LMFDB - Embedded newform 144.2.u.a.131.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(11,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2]))

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

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

chi := DirichletCharacter("144.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.u (of order $12$, degree $4$, 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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			131.19
Character	$\chi$	$=$	144.131
Dual form			144.2.u.a.11.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25087 - 0.659799i) q^{2} +(-1.71297 + 0.256373i) q^{3} +(1.12933 - 1.65064i) q^{4} +(2.03779 - 0.546024i) q^{5} +(-1.97354 + 1.45091i) q^{6} +(-0.0638076 - 0.110518i) q^{7} +(0.323550 - 2.80986i) q^{8} +(2.86855 - 0.878321i) q^{9} +O(q^{10})$	\(q+(1.25087 - 0.659799i) q^{2} +(-1.71297 + 0.256373i) q^{3} +(1.12933 - 1.65064i) q^{4} +(2.03779 - 0.546024i) q^{5} +(-1.97354 + 1.45091i) q^{6} +(-0.0638076 - 0.110518i) q^{7} +(0.323550 - 2.80986i) q^{8} +(2.86855 - 0.878321i) q^{9} +(2.18873 - 2.02753i) q^{10} +(-0.678695 - 0.181856i) q^{11} +(-1.51133 + 3.11703i) q^{12} +(-1.84311 + 0.493860i) q^{13} +(-0.152734 - 0.0961430i) q^{14} +(-3.35069 + 1.45776i) q^{15} +(-1.44923 - 3.72824i) q^{16} +4.32243i q^{17} +(3.00865 - 2.99133i) q^{18} +(-3.97707 + 3.97707i) q^{19} +(1.40005 - 3.98030i) q^{20} +(0.137635 + 0.172956i) q^{21} +(-0.968944 + 0.220325i) q^{22} +(6.81589 + 3.93516i) q^{23} +(0.166142 + 4.89616i) q^{24} +(-0.475689 + 0.274639i) q^{25} +(-1.97963 + 1.83383i) q^{26} +(-4.68856 + 2.23996i) q^{27} +(-0.254485 - 0.0194880i) q^{28} +(-0.926957 - 0.248377i) q^{29} +(-3.22943 + 4.03424i) q^{30} +(-4.91353 - 2.83683i) q^{31} +(-4.27267 - 3.70733i) q^{32} +(1.20921 + 0.137514i) q^{33} +(2.85194 + 5.40679i) q^{34} +(-0.190372 - 0.190372i) q^{35} +(1.78974 - 5.72685i) q^{36} +(-6.64358 + 6.64358i) q^{37} +(-2.35071 + 7.59884i) q^{38} +(3.03058 - 1.31849i) q^{39} +(-0.874924 - 5.90257i) q^{40} +(4.61325 - 7.99038i) q^{41} +(0.286278 + 0.125533i) q^{42} +(2.91294 - 10.8712i) q^{43} +(-1.06665 + 0.914906i) q^{44} +(5.36590 - 3.35613i) q^{45} +(11.1222 + 0.425234i) q^{46} +(5.92267 + 10.2584i) q^{47} +(3.43830 + 6.01482i) q^{48} +(3.49186 - 6.04807i) q^{49} +(-0.413816 + 0.657395i) q^{50} +(-1.10816 - 7.40421i) q^{51} +(-1.26629 + 3.60004i) q^{52} +(0.00259022 + 0.00259022i) q^{53} +(-4.38684 + 5.89539i) q^{54} -1.48233 q^{55} +(-0.331185 + 0.143532i) q^{56} +(5.79299 - 7.83221i) q^{57} +(-1.32338 + 0.300919i) q^{58} +(-1.09748 - 4.09587i) q^{59} +(-1.37780 + 7.17707i) q^{60} +(-1.19213 + 4.44908i) q^{61} +(-8.01790 - 0.306548i) q^{62} +(-0.280105 - 0.260982i) q^{63} +(-7.79063 - 1.81826i) q^{64} +(-3.48621 + 2.01276i) q^{65} +(1.60329 - 0.625822i) q^{66} +(-0.538862 - 2.01106i) q^{67} +(7.13478 + 4.88146i) q^{68} +(-12.6843 - 4.99340i) q^{69} +(-0.363737 - 0.112522i) q^{70} -3.80683i q^{71} +(-1.53984 - 8.34439i) q^{72} +1.87674i q^{73} +(-3.92680 + 12.6937i) q^{74} +(0.744431 - 0.592403i) q^{75} +(2.07328 + 11.0561i) q^{76} +(0.0232076 + 0.0866118i) q^{77} +(2.92091 - 3.64883i) q^{78} +(3.00919 - 1.73736i) q^{79} +(-4.98892 - 6.80604i) q^{80} +(7.45710 - 5.03901i) q^{81} +(0.498509 - 13.0387i) q^{82} +(-0.394284 + 1.47149i) q^{83} +(0.440923 - 0.0318610i) q^{84} +(2.36015 + 8.80821i) q^{85} +(-3.52914 - 15.5204i) q^{86} +(1.65153 + 0.187816i) q^{87} +(-0.730581 + 1.84820i) q^{88} -10.5967 q^{89} +(4.49766 - 7.73848i) q^{90} +(0.172185 + 0.172185i) q^{91} +(14.1929 - 6.80649i) q^{92} +(9.14402 + 3.59971i) q^{93} +(14.1769 + 8.92407i) q^{94} +(-5.93284 + 10.2760i) q^{95} +(8.26943 + 5.25514i) q^{96} +(3.31795 + 5.74685i) q^{97} +(0.377331 - 9.86925i) q^{98} +(-2.10659 + 0.0744506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7}+O(q^{10}) $ 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7	$ 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 16 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} - 10 q^{18} - 8 q^{19} - 48 q^{20} + 2 q^{21} - 2 q^{22} - 12 q^{23} - 16 q^{27} + 8 q^{28} - 6 q^{29} - 34 q^{30} - 6 q^{32} - 8 q^{33} + 2 q^{34} - 26 q^{36} - 8 q^{37} - 6 q^{38} - 32 q^{39} - 2 q^{40} + 48 q^{42} - 2 q^{43} + 6 q^{45} - 40 q^{46} + 42 q^{48} - 24 q^{49} + 72 q^{50} - 12 q^{51} - 2 q^{52} - 38 q^{54} - 16 q^{55} + 36 q^{56} + 16 q^{58} - 42 q^{59} + 70 q^{60} - 2 q^{61} - 44 q^{64} - 12 q^{65} + 104 q^{66} - 2 q^{67} + 96 q^{68} - 10 q^{69} - 16 q^{70} - 10 q^{72} + 78 q^{74} - 56 q^{75} - 14 q^{76} - 6 q^{77} + 12 q^{78} - 8 q^{81} - 36 q^{82} + 54 q^{83} + 158 q^{84} + 8 q^{85} + 54 q^{86} + 48 q^{87} + 22 q^{88} + 64 q^{90} + 20 q^{91} + 108 q^{92} - 34 q^{93} + 6 q^{94} - 58 q^{96} - 4 q^{97} + 46 q^{99}+O(q^{100}) $ 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^10 - 6 * q^11 - 16 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 - 10 * q^18 - 8 * q^19 - 48 * q^20 + 2 * q^21 - 2 * q^22 - 12 * q^23 - 16 * q^27 + 8 * q^28 - 6 * q^29 - 34 * q^30 - 6 * q^32 - 8 * q^33 + 2 * q^34 - 26 * q^36 - 8 * q^37 - 6 * q^38 - 32 * q^39 - 2 * q^40 + 48 * q^42 - 2 * q^43 + 6 * q^45 - 40 * q^46 + 42 * q^48 - 24 * q^49 + 72 * q^50 - 12 * q^51 - 2 * q^52 - 38 * q^54 - 16 * q^55 + 36 * q^56 + 16 * q^58 - 42 * q^59 + 70 * q^60 - 2 * q^61 - 44 * q^64 - 12 * q^65 + 104 * q^66 - 2 * q^67 + 96 * q^68 - 10 * q^69 - 16 * q^70 - 10 * q^72 + 78 * q^74 - 56 * q^75 - 14 * q^76 - 6 * q^77 + 12 * q^78 - 8 * q^81 - 36 * q^82 + 54 * q^83 + 158 * q^84 + 8 * q^85 + 54 * q^86 + 48 * q^87 + 22 * q^88 + 64 * q^90 + 20 * q^91 + 108 * q^92 - 34 * q^93 + 6 * q^94 - 58 * q^96 - 4 * q^97 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.25087	−	0.659799i	0.884496	−	0.466548i
$2$	1.25087	−	0.659799i	0.884496	−	0.466548i
$3$	−1.71297	+	0.256373i	−0.988985	+	0.148017i
$3$	−1.71297	+	0.256373i	−0.988985	+	0.148017i
$4$	1.12933	−	1.65064i	0.564665	−	0.825320i
$5$	2.03779	−	0.546024i	0.911327	−	0.244189i	0.227452	−	0.973789i	$-0.426960\pi$
$5$	2.03779	−	0.546024i	0.911327	−	0.244189i	0.683874	+	0.729600i	$0.260294\pi$
$6$	−1.97354	+	1.45091i	−0.805696	+	0.592330i
$7$	−0.0638076	−	0.110518i	−0.0241170	−	0.0417719i	0.853715	−	0.520741i	$-0.174344\pi$
$7$	−0.0638076	−	0.110518i	−0.0241170	−	0.0417719i	−0.877832	+	0.478969i	$0.841011\pi$
$8$	0.323550	−	2.80986i	0.114392	−	0.993436i
$9$	2.86855	−	0.878321i	0.956182	−	0.292774i
$10$	2.18873	−	2.02753i	0.692138	−	0.641162i
$11$	−0.678695	−	0.181856i	−0.204634	−	0.0548316i	0.155046	−	0.987907i	$-0.450447\pi$
$11$	−0.678695	−	0.181856i	−0.204634	−	0.0548316i	−0.359680	+	0.933076i	$0.617114\pi$
$12$	−1.51133	+	3.11703i	−0.436284	+	0.899809i
$13$	−1.84311	+	0.493860i	−0.511187	+	0.136972i	−0.505187	−	0.863010i	$-0.668576\pi$
$13$	−1.84311	+	0.493860i	−0.511187	+	0.136972i	−0.00599967	+	0.999982i	$0.501910\pi$
$14$	−0.152734	−	0.0961430i	−0.0408200	−	0.0256953i
$15$	−3.35069	+	1.45776i	−0.865144	+	0.376391i
$16$	−1.44923	−	3.72824i	−0.362306	−	0.932059i
$17$			4.32243i			1.04834i	0.851612	+	0.524172i	$0.175625\pi$
$17$			4.32243i			1.04834i	−0.851612	+	0.524172i	$0.824375\pi$
$18$	3.00865	−	2.99133i	0.709146	−	0.705062i
$19$	−3.97707	+	3.97707i	−0.912401	+	0.912401i	−0.996461	−	0.0840594i	$-0.973211\pi$
$19$	−3.97707	+	3.97707i	−0.912401	+	0.912401i	0.0840594	+	0.996461i	$0.473211\pi$
$20$	1.40005	−	3.98030i	0.313060	−	0.890021i
$21$	0.137635	+	0.172956i	0.0300343	+	0.0377420i
$22$	−0.968944	+	0.220325i	−0.206580	+	0.0469735i
$23$	6.81589	+	3.93516i	1.42121	+	0.820537i	0.996403	−	0.0847463i	$-0.0270080\pi$
$23$	6.81589	+	3.93516i	1.42121	+	0.820537i	0.424809	+	0.905283i	$0.360341\pi$
$24$	0.166142	+	4.89616i	0.0339136	+	0.999425i
$25$	−0.475689	+	0.274639i	−0.0951377	+	0.0549278i
$26$	−1.97963	+	1.83383i	−0.388238	+	0.359644i
$27$	−4.68856	+	2.23996i	−0.902314	+	0.431080i
$28$	−0.254485	−	0.0194880i	−0.0480932	−	0.00368288i
$29$	−0.926957	−	0.248377i	−0.172132	−	0.0461225i	0.171724	−	0.985145i	$-0.445066\pi$
$29$	−0.926957	−	0.248377i	−0.172132	−	0.0461225i	−0.343855	+	0.939023i	$0.611733\pi$
$30$	−3.22943	+	4.03424i	−0.589611	+	0.736548i
$31$	−4.91353	−	2.83683i	−0.882496	−	0.509509i	−0.0110152	−	0.999939i	$-0.503506\pi$
$31$	−4.91353	−	2.83683i	−0.882496	−	0.509509i	−0.871480	+	0.490430i	$0.836840\pi$
$32$	−4.27267	−	3.70733i	−0.755309	−	0.655369i
$33$	1.20921	+	0.137514i	0.210496	+	0.0239382i
$34$	2.85194	+	5.40679i	0.489103	+	0.927256i
$35$	−0.190372	−	0.190372i	−0.0321787	−	0.0321787i
$36$	1.78974	−	5.72685i	0.298291	−	0.954475i
$37$	−6.64358	+	6.64358i	−1.09220	+	1.09220i	−0.0969037	+	0.995294i	$0.530894\pi$
$37$	−6.64358	+	6.64358i	−1.09220	+	1.09220i	−0.995294	+	0.0969037i	$0.969106\pi$
$38$	−2.35071	+	7.59884i	−0.381336	+	1.23269i
$39$	3.03058	−	1.31849i	0.485281	−	0.211128i
$40$	−0.874924	−	5.90257i	−0.138338	−	0.933278i
$41$	4.61325	−	7.99038i	0.720469	−	1.24789i	−0.240344	−	0.970688i	$-0.577260\pi$
$41$	4.61325	−	7.99038i	0.720469	−	1.24789i	0.960812	−	0.277200i	$-0.0894066\pi$
$42$	0.286278	+	0.125533i	0.0441737	+	0.0193702i
$43$	2.91294	−	10.8712i	0.444219	−	1.65785i	−0.273772	−	0.961795i	$-0.588271\pi$
$43$	2.91294	−	10.8712i	0.444219	−	1.65785i	0.717991	−	0.696053i	$-0.245062\pi$
$44$	−1.06665	+	0.914906i	−0.160803	+	0.137927i
$45$	5.36590	−	3.35613i	0.799902	−	0.500302i
$46$	11.1222	+	0.425234i	1.63988	+	0.0626973i
$47$	5.92267	+	10.2584i	0.863910	+	1.49634i	0.868125	+	0.496345i	$0.165325\pi$
$47$	5.92267	+	10.2584i	0.863910	+	1.49634i	−0.00421475	+	0.999991i	$0.501342\pi$
$48$	3.43830	+	6.01482i	0.496276	+	0.868165i
$49$	3.49186	−	6.04807i	0.498837	−	0.864011i
$50$	−0.413816	+	0.657395i	−0.0585224	+	0.0929698i
$51$	−1.10816	−	7.40421i	−0.155173	−	1.03680i
$52$	−1.26629	+	3.60004i	−0.175603	+	0.499236i
$53$	0.00259022	+	0.00259022i	0.000355794	+	0.000355794i	0.707285	−	0.706929i	$-0.249920\pi$
$53$	0.00259022	+	0.00259022i	0.000355794	+	0.000355794i	−0.706929	+	0.707285i	$0.749920\pi$
