262	−	0.242896i	−0.371941	−	0.928256i	$-0.621308\pi$
$487$	7.86202	−	5.36024i	0.356262	−	0.242896i	0.728204	+	0.685361i	$0.240355\pi$
$488$	−0.260378	−	0.0392457i	−0.0117868	−	0.00177657i
$489$	1.81161			0.0819237
$490$	−0.979920	+	0.687045i	−0.0442683	+	0.0310375i
$491$	−30.6558			−1.38348			−0.691739	−	0.722148i	$-0.743155\pi$
$491$	−30.6558			−1.38348			−0.691739	+	0.722148i	$0.743155\pi$
$492$	−3.50031	−	0.527587i	−0.157806	−	0.0237855i
$493$	10.9240	−	7.44785i	0.491991	−	0.335434i
$494$	1.12596	+	0.347313i	0.0506594	+	0.0156264i
$495$	−0.853035	−	11.3830i	−0.0383411	−	0.511626i
$496$	−7.37353	+	3.55091i	−0.331081	+	0.159440i
$497$	−0.392168	+	1.77153i	−0.0175911	+	0.0794641i
$498$	−0.206955	−	0.0996643i	−0.00927388	−	0.00446607i
$499$	4.40134	−	11.2144i	0.197031	−	0.502027i	−0.797876	−	0.602821i	$-0.794043\pi$
$499$	4.40134	−	11.2144i	0.197031	−	0.502027i	0.994907	+	0.100794i	$0.0321384\pi$
$500$	−0.0872385	+	1.16412i	−0.00390143	+	0.0520609i
$501$	9.18538	+	23.4040i	0.410373	+	1.04561i
$502$	−0.201424	+	0.0621312i	−0.00899001	+	0.00277305i
$503$	17.8725	−	22.4114i	0.796895	−	0.999275i	−0.202903	−	0.979199i	$-0.565038\pi$
$503$	17.8725	−	22.4114i	0.796895	−	0.999275i	0.999798	−	0.0200761i	$-0.00639085\pi$
$504$	−0.550387	+	0.173722i	−0.0245162	+	0.00773821i
$505$	1.43610	+	1.80082i	0.0639057	+	0.0801353i
$506$	−0.331989	−	0.226346i	−0.0147587	−	0.0100623i
$507$	−3.27287	−	3.03678i	−0.145353	−	0.134868i
$508$	13.4593	−	23.3122i	0.597160	−	1.03431i
$509$	0.735533	+	1.27398i	0.0326019	+	0.0564682i	0.881866	−	0.471500i	$-0.156287\pi$
$509$	0.735533	+	1.27398i	0.0326019	+	0.0564682i	−0.849264	+	0.527968i	$0.822954\pi$
$510$	−0.268137	+	1.17479i	−0.0118733	+	0.0520204i
$511$	−22.3644	−	6.73861i	−0.989341	−	0.298099i
$512$	−0.965774	−	4.23133i	−0.0426816	−	0.187000i
$513$	−3.78712	+	3.51393i	−0.167205	+	0.155144i
$514$	−0.625125	+	0.0942225i	−0.0275731	+	0.00415597i
$515$	47.2105	−	7.11583i	2.08034	−	0.313561i
$516$	17.3921	−	16.1375i	0.765645	−	0.710415i
$517$	8.73371	+	38.2649i	0.384108	+	1.68289i
$518$	0.396278	+	0.119403i	0.0174115	+	0.00524626i
$519$	−2.08435	+	9.13214i	−0.0914929	+	0.400857i
$520$	−1.42791	−	2.47322i	−0.0626182	−	0.108458i
$521$	−10.2560	+	17.7639i	−0.449322	+	0.778249i	−0.998342	−	0.0575607i	$-0.981668\pi$
$521$	−10.2560	+	17.7639i	−0.449322	+	0.778249i	0.549020	+	0.835809i	$0.315001\pi$
$522$	0.0750489	+	0.0696352i	0.00328480	+	0.00304785i
$523$	12.9260	+	8.81279i	0.565214	+	0.385356i	0.811950	−	0.583726i	$-0.198406\pi$
$523$	12.9260	+	8.81279i	0.565214	+	0.385356i	−0.246737	+	0.969083i	$0.579358\pi$
$524$	−3.64023	−	4.56470i	−0.159024	−	0.199410i
$525$	12.1445	−	3.83324i	0.530027	−	0.167296i
$526$	0.726167	−	0.910585i	0.0316624	−	0.0397034i
$527$	−13.8415	+	4.26955i	−0.602947	+	0.185985i
$528$	5.30122	+	13.5073i	0.230706	+	0.587830i
$529$	−1.41372	+	18.8648i	−0.0614662	+	0.820210i
$530$	0.502081	−	1.27928i	0.0218090	−	0.0555684i
$531$	6.16225	+	2.96758i	0.267419	+	0.128782i
$532$	5.89983	−	26.6512i	0.255790	−	1.15548i
$533$	6.67410	−	3.21408i	0.289087	−	0.139217i
$534$	0.0419300	+	0.559517i	0.00181449	+	0.0242127i
$535$	33.0297	+	10.1883i	1.42800	+	0.440479i
$536$	1.55146	−	1.05776i	0.0670127	−	0.0456885i
$537$	−22.0197	−	3.31893i	−0.950218	−	0.143222i
$538$	−0.662236			−0.0285510
$539$	−12.4635	+	22.2547i	−0.536839	+	0.958576i
$540$	6.25594			0.269213
$541$	2.13634	+	0.322002i	0.0918485	+	0.0138439i	0.194806	−	0.980842i	$-0.437592\pi$
$541$	2.13634	+	0.322002i	0.0918485	+	0.0138439i	−0.102957	+	0.994686i	$0.532830\pi$
$542$	−0.642438	+	0.438007i	−0.0275951	+	0.0188140i
$543$	−21.4417	−	6.61388i	−0.920150	−	0.283829i
$544$	−0.344263	−	4.59387i	−0.0147602	−	0.196961i
$545$	35.4622	−	17.0777i	1.51903	−	0.731527i
$546$	0.373146	−	0.474240i	0.0159692	−	0.0202956i
$547$	−25.3153	−	12.1912i	−1.08240	−	0.521258i	−0.194320	−	0.980938i	$-0.562250\pi$
$547$	−25.3153	−	12.1912i	−1.08240	−	0.521258i	−0.888085	+	0.459680i	$0.847964\pi$
$548$	−0.337404	+	0.859692i	−0.0144132	+	0.0367242i
$549$	−0.0902062	+	1.20372i	−0.00384991	+	0.0513734i
$550$	0.349717	+	0.891065i	0.0149120	+	0.0379951i
$551$	−9.26066	+	2.85654i	−0.394517	+	0.121692i
$552$	0.274803	−	0.344593i	0.0116964	−	0.0146668i
$553$	1.18594	+	14.5478i	0.0504315	+	0.618636i
$554$	0.414005	+	0.519145i	0.0175894	+	0.0220564i
$555$	−7.41876	−	5.05803i	−0.314909	−	0.214701i
$556$	8.61097	+	7.98981i	0.365186	+	0.338843i
$557$	−19.4999	+	33.7749i	−0.826239	+	1.43109i	0.0747293	+	0.997204i	$0.476191\pi$
$557$	−19.4999	+	33.7749i	−0.826239	+	1.43109i	−0.900969	+	0.433884i	$0.857143\pi$
$558$	−0.0560822	−	0.0971372i	−0.00237415	−	0.00411215i
$559$	−11.0481	+	48.4048i	−0.467284	+	2.04731i
$560$	−27.1475	+	18.7701i	−1.14719	+	0.793183i
$561$	5.71483	+	25.0383i	0.241280	+	1.05712i
$562$	0.226424	−	0.210091i	0.00955111	−	0.00886214i
$563$	−1.20886	+	0.182207i	−0.0509474	+	0.00767909i	−0.174467	−	0.984663i	$-0.555820\pi$
$563$	−1.20886	+	0.182207i	−0.0509474	+	0.00767909i	0.123519	+	0.992342i	$0.460582\pi$