$54$	−4.38684	+	5.89539i	−0.596973	+	0.802262i
$55$	−1.48233			−0.199878
$56$	−0.331185	+	0.143532i	−0.0442565	+	0.0191803i
$57$	5.79299	−	7.83221i	0.767300	−	1.03740i
$58$	−1.32338	+	0.300919i	−0.173768	+	0.0395125i
$59$	−1.09748	−	4.09587i	−0.142880	−	0.533237i	−0.999841	−	0.0178541i	$-0.994317\pi$
$59$	−1.09748	−	4.09587i	−0.142880	−	0.533237i	0.856960	−	0.515382i	$-0.172350\pi$
$60$	−1.37780	+	7.17707i	−0.177873	+	0.926556i
$61$	−1.19213	+	4.44908i	−0.152636	+	0.569646i	0.846660	+	0.532134i	$0.178610\pi$
$61$	−1.19213	+	4.44908i	−0.152636	+	0.569646i	−0.999296	+	0.0375117i	$0.988057\pi$
$62$	−8.01790	−	0.306548i	−1.01827	−	0.0389317i
$63$	−0.280105	−	0.260982i	−0.0352900	−	0.0328807i
$64$	−7.79063	−	1.81826i	−0.973829	−	0.227282i
$65$	−3.48621	+	2.01276i	−0.432411	+	0.249652i
$66$	1.60329	−	0.625822i	0.197351	−	0.0770334i
$67$	−0.538862	−	2.01106i	−0.0658325	−	0.245690i	0.925166	−	0.379563i	$-0.123925\pi$
$67$	−0.538862	−	2.01106i	−0.0658325	−	0.245690i	−0.990999	+	0.133872i	$0.957259\pi$
$68$	7.13478	+	4.88146i	0.865220	+	0.591964i
$69$	−12.6843	−	4.99340i	−1.52701	−	0.601134i
$70$	−0.363737	−	0.112522i	−0.0434749	−	0.0134490i
$71$		−	3.80683i		−	0.451788i	−0.974152	−	0.225894i	$-0.927470\pi$
$71$		−	3.80683i		−	0.451788i	0.974152	−	0.225894i	$-0.0725303\pi$
$72$	−1.53984	−	8.34439i	−0.181472	−	0.983396i
$73$			1.87674i			0.219656i	0.993951	+	0.109828i	$0.0350300\pi$
$73$			1.87674i			0.219656i	−0.993951	+	0.109828i	$0.964970\pi$
$74$	−3.92680	+	12.6937i	−0.456481	+	1.47561i
$75$	0.744431	−	0.592403i	0.0859595	−	0.0684048i
$76$	2.07328	+	11.0561i	0.237822	+	1.26822i
$77$	0.0232076	+	0.0866118i	0.00264475	+	0.00987033i
$78$	2.92091	−	3.64883i	0.330728	−	0.413149i
$79$	3.00919	−	1.73736i	0.338560	−	0.195468i	−0.321075	−	0.947054i	$-0.604044\pi$
$79$	3.00919	−	1.73736i	0.338560	−	0.195468i	0.659635	+	0.751586i	$0.270711\pi$
$80$	−4.98892	−	6.80604i	−0.557778	−	0.760939i
$81$	7.45710	−	5.03901i	0.828567	−	0.559890i
$82$	0.498509	−	13.0387i	0.0550511	−	1.43989i
$83$	−0.394284	+	1.47149i	−0.0432783	+	0.161517i	−0.984183	−	0.177155i	$-0.943311\pi$
$83$	−0.394284	+	1.47149i	−0.0432783	+	0.161517i	0.940905	+	0.338671i	$0.109977\pi$
$84$	0.440923	−	0.0318610i	0.0481086	−	0.00347632i
$85$	2.36015	+	8.80821i	0.255994	+	0.955384i
$86$	−3.52914	−	15.5204i	−0.380556	−	1.67361i
$87$	1.65153	+	0.187816i	0.177062	+	0.0201360i
$88$	−0.730581	+	1.84820i	−0.0778802	+	0.197019i
$89$	−10.5967			−1.12325			−0.561624	−	0.827392i	$-0.689823\pi$
$89$	−10.5967			−1.12325			−0.561624	+	0.827392i	$0.689823\pi$
$90$	4.49766	−	7.73848i	0.474095	−	0.815708i
$91$	0.172185	+	0.172185i	0.0180499	+	0.0180499i
$92$	14.1929	−	6.80649i	1.47971	−	0.709626i
$93$	9.14402	+	3.59971i	0.948191	+	0.373272i
$94$	14.1769	+	8.92407i	1.46224	+	0.920447i
$95$	−5.93284	+	10.2760i	−0.608697	+	1.05429i
$96$	8.26943	+	5.25514i	0.843995	+	0.536351i
$97$	3.31795	+	5.74685i	0.336886	+	0.583504i	0.983845	−	0.179021i	$-0.0572928\pi$
$97$	3.31795	+	5.74685i	0.336886	+	0.583504i	−0.646959	+	0.762525i	$0.723960\pi$
$98$	0.377331	−	9.86925i	0.0381162	−	0.996945i
$99$	−2.10659	+	0.0744506i	−0.211721	+	0.00748257i
$100$	−0.0838795	+	1.09535i	−0.00838795	+	0.109535i
$101$	3.24008	−	12.0922i	0.322400	−	1.20321i	−0.594499	−	0.804096i	$-0.702650\pi$
$101$	3.24008	−	12.0922i	0.322400	−	1.20321i	0.916899	−	0.399118i	$-0.130684\pi$
$102$	−6.27145	−	8.53051i	−0.620966	−	0.844646i
$103$	−4.21850	+	7.30665i	−0.415661	+	0.719946i	−0.995498	−	0.0947868i	$-0.969783\pi$
$103$	−4.21850	+	7.30665i	−0.415661	+	0.719946i	0.579837	+	0.814733i	$0.303116\pi$
$104$	0.791339	+	5.33867i	0.0775972	+	0.523499i
$105$	0.374908	+	0.277295i	0.0365873	+	0.0270613i
$106$	0.00494904	+	0.00153099i	0.000480693	+	0.000148703i
$107$	7.25071	−	7.25071i	0.700953	−	0.700953i	−0.263662	−	0.964615i	$-0.584930\pi$
$107$	7.25071	−	7.25071i	0.700953	−	0.700953i	0.964615	+	0.263662i	$0.0849304\pi$
$108$	−1.59757	+	10.2688i	−0.153726	+	0.988114i
$109$	10.2850	+	10.2850i	0.985128	+	0.985128i	0.999891	−	0.0147630i	$-0.00469937\pi$
$109$	10.2850	+	10.2850i	0.985128	+	0.985128i	−0.0147630	+	0.999891i	$0.504699\pi$
$110$	−1.85420	+	0.978042i	−0.176791	+	0.0932527i
$111$	9.67702	−	13.0835i	0.918503	−	1.24183i
$112$	−0.319566	+	0.398055i	−0.0301961	+	0.0376127i
$113$	−18.2964	−	10.5634i	−1.72118	−	0.993722i	−0.916526	−	0.399976i	$-0.869019\pi$
$113$	−18.2964	−	10.5634i	−1.72118	−	0.993722i	−0.804652	−	0.593747i	$-0.797648\pi$
$114$	2.07856	−	13.6193i	0.194675	−	1.27556i
$115$	16.0380	+	4.29738i	1.49555	+	0.400732i
$116$	−1.45682	+	1.24957i	−0.135263	+	0.116020i
$117$	−4.85328	+	3.03550i	−0.448685	+	0.280632i
$118$	−4.07526	−	4.39926i	−0.375158	−	0.404985i
$119$	0.477707	−	0.275804i	0.0437913	−	0.0252829i
$120$	3.01198	+	9.88662i	0.274955	+	0.902521i
$121$	−9.09872	−	5.25315i	−0.827157	−	0.477559i
$122$	1.44431	+	6.35176i	0.130761	+	0.575061i
$123$	−5.85384	+	14.8700i	−0.527823	+	1.34078i
$124$	−10.2316	+	4.90675i	−0.918823	+	0.440639i
$125$	−8.27822	+	8.27822i	−0.740426	+	0.740426i
$126$	−0.522570	−	0.141641i	−0.0465543	−	0.0126184i
$127$		−	13.1109i		−	1.16340i	−0.813403	−	0.581700i	$-0.802388\pi$
$127$		−	13.1109i		−	1.16340i	0.813403	−	0.581700i	$-0.197612\pi$
$128$	−10.9447	+	2.86585i	−0.967386	+	0.253308i
$129$	−2.20269	+	19.3689i	−0.193936	+	1.70534i
$130$	−3.03276	+	4.81789i	−0.265990	+	0.422557i
$131$	4.74891	−	1.27247i	0.414914	−	0.111176i	−0.0453222	−	0.998972i	$-0.514431\pi$
$131$	4.74891	−	1.27247i	0.414914	−	0.111176i	0.460236	+	0.887797i	$0.347765\pi$
$132$	1.59258	−	1.84067i	0.138616	−	0.160210i
$133$	0.693305	+	0.185770i	0.0601171	+	0.0161083i
$134$	−2.00094	−	2.16003i	−0.172855	−	0.186598i
$135$	−8.33122	+	7.12462i	−0.717037	+	0.613190i
$136$	12.1454	+	1.39852i	1.04146	+	0.119922i
$137$	3.41217	+	5.91005i	0.291521	+	0.504930i	0.974170	−	0.225817i	$-0.0725053\pi$
$137$	3.41217	+	5.91005i	0.291521	+	0.504930i	−0.682648	+	0.730747i	$0.739172\pi$
$138$	−19.1610	+	2.12302i	−1.63109	+	0.180723i
$139$	10.3427	−	2.77132i	0.877258	−	0.235061i	0.208035	−	0.978121i	$-0.433293\pi$
$139$	10.3427	−	2.77132i	0.877258	−	0.235061i	0.669224	+	0.743061i	$0.266627\pi$
$140$	−0.529228	+	0.0992427i	−0.0447279	+	0.00838754i
$141$	−12.7753	−	16.0539i	−1.07588	−	1.35198i
$142$	−2.51174	−	4.76184i	−0.210781	−	0.399604i
$143$	1.34072			0.112117
$144$	−7.43176	−	9.42173i	−0.619313	−	0.785144i
$145$	−2.02456			−0.168131
$146$	1.23827	+	2.34755i	0.102480	+	0.194285i
$147$	−4.43089	+	11.2554i	−0.365453	+	0.928330i
$148$	3.46336	+	18.4690i	0.284687	+	1.51814i
$149$	−0.204036	+	0.0546714i	−0.0167153	+	0.00447885i	−0.267167	−	0.963650i	$-0.586088\pi$
$149$	−0.204036	+	0.0546714i	−0.0167153	+	0.00447885i	0.250452	+	0.968129i	$0.419421\pi$
$150$	0.540317	−	1.23219i	0.0441167	−	0.100608i
$151$	1.14798	+	1.98835i	0.0934210	+	0.161810i	0.908949	−	0.416908i	$-0.136886\pi$
$151$	1.14798	+	1.98835i	0.0934210	+	0.161810i	−0.815528	+	0.578718i	$0.803553\pi$
$152$	9.88822	+	12.4618i	0.802040	+	1.01078i
$153$	3.79649	+	12.3991i	0.306928	+	1.00241i
$154$	0.0861759	+	0.0930274i	0.00694425	+	0.00749636i
$155$	−11.5617	−	3.09795i	−0.928658	−	0.248833i
$156$	1.24617	−	6.49141i	0.0997736	−	0.519729i
$157$	−16.2150	+	4.34480i	−1.29410	+	0.346753i	−0.839216	−	0.543799i	$-0.816985\pi$
$157$	−16.2150	+	4.34480i	−1.29410	+	0.346753i	−0.454883	+	0.890551i	$0.650319\pi$
$158$	2.61779	−	4.15866i	0.208260	−	0.330845i
$159$	−0.00510103	−	0.00377291i	−0.000404538	−	0.000299211i
$160$	−10.7311	−	5.22176i	−0.848367	−	0.412817i
$161$		−	1.00437i		−	0.0791556i
$162$	6.00310	−	11.2233i	0.471648	−	0.881787i
$163$	0.490399	−	0.490399i	0.0384110	−	0.0384110i	−0.687640	−	0.726051i	$-0.741353\pi$
$163$	0.490399	−	0.490399i	0.0384110	−	0.0384110i	0.726051	+	0.687640i	$0.241353\pi$
$164$	−7.97936	−	16.6386i	−0.623084	−	1.29926i
$165$	2.53920	−	0.380031i	0.197676	−	0.0295854i
$166$	0.477690	+	2.10078i	0.0370759	+	0.163052i
$167$	9.34175	+	5.39346i	0.722887	+	0.417359i	0.815814	−	0.578314i	$-0.196289\pi$
$167$	9.34175	+	5.39346i	0.722887	+	0.417359i	−0.0929276	+	0.995673i	$0.529622\pi$
$168$	0.530513	−	0.330774i	0.0409300	−	0.0255198i
$169$	−8.10518	+	4.67953i	−0.623475	+	0.359963i
$170$	8.76388	+	9.46066i	0.672159	+	0.725599i
$171$	−7.91525	+	14.9015i	−0.605294	+	1.13955i
$172$	−14.6548	−	17.0854i	−1.11742	−	1.30275i
$173$	4.61598	+	1.23685i	0.350946	+	0.0940358i	0.429986	−	0.902836i	$-0.358519\pi$
$173$	4.61598	+	1.23685i	0.350946	+	0.0940358i	−0.0790394	+	0.996871i	$0.525185\pi$
$174$	2.18976	−	0.854744i	0.166005	−	0.0647980i
$175$	0.0607051	+	0.0350481i	0.00458888	+	0.00264939i
$176$	0.305581	+	2.79388i	0.0230340	+	0.210597i
$177$	2.93003	+	6.73474i	0.220235	+	0.506214i
$178$	−13.2551	+	6.99170i	−0.993509	+	0.524050i
$179$	3.52882	+	3.52882i	0.263756	+	0.263756i	0.826578	−	0.562822i	$-0.190284\pi$
$179$	3.52882	+	3.52882i	0.263756	+	0.263756i	−0.562822	+	0.826578i	$0.690284\pi$
$180$	0.520121	−	12.6474i	0.0387675	−	0.942678i
$181$	7.34860	−	7.34860i	0.546217	−	0.546217i	−0.379127	−	0.925344i	$-0.623776\pi$
$181$	7.34860	−	7.34860i	0.546217	−	0.546217i	0.925344	+	0.379127i	$0.123776\pi$
$182$	0.328987	+	0.101773i	0.0243862	+	0.00754390i
$183$	0.901454	−	7.92677i	0.0666374	−	0.585964i
$184$	13.2625	−	17.8785i	0.977726	−	1.31802i
$185$	−9.91065	+	17.1658i	−0.728646	+	1.26205i
$186$	13.8130	−	1.53047i	1.01282	−	0.112219i
$187$	0.786059	−	2.93361i	0.0574824	−	0.214527i
$188$	23.6215	+	1.80889i	1.72278	+	0.131927i
$189$	0.546722	+	0.375244i	0.0397681	+	0.0272950i
$190$	−0.641105	+	16.7684i	−0.0465106	+	1.21651i
$191$	−2.58888	−	4.48407i	−0.187325	−	0.324456i	0.757033	−	0.653377i	$-0.226648\pi$
$191$	−2.58888	−	4.48407i	−0.187325	−	0.324456i	−0.944357	+	0.328921i	$0.893315\pi$
$192$	13.8113	+	1.11732i	0.996744	+	0.0806354i
$193$	13.2173	−	22.8930i	0.951401	−	1.64787i	0.209003	−	0.977915i	$-0.432978\pi$
$193$	13.2173	−	22.8930i	0.951401	−	1.64787i	0.742398	−	0.669960i	$-0.233689\pi$
$194$	7.94207	+	4.99936i	0.570208	+	0.358933i
$195$	5.45576	−	4.34158i	0.390695	−	0.310907i
$196$	−6.03973	−	12.5941i	−0.431410	−	0.899577i
$197$	5.14652	+	5.14652i	0.366674	+	0.366674i	0.866263	−	0.499588i	$-0.166515\pi$
$197$	5.14652	+	5.14652i	0.366674	+	0.366674i	−0.499588	+	0.866263i	$0.666515\pi$
$198$	−2.58594	+	1.48306i	−0.183775	+	0.105396i
$199$	−1.37436			−0.0974261			−0.0487130	−	0.998813i	$-0.515512\pi$
$199$	−1.37436			−0.0974261			−0.0487130	+	0.998813i	$0.515512\pi$
$200$	0.617788	+	1.42548i	0.0436842	+	0.100797i
$201$	1.43864	+	3.30674i	0.101474	+	0.233240i
$202$	−3.92549	−	17.2635i	−0.276196	−	1.21465i
$203$	0.0316967	+	0.118294i	0.00222468	+	0.00830260i
$204$	−13.4732	−	6.53263i	−0.943310	−	0.457376i
$205$	5.03789	−	18.8017i	0.351861	−	1.31316i
$206$	−0.455852	+	11.9230i	−0.0317607	+	0.830715i
$207$	23.0080	+	5.30163i	1.59917	+	0.368489i
$208$	4.51231	+	6.15583i	0.312872	+	0.426830i
$209$	3.42246	−	1.97596i	0.236737	−	0.136680i
$210$	0.651919	+	0.0994954i	0.0449867	+	0.00686583i
$211$	−2.98444	−	11.1381i	−0.205457	−	0.766776i	−0.989310	−	0.145829i	$-0.953415\pi$
$211$	−2.98444	−	11.1381i	−0.205457	−	0.766776i	0.783853	−	0.620947i	$-0.213252\pi$
$212$	0.00720073	−	0.00135031i	0.000494548	−	9.27394e-5i
$213$	0.975971	+	6.52100i	0.0668724	+	0.446811i
$214$	4.28566	−	13.8537i	0.292961	−	0.947018i
$215$		−	23.7438i		−	1.61931i
$216$	4.77699	+	13.8989i	0.325033	+	0.945703i
$217$			0.724045i			0.0491514i
$218$	19.6513	+	6.07914i	1.33095	+	0.411732i
$219$	−0.481147	−	3.21481i	−0.0325129	−	0.217237i
$220$	−1.67404	+	2.44680i	−0.112864	+	0.164963i
$221$	−2.13468	−	7.96672i	−0.143594	−	0.535900i
$222$	3.47218	−	22.7506i	0.233037	−	1.52692i
$223$	−17.9819	+	10.3819i	−1.20416	+	0.695220i	−0.961477	−	0.274886i	$-0.911360\pi$
$223$	−17.9819	+	10.3819i	−1.20416	+	0.695220i	−0.242680	+	0.970106i	$0.578026\pi$
$224$	−0.137097	+	0.708763i	−0.00916019	+	0.0473562i
$225$	−1.12331	+	1.20562i	−0.0748876	+	0.0803748i
$226$	−29.8560	−	1.14149i	−1.98599	−	0.0759305i
$227$	2.05090	−	7.65406i	0.136123	−	0.508018i	−0.863868	−	0.503718i	$-0.831965\pi$
$227$	2.05090	−	7.65406i	0.136123	−	0.508018i	0.999991	−	0.00429906i	$-0.00136844\pi$
$228$	−6.38597	−	18.4073i	−0.422921	−	1.21905i
$229$	−0.120227	−	0.448692i	−0.00794481	−	0.0296504i	0.961840	−	0.273614i	$-0.0882190\pi$
$229$	−0.120227	−	0.448692i	−0.00794481	−	0.0296504i	−0.969784	+	0.243963i	$0.921552\pi$
$230$	22.8968	−	5.20643i	1.50977	−	0.343302i
$231$	−0.0619589	−	0.142414i	−0.00407659	−	0.00937014i
$232$	−0.997823	+	2.52426i	−0.0655103	+	0.165726i
$233$	9.13737			0.598609			0.299305	−	0.954158i	$-0.403245\pi$
$233$	9.13737			0.598609			0.299305	+	0.954158i	$0.403245\pi$
$234$	−4.06798	+	6.99919i	−0.265932	+	0.457551i
$235$	17.6705	+	17.6705i	1.15269	+	1.15269i
$236$	−8.00023	−	2.81404i	−0.520770	−	0.183178i
$237$	−4.70925	+	3.74752i	−0.305898	+	0.243428i
$238$	0.415572	−	0.660185i	0.0269375	−	0.0427934i
$239$	−3.65824	+	6.33626i	−0.236632	+	0.409859i	−0.959746	−	0.280870i	$-0.909377\pi$
$239$	−3.65824	+	6.33626i	−0.236632	+	0.409859i	0.723114	+	0.690729i	$0.242710\pi$
$240$	10.2908	+	10.3795i	0.664266	+	0.669996i
$241$	−1.24858	−	2.16261i	−0.0804282	−	0.139306i	0.823006	−	0.568033i	$-0.192295\pi$
$241$	−1.24858	−	2.16261i	−0.0804282	−	0.139306i	−0.903434	+	0.428727i	$0.858962\pi$
$242$	−14.8473	−	0.567657i	−0.954421	−	0.0364904i
$243$	−11.4819	+	10.5435i	−0.736567	+	0.676365i
$244$	5.99752	+	6.99225i	0.383952	+	0.447633i
$245$	3.81327	−	14.2313i	0.243621	−	0.909206i
$246$	2.48885	+	22.4628i	0.158683	+	1.43217i
$247$	5.36605	−	9.29428i	0.341434	−	0.591381i
$248$	−9.56086	+	12.8885i	−0.607115	+	0.818419i
$249$	0.298147	−	2.62170i	0.0188943	−	0.166144i
$250$	−4.89298	+	15.8169i	−0.309459	+	1.00035i
$251$	−2.77626	+	2.77626i	−0.175236	+	0.175236i	−0.789275	−	0.614039i	$-0.789544\pi$
$251$	−2.77626	+	2.77626i	−0.175236	+	0.175236i	0.614039	+	0.789275i	$0.289544\pi$
$252$	−0.747120	+	0.167618i	−0.0470641	+	0.0105589i
$253$	−3.91028	−	3.91028i	−0.245837	−	0.245837i
$254$	−8.65053	−	16.3999i	−0.542783	−	1.02902i
$255$	−6.30106	−	14.4831i	−0.394588	−	0.906969i
$256$	−11.7995	+	10.8061i	−0.737468	+	0.675382i
$257$	−9.61957	−	5.55386i	−0.600052	−	0.346440i	0.169010	−	0.985614i	$-0.445943\pi$
$257$	−9.61957	−	5.55386i	−0.600052	−	0.346440i	−0.769062	+	0.639174i	$0.779276\pi$
$258$	10.0243	+	25.6812i	0.624088	+	1.59884i
$259$	1.15815	+	0.310324i	0.0719637	+	0.0192826i
$260$	−0.614733	+	8.02755i	−0.0381241	+	0.497847i
$261$	−2.87717	+	0.101684i	−0.178093	+	0.00629409i
$262$	5.10067	−	4.72501i	0.315121	−	0.291912i
$263$	−16.6320	+	9.60247i	−1.02557	+	0.592114i	−0.915713	−	0.401834i	$-0.868373\pi$
$263$	−16.6320	+	9.60247i	−1.02557	+	0.592114i	−0.109858	+	0.993947i	$0.535040\pi$
$264$	0.777635	−	3.35321i	0.0478601	−	0.206376i
$265$	0.00669264	+	0.00386400i	0.000411125	+	0.000237363i
$266$	0.989802	−	0.225068i	0.0606887	−	0.0137998i
$267$	18.1519	−	2.71671i	1.11088	−	0.166260i
$268$	−3.92809	−	1.38169i	−0.239947	−	0.0843999i
$269$	7.66476	−	7.66476i	0.467329	−	0.467329i	−0.433719	−	0.901048i	$-0.642799\pi$
$269$	7.66476	−	7.66476i	0.467329	−	0.467329i	0.901048	+	0.433719i	$0.142799\pi$
$270$	−5.72042	+	14.4089i	−0.348133	+	0.876897i
$271$		−	12.9801i		−	0.788486i	−0.919006	−	0.394243i	$-0.871007\pi$
$271$		−	12.9801i		−	0.788486i	0.919006	−	0.394243i	$-0.128993\pi$
$272$	16.1151	−	6.26418i	0.977119	−	0.379822i
$273$	−0.339091	−	0.250804i	−0.0205227	−	0.0151794i
$274$	8.16761	+	5.14133i	0.493423	+	0.310599i
$275$	0.372792	−	0.0998893i	0.0224802	−	0.00602355i
$276$	−22.5671	+	15.2980i	−1.35838	+	0.920832i
$277$	23.9833	+	6.42631i	1.44102	+	0.386119i	0.892890	−	0.450276i	$-0.148674\pi$
$277$	23.9833	+	6.42631i	1.44102	+	0.386119i	0.548127	+	0.836395i	$0.315341\pi$
$278$	11.1088	−	10.2907i	0.666264	−	0.617194i
$279$	−16.5863	−	3.82191i	−0.992997	−	0.228812i
$280$	−0.596513	+	0.473324i	−0.0356485	+	0.0282865i
$281$	3.69120	+	6.39334i	0.220198	+	0.381395i	0.954868	−	0.297030i	$-0.0959962\pi$
$281$	3.69120	+	6.39334i	0.220198	+	0.381395i	−0.734670	+	0.678425i	$0.762663\pi$
$282$	−26.5726	−	11.6521i	−1.58237	−	0.693872i
$283$	−5.99708	+	1.60691i	−0.356490	+	0.0955211i	−0.432619	−	0.901577i	$-0.642410\pi$
$283$	−5.99708	+	1.60691i	−0.356490	+	0.0955211i	0.0761294	+	0.997098i	$0.475744\pi$
$284$	−6.28371	−	4.29917i	−0.372870	−	0.255109i
$285$	7.52830	−	19.1235i	0.445938	−	1.13278i
$286$	1.67706	−	0.884606i	0.0991667	−	0.0523078i
$287$	−1.17744			−0.0695022
$288$	−15.5126	−	6.88185i	−0.914088	−	0.405517i
$289$	−1.68344			−0.0990261
$290$	−2.53246	+	1.33580i	−0.148711	+	0.0784411i
$291$	−7.15689	−	8.99356i	−0.419544	−	0.527212i
$292$	3.09783	+	2.11946i	0.181287	+	0.124032i
$293$	24.0140	−	6.43453i	1.40291	−	0.375909i	0.523522	−	0.852012i	$-0.324618\pi$
$293$	24.0140	−	6.43453i	1.40291	−	0.375909i	0.879390	+	0.476103i	$0.157951\pi$
$294$	1.88386	+	17.0025i	0.109869	+	0.991605i
$295$	−4.47288	−	7.74726i	−0.260421	−	0.451063i
$296$	16.5180	+	20.8171i	0.960089	+	1.20997i
$297$	3.58945	−	0.667607i	0.208281	−	0.0387385i
$298$	−0.219150	+	0.203009i	−0.0126950	+	0.0117600i
$299$	−14.5058	−	3.88683i	−0.838895	−	0.224781i
$300$	−0.137135	−	1.89781i	−0.00791750	−	0.109570i
$301$	−1.38734	+	0.371735i	−0.0799647	+	0.0214265i
$302$	2.74788	+	1.72973i	0.158123	+	0.0995347i
$303$	−2.45006	+	21.5442i	−0.140753	+	1.23768i
$304$	20.5911	+	9.06377i	1.18098	+	0.519843i
$305$			9.71720i			0.556406i
$306$	12.9298	+	13.0047i	0.739148	+	0.743429i
$307$	−17.3773	+	17.3773i	−0.991773	+	0.991773i	−0.999966	−	0.00819381i	$-0.997392\pi$
$307$	−17.3773	+	17.3773i	−0.991773	+	0.991773i	0.00819381	+	0.999966i	$0.497392\pi$
$308$	0.169174	+	0.0595060i	0.00963958	+	0.00339067i
$309$	5.35294	−	13.5976i	0.304518	−	0.773541i
$310$	−16.5062	+	3.75328i	−0.937487	+	0.213172i
$311$	−11.9437	−	6.89568i	−0.677264	−	0.391018i	0.121560	−	0.992584i	$-0.461210\pi$
$311$	−11.9437	−	6.89568i	−0.677264	−	0.391018i	−0.798823	+	0.601566i	$0.794544\pi$
$312$	−2.72423	−	8.94211i	−0.154229	−	0.506247i
$313$	17.6368	−	10.1826i	0.996890	−	0.575555i	0.0895635	−	0.995981i	$-0.471453\pi$
$313$	17.6368	−	10.1826i	0.996890	−	0.575555i	0.907327	+	0.420426i	$0.138119\pi$
$314$	−17.4161	+	16.1334i	−0.982848	+	0.910461i
$315$	−0.713298	−	0.378883i	−0.0401898	−	0.0213476i
$316$	0.530619	−	6.92914i	0.0298497	−	0.389795i
$317$	20.3136	+	5.44301i	1.14092	+	0.305710i	0.779322	−	0.626623i	$-0.215563\pi$
$317$	20.3136	+	5.44301i	1.14092	+	0.305710i	0.361601	+	0.932333i	$0.382230\pi$
$318$	−0.00887007	−	0.00135374i	−0.000497409	−	7.59142e-5i
$319$	0.583952	+	0.337145i	0.0326950	+	0.0188765i
$320$	−16.8685	+	0.548641i	−0.942976	+	0.0306700i
$321$	−10.5614	+	14.2792i	−0.589479	+	0.796985i
$322$	−0.662684	−	1.25633i	−0.0369299	−	0.0700128i
$323$	−17.1906	−	17.1906i	−0.956511	−	0.956511i
$324$	0.103945	−	17.9997i	0.00577473	−	0.999983i
$325$	0.741113	−	0.741113i	0.0411096	−	0.0411096i
$326$	0.289859	−	0.936989i	0.0160538	−	0.0518950i
$327$	−20.2548	−	14.9812i	−1.12009	−	0.828461i
$328$	−20.9592	−	15.5479i	−1.15728	−	0.858488i
$329$	0.755823	−	1.30912i	0.0416699	−	0.0721743i
$330$	2.92545	−	2.15073i	0.161041	−	0.118394i
$331$	−4.57199	+	17.0629i	−0.251299	+	0.937862i	0.718813	+	0.695204i	$0.244686\pi$
$331$	−4.57199	+	17.0629i	−0.251299	+	0.937862i	−0.970112	+	0.242658i	$0.921981\pi$
$332$	1.98362	+	2.31262i	0.108865	+	0.126921i
$333$	−13.2222	+	24.8926i	−0.724573	+	1.36411i
$334$	15.2439	+	0.582819i	0.834108	+	0.0318904i
$335$	−2.19618	−	3.80389i	−0.119990	−	0.207829i
$336$	0.445356	−	0.763786i	0.0242962	−	0.0416679i
$337$	−4.82538	+	8.35780i	−0.262855	+	0.455279i	−0.966999	−	0.254778i	$-0.917997\pi$
$337$	−4.82538	+	8.35780i	−0.262855	+	0.455279i	0.704144	+	0.710057i	$0.251331\pi$
$338$	−7.05094	+	11.2012i	−0.383521	+	0.609267i
$339$	34.0493	+	13.4041i	1.84931	+	0.728012i