$564$	−21.2702	+	3.20596i	−0.895635	+	0.134995i
$565$	33.2977	−	30.8958i	1.40085	−	1.29979i
$566$	−0.126411	−	0.553843i	−0.00531345	−	0.0232798i
$567$	0.982690	+	2.45649i	0.0412691	+	0.103163i
$568$	0.0332891	−	0.145849i	0.00139678	−	0.00611969i
$569$	14.2617	+	24.7020i	0.597883	+	1.03556i	0.993133	+	0.116990i	$0.0373245\pi$
$569$	14.2617	+	24.7020i	0.597883	+	1.03556i	−0.395250	+	0.918573i	$0.629342\pi$
$570$	0.441630	−	0.764926i	0.0184979	−	0.0320392i
$571$	15.5214	+	14.4018i	0.649552	+	0.602696i	0.934550	−	0.355832i	$-0.115803\pi$
$571$	15.5214	+	14.4018i	0.649552	+	0.602696i	−0.284998	+	0.958528i	$0.591993\pi$
$572$	−25.1264	−	17.1309i	−1.05059	−	0.716279i
$573$	−0.918298	−	1.15151i	−0.0383625	−	0.0481050i
$574$	0.129422	+	0.220818i	0.00540199	+	0.00921677i
$575$	−6.06362	+	7.60354i	−0.252870	+	0.317090i
$576$	−7.57636	+	2.33700i	−0.315682	+	0.0973749i
$577$	−7.26995	−	18.5235i	−0.302652	−	0.771144i	−0.998592	−	0.0530446i	$-0.983107\pi$
$577$	−7.26995	−	18.5235i	−0.302652	−	0.771144i	0.695940	−	0.718100i	$-0.254988\pi$
$578$	0.133267	−	1.77833i	0.00554318	−	0.0739686i
$579$	0.671402	−	1.71071i	0.0279025	−	0.0710945i
$580$	10.5732	+	5.09179i	0.439028	+	0.211425i
$581$	−2.54884	−	10.8399i	−0.105744	−	0.449714i
$582$	0.427801	−	0.206018i	0.0177329	−	0.00853972i
$583$	−2.18886	−	29.2083i	−0.0906532	−	1.20968i
$584$	1.84028	+	0.567650i	0.0761512	+	0.0234895i
$585$	−10.8167	+	7.37472i	−0.447217	+	0.304907i
$586$	−0.323846	−	0.0488119i	−0.0133779	−	0.00201640i
$587$	12.1851			0.502934			0.251467	−	0.967866i	$-0.419087\pi$
$587$	12.1851			0.502934			0.251467	+	0.967866i	$0.419087\pi$
$588$	−11.6521	−	7.72297i	−0.480526	−	0.318490i
$589$	10.6175			0.437488
$590$	−1.15629	−	0.174283i	−0.0476037	−	0.00717510i
$591$	16.2280	−	11.0641i	0.667531	−	0.455115i
$592$	10.9068	+	3.36429i	0.448266	+	0.138272i
$593$	2.09855	+	28.0032i	0.0861770	+	1.14995i	0.857839	+	0.513919i	$0.171807\pi$
$593$	2.09855	+	28.0032i	0.0861770	+	1.14995i	−0.771662	+	0.636033i	$0.780574\pi$
$594$	−0.179175	+	0.0862860i	−0.00735163	+	0.00354036i
$595$	−52.4639	+	25.6893i	−2.15081	+	1.05316i
$596$	3.38554	+	1.63039i	0.138677	+	0.0667833i
$597$	6.12345	−	15.6023i	0.250616	−	0.638560i
$598$	−0.0344376	+	0.459538i	−0.00140826	+	0.0187919i
$599$	13.3939	+	34.1272i	0.547262	+	1.39440i	0.890427	+	0.455125i	$0.150406\pi$
$599$	13.3939	+	34.1272i	0.547262	+	1.39440i	−0.343166	+	0.939275i	$0.611499\pi$
$600$	−1.00336	+	0.309496i	−0.0409620	+	0.0126351i
$601$	−5.36846	+	6.73183i	−0.218984	+	0.274597i	−0.879173	−	0.476502i	$-0.841905\pi$
$601$	−5.36846	+	6.73183i	−0.218984	+	0.274597i	0.660189	+	0.751099i	$0.270476\pi$
$602$	−1.69797	−	0.244581i	−0.0692041	−	0.00996836i
$603$	−5.36687	−	6.72985i	−0.218556	−	0.274061i
$604$	−5.30425	−	3.61637i	−0.215827	−	0.147148i
$605$	5.23049	+	4.85319i	0.212650	+	0.197310i
$606$	0.0200642	−	0.0347522i	0.000815052	−	0.00141171i
$607$	−18.9755	−	32.8664i	−0.770190	−	1.33401i	−0.937459	−	0.348097i	$-0.886828\pi$
$607$	−18.9755	−	32.8664i	−0.770190	−	1.33401i	0.167269	−	0.985911i	$-0.446505\pi$
$608$	−0.751395	+	3.29208i	−0.0304731	+	0.133511i
$609$	−0.338514	+	4.95155i	−0.0137173	+	0.200647i
$610$	−0.0459226	−	0.201200i	−0.00185935	−	0.00814635i
$611$	32.9975	−	30.6172i	1.33494	−	1.23864i
$612$	−13.9180	+	2.09780i	−0.562601	+	0.0847984i
$613$	−46.9159	+	7.07143i	−1.89492	+	0.285613i	−0.990119	−	0.140231i	$-0.955215\pi$
$613$	−46.9159	+	7.07143i	−1.89492	+	0.285613i	−0.904797	+	0.425844i	$0.859977\pi$
$614$	−0.302478	+	0.280658i	−0.0122070	+	0.0113264i
$615$	−1.23561	−	5.41358i	−0.0498247	−	0.218296i
$616$	1.03960	−	1.82815i	0.0418865	−	0.0736581i
$617$	−5.55632	+	24.3438i	−0.223689	+	0.980046i	0.730985	+	0.682393i	$0.239061\pi$
$617$	−5.55632	+	24.3438i	−0.223689	+	0.980046i	−0.954674	+	0.297653i	$0.903796\pi$
$618$	−0.415893	−	0.720349i	−0.0167297	−	0.0289767i
$619$	3.35823	−	5.81662i	0.134979	−	0.233790i	−0.790611	−	0.612319i	$-0.790237\pi$
$619$	3.35823	−	5.81662i	0.134979	−	0.233790i	0.925589	+	0.378529i	$0.123570\pi$
$620$	−9.42490	−	8.74503i	−0.378513	−	0.351209i
$621$	−1.66939	−	1.13817i	−0.0669901	−	0.0456731i
$622$	0.406673	+	0.509951i	0.0163061	+	0.0204472i
$623$	−19.8178	+	18.6309i	−0.793983	+	0.746432i
$624$	10.3759	−	13.0110i	0.415369	−	0.520856i
$625$	−24.7476	+	7.63363i	−0.989905	+	0.305345i
$626$	−0.190383	−	0.485089i	−0.00760925	−	0.0193880i
$627$	1.40680	−	18.7724i	0.0561820	−	0.749697i
$628$	−2.91553	+	7.42865i	−0.116342	+	0.296435i
$629$	18.2011	+	8.76518i	0.725724	+	0.349490i
$630$	−0.284336	−	0.351801i	−0.0113282	−	0.0140161i
$631$	−9.03262	+	4.34988i	−0.359583	+	0.173166i	−0.604948	−	0.796265i	$-0.706806\pi$
$631$	−9.03262	+	4.34988i	−0.359583	+	0.173166i	0.245366	+	0.969431i	$0.421092\pi$
$632$	−0.0899342	−	1.20009i	−0.00357739	−	0.0477369i
$633$	−3.67297	−	1.13296i	−0.145987	−	0.0450312i
$634$	0.640609	−	0.436760i	0.0254418	−	0.0173460i
$635$	41.7544	+	6.29346i	1.65697	+	0.249748i
$636$	16.0525			0.636524
$637$	29.2511	−	0.382666i	1.15897	−	0.0151618i