$340$	17.2046	+	6.05161i	0.933049	+	0.328195i
$341$	2.81889	+	2.81889i	0.152652	+	0.152652i
$342$	−0.0688997	+	23.8623i	−0.00372567	+	1.29032i
$343$	−1.78454			−0.0963558
$344$	−29.6042	−	11.7023i	−1.59615	−	0.630948i
$345$	−28.5744	−	3.24956i	−1.53840	−	0.174950i
$346$	6.59004	−	1.49849i	0.354283	−	0.0805592i
$347$	4.93125	+	18.4037i	0.264723	+	0.987960i	0.962420	+	0.271567i	$0.0875418\pi$
$347$	4.93125	+	18.4037i	0.264723	+	0.987960i	−0.697696	+	0.716393i	$0.745792\pi$
$348$	2.17514	−	2.51397i	0.116600	−	0.134763i
$349$	4.68226	−	17.4744i	0.250636	−	0.935385i	−0.719831	−	0.694150i	$-0.755781\pi$
$349$	4.68226	−	17.4744i	0.250636	−	0.935385i	0.970467	−	0.241236i	$-0.0775527\pi$
$350$	0.0990587	+	0.00378731i	0.00529491	+	0.000202440i
$351$	7.53530	−	6.44398i	0.402205	−	0.343954i
$352$	2.22564	+	3.29315i	0.118627	+	0.175526i
$353$	5.65589	−	3.26543i	0.301033	−	0.173801i	−0.341874	−	0.939746i	$-0.611062\pi$
$353$	5.65589	−	3.26543i	0.301033	−	0.173801i	0.642907	+	0.765944i	$0.277728\pi$
$354$	8.10865	+	6.49102i	0.430970	+	0.344994i
$355$	−2.07862	−	7.75752i	−0.110322	−	0.411726i
$356$	−11.9672	+	17.4914i	−0.634259	+	0.927040i
$357$	−0.747590	+	0.594916i	−0.0395667	+	0.0314863i
$358$	6.74239	+	2.08577i	0.356346	+	0.110236i
$359$			22.8075i			1.20373i	0.798597	+	0.601866i	$0.205576\pi$
$359$			22.8075i			1.20373i	−0.798597	+	0.601866i	$0.794424\pi$
$360$	−7.69411	−	16.1633i	−0.405515	−	0.851881i
$361$		−	12.6341i		−	0.664952i
$362$	4.34351	−	14.0407i	0.228290	−	0.737963i
$363$	16.9326	+	6.66583i	0.888732	+	0.349865i
$364$	0.478669	−	0.0897616i	0.0250891	−	0.00470479i
$365$	1.02475	+	3.82440i	0.0536377	+	0.200178i
$366$	−4.10248	−	10.5101i	−0.214440	−	0.549372i
$367$	−20.7702	+	11.9917i	−1.08419	+	0.625959i	−0.932025	−	0.362395i	$-0.881959\pi$
$367$	−20.7702	+	11.9917i	−1.08419	+	0.625959i	−0.152169	+	0.988355i	$0.548626\pi$
$368$	4.79343	−	31.1142i	0.249875	−	1.62194i
$369$	6.21519	−	26.9727i	0.323550	−	1.40414i
$370$	−1.07095	+	28.0111i	−0.0556759	+	1.45623i
$371$	0.000120990	0	0.000451542i	6.28150e−6	0	2.34429e-5i
$372$	16.2684	−	11.0282i	0.843479	−	0.571787i
$373$	6.20866	+	23.1710i	0.321472	+	1.19975i	0.917811	+	0.397018i	$0.129955\pi$
$373$	6.20866	+	23.1710i	0.321472	+	1.19975i	−0.596338	+	0.802733i	$0.703378\pi$
$374$	−0.952341	−	4.18820i	−0.0492444	−	0.216567i
$375$	12.0580	−	16.3027i	0.622674	−	0.841866i
$376$	30.7409	−	13.3228i	1.58534	−	0.687070i
$377$	1.83115			0.0943089
$378$	0.931461	+	0.108653i	0.0479092	+	0.00558853i
$379$	9.96634	+	9.96634i	0.511936	+	0.511936i	0.915119	−	0.403183i	$-0.132096\pi$
$379$	9.96634	+	9.96634i	0.511936	+	0.511936i	−0.403183	+	0.915119i	$0.632096\pi$
$380$	10.2618	+	21.3980i	0.526420	+	1.09769i
$381$	3.36128	+	22.4585i	0.172203	+	1.15059i
$382$	−6.19692	−	3.90083i	−0.317062	−	0.199584i
$383$	2.30770	−	3.99705i	0.117918	−	0.204240i	−0.801024	−	0.598632i	$-0.795711\pi$
$383$	2.30770	−	3.99705i	0.117918	−	0.204240i	0.918942	+	0.394392i	$0.129045\pi$
$384$	18.0133	−	7.71506i	0.919236	−	0.393708i
$385$	0.0945842	+	0.163825i	0.00482046	+	0.00834927i
$386$	1.42826	−	37.3568i	0.0726967	−	1.90141i
$387$	−1.19254	−	33.7431i	−0.0606202	−	1.71526i
$388$	13.2330	+	1.01336i	0.671806	+	0.0514455i
$389$	−3.31091	+	12.3565i	−0.167870	+	0.626498i	0.829787	+	0.558080i	$0.188462\pi$
$389$	−3.31091	+	12.3565i	−0.167870	+	0.626498i	−0.997657	+	0.0684178i	$0.978205\pi$
$390$	3.95985	−	9.03043i	0.200515	−	0.457274i
$391$	−17.0095	+	29.4612i	−0.860205	+	1.48992i
$392$	−15.8645	−	11.7685i	−0.801276	−	0.594398i
$393$	−7.80852	+	3.39719i	−0.393887	+	0.171366i
$394$	9.83328	+	3.04194i	0.495393	+	0.153251i
$395$	5.18345	−	5.18345i	0.260808	−	0.260808i
$396$	−2.25615	+	3.56131i	−0.113376	+	0.178962i
$397$	−3.70313	−	3.70313i	−0.185855	−	0.185855i	0.608047	−	0.793901i	$-0.291953\pi$
$397$	−3.70313	−	3.70313i	−0.185855	−	0.185855i	−0.793901	+	0.608047i	$0.791953\pi$
$398$	−1.71915	+	0.906804i	−0.0861730	+	0.0454540i
$399$	−1.23524	−	0.140475i	−0.0618392	−	0.00703252i
$400$	1.71330	+	1.37547i	0.0856650	+	0.0687733i
$401$	11.5871	+	6.68983i	0.578633	+	0.334074i	0.760590	−	0.649232i	$-0.224910\pi$
$401$	11.5871	+	6.68983i	0.578633	+	0.334074i	−0.181957	+	0.983307i	$0.558243\pi$
$402$	3.98133	+	3.18708i	0.198571	+	0.158957i
$403$	10.4572	+	2.80199i	0.520908	+	0.139577i
$404$	−16.3007	−	19.0043i	−0.810989	−	0.945497i
$405$	12.4446	−	14.3402i	0.618376	−	0.712570i
$406$	0.117699	+	0.127056i	0.00584128	+	0.00630570i
$407$	5.71713	−	3.30079i	0.283388	−	0.163614i
$408$	−21.1633	+	0.718138i	−1.04774	+	0.0355531i
$409$	24.1053	+	13.9172i	1.19193	+	0.688161i	0.958744	−	0.284272i	$-0.0917518\pi$
$409$	24.1053	+	13.9172i	1.19193	+	0.688161i	0.233185	+	0.972432i	$0.425085\pi$
$410$	−6.10359	−	26.8423i	−0.301435	−	1.32565i
$411$	−7.36013	−	9.24896i	−0.363048	−	0.456217i
$412$	7.29658	+	15.2148i	0.359477	+	0.749582i
$413$	−0.382639	+	0.382639i	−0.0188285	+	0.0188285i
$414$	32.2780	−	8.54904i	1.58638	−	0.420162i
$415$			3.21387i			0.157763i
$416$	9.70590	+	4.72290i	0.475871	+	0.231559i
$417$	−17.0063	+	7.39880i	−0.832802	+	0.362321i
$418$	2.97731	−	4.72980i	0.145625	−	0.231342i
$419$	9.97902	−	2.67387i	0.487507	−	0.130627i	−0.00668892	−	0.999978i	$-0.502129\pi$
$419$	9.97902	−	2.67387i	0.487507	−	0.130627i	0.494196	+	0.869350i	$0.335462\pi$
$420$	0.881110	−	0.305680i	0.0429938	−	0.0149157i
$421$	−29.8528	−	7.99904i	−1.45494	−	0.389849i	−0.557199	−	0.830379i	$-0.688124\pi$
$421$	−29.8528	−	7.99904i	−1.45494	−	0.389849i	−0.897738	+	0.440529i	$0.854791\pi$
$422$	−11.0820	−	11.9631i	−0.539464	−	0.582354i
$423$	25.9996	+	24.2246i	1.26414	+	1.17784i
$424$	0.00811622	−	0.00644009i	0.000394158	−	0.000312758i
$425$	−1.18711	−	2.05613i	−0.0575833	−	0.0997371i
$426$	5.52336	+	7.51295i	0.267608	+	0.364004i
$427$	0.567770	−	0.152134i	0.0274763	−	0.00736226i
$428$	−3.77987	−	20.1568i	−0.182707	−	0.974314i
$429$	−2.29662	+	0.343725i	−0.110882	+	0.0165952i
$430$	−15.6661	−	29.7003i	−0.755488	−	1.43228i
$431$	14.8449			0.715053			0.357526	−	0.933903i	$-0.383620\pi$
$431$	14.8449			0.715053			0.357526	+	0.933903i	$0.383620\pi$
$432$	15.1459	+	14.2338i	0.728706	+	0.684826i
$433$	−32.1617			−1.54559			−0.772796	−	0.634654i	$-0.781143\pi$
$433$	−32.1617			−1.54559			−0.772796	+	0.634654i	$0.781143\pi$
$434$	0.477724	+	0.905683i	0.0229315	+	0.0434742i
$435$	3.46802	−	0.519044i	0.166279	−	0.0248863i
$436$	28.5921	−	5.36169i	1.36931	−	0.256778i
$437$	−42.7576	+	11.4569i	−2.04537	+	0.548056i
$438$	−2.72298	−	3.70383i	−0.130109	−	0.176976i
$439$	−0.140035	−	0.242548i	−0.00668352	−	0.0115762i	0.862664	−	0.505777i	$-0.168794\pi$
$439$	−0.140035	−	0.242548i	−0.00668352	−	0.0115762i	−0.869348	+	0.494201i	$0.835461\pi$
$440$	−0.479609	+	4.16515i	−0.0228644	+	0.198566i
$441$	4.70440	−	20.4161i	0.224019	−	0.972197i
$442$	−7.92663	−	8.55684i	−0.377031	−	0.407007i
$443$	−24.2588	−	6.50011i	−1.15257	−	0.308830i	−0.368574	−	0.929598i	$-0.620154\pi$
$443$	−24.2588	−	6.50011i	−1.15257	−	0.308830i	−0.783994	+	0.620768i	$0.786821\pi$
$444$	−10.6676	−	30.7489i	−0.506261	−	1.45928i
$445$	−21.5938	+	5.78605i	−1.02365	+	0.274285i
$446$	−15.6430	+	24.8507i	−0.740717	+	1.17672i
$447$	0.335492	−	0.145960i	0.0158682	−	0.00690367i
$448$	0.296151	+	0.977024i	0.0139918	+	0.0461601i
$449$			14.2885i			0.674318i	0.941448	+	0.337159i	$0.109466\pi$
$449$			14.2885i			0.674318i	−0.941448	+	0.337159i	$0.890534\pi$
$450$	−0.609646	+	2.24923i	−0.0287390	+	0.106030i
$451$	−4.58408	+	4.58408i	−0.215856	+	0.215856i
$452$	−38.0990	+	18.2711i	−1.79203	+	0.859402i
$453$	−2.47621	−	3.11168i	−0.116343	−	0.146200i
$454$	−2.48474	−	10.9274i	−0.116615	−	0.512847i
$455$	0.444893	+	0.256859i	0.0208569	+	0.0120417i
$456$	−20.1331	−	18.8116i	−0.942819	−	0.880934i
$457$	−24.1097	+	13.9198i	−1.12781	+	0.651139i	−0.943382	−	0.331708i	$-0.892375\pi$
$457$	−24.1097	+	13.9198i	−1.12781	+	0.651139i	−0.184424	+	0.982847i	$0.559042\pi$
$458$	−0.446434	−	0.481928i	−0.0208605	−	0.0225190i
$459$	−9.68207	−	20.2660i	−0.451921	−	0.945935i
$460$	25.2057	−	21.6199i	1.17522	−	1.00803i
$461$	16.1887	+	4.33776i	0.753985	+	0.202030i	0.615285	−	0.788305i	$-0.289041\pi$
$461$	16.1887	+	4.33776i	0.753985	+	0.202030i	0.138700	+	0.990334i	$0.455708\pi$
$462$	−0.171467	−	0.137260i	−0.00797735	−	0.00638592i
$463$	26.1951	+	15.1238i	1.21739	+	0.702861i	0.964359	−	0.264597i	$-0.0852389\pi$
$463$	26.1951	+	15.1238i	1.21739	+	0.702861i	0.253032	+	0.967458i	$0.418572\pi$
$464$	0.417361	+	3.81587i	0.0193755	+	0.177147i
$465$	20.5991	+	2.34259i	0.955261	+	0.108635i
$466$	11.4296	−	6.02883i	0.529467	−	0.279280i
$467$	15.9369	+	15.9369i	0.737469	+	0.737469i	0.972088	−	0.234618i	$-0.0753840\pi$
$467$	15.9369	+	15.9369i	0.737469	+	0.737469i	−0.234618	+	0.972088i	$0.575384\pi$
$468$	−0.470432	+	11.4391i	−0.0217457	+	0.528772i
$469$	−0.187875	+	0.187875i	−0.00867527	+	0.00867527i
$470$	33.7623	+	10.4444i	1.55734	+	0.481765i
$471$	26.6620	−	11.5996i	1.22852	−	0.534482i
$472$	−11.8639	+	1.75856i	−0.546081	+	0.0809443i
$473$	−3.95399	+	6.84851i	−0.181805	+	0.314895i
$474$	−3.41802	+	7.79480i	−0.156995	+	0.358027i
$475$	0.799588	−	2.98410i	0.0366876	−	0.136920i
$476$	0.0842354	−	1.10000i	0.00386092	−	0.0504183i
$477$	0.00970520	+	0.00515511i	0.000444371	+	0.000236036i
$478$	−0.395311	+	10.3395i	−0.0180811	+	0.472919i
$479$	−14.8100	−	25.6516i	−0.676684	−	1.17205i	−0.975973	−	0.217889i	$-0.930083\pi$
$479$	−14.8100	−	25.6516i	−0.676684	−	1.17205i	0.299289	−	0.954163i	$-0.403251\pi$
$480$	19.7208	+	6.19356i	0.900126	+	0.282696i
$481$	8.96385	−	15.5258i	0.408716	−	0.707917i
$482$	−2.98869	−	1.88132i	−0.136131	−	0.0856916i
$483$	0.257494	+	1.72046i	0.0117164	+	0.0782837i
$484$	−18.9465	+	9.08618i	−0.861206	+	0.413008i
$485$	9.89919	+	9.89919i	0.449499	+	0.449499i
$486$	−7.40579	+	20.7643i	−0.335933	+	0.941886i
$487$	25.6320			1.16150			0.580749	−	0.814083i	$-0.302760\pi$