$638$	−0.373054			−0.0147693
$639$	−0.678127	−	0.102211i	−0.0268263	−	0.00404341i
$640$	4.50352	−	3.07045i	0.178017	−	0.121370i
$641$	−12.7930	−	3.94613i	−0.505295	−	0.155863i	0.0316188	−	0.999500i	$-0.489934\pi$
$641$	−12.7930	−	3.94613i	−0.505295	−	0.155863i	−0.536914	+	0.843637i	$0.680410\pi$
$642$	−0.0450020	−	0.600510i	−0.00177609	−	0.0237002i
$643$	−4.62883	+	2.22913i	−0.182543	+	0.0879082i	−0.522923	−	0.852380i	$-0.675159\pi$
$643$	−4.62883	+	2.22913i	−0.182543	+	0.0879082i	0.340380	+	0.940288i	$0.389444\pi$
$644$	10.6751	−	0.0698238i	0.420659	−	0.00275144i
$645$	33.5316	+	16.1480i	1.32031	+	0.635826i
$646$	−0.726020	+	1.84987i	−0.0285649	+	0.0727821i
$647$	−1.15215	+	15.3744i	−0.0452958	+	0.604430i	0.927658	+	0.373431i	$0.121819\pi$
$647$	−1.15215	+	15.3744i	−0.0452958	+	0.604430i	−0.972954	+	0.230999i	$0.925800\pi$
$648$	−0.0796967	−	0.203064i	−0.00313078	−	0.00797710i
$649$	−23.8152	+	7.34603i	−0.934830	+	0.288357i
$650$	0.684490	−	0.858323i	0.0268479	−	0.0336662i
$651$	1.95339	−	5.07450i	0.0765594	−	0.198885i
$652$	−2.25567	−	2.82852i	−0.0883390	−	0.110774i
$653$	26.2120	+	17.8710i	1.02576	+	0.699348i	0.954531	−	0.298112i	$-0.0963570\pi$
$653$	26.2120	+	17.8710i	1.02576	+	0.699348i	0.0712244	+	0.997460i	$0.477309\pi$
$654$	−0.502673	−	0.466413i	−0.0196561	−	0.0182382i
$655$	4.57927	−	7.93153i	0.178927	−	0.309911i
$656$	3.52930	+	6.11292i	0.137796	+	0.238670i
$657$	1.96448	−	8.60697i	0.0766418	−	0.335790i
$658$	1.14703	+	1.05041i	0.0447158	+	0.0409492i
$659$	−3.15915	−	13.8411i	−0.123063	−	0.539174i	−0.998445	−	0.0557423i	$-0.982247\pi$
$659$	−3.15915	−	13.8411i	−0.123063	−	0.539174i	0.875382	−	0.483431i	$-0.160610\pi$
$660$	−16.7105	+	15.5050i	−0.650454	+	0.603533i
$661$	18.3368	−	2.76382i	0.713217	−	0.107500i	0.217596	−	0.976039i	$-0.430179\pi$
$661$	18.3368	−	2.76382i	0.713217	−	0.107500i	0.495621	+	0.868539i	$0.334940\pi$
$662$	−0.799871	+	0.120561i	−0.0310879	+	0.00468574i
$663$	21.5917	−	20.0342i	0.838552	−	0.778062i
$664$	0.204303	+	0.895108i	0.00792848	+	0.0347369i
$665$	42.2977	−	6.65858i	1.64023	−	0.258209i
$666$	−0.0348091	+	0.152508i	−0.00134882	+	0.00590958i
$667$	−1.89507	−	3.28236i	−0.0733774	−	0.127093i
$668$	25.1045	−	43.4823i	0.971322	−	1.68238i
$669$	−4.92801	−	4.57252i	−0.190528	−	0.176784i
$670$	1.21594	+	0.829015i	0.0469759	+	0.0320276i
$671$	−2.74241	−	3.43887i	−0.105869	−	0.132756i
$672$	1.43516	+	0.964788i	0.0553626	+	0.0372175i
$673$	3.02984	−	3.79930i	0.116792	−	0.146452i	−0.719999	−	0.693975i	$-0.755858\pi$
$673$	3.02984	−	3.79930i	0.116792	−	0.146452i	0.836791	+	0.547523i	$0.184429\pi$
$674$	−0.383739	+	0.118368i	−0.0147811	+	0.00455936i
$675$	1.75853	+	4.48066i	0.0676859	+	0.172461i
$676$	−0.666304	+	8.89121i	−0.0256271	+	0.341970i
$677$	−5.89531	+	15.0210i	−0.226575	+	0.577304i	−0.998277	−	0.0586805i	$-0.981311\pi$
$677$	−5.89531	+	15.0210i	−0.226575	+	0.577304i	0.771702	+	0.635985i	$0.219406\pi$
$678$	−0.712993	−	0.343359i	−0.0273823	−	0.0131866i
$679$	20.8038	+	9.85146i	0.798375	+	0.378064i
$680$	4.33943	−	2.08976i	0.166409	−	0.0801386i
$681$	−0.842568	−	11.2433i	−0.0322873	−	0.430844i
$682$	0.390553	+	0.120470i	0.0149551	+	0.00461302i
$683$	12.4509	−	8.48887i	0.476420	−	0.324818i	−0.301190	−	0.953564i	$-0.597384\pi$
$683$	12.4509	−	8.48887i	0.476420	−	0.324818i	0.777610	+	0.628746i	$0.216432\pi$
$684$	10.2018	+	1.53768i	0.390077	+	0.0587947i
$685$	−1.44870			−0.0553521
$686$	0.0952971	+	1.00627i	0.00363846	+	0.0384195i
$687$	−13.0334			−0.497257
$688$	−46.7814	−	7.05116i	−1.78352	−	0.268823i
$689$	−27.7554	+	18.9233i	−1.05739	+	0.720920i
$690$	0.330088	+	0.101819i	0.0125662	+	0.00387617i
$691$	−0.818747	−	10.9254i	−0.0311466	−	0.415622i	−0.990883	−	0.134722i	$-0.956986\pi$
$691$	−0.818747	−	10.9254i	−0.0311466	−	0.415622i	0.959737	−	0.280901i	$-0.0906331\pi$
$692$	16.8536	−	8.11627i	0.640678	−	0.308534i
$693$	−8.71318	−	4.12606i	−0.330986	−	0.156736i
$694$	−1.65230	−	0.795706i	−0.0627205	−	0.0302046i
$695$	−6.73198	+	17.1528i	−0.255358	+	0.650643i
$696$	0.0305803	−	0.408066i	0.00115914	−	0.0154677i
$697$	4.56427	+	11.6296i	0.172884	+	0.440502i
$698$	−1.38458	+	0.427085i	−0.0524070	+	0.0161654i
$699$	−16.1086	+	20.1996i	−0.609285	+	0.764019i
$700$	−21.1063	−	14.1887i	−0.797743	−	0.536283i
$701$	−28.4459	−	35.6700i	−1.07439	−	1.34724i	−0.934053	−	0.357133i	$-0.883754\pi$
$701$	−28.4459	−	35.6700i	−1.07439	−	1.34724i	−0.140333	−	0.990104i	$-0.544817\pi$
$702$	0.188448	+	0.128482i	0.00711251	+	0.00484923i
$703$	−10.8549	−	10.0718i	−0.409399	−	0.379867i
$704$	14.4454	−	25.0201i	0.544430	−	0.942980i
$705$	−16.8712	−	29.2218i	−0.635406	−	1.10056i
$706$	0.355410	−	1.55715i	0.0133760	−	0.0586042i
$707$	1.92167	−	0.302513i	0.0722720	−	0.0113772i
$708$	−3.03937	−	13.3163i	−0.114226	−	0.500459i
$709$	26.0650	−	24.1848i	0.978891	−	0.908278i	−0.0169068	−	0.999857i	$-0.505382\pi$
$709$	26.0650	−	24.1848i	0.978891	−	0.908278i	0.995798	+	0.0915789i	$0.0291914\pi$
$710$	0.115938	−	0.0174749i	0.00435108	−	0.000655820i
$711$	−5.45518	+	0.822237i	−0.204585	+	0.0308363i
$712$	1.64400	−	1.52541i	0.0616114	−	0.0571670i
$713$	0.923999	+	4.04830i	0.0346040	+	0.151610i
$714$	0.750548	+	0.687327i	0.0280886	+	0.0257225i
$715$	10.6151	−	46.5077i	0.396981	−	1.73929i
$716$	22.2352	+	38.5125i	0.830969	+	1.43928i
$717$	−10.2638	+	17.7774i	−0.383308	+	0.663909i
$718$	0.548168	+	0.508626i	0.0204574	+	0.0189817i
$719$	−26.9470	−	18.3722i	−1.00495	−	0.685166i	−0.0553014	−	0.998470i	$-0.517612\pi$
$719$	−26.9470	−	18.3722i	−1.00495	−	0.685166i	−0.949653	+	0.313303i	$0.898564\pi$
$720$	−7.77777	−	9.75302i	−0.289860	−	0.363474i
$721$	14.4859	−	37.6314i	0.539484	−	1.40147i
$722$	0.261672	−	0.328127i	0.00973843	−	0.0122116i
$723$	−19.3317	+	5.96303i	−0.718952	+	0.221767i
$724$	16.3710	+	41.7127i	0.608424	+	1.55024i
$725$	−0.674763	+	9.00409i	−0.0250601	+	0.334404i
$726$	0.0454153	−	0.115716i	0.00168552	−	0.00429463i
$727$	−23.2666	−	11.2046i	−0.862910	−	0.415555i	−0.0505564	−	0.998721i	$-0.516099\pi$
$727$	−23.2666	−	11.2046i	−0.862910	−	0.415555i	−0.812353	+	0.583166i	$0.801814\pi$
$728$	−2.41192	+	0.0157758i	−0.0893916	+	0.000584691i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	0.112795	+	1.50514i	0.00417471	+	0.0557077i
$731$	−80.0147	−	24.6813i	−2.95945	−	0.912870i
$732$	1.99172	−	1.35793i	0.0736162	−	0.0501907i
$733$	12.6661	+	1.90910i	0.467832	+	0.0705143i	0.378728	−	0.925508i	$-0.376362\pi$
$733$	12.6661	+	1.90910i	0.467832	+	0.0705143i	0.0891038	+	0.996022i	$0.471600\pi$
$734$	−0.0158793			−0.000586116
$735$	4.59946	−	21.4406i	0.169654	−	0.790850i
$736$	−1.32061			−0.0486783
$737$	31.0153	+	4.67480i	1.14246	+	0.172198i
$738$	−0.0799306	+	0.0544957i	−0.00294229	+	0.00200602i
$739$	−10.2067	−	3.14836i	−0.375461	−	0.115814i	0.101280	−	0.994858i	$-0.467706\pi$
$739$	−10.2067	−	3.14836i	−0.375461	−	0.115814i	−0.476742	+	0.879043i	$0.658182\pi$
$740$	1.34000	+	17.8810i	0.0492593	+	0.657320i
$741$	−19.4520	+	9.36759i	−0.714587	+	0.344127i
$742$	−0.729596	−	0.902708i	−0.0267843	−	0.0331395i
$743$	16.0697	+	7.73874i	0.589538	+	0.283907i	0.704775	−	0.709431i	$-0.251048\pi$
$743$	16.0697	+	7.73874i	0.589538	+	0.283907i	−0.115236	+	0.993338i	$0.536762\pi$
$744$	−0.163791	+	0.417332i	−0.00600487	+	0.0153002i
$745$	−0.440494	+	5.87799i	−0.0161385	+	0.215353i
$746$	−0.125686	−	0.320242i	−0.00460168	−	0.0117249i
$747$	4.02184	−	1.24057i	0.147151	−	0.0453902i
$748$	31.9775	−	40.0985i	1.16921	−	1.46615i
$749$	21.2697	−	19.9959i	0.777178	−	0.730634i
$750$	0.0198914	+	0.0249430i	0.000726330	+	0.000910789i
$751$	−26.5121	−	18.0757i	−0.967442	−	0.659591i	−0.0270322	−	0.999635i	$-0.508606\pi$
$751$	−26.5121	−	18.0757i	−0.967442	−	0.659591i	−0.940410	+	0.340044i	$0.889558\pi$
$752$	31.4425	+	29.1744i	1.14659	+	1.06388i
$753$	1.93114	−	3.34483i	0.0703745	−	0.121892i
$754$	0.213924	+	0.370528i	0.00779067	+	0.0134938i
$755$	2.24087	−	9.81788i	0.0815535	−	0.357309i
$756$	2.61183	−	4.59293i	0.0949912	−	0.167043i
$757$	1.47805	+	6.47576i	0.0537206	+	0.235365i	0.994659	−	0.103211i	$-0.0329117\pi$
$757$	1.47805	+	6.47576i	0.0537206	+	0.235365i	−0.940939	+	0.338577i	$0.890055\pi$
$758$	0.315724	−	0.292949i	0.0114676	−	0.0106404i
$759$	7.28005	−	1.09729i	0.264249	−	0.0398292i
$760$	−3.49098	+	0.526180i	−0.126631	+	0.0190866i
$761$	−38.8169	+	36.0168i	−1.40711	+	1.30561i	−0.512551	+	0.858657i	$0.671299\pi$
$761$	−38.8169	+	36.0168i	−1.40711	+	1.30561i	−0.894559	+	0.446950i	$0.852510\pi$
$762$	−0.163699	−	0.717213i	−0.00593019	−	0.0259819i
$763$	2.26735	−	33.1652i	0.0820835	−	1.20066i
$764$	−0.654498	+	2.86754i	−0.0236789	+	0.103744i
$765$	−11.0395	−	19.1210i	−0.399135	−	0.691323i
$766$	−0.434193	+	0.752044i	−0.0156880	+	0.0271725i
$767$	20.9530	+	19.4415i	0.756567	+	0.701992i
$768$	13.0234	+	8.87919i	0.469941	+	0.320400i
$769$	−14.4964	−	18.1779i	−0.522752	−	0.655511i	0.448438	−	0.893814i	$-0.351980\pi$
$769$	−14.4964	−	18.1779i	−0.522752	−	0.655511i	−0.971191	+	0.238303i	$0.923409\pi$
$770$	1.63142	+	0.234995i	0.0587924	+	0.00846862i
$771$	7.22219	−	9.05634i	0.260101	−	0.326156i
$772$	−3.50696	+	1.08175i	−0.126218	+	0.0389332i
$773$	−15.7117	−	40.0329i	−0.565112	−	1.43988i	−0.872650	−	0.488346i	$-0.837600\pi$
$773$	−15.7117	−	40.0329i	−0.565112	−	1.43988i	0.307538	−	0.951536i	$-0.400495\pi$
$774$	0.0484547	−	0.646583i	0.00174167	−	0.0232410i
$775$	3.61410	−	9.20857i	0.129822	−	0.330781i
$776$	−1.70993	−	0.823459i	−0.0613829	−	0.0295604i
$777$	−6.81076	+	3.33494i	−0.244335	+	0.119640i
$778$	0.629654	−	0.303225i	0.0225742	−	0.0108712i
$779$	−0.684339	−	9.13187i	−0.0245190	−	0.327183i
$780$	24.9826	+	7.70610i	0.894519	+	0.275923i
$781$	2.06470	−	1.40769i	0.0738807	−	0.0503710i
$782$	−0.768510	−	0.115834i	−0.0274819	−	0.00414222i
$783$	−1.87588			−0.0670384
$784$	2.44653	+	27.7674i	0.0873762	+	0.991692i
$785$	−12.5183			−0.446798
$786$	−0.157777	−	0.0237811i	−0.00562773	−	0.000848243i
$787$	−11.0140	+	7.50922i	−0.392607	+	0.267675i	−0.743494	−	0.668743i	$-0.766833\pi$
$787$	−11.0140	+	7.50922i	−0.392607	+	0.267675i	0.350887	+	0.936418i	$0.385880\pi$