$487$	25.6320			1.16150			0.580749	+	0.814083i	$0.302760\pi$
$488$	12.1156	+	4.78921i	0.548446	+	0.216797i
$489$	−0.714315	+	0.965765i	−0.0323024	+	0.0436734i
$490$	−4.61993	−	20.3175i	−0.208707	−	0.917850i
$491$	−1.40692	−	5.25069i	−0.0634933	−	0.236960i	0.926885	−	0.375345i	$-0.122476\pi$
$491$	−1.40692	−	5.25069i	−0.0634933	−	0.236960i	−0.990379	+	0.138385i	$0.955809\pi$
$492$	17.9341	+	26.4558i	0.808533	+	1.19272i
$493$	1.07360	−	4.00671i	0.0483523	−	0.180453i
$494$	0.579857	−	15.1664i	0.0260890	−	0.682369i
$495$	−4.25214	+	1.30196i	−0.191119	+	0.0585190i
$496$	−3.45555	+	22.4300i	−0.155159	+	1.00714i
$497$	−0.420724	+	0.242905i	−0.0188720	+	0.0108958i
$498$	−1.35685	−	3.47611i	−0.0608021	−	0.155768i
$499$	5.78179	+	21.5779i	0.258829	+	0.965961i	0.965920	+	0.258840i	$0.0833401\pi$
$499$	5.78179	+	21.5779i	0.258829	+	0.965961i	−0.707092	+	0.707122i	$0.749993\pi$
$500$	4.31551	+	23.0132i	0.192996	+	1.02918i
$501$	−17.3849	−	6.84387i	−0.776700	−	0.305762i
$502$	−1.64096	+	5.30451i	−0.0732395	+	0.236752i
$503$			24.7337i			1.10282i	0.834235	+	0.551410i	$0.185910\pi$
$503$			24.7337i			1.10282i	−0.834235	+	0.551410i	$0.814090\pi$
$504$	−0.823952	+	0.702616i	−0.0367018	+	0.0312970i
$505$		−	26.4104i		−	1.17525i
$506$	−7.47123	−	2.31124i	−0.332137	−	0.102747i
$507$	12.6842	−	10.0938i	0.563327	−	0.448284i
$508$	−21.6413	−	14.8065i	−0.960178	−	0.656932i
$509$	−2.31048	−	8.62284i	−0.102410	−	0.382201i	0.895628	−	0.444804i	$-0.146726\pi$
$509$	−2.31048	−	8.62284i	−0.102410	−	0.382201i	−0.998039	+	0.0626029i	$0.980060\pi$
$510$	−17.4377	−	13.9590i	−0.772156	−	0.618116i
$511$	0.207414	−	0.119751i	0.00917545	−	0.00529745i
$512$	−7.62971	+	21.3023i	−0.337189	+	0.941437i
$513$	9.73824	−	27.5552i	0.429954	−	1.21659i
$514$	−15.6972	−	0.600152i	−0.692375	−	0.0264716i
$515$	−4.60680	+	17.1928i	−0.203000	+	0.757606i
$516$	29.4836	+	25.5097i	1.29794	+	1.12300i
$517$	−2.15414	−	8.03937i	−0.0947391	−	0.353571i
$518$	1.65344	−	0.375970i	0.0726479	−	0.0165192i
$519$	−8.22413	−	0.935271i	−0.360999	−	0.0410538i
$520$	4.52762	+	10.4470i	0.198549	+	0.458131i
$521$	14.1129			0.618299			0.309149	−	0.951013i	$-0.399956\pi$
$521$	14.1129			0.618299			0.309149	+	0.951013i	$0.399956\pi$
$522$	−3.53187	+	2.02555i	−0.154586	+	0.0886559i
$523$	−27.5776	−	27.5776i	−1.20588	−	1.20588i	−0.972349	−	0.233534i	$-0.924971\pi$
$523$	−27.5776	−	27.5776i	−1.20588	−	1.20588i	−0.233534	−	0.972349i	$-0.575029\pi$
$524$	3.26270	−	9.27577i	0.142532	−	0.405214i
$525$	−0.112972	−	0.0444733i	−0.00493048	−	0.00194097i
$526$	−14.4687	+	22.9852i	−0.630863	+	1.00220i
$527$	12.2620	−	21.2384i	0.534141	−	0.925159i
$528$	−1.23973	−	4.70750i	−0.0539523	−	0.204868i
$529$	19.4709	+	33.7246i	0.846561	+	1.46629i
$530$	0.0109211		0.000417544i	0.000474380		1.81370e-5i
$531$	−6.74567	−	10.7852i	−0.292737	−	0.468039i
$532$	1.08961	−	0.934600i	0.0472406	−	0.0405201i
$533$	−4.55660	+	17.0054i	−0.197368	+	0.736588i
$534$	20.9131	−	15.3748i	0.904997	−	0.665334i
$535$	10.8164	−	18.7345i	0.467632	−	0.809962i
$536$	−5.82515	+	0.863450i	−0.251608	+	0.0372953i
$537$	−6.94946	−	5.14007i	−0.299891	−	0.221810i
$538$	4.53038	−	14.6448i	0.195319	−	0.631381i
$539$	−3.46978	+	3.46978i	−0.149454	+	0.149454i
$540$	2.35149	+	21.7979i	0.101192	+	0.938032i
$541$	7.82995	+	7.82995i	0.336636	+	0.336636i	0.855100	−	0.518464i	$-0.173496\pi$
$541$	7.82995	+	7.82995i	0.336636	+	0.336636i	−0.518464	+	0.855100i	$0.673496\pi$
$542$	−8.56427	−	16.2364i	−0.367867	−	0.697412i
$543$	−10.7040	+	14.4719i	−0.459351	+	0.621050i
$544$	16.0247	−	18.4684i	0.687052	−	0.791824i
$545$	26.5746	+	15.3429i	1.13833	+	0.657216i
$546$	−0.589638	−	0.0899901i	−0.0252342	−	0.00385122i
$547$	−21.7416	−	5.82566i	−0.929606	−	0.249087i	−0.237919	−	0.971285i	$-0.576465\pi$
$547$	−21.7416	−	5.82566i	−0.929606	−	0.249087i	−0.691686	+	0.722198i	$0.743132\pi$
$548$	13.6088	+	1.04214i	0.581340	+	0.0445178i
$549$	0.488049	+	13.8094i	0.0208294	+	0.589373i
$550$	0.400406	−	0.370916i	0.0170734	−	0.0158159i
$551$	4.67438	−	2.69876i	0.199135	−	0.114971i
$552$	−18.1348	+	34.0255i	−0.771866	+	1.44822i
$553$	−0.384019	−	0.221713i	−0.0163301	−	0.00942821i
$554$	34.2400	−	7.78571i	1.45472	−	0.330783i
$555$	12.5758	−	31.9453i	0.533814	−	1.35600i
$556$	7.10589	−	20.2019i	0.301357	−	0.856750i
$557$	−25.5918	+	25.5918i	−1.08436	+	1.08436i	−0.0882628	+	0.996097i	$0.528132\pi$
$557$	−25.5918	+	25.5918i	−1.08436	+	1.08436i	−0.996097	+	0.0882628i	$0.971868\pi$
$558$	−23.2690	+	6.16294i	−0.985053	+	0.260898i
$559$			21.4755i			0.908315i
$560$	−0.433859	+	0.985643i	−0.0183339	+	0.0416510i
$561$	−0.594397	+	5.22672i	−0.0250955	+	0.220672i
$562$	8.83552	+	5.56176i	0.372704	+	0.234609i
$563$	11.3728	−	3.04735i	0.479308	−	0.128430i	−0.0110721	−	0.999939i	$-0.503524\pi$
$563$	11.3728	−	3.04735i	0.479308	−	0.128430i	0.490381	+	0.871508i	$0.336858\pi$
$564$	−40.9268	+	2.95736i	−1.72333	+	0.124527i
$565$	−43.0520	−	11.5357i	−1.81121	−	0.485313i
$566$	−6.44131	+	5.96690i	−0.270748	+	0.250808i
$567$	−1.03272	−	0.502617i	−0.0433702	−	0.0211079i
$568$	−10.6967	−	1.23170i	−0.448822	−	0.0516810i
$569$	0.819418	+	1.41927i	0.0343518	+	0.0594990i	0.882690	−	0.469955i	$-0.155730\pi$
$569$	0.819418	+	1.41927i	0.0343518	+	0.0594990i	−0.848338	+	0.529454i	$0.822397\pi$
$570$	−3.20077	−	28.8881i	−0.134066	−	1.20999i
$571$	−32.7015	+	8.76233i	−1.36851	+	0.366692i	−0.866936	−	0.498420i	$-0.833914\pi$
$571$	−32.7015	+	8.76233i	−1.36851	+	0.366692i	−0.501578	+	0.865112i	$0.667247\pi$
$572$	1.51412	−	2.21305i	0.0633083	−	0.0925321i
$573$	5.58427	+	7.01737i	0.233286	+	0.293155i
$574$	−1.47282	+	0.776875i	−0.0614744	+	0.0324261i
$575$	−4.32299			−0.180281
$576$	−23.9448	+	1.62692i	−0.997700	+	0.0677881i
$577$	−16.0429			−0.667873			−0.333936	−	0.942596i	$-0.608377\pi$
$577$	−16.0429			−0.667873			−0.333936	+	0.942596i	$0.608377\pi$
$578$	−2.10576	+	1.11073i	−0.0875882	+	0.0462005i
$579$	−16.7717	+	42.6036i	−0.697007	+	1.77055i
$580$	−2.28640	+	3.34182i	−0.0949376	+	0.138762i
$581$	0.187784	−	0.0503166i	0.00779060	−	0.00208749i
$582$	−14.8862	−	6.52763i	−0.617055	−	0.270579i
$583$	−0.00128692	−	0.00222901i	−5.32988e−5	−	9.23163e-5i
$584$	5.27339	+	0.607220i	0.218214	+	0.0251269i
$585$	−8.23249	+	8.83571i	−0.340372	+	0.365312i
$586$	25.7928	−	23.8931i	1.06549	−	0.987016i
$587$	36.9837	+	9.90974i	1.52648	+	0.409019i	0.921869	−	0.387502i	$-0.126662\pi$
$587$	36.9837	+	9.90974i	1.52648	+	0.409019i	0.604611	+	0.796521i	$0.293329\pi$
$588$	13.5747	+	20.0249i	0.559810	+	0.825812i
$589$	30.8237	−	8.25918i	1.27007	−	0.340313i
$590$	−10.7066	−	6.73958i	−0.440784	−	0.277464i
$591$	−10.1353	−	7.49641i	−0.416910	−	0.308361i
$592$	34.3969	+	15.1408i	1.41370	+	0.622282i
$593$		−	32.2597i		−	1.32475i	−0.749173	−	0.662374i	$-0.769549\pi$
$593$		−	32.2597i		−	1.32475i	0.749173	−	0.662374i	$-0.230451\pi$
$594$	4.04943	−	3.20340i	0.166150	−	0.131437i
$595$	0.822870	−	0.822870i	0.0337344	−	0.0337344i
$596$	−0.140182	+	0.398533i	−0.00574206	+	0.0163245i
$597$	2.35425	−	0.352351i	0.0963529	−	0.0144207i
$598$	−20.7094	+	4.70904i	−0.846870	+	0.192567i
$599$	11.7417	+	6.77905i	0.479751	+	0.276984i	0.720313	−	0.693649i	$-0.243998\pi$
$599$	11.7417	+	6.77905i	0.479751	+	0.276984i	−0.240562	+	0.970634i	$0.577332\pi$
$600$	−1.42371	−	2.28342i	−0.0581227	−	0.0932202i
$601$	−0.496416	+	0.286606i	−0.0202492	+	0.0116909i	−0.510090	−	0.860121i	$-0.670388\pi$
$601$	−0.496416	+	0.286606i	−0.0202492	+	0.0116909i	0.489841	+	0.871812i	$0.337055\pi$
$602$	−1.49010	+	1.38035i	−0.0607319	+	0.0562590i
$603$	−3.31211	−	5.29553i	−0.134880	−	0.215651i
$604$	4.57850	+	0.350612i	0.186297	+	0.0142662i
$605$	−21.4096	−	5.73669i	−0.870425	−	0.233230i
$606$	11.1501	+	28.5655i	0.452944	+	1.16039i
$607$	29.1103	+	16.8068i	1.18155	+	0.682168i	0.956373	−	0.292149i	$-0.0943705\pi$
$607$	29.1103	+	16.8068i	1.18155	+	0.682168i	0.225178	+	0.974318i	$0.427704\pi$
$608$	31.7370	−	2.24843i	1.28710	−	0.0911858i
$609$	−0.0846230	−	0.194508i	−0.00342910	−	0.00788185i
$610$	6.41140	+	12.1549i	0.259590	+	0.492138i
$611$	−15.9823	−	15.9823i	−0.646576	−	0.646576i
$612$	24.7539	+	7.73605i	1.00062	+	0.312711i
$613$	26.5621	−	26.5621i	1.07283	−	1.07283i	0.0757042	−	0.997130i	$-0.475880\pi$
$613$	26.5621	−	26.5621i	1.07283	−	1.07283i	0.997130	−	0.0757042i	$-0.0241205\pi$
$614$	−10.2711	+	33.2021i	−0.414509	+	1.33993i
$615$	−3.80951	+	33.4983i	−0.153614	+	1.35078i
$616$	0.250876	−	0.0371868i	0.0101081	−	0.00149830i
$617$	11.8730	−	20.5647i	0.477991	−	0.827904i	−0.521691	−	0.853134i	$-0.674699\pi$
$617$	11.8730	−	20.5647i	0.477991	−	0.827904i	0.999682	+	0.0252305i	$0.00803196\pi$
$618$	−2.27588	−	20.5406i	−0.0915493	−	0.826266i
$619$	4.60330	−	17.1798i	0.185022	−	0.690513i	−0.809603	−	0.586977i	$-0.800318\pi$
$619$	4.60330	−	17.1798i	0.185022	−	0.690513i	0.994626	−	0.103535i	$-0.0330155\pi$
$620$	−18.1706	+	15.5856i	−0.729748	+	0.625933i
$621$	−40.7713	−	3.18290i	−1.63610	−	0.127725i
$622$	−19.4897	−	0.745149i	−0.781466	−	0.0298778i
$623$	0.676151	+	1.17113i	0.0270894	+	0.0469202i
$624$	−9.30765	−	9.38793i	−0.372604	−	0.375818i
$625$	−10.9760	+	19.0109i	−0.439038	+	0.760436i
$626$	15.3428	−	24.3738i	0.613221	−	0.974173i
$627$	−5.35600	+	4.26219i	−0.213898	+	0.170216i
$628$	−11.1404	+	31.6719i	−0.444550	+	1.26384i
$629$	−28.7164	−	28.7164i	−1.14500	−	1.14500i
$630$	−1.14223	−	0.00329805i	−0.0455074	−	0.000131398i
$631$	16.0572			0.639228			0.319614	−	0.947548i	$-0.396447\pi$
$631$	16.0572			0.639228			0.319614	+	0.947548i	$0.396447\pi$
$632$	−3.90811	−	9.01753i	−0.155456	−	0.358698i
$633$	7.96776	+	18.3141i	0.316690	+	0.727919i
$634$	29.0008	−	6.59441i	1.15177	−	0.261897i
$635$	−7.15884	−	26.7172i	−0.284090	−	1.06024i
$636$	−0.0119885	+	0.00415911i	−0.000475374	+	0.000164920i
$637$	−3.44897	+	12.8717i	−0.136653	+	0.509997i
$638$	0.952893	+	0.0364320i	0.0377254	+	0.00144235i
$639$	−3.34362	−	10.9201i	−0.132272	−	0.431991i
$640$	−20.7382	+	11.8161i	−0.819749	+	0.467071i