$788$	−37.4806	−	11.5612i	−1.33519	−	0.411851i
$789$	1.59477	+	21.2807i	0.0567752	+	0.757613i
$790$	0.849791	−	0.409238i	0.0302342	−	0.0145600i
$791$	−8.78115	−	37.3451i	−0.312222	−	1.32784i
$792$	0.716165	+	0.344887i	0.0254478	+	0.0122550i
$793$	−1.84298	+	4.69583i	−0.0654460	+	0.166754i
$794$	−0.0304551	+	0.406395i	−0.00108081	+	0.0144224i
$795$	9.19959	+	23.4402i	0.326276	+	0.831337i
$796$	−31.9849	+	9.86603i	−1.13367	+	0.349692i
$797$	3.27047	−	4.10104i	0.115846	−	0.145266i	−0.720527	−	0.693427i	$-0.756100\pi$
$797$	3.27047	−	4.10104i	0.115846	−	0.145266i	0.836373	+	0.548160i	$0.184672\pi$
$798$	−0.377208	−	0.643586i	−0.0133530	−	0.0227827i
$799$	47.3333	+	59.3541i	1.67453	+	2.09980i
$800$	2.59945	+	1.77227i	0.0919043	+	0.0626593i
$801$	−7.53631	−	6.99268i	−0.266283	−	0.247074i
$802$	−0.776131	+	1.34430i	−0.0274061	+	0.0474688i
$803$	16.0846	+	27.8593i	0.567612	+	0.983132i
$804$	−3.82513	+	16.7590i	−0.134902	+	0.591043i
$805$	6.21981	+	15.5480i	0.219219	+	0.547996i
$806$	−0.104305	−	0.456992i	−0.00367400	−	0.0160968i
$807$	8.89492	−	8.25328i	0.313116	−	0.290529i
$808$	−0.158603	+	0.0239055i	−0.00557962	+	0.000840992i
$809$	21.3732	−	3.22150i	0.751443	−	0.113262i	0.237857	−	0.971300i	$-0.423555\pi$
$809$	21.3732	−	3.22150i	0.751443	−	0.113262i	0.513586	+	0.858038i	$0.328317\pi$
$810$	0.125328	−	0.116288i	0.00440359	−	0.00408594i
$811$	3.33132	+	14.5955i	0.116978	+	0.512516i	0.999136	+	0.0415615i	$0.0132332\pi$
$811$	3.33132	+	14.5955i	0.116978	+	0.512516i	−0.882158	+	0.470954i	$0.843910\pi$
$812$	8.15251	−	5.63675i	0.286097	−	0.197811i
$813$	3.17023	−	13.8897i	0.111185	−	0.487133i
$814$	−0.285005	−	0.493644i	−0.00998943	−	0.0173022i
$815$	2.83755	−	4.91478i	0.0993951	−	0.172157i
$816$	20.5742	+	19.0900i	0.720240	+	0.668285i
$817$	50.7124	+	34.5752i	1.77420	+	1.20963i
$818$	−0.391440	−	0.490850i	−0.0136864	−	0.0171622i
$819$	0.898375	+	11.0203i	0.0313918	+	0.385079i
$820$	−6.91391	+	8.66977i	−0.241444	+	0.302762i
$821$	47.4227	−	14.6280i	1.65506	−	0.510519i	0.680144	−	0.733078i	$-0.261917\pi$
$821$	47.4227	−	14.6280i	1.65506	−	0.510519i	0.974919	+	0.222559i	$0.0714410\pi$
$822$	0.00922090	+	0.0234945i	0.000321616	+	0.000819464i
$823$	2.43607	−	32.5071i	0.0849162	−	1.13313i	−0.778164	−	0.628061i	$-0.783849\pi$
$823$	2.43607	−	32.5071i	0.0849162	−	1.13313i	0.863080	−	0.505067i	$-0.168532\pi$
$824$	−1.21464	+	3.09485i	−0.0423139	+	0.107814i
$825$	−15.8024	−	7.61003i	−0.550169	−	0.264947i
$826$	−0.610699	+	0.776153i	−0.0212489	+	0.0270058i
$827$	−23.0516	+	11.1011i	−0.801584	+	0.386022i	−0.789381	−	0.613903i	$-0.789599\pi$
$827$	−23.0516	+	11.1011i	−0.801584	+	0.386022i	−0.0122024	+	0.999926i	$0.503884\pi$
$828$	0.301529	+	4.02363i	0.0104789	+	0.139831i
$829$	−31.7103	−	9.78132i	−1.10134	−	0.339719i	−0.309781	−	0.950808i	$-0.600256\pi$
$829$	−31.7103	−	9.78132i	−1.10134	−	0.339719i	−0.791562	+	0.611088i	$0.790732\pi$
$830$	−0.594541	+	0.405351i	−0.0206368	+	0.0140699i
$831$	−12.0307	−	1.81334i	−0.417342	−	0.0629042i
$832$	−33.1343			−1.14872
$833$	−3.04305	+	49.2427i	−0.105435	+	1.70616i
$834$	0.321026			0.0111162
$835$	77.8808	+	11.7386i	2.69518	+	0.406232i
$836$	−31.0616	+	21.1774i	−1.07429	+	0.732437i
$837$	1.96387	+	0.605775i	0.0678814	+	0.0209386i
$838$	0.0240315	+	0.320679i	0.000830156	+	0.0110777i
$839$	−30.4723	+	14.6747i	−1.05202	+	0.506627i	−0.878271	−	0.478163i	$-0.841303\pi$
$839$	−30.4723	+	14.6747i	−1.05202	+	0.506627i	−0.173750	+	0.984790i	$0.555589\pi$
$840$	−0.390782	+	1.76527i	−0.0134833	+	0.0609077i
$841$	22.9577	+	11.0558i	0.791644	+	0.381235i
$842$	0.771217	−	1.96503i	0.0265779	−	0.0677194i
$843$	−0.422939	+	5.64373i	−0.0145668	+	0.194380i
$844$	2.80437	+	7.14541i	0.0965303	+	0.245955i
$845$	−13.3650	+	4.12255i	−0.459769	+	0.141820i
$846$	−0.366523	+	0.459605i	−0.0126013	+	0.0158015i
$847$	5.74678	−	1.81389i	0.197462	−	0.0623261i
$848$	−19.9575	−	25.0259i	−0.685343	−	0.859393i
$849$	8.60032	+	5.86360i	0.295162	+	0.201238i
$850$	1.35726	+	1.25935i	0.0465536	+	0.0431954i
$851$	2.89559	−	5.01531i	0.0992596	−	0.171923i
$852$	0.684766	+	1.18605i	0.0234597	+	0.0406334i
$853$	9.11687	−	39.9436i	0.312156	−	1.36764i	−0.538812	−	0.842426i	$-0.681127\pi$
$853$	9.11687	−	39.9436i	0.312156	−	1.36764i	0.850968	−	0.525217i	$-0.176016\pi$
$854$	−0.166888	−	0.0502851i	−0.00571079	−	0.00172072i
$855$	3.60126	+	15.7781i	0.123160	+	0.539601i
$856$	−1.76444	+	1.63716i	−0.0603074	+	0.0559571i
$857$	35.5640	−	5.36040i	1.21484	−	0.183108i	0.489813	−	0.871827i	$-0.337065\pi$
$857$	35.5640	−	5.36040i	1.21484	−	0.183108i	0.725028	+	0.688719i	$0.241827\pi$
$858$	−0.821807	+	0.123867i	−0.0280560	+	0.00422876i
$859$	−34.7005	+	32.1974i	−1.18397	+	1.09856i	−0.190826	+	0.981624i	$0.561117\pi$
$859$	−34.7005	+	32.1974i	−1.18397	+	1.09856i	−0.993139	+	0.116936i	$0.962693\pi$
$860$	−16.5386	−	72.4603i	−0.563961	−	2.47088i
$861$	−4.49036	−	1.35299i	−0.153031	−	0.0461098i
$862$	−0.121797	+	0.533627i	−0.00414841	+	0.0181754i