$641$	35.3930	−	20.4342i	1.39794	−	0.807102i	0.403764	−	0.914863i	$-0.367702\pi$
$641$	35.3930	−	20.4342i	1.39794	−	0.807102i	0.994177	+	0.107761i	$0.0343683\pi$
$642$	−3.78949	+	24.8297i	−0.149559	+	0.979950i
$643$	−8.91467	−	33.2700i	−0.351560	−	1.31204i	−0.884758	−	0.466050i	$-0.845677\pi$
$643$	−8.91467	−	33.2700i	−0.351560	−	1.31204i	0.533198	−	0.845991i	$-0.320990\pi$
$644$	−1.65786	−	1.13427i	−0.0653287	−	0.0446964i
$645$	6.08728	+	40.6725i	0.239686	+	1.60148i
$646$	−32.8455	−	10.1608i	−1.29229	−	0.399771i
$647$		−	28.1696i		−	1.10746i	−0.832696	−	0.553730i	$-0.813204\pi$
$647$		−	28.1696i		−	1.10746i	0.832696	−	0.553730i	$-0.186796\pi$
$648$	−11.7462	−	22.5838i	−0.461433	−	0.887175i
$649$			2.97943i			0.116953i
$650$	0.438047	−	1.41602i	0.0171816	−	0.0555408i
$651$	−0.185626	−	1.24027i	−0.00727525	−	0.0486099i
$652$	−0.255650	−	1.36330i	−0.0100120	−	0.0533908i
$653$	2.17456	+	8.11558i	0.0850972	+	0.317587i	0.995333	−	0.0965042i	$-0.0307661\pi$
$653$	2.17456	+	8.11558i	0.0850972	+	0.317587i	−0.910235	+	0.414091i	$0.864099\pi$
$654$	−35.2206	−	5.37534i	−1.37723	−	0.210192i
$655$	8.98247	−	5.18603i	0.350974	−	0.202635i
$656$	−36.4757	−	5.61941i	−1.42414	−	0.219401i
$657$	1.64838	+	5.38352i	0.0643096	+	0.210031i
$658$	0.0816744	−	2.13623i	0.00318400	−	0.0832789i
$659$	−6.62788	+	24.7356i	−0.258186	+	0.963562i	0.708105	+	0.706107i	$0.249550\pi$
$659$	−6.62788	+	24.7356i	−0.258186	+	0.963562i	−0.966290	+	0.257455i	$0.917116\pi$
$660$	2.24030	−	4.62048i	0.0872034	−	0.179852i
$661$	−5.44473	−	20.3200i	−0.211775	−	0.790357i	−0.987277	−	0.159011i	$-0.949170\pi$
$661$	−5.44473	−	20.3200i	−0.211775	−	0.790357i	0.775501	−	0.631346i	$-0.217497\pi$
$662$	5.53914	+	24.3600i	0.215285	+	0.946778i
$663$	5.69910	+	13.0995i	0.221335	+	0.508742i
$664$	4.00710	+	1.58398i	0.155506	+	0.0614704i
$665$	1.51424			0.0587198
$666$	−0.115095	+	39.8613i	−0.00445984	+	1.54459i
$667$	−5.34063	−	5.34063i	−0.206790	−	0.206790i
$668$	19.4526	−	9.32887i	0.752644	−	0.360945i
$669$	28.1408	−	22.3939i	1.08799	−	0.865798i
$670$	−5.25692	−	3.30912i	−0.203093	−	0.127842i
$671$	1.61818	−	2.80277i	0.0624691	−	0.108200i
$672$	0.0531355	−	1.24924i	0.00204975	−	0.0481905i
$673$	−12.5221	−	21.6890i	−0.482693	−	0.836048i	0.517110	−	0.855919i	$-0.327008\pi$
$673$	−12.5221	−	21.6890i	−0.482693	−	0.836048i	−0.999803	+	0.0198709i	$0.993674\pi$
$674$	−0.521432	+	13.6383i	−0.0200848	+	0.525327i
$675$	1.61511	−	2.35318i	0.0621658	−	0.0905741i
$676$	−1.42921	+	18.6635i	−0.0549696	+	0.717825i
$677$	−4.91241	+	18.3334i	−0.188799	+	0.704608i	0.804986	+	0.593294i	$0.202173\pi$
$677$	−4.91241	+	18.3334i	−0.188799	+	0.704608i	−0.993785	+	0.111314i	$0.964494\pi$
$678$	51.4352	−	5.69896i	1.97536	−	0.218867i
$679$	0.423420	−	0.733386i	0.0162494	−	0.0281448i
$680$	25.5135	−	3.78180i	0.978396	−	0.145026i
$681$	−1.55083	+	13.6370i	−0.0594281	+	0.522570i
$682$	5.38596	+	1.66615i	0.206239	+	0.0638003i
$683$	3.70253	−	3.70253i	0.141673	−	0.141673i	−0.632713	−	0.774386i	$-0.718059\pi$
$683$	3.70253	−	3.70253i	0.141673	−	0.141673i	0.774386	+	0.632713i	$0.218059\pi$
$684$	15.6581	+	29.8940i	0.598704	+	1.14303i
$685$	10.1803	+	10.1803i	0.388969	+	0.388969i
$686$	−2.23221	+	1.17743i	−0.0852263	+	0.0449547i
$687$	0.320978	+	0.737774i	0.0122461	+	0.0281478i
$688$	−44.7520	+	4.89475i	−1.70616	+	0.186611i
$689$	−0.00605326	−	0.00349485i	−0.000230611	−	0.000133143i
$690$	−37.8868	+	14.7886i	−1.44233	+	0.562993i
$691$	8.18783	+	2.19392i	0.311480	+	0.0834607i	0.411173	−	0.911558i	$-0.365119\pi$
$691$	8.18783	+	2.19392i	0.311480	+	0.0834607i	−0.0996929	+	0.995018i	$0.531786\pi$
$692$	7.25455	−	6.22251i	0.275777	−	0.236544i
$693$	0.142645	+	0.228066i	0.00541863	+	0.00866352i
$694$	18.3110	+	19.7669i	0.695078	+	0.750340i
$695$	19.5631	−	11.2947i	0.742070	−	0.428434i
$696$	1.06209	−	4.57980i	0.0402584	−	0.173597i
$697$	34.5379	+	19.9405i	1.30822	+	0.755299i
$698$	−5.67274	−	24.9475i	−0.214716	−	0.944278i
$699$	−15.6521	+	2.34258i	−0.592015	+	0.0886045i
$700$	0.126408	−	0.0606214i	0.00477777	−	0.00229127i
$701$	16.2977	−	16.2977i	0.615557	−	0.615557i	−0.328831	−	0.944389i	$-0.606655\pi$
$701$	16.2977	−	16.2977i	0.615557	−	0.615557i	0.944389	+	0.328831i	$0.106655\pi$
$702$	5.17392	−	13.0323i	0.195277	−	0.491874i
$703$		−	52.8439i		−	1.99304i
$704$	4.95680	+	2.65081i	0.186816	+	0.0999063i
$705$	−34.7992	−	25.7388i	−1.31062	−	0.969378i
$706$	4.92023	−	7.81637i	0.185175	−	0.294173i
$707$	−1.54314	+	0.413484i	−0.0580359	+	0.0155507i
$708$	14.4256	+	2.76932i	0.542147	+	0.104077i
$709$	−18.6437	−	4.99557i	−0.700180	−	0.187613i	−0.108869	−	0.994056i	$-0.534723\pi$
$709$	−18.6437	−	4.99557i	−0.700180	−	0.187613i	−0.591311	+	0.806443i	$0.701390\pi$
$710$	−7.71848	−	8.33214i	−0.289669	−	0.312700i
$711$	7.10604	−	7.62672i	0.266497	−	0.286024i
$712$	−3.42856	+	29.7753i	−0.128491	+	1.11588i
$713$	−22.3267	−	38.6710i	−0.836142	−	1.44824i
$714$	−0.542609	+	1.23742i	−0.0203066	+	0.0463093i
$715$	2.73210	−	0.732065i	0.102175	−	0.0273777i
$716$	9.81001	−	1.83961i	0.366617	−	0.0687493i
$717$	4.64202	−	11.7917i	0.173359	−	0.440370i
$718$	15.0483	+	28.5291i	0.561599	+	1.06470i
$719$	−24.2401			−0.904003			−0.452002	−	0.892017i	$-0.649290\pi$
$719$	−24.2401			−0.904003			−0.452002	+	0.892017i	$0.649290\pi$
$720$	−20.2888	−	15.1416i	−0.756120	−	0.564293i
$721$	1.07669			0.0400980
$722$	−8.33596	−	15.8036i	−0.310232	−	0.588148i
$723$	2.69322	+	3.38438i	0.100162	+	0.125866i
$724$	−3.83090	−	20.4289i	−0.142374	−	0.759234i
$725$	0.509157	−	0.136428i	0.0189096	−	0.00506682i
$726$	25.5786	−	2.83408i	0.949309	−	0.105182i
$727$	−8.10074	−	14.0309i	−0.300440	−	0.520377i	0.675796	−	0.737089i	$-0.263800\pi$
$727$	−8.10074	−	14.0309i	−0.300440	−	0.520377i	−0.976236	+	0.216712i	$0.930467\pi$
$728$	0.539526	−	0.428105i	0.0199962	−	0.0158666i
$729$	16.9652	−	21.0044i	0.628340	−	0.777939i
$730$	3.80516	+	4.10769i	0.140835	+	0.152032i
$731$	46.9902	+	12.5910i	1.73800	+	0.465694i
$732$	−12.0662	−	10.4399i	−0.445980	−	0.385871i
$733$	8.04180	−	2.15479i	0.297031	−	0.0795891i	−0.107226	−	0.994235i	$-0.534197\pi$
$733$	8.04180	−	2.15479i	0.297031	−	0.0795891i	0.404257	+	0.914646i	$0.367530\pi$
$734$	−18.0686	+	28.7041i	−0.666924	+	1.05949i
$735$	−2.88349	+	25.3555i	−0.106359	+	0.935251i
$736$	−14.5332	−	42.0824i	−0.535700	−	1.55118i
$737$			1.46289i			0.0538863i
$738$	−10.0222	−	37.8400i	−0.368922	−	1.39291i
$739$	22.8405	−	22.8405i	0.840203	−	0.840203i	−0.148682	−	0.988885i	$-0.547503\pi$
$739$	22.8405	−	22.8405i	0.840203	−	0.840203i	0.988885	+	0.148682i	$0.0475030\pi$
$740$	17.1421	+	35.7447i	0.630155	+	1.31400i
$741$	−6.80909	+	17.2966i	−0.250138	+	0.635405i
$742$	−0.000146584	0	0.000644647i	−5.38128e−6	0	2.36657e-5i
$743$	−7.19608	−	4.15466i	−0.263999	−	0.152420i	0.362159	−	0.932116i	$-0.382040\pi$
$743$	−7.19608	−	4.15466i	−0.263999	−	0.152420i	−0.626157	+	0.779697i	$0.715373\pi$
$744$	13.0732	−	24.5287i	0.479287	−	0.899267i
$745$	−0.385931	+	0.222817i	−0.0141394	+	0.00816339i
$746$	23.0544	+	24.8874i	0.844083	+	0.911192i
$747$	0.161417	+	4.56734i	0.00590595	+	0.167110i
$748$	−3.95462	−	4.61052i	−0.144595	−	0.168577i
$749$	−1.26399	−	0.338684i	−0.0461850	−	0.0123752i
$750$	4.32650	−	28.3483i	0.157981	−	1.03513i
$751$	28.0215	+	16.1782i	1.02252	+	0.590352i	0.914833	−	0.403833i	$-0.132322\pi$
$751$	28.0215	+	16.1782i	1.02252	+	0.590352i	0.107687	+	0.994185i	$0.465656\pi$
$752$	29.6623	−	36.9478i	1.08167	−	1.34735i
$753$	4.04390	−	5.46742i	0.147368	−	0.199244i
$754$	2.29052	−	1.20819i	0.0834158	−	0.0439996i
$755$	3.42502	+	3.42502i	0.124649	+	0.124649i
$756$	1.23682	−	0.478666i	0.0449828	−	0.0174089i
$757$	3.76265	−	3.76265i	0.136756	−	0.136756i	−0.635415	−	0.772171i	$-0.719171\pi$
$757$	3.76265	−	3.76265i	0.136756	−	0.136756i	0.772171	+	0.635415i	$0.219171\pi$
$758$	19.0423	+	5.89077i	0.691649	+	0.213962i
$759$	7.70069	+	5.69570i	0.279517	+	0.206741i
$760$	26.9545	+	19.9953i	0.977743	+	0.725304i
$761$	13.1168	−	22.7190i	0.475485	−	0.823564i	−0.524121	−	0.851644i	$-0.675606\pi$
$761$	13.1168	−	22.7190i	0.475485	−	0.823564i	0.999606	+	0.0280801i	$0.00893934\pi$
$762$	19.0226	+	25.8748i	0.689117	+	0.937347i
$763$	0.480419	−	1.79295i	0.0173923	−	0.0649090i
$764$	−10.3253	−	0.790689i	−0.373556	−	0.0286061i
$765$	14.5066	+	23.1938i	0.524489	+	0.838572i
$766$	0.249371	−	6.52239i	0.00901012	−	0.235664i
$767$	4.04557	+	7.00713i	0.146077	+	0.253013i
$768$	17.4418	−	21.5356i	0.629376	−	0.777101i
$769$	−9.31591	+	16.1356i	−0.335940	+	0.581865i	−0.983665	−	0.180009i	$-0.942387\pi$
$769$	−9.31591	+	16.1356i	−0.335940	+	0.581865i	0.647725	+	0.761874i	$0.275721\pi$
$770$	0.226403	+	0.142516i	0.00815901	+	0.00513592i
$771$	17.9019	+	7.04741i	0.644722	+	0.253806i
$772$	−22.8614	−	47.6707i	−0.822801	−	1.71571i
$773$	−4.69430	−	4.69430i	−0.168842	−	0.168842i	0.617628	−	0.786470i	$-0.288094\pi$
$773$	−4.69430	−	4.69430i	−0.168842	−	0.168842i	−0.786470	+	0.617628i	$0.788094\pi$
$774$	−23.7554	−	41.4213i	−0.853870	−	1.48886i
$775$	3.11641			0.111945
$776$	17.2214	−	7.46357i	0.618211	−	0.267927i
$777$	−2.06343	−	0.234659i	−0.0740252	−	0.00841834i
$778$	4.01129	+	17.6408i	0.143812	+	0.632454i
$779$	13.4311	+	50.1255i	0.481218	+	1.79593i
$780$	−1.00503	−	13.9086i	−0.0359859	−	0.498006i
$781$	−0.692294	+	2.58368i	−0.0247722	+	0.0924512i
$782$	−1.83805	+	48.0749i	−0.0657284	+	1.71915i
$783$	4.90245	−	0.911813i	0.175199	−	0.0325855i
$784$	−27.6091	−	4.25344i	−0.986041	−	0.151909i
$785$	−30.6704	+	17.7076i	−1.09467	+	0.632010i
$786$	−7.52594	+	9.40148i	−0.268441	+	0.335340i
$787$	−11.7352	−	43.7964i	−0.418315	−	1.56117i	−0.778101	−	0.628139i	$-0.783817\pi$
$787$	−11.7352	−	43.7964i	−0.418315	−	1.56117i	0.359786	−	0.933035i	$-0.382850\pi$
$788$	14.3072	−	2.68293i	0.509672	−	0.0955755i
$789$	26.0283	−	20.7128i	0.926631	−	0.737394i
$790$	3.06377	−	9.90384i	0.109004	−	0.352363i
$791$			2.69611i			0.0958625i
$792$	−0.472392	+	5.94332i	−0.0167857	+	0.211187i
$793$		−	8.78888i		−	0.312102i
$794$	−7.07544	−	2.18880i	−0.251098	−	0.0776775i
$795$	−0.0124549	−	0.00490310i	−0.000441731	−	0.000173895i
$796$	−1.55211	+	2.26858i	−0.0550131	+	0.0804077i
$797$	−9.77347	−	36.4751i	−0.346194	−	1.29201i	−0.891211	−	0.453589i	$-0.850143\pi$
$797$	−9.77347	−	36.4751i	−0.346194	−	1.29201i	0.545017	−	0.838425i	$-0.316523\pi$
$798$	−1.63780	+	0.639294i	−0.0579776	+	0.0226308i
$799$	−44.3411	+	25.6004i	−1.56868	+	0.905676i
$800$	3.05064	+	0.590090i	0.107856	+	0.0208628i
$801$	−30.3971	+	9.30731i	−1.07403	+	0.328858i
$802$	18.9079	+	0.722905i	0.667660	+	0.0255266i
$803$	0.341296	−	1.27374i	0.0120441	−	0.0449492i
$804$	7.08294	+	1.35973i	0.249796	+	0.0479540i
$805$	−0.548411	−	2.04670i	−0.0193289	−	0.0721366i
$806$	14.9293	−	3.39472i	0.525861	−	0.119574i
$807$	−11.1645	+	15.0946i	−0.393008	+	0.531353i
$808$	−32.9290	−	13.0166i	−1.15844	−	0.457922i
$809$	−24.0071			−0.844045			−0.422023	−	0.906585i	$-0.638680\pi$
$809$	−24.0071			−0.844045			−0.422023	+	0.906585i	$0.638680\pi$
$810$	6.10486	−	26.1486i	0.214503	−	0.918767i
$811$	−0.243845	−	0.243845i	−0.00856256	−	0.00856256i	0.702813	−	0.711375i	$-0.251927\pi$
$811$	−0.243845	−	0.243845i	−0.00856256	−	0.00856256i	−0.711375	+	0.702813i	$0.751927\pi$
$812$	0.231057	+	0.0812729i	0.00810850	+	0.00285212i
$813$	3.32776	+	22.2346i	0.116710	+	0.779800i
$814$	4.97351	−	7.90100i	0.174321	−	0.276930i
$815$	0.731560	−	1.26710i	0.0256254	−	0.0443846i
$816$	−25.9987	+	14.8618i	−0.910135	+	0.520269i
$817$	31.6507	+	54.8205i	1.10732	+	1.91793i
$818$	39.3350	+	1.50389i	1.37532	+	0.0525824i
$819$	0.645154	+	0.342686i	0.0225435	+	0.0119744i
$820$	−25.3453	−	29.5490i	−0.885097	−	1.03190i
$821$	−12.4067	+	46.3025i	−0.432998	+	1.61597i	0.312815	+	0.949814i	$0.398728\pi$
$821$	−12.4067	+	46.3025i	−0.432998	+	1.61597i	−0.745813	+	0.666156i	$0.767939\pi$
$822$	−15.3090	−	6.71300i	−0.533962	−	0.234143i
$823$	−0.737958	+	1.27818i	−0.0257236	+	0.0445546i	−0.878601	−	0.477557i	$-0.841522\pi$
$823$	−0.737958	+	1.27818i	−0.0257236	+	0.0445546i	0.852877	+	0.522112i	$0.174856\pi$
$824$	19.1658	+	14.2175i	0.667672	+	0.495289i
$825$	−0.612973	+	0.266682i	−0.0213410	+	0.00928466i
$826$	−0.226165	+	0.731096i	−0.00786930	+	0.0254381i
$827$	−11.5464	+	11.5464i	−0.401509	+	0.401509i	−0.878764	−	0.477256i	$-0.841632\pi$
$827$	−11.5464	+	11.5464i	−0.401509	+	0.401509i	0.477256	+	0.878764i	$0.341632\pi$
$828$	34.7347	−	31.9907i	1.20712	−	1.11175i
$829$	34.7961	+	34.7961i	1.20852	+	1.20852i	0.971507	+	0.237010i	$0.0761675\pi$
$829$	34.7961	+	34.7961i	1.20852	+	1.20852i	0.237010	+	0.971507i	$0.423833\pi$
$830$	2.12051	+	4.02012i	0.0736039	+	0.139540i
$831$	−42.7303	−	4.85940i	−1.48230	−	0.168571i
$832$	15.2569	−	0.496227i	0.528940	−	0.0172036i
$833$	26.1424	+	15.0933i	0.905781	+	0.522953i
$834$	−16.3909	+	20.4757i	−0.567570	+	0.709014i
$835$	21.9815	+	5.88992i	0.760700	+	0.203829i
$836$	0.603493	−	7.88077i	0.0208722	−	0.272562i
$837$	29.3917	+	2.29453i	1.01593	+	0.0793106i
$838$	10.7182	−	9.92880i	0.370254	−	0.342985i
$839$	−41.3065	+	23.8483i	−1.42606	+	0.823335i	−0.996807	−	0.0798497i	$-0.974556\pi$
$839$	−41.3065	+	23.8483i	−1.42606	+	0.823335i	−0.429252	+	0.903185i	$0.641223\pi$
$840$	0.900463	−	0.963720i	0.0310689	−	0.0332515i
$841$	−24.3172	−	14.0395i	−0.838523	−	0.484122i
$842$	−42.6196	+	9.69114i	−1.46877	+	0.333979i
$843$	−7.96200	−	10.0053i	−0.274226	−	0.344601i
$844$	−21.7553	−	7.65233i	−0.748850	−	0.263404i
$845$	−13.9615	+	13.9615i	−0.480290	+	0.480290i
$846$	48.5054	+	13.1472i	1.66765	+	0.452010i
$847$			1.34076i			0.0460692i
$848$	0.00590313	−	0.0134108i	0.000202714	−	0.000460527i
$849$	9.86087	−	4.29009i	0.338424	−	0.147236i
$850$	−2.84155	−	1.78869i	−0.0974643	−	0.0613517i
$851$	−71.4254	+	19.1384i	−2.44843	+	0.656055i
$852$	11.8660	+	5.75338i	0.406523	+	0.197108i
$853$	42.5120	+	11.3911i	1.45558	+	0.390023i	0.897962	−	0.440072i	$-0.145047\pi$
$853$	42.5120	+	11.3911i	1.45558	+	0.390023i	0.557622	+	0.830095i	$0.311714\pi$
$854$	0.609827	−	0.564913i	0.0208678	−	0.0193309i
$855$	−7.99302	+	34.6881i	−0.273355	+	1.18631i
$856$	−18.0275	−	22.7195i	−0.616168	−	0.776535i
$857$	4.36756	+	7.56483i	0.149193	+	0.258410i	0.930929	−	0.365199i	$-0.118999\pi$
$857$	4.36756	+	7.56483i	0.149193	+	0.258410i	−0.781736	+	0.623609i	$0.785666\pi$
$858$	−2.64597	+	1.94526i	−0.0903318	+	0.0664100i
$859$	−48.4800	+	12.9902i	−1.65411	+	0.443219i	−0.960761	−	0.277378i	$-0.910534\pi$
$859$	−48.4800	+	12.9902i	−1.65411	+	0.443219i	−0.693354	+	0.720597i	$0.743868\pi$
$860$	−39.1925	−	26.8146i	−1.33645	−	0.914370i
$861$	2.01693	−	0.301865i	0.0687366	−	0.0102875i
$862$	18.5690	−	9.79464i	0.632461	−	0.333607i
$863$	−3.87853			−0.132027			−0.0660134	−	0.997819i	$-0.521028\pi$
$863$	−3.87853			−0.132027			−0.0660134	+	0.997819i	$0.521028\pi$
$864$	28.3369	+	7.81140i	0.964042	+	0.265749i
$865$	10.0817			0.342789
$866$	−40.2300	+	21.2203i	−1.36707	+	0.721094i
$867$	2.88369	−	0.431590i	0.0979353	−	0.0146576i
$868$	1.19514	+	0.817686i	0.0405656	+	0.0277541i
$869$	−2.35827	+	0.631896i	−0.0799988	+	0.0214356i
$870$	3.99556	−	2.93745i	0.135462	−	0.0995889i
$871$	1.98636	+	3.44049i	0.0673054	+	0.116576i
$872$	32.2272	−	25.5718i	1.09135	−	0.865970i
$873$	14.5653	+	13.5709i	0.492959	+	0.459305i
$874$	−45.9248	+	42.5424i	−1.55343	+	1.43902i
$875$	1.44311	+	0.386679i	0.0487859	+	0.0130721i
$876$	−5.84987	−	2.83638i	−0.197649	−	0.0958324i
$877$	−20.2871	+	5.43592i	−0.685047	+	0.183558i	−0.584524	−	0.811377i	$-0.698719\pi$
$877$	−20.2871	+	5.43592i	−0.685047	+	0.183558i	−0.100524	+	0.994935i	$0.532052\pi$
$878$	−0.335198	−	0.211000i	−0.0113124	−	0.00712091i
$879$	−39.4856	+	17.1787i	−1.33182	+	0.579424i
$880$	2.14824	+	5.52649i	0.0724170	+	0.186298i
$881$		−	7.45496i		−	0.251164i	−0.992083	−	0.125582i	$-0.959920\pi$
$881$		−	7.45496i		−	0.251164i	0.992083	−	0.125582i	$-0.0400798\pi$
$882$	−7.58598	−	28.6418i	−0.255433	−	0.964420i
$883$	−9.55597	+	9.55597i	−0.321584	+	0.321584i	−0.849375	−	0.527791i	$-0.823021\pi$
$883$	−9.55597	+	9.55597i	−0.321584	+	0.321584i	0.527791	+	0.849375i	$0.323021\pi$
$884$	−15.5609	−	5.47348i	−0.523371	−	0.184093i
$885$	9.64811	+	12.1241i	0.324318	+	0.407547i
$886$	−34.6332	+	7.87514i	−1.16353	+	0.264570i
$887$	−41.0581	−	23.7049i	−1.37860	−	0.795934i	−0.386607	−	0.922245i	$-0.626353\pi$
$887$	−41.0581	−	23.7049i	−1.37860	−	0.795934i	−0.991991	+	0.126311i	$0.959686\pi$
$888$	−33.6318	−	31.4243i	−1.12861	−	1.05453i
$889$	−1.44899	+	0.836573i	−0.0485975	+	0.0280578i
$890$	−23.1934	+	21.4852i	−0.777444	+	0.720185i
$891$	−5.97747	+	2.06383i	−0.200253	+	0.0691409i
$892$	−3.17080	+	41.4062i	−0.106166	+	1.38638i
$893$	−64.3530	−	17.2433i	−2.15349	−	0.577027i
$894$	0.323351	−	0.403934i	0.0108145	−	0.0135096i
$895$	9.11780	+	5.26416i	0.304774	+	0.175962i
$896$	1.01508	+	1.02673i	0.0339116	+	0.0343005i
$897$	25.8446	+	2.93912i	0.862926	+	0.0981342i
$898$	9.42757	+	17.8731i	0.314602	+	0.596431i
$899$	3.85003	+	3.85003i	0.128406	+	0.128406i
$900$	0.721456	+	3.21573i	0.0240485	+	0.107191i
$901$	−0.0111960	+	0.0111960i	−0.000372994	+	0.000372994i
$902$	−2.70950	+	8.75865i	−0.0902165	+	0.291631i
$903$	2.28116	−	0.992448i	0.0759124	−	0.0330266i
$904$	−35.6015	+	47.9925i	−1.18409	+	1.59621i
$905$	10.9624	−	18.9874i	0.364402	−	0.631162i
$906$	−5.15049	−	2.25849i	−0.171114	−	0.0750335i
$907$	−3.66301	+	13.6705i	−0.121628	+	0.453923i	−0.999697	−	0.0246114i	$-0.992165\pi$
$907$	−3.66301	+	13.6705i	−0.121628	+	0.453923i	0.878069	+	0.478534i	$0.158832\pi$
$908$	−10.3180	−	12.0293i	−0.342413	−	0.399205i
$909$	−1.32647	−	37.5327i	−0.0439963	−	1.24488i
$910$	0.725977	+	0.0277563i	0.0240659	+	0.000920111i
$911$	20.0062	+	34.6517i	0.662834	+	1.14806i	0.979868	+	0.199648i	$0.0639799\pi$
$911$	20.0062	+	34.6517i	0.662834	+	1.14806i	−0.317034	+	0.948414i	$0.602687\pi$
$912$	−37.5957	−	10.2470i	−1.24492	−	0.339311i
$913$	0.535197	−	0.926988i	0.0177124	−	0.0306788i
$914$	−20.9738	+	33.3193i	−0.693751	+	1.10211i
$915$	−2.49123	−	16.6453i	−0.0823576	−	0.550277i
$916$	−0.876405	−	0.308271i	−0.0289572	−	0.0101856i
$917$	−0.443647	−	0.443647i	−0.0146505	−	0.0146505i
$918$	−25.4825	−	18.9618i	−0.841046	−	0.625833i
$919$	−18.6876			−0.616446			−0.308223	−	0.951314i	$-0.599734\pi$
$919$	−18.6876			−0.616446			−0.308223	+	0.951314i	$0.599734\pi$
$920$	17.2641	−	43.6742i	0.569182	−	1.43990i
$921$	25.3117	−	34.2218i	0.834049	−	1.12765i
$922$	23.1120	−	5.25536i	0.761153	−	0.173076i
$923$	1.88004	+	7.01641i	0.0618823	+	0.230948i
$924$	−0.305046	−	0.0585604i	−0.0100353	−	0.00192650i
$925$	1.33569	−	4.98486i	0.0439172	−	0.163901i
$926$	42.7452	+	1.63428i	1.40470	+	0.0537057i
$927$	−5.68337	+	24.6647i	−0.186666	+	0.810094i
$928$	3.03977	+	4.49777i	0.0997853	+	0.147646i
$929$	−8.76538	+	5.06070i	−0.287583	+	0.166036i	−0.636851	−	0.770987i	$-0.719763\pi$
$929$	−8.76538	+	5.06070i	−0.287583	+	0.166036i	0.349268	+	0.937023i	$0.386430\pi$
$930$	27.3123	−	10.6610i	0.895607	−	0.349588i
$931$	10.1662	+	37.9409i	0.333185	+	1.24346i
$932$	10.3191	−	15.0825i	0.338014	−	0.494044i
$933$	22.2270	+	8.75007i	0.727681	+	0.286464i
$934$	30.4500	+	9.41974i	0.996354	+	0.308223i
$935$		−	6.40729i		−	0.209541i
$936$	6.95906	+	14.6192i	0.227464	+	0.477842i
$937$			19.1375i			0.625194i	0.949886	+	0.312597i	$0.101199\pi$
$937$			19.1375i			0.625194i	−0.949886	+	0.312597i	$0.898801\pi$
$938$	−0.111047	+	0.358966i	−0.00362580	+	0.0117207i
$939$	−27.6008	+	21.9641i	−0.900717	+	0.716772i
$940$	49.1234	−	9.21178i	1.60223	−	0.300455i
$941$	11.1081	+	41.4559i	0.362113	+	1.35142i	0.871292	+	0.490764i	$0.163282\pi$
$941$	11.1081	+	41.4559i	0.362113	+	1.35142i	−0.509179	+	0.860660i	$0.670051\pi$
$942$	25.6971	−	32.1011i	0.837257	−	1.04591i
$943$	62.8868	−	36.3077i	2.04788	−	1.18234i
$944$	−13.6799	+	10.0275i	−0.445241	+	0.326368i
$945$	1.31899	+	0.466145i	0.0429069	+	0.0151637i