$863$	−18.2547	−	31.6181i	−0.621398	−	1.07629i	−0.989226	−	0.146399i	$-0.953232\pi$
$863$	−18.2547	−	31.6181i	−0.621398	−	1.07629i	0.367828	−	0.929894i	$-0.380102\pi$
$864$	−0.326809	+	0.566049i	−0.0111183	+	0.0192574i
$865$	21.5102	+	19.9586i	0.731369	+	0.678611i
$866$	1.33503	+	0.910210i	0.0453663	+	0.0309302i
$867$	20.3728	+	25.5467i	0.691898	+	0.867613i
$868$	−10.3552	+	3.26848i	−0.351479	+	0.110940i
$869$	12.5337	−	15.7167i	0.425176	−	0.533153i
$870$	0.306467	−	0.0945324i	0.0103902	−	0.00320495i
$871$	−13.1423	−	33.4860i	−0.445310	−	1.13463i
$872$	−0.204825	+	2.73320i	−0.00693625	+	0.0925578i
$873$	−3.17852	+	8.09874i	−0.107577	+	0.274101i
$874$	0.513263	+	0.247174i	0.0173614	+	0.00836080i
$875$	−0.334282	+	1.51005i	−0.0113008	+	0.0510489i
$876$	−15.8844	+	7.64951i	−0.536683	+	0.258453i
$877$	2.49581	+	33.3043i	0.0842775	+	1.12461i	0.865687	+	0.500586i	$0.166882\pi$
$877$	2.49581	+	33.3043i	0.0842775	+	1.12461i	−0.781409	+	0.624019i	$0.785499\pi$
$878$	0.0528330	+	0.0162968i	0.00178303	+	0.000549991i
$879$	4.95811	−	3.38038i	0.167233	−	0.114017i
$880$	44.9479	+	6.77481i	1.51519	+	0.228379i
$881$	−1.62805			−0.0548505			−0.0274253	−	0.999624i	$-0.508731\pi$
$881$	−1.62805			−0.0548505			−0.0274253	+	0.999624i	$0.508731\pi$
$882$	−0.376991	+	0.0618761i	−0.0126939	+	0.00208348i
$883$	11.1297			0.374543			0.187272	−	0.982308i	$-0.440036\pi$
$883$	11.1297			0.374543			0.187272	+	0.982308i	$0.440036\pi$
$884$	−58.1643	−	8.76686i	−1.95628	−	0.294861i
$885$	17.7029	−	12.0696i	0.595077	−	0.405717i
$886$	−0.361185	−	0.111411i	−0.0121343	−	0.00374292i
$887$	1.58004	+	21.0842i	0.0530525	+	0.707937i	0.958793	+	0.284105i	$0.0916963\pi$
$887$	1.58004	+	21.0842i	0.0530525	+	0.707937i	−0.905741	+	0.423832i	$0.860685\pi$
$888$	0.563336	−	0.271288i	0.0189043	−	0.00910384i
$889$	22.0527	−	28.0274i	0.739625	−	0.940008i
$890$	1.58361	+	0.762628i	0.0530828	+	0.0255633i
$891$	1.33125	−	3.39197i	0.0445986	−	0.113635i
$892$	−1.00326	+	13.3876i	−0.0335917	+	0.448251i
$893$	−20.3300	−	51.8001i	−0.680319	−	1.73342i
$894$	0.0981305	−	0.0302693i	0.00328197	−	0.00101236i
$895$	−43.4938	+	54.5395i	−1.45384	+	1.82306i
$896$	−0.374036	−	4.58825i	−0.0124957	−	0.153283i
$897$	−5.26455	−	6.60154i	−0.175778	−	0.220419i
$898$	1.58597	+	1.08129i	0.0529244	+	0.0360833i
$899$	2.82611	+	2.62224i	0.0942560	+	0.0874567i
$900$	4.80623	−	8.32463i	0.160208	−	0.277488i
$901$	−28.3271	−	49.0639i	−0.943711	−	1.63456i
$902$	0.0784404	−	0.343670i	0.00261178	−	0.0114430i
$903$	25.8547	−	17.8763i	0.860390	−	0.594885i
$904$	0.703854	+	3.08379i	0.0234098	+	0.102565i
$905$	−51.5275	+	47.8105i	−1.71283	+	1.58928i
$906$	−0.173485	+	0.0261487i	−0.00576366	+	0.000868733i
$907$	−49.4012	+	7.44603i	−1.64034	+	0.247241i	−0.903425	−	0.428745i	$-0.858956\pi$
$907$	−49.4012	+	7.44603i	−1.64034	+	0.247241i	−0.736914	+	0.675987i	$0.763718\pi$
$908$	−16.5054	+	15.3148i	−0.547752	+	0.508239i
$909$	0.163613	+	0.716835i	0.00542670	+	0.0237759i
$910$	−0.702121	−	1.75513i	−0.0232751	−	0.0581821i
$911$	−0.952407	+	4.17277i	−0.0315547	+	0.138250i	−0.988252	−	0.152836i	$-0.951159\pi$
$911$	−0.952407	+	4.17277i	−0.0315547	+	0.138250i	0.956697	+	0.291086i	$0.0940166\pi$
$912$	−10.2863	−	17.8164i	−0.340614	−	0.589961i
$913$	−7.66819	+	13.2817i	−0.253780	+	0.439560i
$914$	−0.751555	−	0.697341i	−0.0248592	−	0.0230660i
$915$	3.12432	+	2.13013i	0.103287	+	0.0704198i
$916$	16.2282	+	20.3496i	0.536196	+	0.672368i
$917$	−3.91128	−	6.67335i	−0.129162	−	0.220374i
$918$	−0.239831	+	0.300739i	−0.00791561	+	0.00992586i
$919$	−35.3356	+	10.8996i	−1.16561	+	0.359544i	−0.816393	−	0.577496i	$-0.804030\pi$
$919$	−35.3356	+	10.8996i	−1.16561	+	0.359544i	−0.349221	+	0.937041i	$0.613554\pi$
$920$	−0.504430	−	1.28527i	−0.0166306	−	0.0423740i
$921$	0.565000	−	7.53941i	0.0186174	−	0.248432i
$922$	−0.378687	+	0.964879i	−0.0124714	+	0.0317766i
$923$	−2.58214	−	1.24349i	−0.0849922	−	0.0409301i
$924$	4.40682	+	18.7416i	0.144974	+	0.616555i
$925$	−12.4302	+	5.98606i	−0.408702	+	0.196820i
$926$	0.115778	+	1.54496i	0.00380472	+	0.0507704i
$927$	14.5637	+	4.49229i	0.478333	+	0.147546i
$928$	−1.01306	+	0.690690i	−0.0332552	+	0.0226730i
$929$	34.1641	+	5.14940i	1.12089	+	0.168946i	0.683235	−	0.730198i	$-0.260572\pi$
$929$	34.1641	+	5.14940i	1.12089	+	0.168946i	0.437651	+	0.899145i	$0.355810\pi$
$930$	−0.351370			−0.0115219
$931$	12.7706	−	33.8337i	0.418538	−	1.10885i
$932$	51.5956			1.69007
$933$	−11.8177	−	1.78123i	−0.386893	−	0.0583148i
$934$	−0.391864	+	0.267169i	−0.0128222	+	0.00874202i
$935$	76.8787	+	23.7139i	2.51420	+	0.775529i
$936$	−0.0681268	−	0.909089i	−0.00222679	−	0.0297145i
$937$	−5.75905	+	2.77341i	−0.188140	+	0.0906035i	−0.525582	−	0.850743i	$-0.676153\pi$
$937$	−5.75905	+	2.77341i	−0.188140	+	0.0906035i	0.337442	+	0.941346i	$0.390438\pi$
$938$	1.11629	−	0.546600i	0.0364481	−	0.0178471i
$939$	8.60270	+	4.14284i	0.280739	+	0.135197i
$940$	−24.6182	+	62.7262i	−0.802958	+	2.04590i
$941$	1.41592	−	18.8942i	0.0461578	−	0.615933i	−0.925379	−	0.379044i	$-0.876253\pi$
$941$	1.41592	−	18.8942i	0.0461578	−	0.615933i	0.971537	−	0.236890i	$-0.0761279\pi$
$942$	0.0796783	+	0.203017i	0.00259606	+	0.00661465i
$943$	3.42229	−	1.05564i	0.111445	−	0.0343763i
$944$	−16.9815	+	21.2941i	−0.552700	+	0.693064i
$945$	8.20350	+	1.18166i	0.266860	+	0.0384393i
$946$	1.47310	+	1.84721i	0.0478945	+	0.0600578i
$947$	−15.0261	−	10.2446i	−0.488283	−	0.332905i	0.294025	−	0.955798i	$-0.405005\pi$
$947$	−15.0261	−	10.2446i	−0.488283	−	0.332905i	−0.782308	+	0.622892i	$0.785957\pi$
$948$	8.07616	+	7.49358i	0.262301	+	0.243380i
$949$	18.4471	−	31.9513i	0.598819	−	1.03718i
$950$	−0.678580	−	1.17533i	−0.0220160	−	0.0381329i
$951$	−3.16121	+	13.8502i	−0.102509	+	0.449122i
$952$	0.277450	−	4.05835i	0.00899222	−	0.131532i
$953$	10.9998	+	48.1934i	0.356319	+	1.56114i	0.762280	+	0.647247i	$0.224080\pi$
$953$	10.9998	+	48.1934i	0.356319	+	1.56114i	−0.405961	+	0.913890i	$0.633063\pi$
$954$	0.321588	−	0.298390i	0.0104118	−	0.00966075i
$955$	−4.56232	+	0.687660i	−0.147633	+	0.0222521i
$956$	40.5361	−	6.10984i	1.31103	−	0.197606i
$957$	5.01073	−	4.64927i	0.161974	−	0.150290i
$958$	−0.0771942	−	0.338210i	−0.00249403	−	0.0109271i
$959$	−0.604827	+	1.06360i	−0.0195309	+	0.0343453i
$960$	−5.52684	+	24.2147i	−0.178378	+	0.781526i
$961$	13.3881	+	23.1889i	0.431875	+	0.748029i
$962$	−0.326868	+	0.566152i	−0.0105386	+	0.0182535i
$963$	8.08845	+	7.50499i	0.260647	+	0.241845i
$964$	33.3806	+	22.7585i	1.07512	+	0.733002i
$965$	−3.58941	−	4.50098i	−0.115547	−	0.144892i
$966$	0.212563	−	0.199832i	0.00683909	−	0.00642950i
$967$	−17.4747	+	21.9126i	−0.561949	+	0.704662i	−0.978917	−	0.204260i	$-0.934521\pi$
$967$	−17.4747	+	21.9126i	−0.561949	+	0.704662i	0.416968	+	0.908921i	$0.363093\pi$
$968$	−0.474792	+	0.146454i	−0.0152604	+	0.00470721i
$969$	−13.3028	−	33.8950i	−0.427348	−	1.08886i
$970$	0.111157	−	1.48329i	0.00356904	−	0.0476255i
$971$	15.2847	−	38.9448i	0.490509	−	1.24980i	−0.444693	−	0.895683i	$-0.646687\pi$
$971$	15.2847	−	38.9448i	0.490509	−	1.24980i	0.935202	−	0.354114i	$-0.115218\pi$
$972$	1.79925	+	0.866475i	0.0577111	+	0.0277922i
$973$	9.78253	+	12.1036i	0.313613	+	0.388025i
$974$	−0.467890	+	0.225324i	−0.0149922	+	0.00721985i
$975$	1.50324	+	20.0593i	0.0481422	+	0.642413i
$976$	−4.59326	−	1.41683i	−0.147027	−	0.0453517i
$977$	19.3849	−	13.2164i	0.620179	−	0.422831i	−0.212053	−	0.977258i	$-0.568015\pi$
$977$	19.3849	−	13.2164i	0.620179	−	0.422831i	0.832232	+	0.554427i	$0.187063\pi$
$978$	−0.0977668	−	0.0147360i	−0.00312624	−	0.000471204i
$979$	37.4616			1.19728
$980$	−39.2029	+	19.5149i	−1.25229	+	0.623382i
$981$	12.5645			0.401154
$982$	1.65440	+	0.249360i	0.0527940	+	0.00795741i
$983$	37.6494	−	25.6689i	1.20083	−	0.818711i	0.213430	−	0.976958i	$-0.431537\pi$
$983$	37.6494	−	25.6689i	1.20083	−	0.818711i	0.987400	+	0.158247i	$0.0505842\pi$
$984$	0.369494	+	0.113974i	0.0117790	+	0.00363335i
$985$	−4.59795	−	61.3554i	−0.146503	−	1.95495i
$986$	−0.650116	+	0.313079i	−0.0207039	+	0.00997047i
$987$	−28.4974	+	0.186396i	−0.907083	+	0.00593304i
$988$	38.8461	+	18.7073i	1.23586	+	0.595158i
$989$	−8.76970	+	22.3448i	−0.278860	+	0.710524i
$990$	−0.0465556	+	0.621242i	−0.00147963	+	0.0197444i
$991$	6.43100	+	16.3859i	0.204287	+	0.520516i	0.995895	−	0.0905137i	$-0.0288509\pi$
$991$	6.43100	+	16.3859i	0.204287	+	0.520516i	−0.791608	+	0.611030i	$0.790756\pi$
$992$	1.28362	−	0.395945i	0.0407550	−	0.0125713i
$993$	9.24106	−	11.5879i	0.293256	−	0.367732i
$994$	0.0355741	−	0.0924141i	0.00112834	−	0.00293120i
$995$	−32.7369	−	41.0507i	−1.03783	−	1.30140i
$996$	−6.94463	−	4.73477i	−0.220049	−	0.150027i
$997$	−41.4463	−	38.4566i	−1.31262	−	1.21793i	−0.959287	−	0.282433i	$-0.908858\pi$
$997$	−41.4463	−	38.4566i	−1.31262	−	1.21793i	−0.353331	−	0.935498i	$-0.614951\pi$
$998$	−0.328747	+	0.569407i	−0.0104063	+	0.0180243i
$999$	−1.43313	−	2.48226i	−0.0453423	−	0.0785351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.m.b.88.3	✓	60
3.2	odd	2		441.2.bb.e.235.3		60
49.17	odd	42		7203.2.a.m.1.15		30
49.32	even	21		7203.2.a.n.1.15		30
49.44	even	21	inner	147.2.m.b.142.3	yes	60
147.44	odd	42		441.2.bb.e.289.3		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.88.3	✓	60	1.1	even	1	trivial
147.2.m.b.142.3	yes	60	49.44	even	21	inner
441.2.bb.e.235.3		60	3.2	odd	2
441.2.bb.e.289.3		60	147.44	odd	42
7203.2.a.m.1.15		30	49.17	odd	42
7203.2.a.n.1.15		30	49.32	even	21