$946$	−0.427269	+	11.1754i	−0.0138917	+	0.363344i
$947$	12.0721	−	45.0535i	0.392289	−	1.46404i	−0.434060	−	0.900884i	$-0.642919\pi$
$947$	12.0721	−	45.0535i	0.392289	−	1.46404i	0.826349	−	0.563159i	$-0.190414\pi$
$948$	0.867512	+	12.0055i	0.0281755	+	0.389919i
$949$	−0.926848	−	3.45904i	−0.0300867	−	0.112285i
$950$	−0.968731	−	4.26028i	−0.0314298	−	0.138222i
$951$	−36.1920	−	4.11585i	−1.17361	−	0.133466i
$952$	−0.620410	−	1.43153i	−0.0201076	−	0.0463960i
$953$	−20.2249			−0.655149			−0.327575	−	0.944825i	$-0.606231\pi$
$953$	−20.2249			−0.655149			−0.327575	+	0.944825i	$0.606231\pi$
$954$	0.0155412		4.48736e-5i	0.000503166		1.45284e-6i
$955$	−7.72399	−	7.72399i	−0.249943	−	0.249943i
$956$	6.32752	+	13.1942i	0.204647	+	0.426730i
$957$	−1.08673	−	0.427810i	−0.0351289	−	0.0138291i
$958$	−35.4502	−	22.3151i	−1.14534	−	0.720969i
$959$	0.435445	−	0.754212i	0.0140612	−	0.0243548i
$960$	28.7546	−	5.26443i	0.928049	−	0.169909i
$961$	0.595170	+	1.03087i	0.0191990	+	0.0332537i
$962$	0.968635	−	25.3351i	0.0312301	−	0.816836i
$963$	14.4305	−	27.1675i	0.465018	−	0.875459i
$964$	−4.97974	−	0.381338i	−0.160387	−	0.0122821i
$965$	14.4339	−	53.8680i	0.464644	−	1.73407i
$966$	1.45725	+	1.98217i	0.0468862	+	0.0637753i
$967$	15.9815	−	27.6807i	0.513930	−	0.890152i	−0.485940	−	0.873992i	$-0.661523\pi$
$967$	15.9815	−	27.6807i	0.513930	−	0.890152i	0.999869	−	0.0161601i	$-0.00514413\pi$
$968$	−17.7045	+	23.8665i	−0.569045	+	0.767098i
$969$	33.8542	+	25.0398i	1.08755	+	0.804395i
$970$	18.9140	+	5.85108i	0.607293	+	0.187867i
$971$	4.69660	−	4.69660i	0.150721	−	0.150721i	−0.627719	−	0.778440i	$-0.716011\pi$
$971$	4.69660	−	4.69660i	0.150721	−	0.150721i	0.778440	+	0.627719i	$0.216011\pi$
$972$	4.43659	+	30.8596i	0.142304	+	0.989823i
$973$	−0.966226	−	0.966226i	−0.0309758	−	0.0309758i
$974$	32.0622	−	16.9120i	1.02734	−	0.541895i
$975$	−1.07950	+	1.45951i	−0.0345718	+	0.0467417i
$976$	18.3149	−	2.00319i	0.586245	−	0.0641205i
$977$	−22.7888	−	13.1571i	−0.729079	−	0.420934i	0.0890064	−	0.996031i	$-0.471631\pi$
$977$	−22.7888	−	13.1571i	−0.729079	−	0.420934i	−0.818085	+	0.575097i	$0.804964\pi$
$978$	−0.256301	+	1.67935i	−0.00819559	+	0.0536996i
$979$	7.19193	+	1.92707i	0.229855	+	0.0615895i
$980$	−19.1844	−	22.3662i	−0.612822	−	0.714463i
$981$	38.5367	+	20.4695i	1.23038	+	0.653542i
$982$	−5.22426	−	5.63962i	−0.166713	−	0.179968i
$983$	19.6448	−	11.3420i	0.626573	−	0.361752i	−0.152851	−	0.988249i	$-0.548845\pi$
$983$	19.6448	−	11.3420i	0.626573	−	0.361752i	0.779424	+	0.626497i	$0.215512\pi$
$984$	39.8887	+	21.2597i	1.27160	+	0.677734i
$985$	13.2976	+	7.67740i	0.423698	+	0.244622i
$986$	−1.30070	−	5.72022i	−0.0414228	−	0.182169i
$987$	−0.959079	+	2.43627i	−0.0305278	+	0.0775472i
$988$	−9.28146	−	19.3537i	−0.295283	−	0.615724i
$989$	62.6343	−	62.6343i	1.99165	−	1.99165i
$990$	−4.45982	+	4.43414i	−0.141742	+	0.140926i
$991$			13.0577i			0.414793i	0.978257	+	0.207396i	$0.0664990\pi$
$991$			13.0577i			0.414793i	−0.978257	+	0.207396i	$0.933501\pi$
$992$	10.4769	+	30.3369i	0.332641	+	0.963197i
$993$	3.45722	−	30.4004i	0.109711	−	0.964728i
$994$	−0.366000	+	0.581435i	−0.0116088	+	0.0184420i
$995$	−2.80066	+	0.750435i	−0.0887870	+	0.0237904i
$996$	−3.99078	−	3.45290i	−0.126453	−	0.109409i
$997$	7.68222	+	2.05844i	0.243298	+	0.0651916i	0.378407	−	0.925639i	$-0.376472\pi$
$997$	7.68222	+	2.05844i	0.243298	+	0.0651916i	−0.135109	+	0.990831i	$0.543139\pi$
$998$	21.4694	+	23.1763i	0.679601	+	0.733633i
$999$	16.2675	−	46.0301i	0.514680	−	1.45633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.u.a.131.19	yes	88
3.2	odd	2		432.2.v.a.179.4		88
4.3	odd	2		576.2.y.a.239.22		88
9.2	odd	6	inner	144.2.u.a.83.19	yes	88
9.7	even	3		432.2.v.a.35.4		88
12.11	even	2		1728.2.z.a.1583.5		88
16.5	even	4		576.2.y.a.527.11		88
16.11	odd	4	inner	144.2.u.a.59.19	yes	88
36.7	odd	6		1728.2.z.a.1007.5		88
36.11	even	6		576.2.y.a.47.11		88
48.5	odd	4		1728.2.z.a.719.5		88
48.11	even	4		432.2.v.a.395.4		88
144.11	even	12	inner	144.2.u.a.11.19	✓	88
144.43	odd	12		432.2.v.a.251.4		88
144.101	odd	12		576.2.y.a.335.22		88
144.133	even	12		1728.2.z.a.143.5		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.19	✓	88	144.11	even	12	inner
144.2.u.a.59.19	yes	88	16.11	odd	4	inner
144.2.u.a.83.19	yes	88	9.2	odd	6	inner
144.2.u.a.131.19	yes	88	1.1	even	1	trivial
432.2.v.a.35.4		88	9.7	even	3
432.2.v.a.179.4		88	3.2	odd	2
432.2.v.a.251.4		88	144.43	odd	12
432.2.v.a.395.4		88	48.11	even	4
576.2.y.a.47.11		88	36.11	even	6
576.2.y.a.239.22		88	4.3	odd	2
576.2.y.a.335.22		88	144.101	odd	12
576.2.y.a.527.11		88	16.5	even	4
1728.2.z.a.143.5		88	144.133	even	12
1728.2.z.a.719.5		88	48.5	odd	4
1728.2.z.a.1007.5		88	36.7	odd	6
1728.2.z.a.1583.5		88	12.11	even	2

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25087 - 0.659799i) q^{2} +(-1.71297 + 0.256373i) q^{3} +(1.12933 - 1.65064i) q^{4} +(2.03779 - 0.546024i) q^{5} +(-1.97354 + 1.45091i) q^{6} +(-0.0638076 - 0.110518i) q^{7} +(0.323550 - 2.80986i) q^{8} +(2.86855 - 0.878321i) q^{9} +O(q^{10})\)	\(q+(1.25087 - 0.659799i) q^{2} +(-1.71297 + 0.256373i) q^{3} +(1.12933 - 1.65064i) q^{4} +(2.03779 - 0.546024i) q^{5} +(-1.97354 + 1.45091i) q^{6} +(-0.0638076 - 0.110518i) q^{7} +(0.323550 - 2.80986i) q^{8} +(2.86855 - 0.878321i) q^{9} +(2.18873 - 2.02753i) q^{10} +(-0.678695 - 0.181856i) q^{11} +(-1.51133 + 3.11703i) q^{12} +(-1.84311 + 0.493860i) q^{13} +(-0.152734 - 0.0961430i) q^{14} +(-3.35069 + 1.45776i) q^{15} +(-1.44923 - 3.72824i) q^{16} +4.32243i q^{17} +(3.00865 - 2.99133i) q^{18} +(-3.97707 + 3.97707i) q^{19} +(1.40005 - 3.98030i) q^{20} +(0.137635 + 0.172956i) q^{21} +(-0.968944 + 0.220325i) q^{22} +(6.81589 + 3.93516i) q^{23} +(0.166142 + 4.89616i) q^{24} +(-0.475689 + 0.274639i) q^{25} +(-1.97963 + 1.83383i) q^{26} +(-4.68856 + 2.23996i) q^{27} +(-0.254485 - 0.0194880i) q^{28} +(-0.926957 - 0.248377i) q^{29} +(-3.22943 + 4.03424i) q^{30} +(-4.91353 - 2.83683i) q^{31} +(-4.27267 - 3.70733i) q^{32} +(1.20921 + 0.137514i) q^{33} +(2.85194 + 5.40679i) q^{34} +(-0.190372 - 0.190372i) q^{35} +(1.78974 - 5.72685i) q^{36} +(-6.64358 + 6.64358i) q^{37} +(-2.35071 + 7.59884i) q^{38} +(3.03058 - 1.31849i) q^{39} +(-0.874924 - 5.90257i) q^{40} +(4.61325 - 7.99038i) q^{41} +(0.286278 + 0.125533i) q^{42} +(2.91294 - 10.8712i) q^{43} +(-1.06665 + 0.914906i) q^{44} +(5.36590 - 3.35613i) q^{45} +(11.1222 + 0.425234i) q^{46} +(5.92267 + 10.2584i) q^{47} +(3.43830 + 6.01482i) q^{48} +(3.49186 - 6.04807i) q^{49} +(-0.413816 + 0.657395i) q^{50} +(-1.10816 - 7.40421i) q^{51} +(-1.26629 + 3.60004i) q^{52} +(0.00259022 + 0.00259022i) q^{53} +(-4.38684 + 5.89539i) q^{54} -1.48233 q^{55} +(-0.331185 + 0.143532i) q^{56} +(5.79299 - 7.83221i) q^{57} +(-1.32338 + 0.300919i) q^{58} +(-1.09748 - 4.09587i) q^{59} +(-1.37780 + 7.17707i) q^{60} +(-1.19213 + 4.44908i) q^{61} +(-8.01790 - 0.306548i) q^{62} +(-0.280105 - 0.260982i) q^{63} +(-7.79063 - 1.81826i) q^{64} +(-3.48621 + 2.01276i) q^{65} +(1.60329 - 0.625822i) q^{66} +(-0.538862 - 2.01106i) q^{67} +(7.13478 + 4.88146i) q^{68} +(-12.6843 - 4.99340i) q^{69} +(-0.363737 - 0.112522i) q^{70} -3.80683i q^{71} +(-1.53984 - 8.34439i) q^{72} +1.87674i q^{73} +(-3.92680 + 12.6937i) q^{74} +(0.744431 - 0.592403i) q^{75} +(2.07328 + 11.0561i) q^{76} +(0.0232076 + 0.0866118i) q^{77} +(2.92091 - 3.64883i) q^{78} +(3.00919 - 1.73736i) q^{79} +(-4.98892 - 6.80604i) q^{80} +(7.45710 - 5.03901i) q^{81} +(0.498509 - 13.0387i) q^{82} +(-0.394284 + 1.47149i) q^{83} +(0.440923 - 0.0318610i) q^{84} +(2.36015 + 8.80821i) q^{85} +(-3.52914 - 15.5204i) q^{86} +(1.65153 + 0.187816i) q^{87} +(-0.730581 + 1.84820i) q^{88} -10.5967 q^{89} +(4.49766 - 7.73848i) q^{90} +(0.172185 + 0.172185i) q^{91} +(14.1929 - 6.80649i) q^{92} +(9.14402 + 3.59971i) q^{93} +(14.1769 + 8.92407i) q^{94} +(-5.93284 + 10.2760i) q^{95} +(8.26943 + 5.25514i) q^{96} +(3.31795 + 5.74685i) q^{97} +(0.377331 - 9.86925i) q^{98} +(-2.10659 + 0.0744506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7}+O(q^{10}) \) 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7	\( 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 16 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} - 10 q^{18} - 8 q^{19} - 48 q^{20} + 2 q^{21} - 2 q^{22} - 12 q^{23} - 16 q^{27} + 8 q^{28} - 6 q^{29} - 34 q^{30} - 6 q^{32} - 8 q^{33} + 2 q^{34} - 26 q^{36} - 8 q^{37} - 6 q^{38} - 32 q^{39} - 2 q^{40} + 48 q^{42} - 2 q^{43} + 6 q^{45} - 40 q^{46} + 42 q^{48} - 24 q^{49} + 72 q^{50} - 12 q^{51} - 2 q^{52} - 38 q^{54} - 16 q^{55} + 36 q^{56} + 16 q^{58} - 42 q^{59} + 70 q^{60} - 2 q^{61} - 44 q^{64} - 12 q^{65} + 104 q^{66} - 2 q^{67} + 96 q^{68} - 10 q^{69} - 16 q^{70} - 10 q^{72} + 78 q^{74} - 56 q^{75} - 14 q^{76} - 6 q^{77} + 12 q^{78} - 8 q^{81} - 36 q^{82} + 54 q^{83} + 158 q^{84} + 8 q^{85} + 54 q^{86} + 48 q^{87} + 22 q^{88} + 64 q^{90} + 20 q^{91} + 108 q^{92} - 34 q^{93} + 6 q^{94} - 58 q^{96} - 4 q^{97} + 46 q^{99}+O(q^{100}) \) 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^10 - 6 * q^11 - 16 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 - 10 * q^18 - 8 * q^19 - 48 * q^20 + 2 * q^21 - 2 * q^22 - 12 * q^23 - 16 * q^27 + 8 * q^28 - 6 * q^29 - 34 * q^30 - 6 * q^32 - 8 * q^33 + 2 * q^34 - 26 * q^36 - 8 * q^37 - 6 * q^38 - 32 * q^39 - 2 * q^40 + 48 * q^42 - 2 * q^43 + 6 * q^45 - 40 * q^46 + 42 * q^48 - 24 * q^49 + 72 * q^50 - 12 * q^51 - 2 * q^52 - 38 * q^54 - 16 * q^55 + 36 * q^56 + 16 * q^58 - 42 * q^59 + 70 * q^60 - 2 * q^61 - 44 * q^64 - 12 * q^65 + 104 * q^66 - 2 * q^67 + 96 * q^68 - 10 * q^69 - 16 * q^70 - 10 * q^72 + 78 * q^74 - 56 * q^75 - 14 * q^76 - 6 * q^77 + 12 * q^78 - 8 * q^81 - 36 * q^82 + 54 * q^83 + 158 * q^84 + 8 * q^85 + 54 * q^86 + 48 * q^87 + 22 * q^88 + 64 * q^90 + 20 * q^91 + 108 * q^92 - 34 * q^93 + 6 * q^94 - 58 * q^96 - 4 * q^97 + 46 * q^99

Introduction

L-functions

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