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0539669 - 0.00813420i) q^{2} +(0.826239 - 0.563320i) q^{3} +(-1.90830 - 0.588632i) q^{4} +(-0.234102 - 3.12387i) q^{5} +(-0.0491717 + 0.0236798i) q^{6} +(-2.39120 - 1.13233i) q^{7} +(0.196540 + 0.0946488i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})\)	\(q+(-0.0539669 - 0.00813420i) q^{2} +(0.826239 - 0.563320i) q^{3} +(-1.90830 - 0.588632i) q^{4} +(-0.234102 - 3.12387i) q^{5} +(-0.0491717 + 0.0236798i) q^{6} +(-2.39120 - 1.13233i) q^{7} +(0.196540 + 0.0946488i) q^{8} +(0.365341 - 0.930874i) q^{9} +(-0.0127765 + 0.170490i) q^{10} +(1.33125 + 3.39197i) q^{11} +(-1.90830 + 0.588632i) q^{12} +(2.60561 - 3.26734i) q^{13} +(0.119835 + 0.0805589i) q^{14} +(-1.95317 - 2.44919i) q^{15} +(3.29020 + 2.24322i) q^{16} +(5.16661 + 4.79392i) q^{17} +(-0.0272882 + 0.0472646i) q^{18} +(-2.58312 - 4.47409i) q^{19} +(-1.39208 + 6.09909i) q^{20} +(-2.61357 + 0.411432i) q^{21} +(-0.0442525 - 0.193883i) q^{22} +(1.48110 - 1.37426i) q^{23} +(0.215707 - 0.0325126i) q^{24} +(-4.75963 + 0.717399i) q^{25} +(-0.167194 + 0.155133i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(3.89659 + 3.56837i) q^{28} +(0.417422 - 1.82884i) q^{29} +(0.0854840 + 0.148063i) q^{30} +(-1.02759 + 1.77984i) q^{31} +(-0.479136 - 0.444573i) q^{32} +(3.01070 + 2.05266i) q^{33} +(-0.239831 - 0.300739i) q^{34} +(-2.97748 + 7.73488i) q^{35} +(-1.24512 + 1.56133i) q^{36} +(2.73892 - 0.844846i) q^{37} +(0.103010 + 0.262464i) q^{38} +(0.312303 - 4.16740i) q^{39} +(0.249661 - 0.636125i) q^{40} +(1.59703 + 0.769087i) q^{41} +(0.144393 - 0.000944441i) q^{42} +(-10.7040 + 5.15476i) q^{43} +(-0.543801 - 7.25652i) q^{44} +(-2.99346 - 0.923360i) q^{45} +(-0.0911091 + 0.0621172i) q^{46} +(10.6509 + 1.60537i) q^{47} +3.98214 q^{48} +(4.43565 + 5.41526i) q^{49} +0.262698 q^{50} +(6.96936 + 1.05046i) q^{51} +(-6.89555 + 4.70131i) q^{52} +(-7.68111 - 2.36931i) q^{53} +(0.00407850 + 0.0544238i) q^{54} +(10.2844 - 4.95273i) q^{55} +(-0.362793 - 0.448873i) q^{56} +(-4.65461 - 2.24154i) q^{57} +(-0.0374031 + 0.0953017i) q^{58} +(-0.511123 + 6.82046i) q^{59} +(2.28555 + 5.82349i) q^{60} +(-1.15347 + 0.355797i) q^{61} +(0.0699333 - 0.0876936i) q^{62} +(-1.92766 + 1.81221i) q^{63} +(-4.94340 - 6.19883i) q^{64} +(-10.8167 - 7.37472i) q^{65} +(-0.145781 - 0.135265i) q^{66} +(4.30390 - 7.45457i) q^{67} +(-7.03759 - 12.1895i) q^{68} +(0.449595 - 1.96981i) q^{69} +(0.223602 - 0.393208i) q^{70} +(-0.152602 - 0.668593i) q^{71} +(0.159910 - 0.148375i) q^{72} +(8.72971 - 1.31579i) q^{73} +(-0.154683 + 0.0233148i) q^{74} +(-3.52847 + 3.27394i) q^{75} +(2.29576 + 10.0584i) q^{76} +(0.657558 - 9.61829i) q^{77} +(-0.0507525 + 0.222361i) q^{78} +(-2.75840 - 4.77769i) q^{79} +(6.23729 - 10.8033i) q^{80} +(-0.733052 - 0.680173i) q^{81} +(-0.0799306 - 0.0544957i) q^{82} +(2.62416 + 3.29059i) q^{83} +(5.22965 + 0.753294i) q^{84} +(13.7661 - 17.2621i) q^{85} +(0.619590 - 0.191118i) q^{86} +(-0.685335 - 1.74620i) q^{87} +(-0.0594017 + 0.792661i) q^{88} +(3.75598 - 9.57007i) q^{89} +(0.154037 + 0.0741803i) q^{90} +(-9.93025 + 4.86242i) q^{91} +(-3.63533 + 1.75068i) q^{92} +(0.153584 + 2.04943i) q^{93} +(-0.561740 - 0.173274i) q^{94} +(-13.3718 + 9.11672i) q^{95} +(-0.646317 - 0.0974166i) q^{96} -8.70015 q^{97} +(-0.195329 - 0.328325i) q^{98} +3.64386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9} - 34 q^{10} - 11 q^{11} + 5 q^{12} - 2 q^{13} + 40 q^{14} - 3 q^{15} - 31 q^{16} - 9 q^{17} - 6 q^{18} - 29 q^{19} - 43 q^{20} - 11 q^{21} + 9 q^{22} - 4 q^{23} - 24 q^{24} + 55 q^{25} + 36 q^{26} - 10 q^{27} - 57 q^{28} + 4 q^{29} - 20 q^{30} - 39 q^{31} - 92 q^{32} - 18 q^{33} - 36 q^{34} - 33 q^{35} - 10 q^{36} - 24 q^{37} + 118 q^{38} - 6 q^{39} + 35 q^{41} + 38 q^{42} + 2 q^{43} + 40 q^{44} + 12 q^{45} - 40 q^{46} - 5 q^{47} + 76 q^{48} + 129 q^{49} - 176 q^{50} + 54 q^{51} - 6 q^{52} + 26 q^{53} + q^{54} + 2 q^{55} + 63 q^{56} - 12 q^{57} + 11 q^{58} - 41 q^{59} + 32 q^{60} + 6 q^{61} + 36 q^{62} - q^{63} + 74 q^{64} - 51 q^{65} - 15 q^{66} - 55 q^{67} - 22 q^{68} + 8 q^{69} - 68 q^{70} - 66 q^{71} - 24 q^{72} + 24 q^{73} + 28 q^{74} + 41 q^{75} + 3 q^{76} - 34 q^{77} - 30 q^{78} - 51 q^{79} - 5 q^{80} + 5 q^{81} - 41 q^{82} + 30 q^{83} - 30 q^{84} + 68 q^{85} + 110 q^{86} + 19 q^{87} + 129 q^{88} + 75 q^{89} - 16 q^{90} + 5 q^{91} - 4 q^{93} + 38 q^{94} + 36 q^{95} - 57 q^{96} - 168 q^{97} + 227 q^{98} + 36 q^{99}+O(q^{100}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9 - 34 * q^10 - 11 * q^11 + 5 * q^12 - 2 * q^13 + 40 * q^14 - 3 * q^15 - 31 * q^16 - 9 * q^17 - 6 * q^18 - 29 * q^19 - 43 * q^20 - 11 * q^21 + 9 * q^22 - 4 * q^23 - 24 * q^24 + 55 * q^25 + 36 * q^26 - 10 * q^27 - 57 * q^28 + 4 * q^29 - 20 * q^30 - 39 * q^31 - 92 * q^32 - 18 * q^33 - 36 * q^34 - 33 * q^35 - 10 * q^36 - 24 * q^37 + 118 * q^38 - 6 * q^39 + 35 * q^41 + 38 * q^42 + 2 * q^43 + 40 * q^44 + 12 * q^45 - 40 * q^46 - 5 * q^47 + 76 * q^48 + 129 * q^49 - 176 * q^50 + 54 * q^51 - 6 * q^52 + 26 * q^53 + q^54 + 2 * q^55 + 63 * q^56 - 12 * q^57 + 11 * q^58 - 41 * q^59 + 32 * q^60 + 6 * q^61 + 36 * q^62 - q^63 + 74 * q^64 - 51 * q^65 - 15 * q^66 - 55 * q^67 - 22 * q^68 + 8 * q^69 - 68 * q^70 - 66 * q^71 - 24 * q^72 + 24 * q^73 + 28 * q^74 + 41 * q^75 + 3 * q^76 - 34 * q^77 - 30 * q^78 - 51 * q^79 - 5 * q^80 + 5 * q^81 - 41 * q^82 + 30 * q^83 - 30 * q^84 + 68 * q^85 + 110 * q^86 + 19 * q^87 + 129 * q^88 + 75 * q^89 - 16 * q^90 + 5 * q^91 - 4 * q^93 + 38 * q^94 + 36 * q^95 - 57 * q^96 - 168 * q^97 + 227 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

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Database

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