LMFDB - Embedded newform 192.2.s.a.59.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8]))

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

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

chi := DirichletCharacter("192.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			59.15
Character	$\chi$	$=$	192.59
Dual form			192.2.s.a.179.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.246732 + 1.39252i) q^{2} +(-0.701166 + 1.58378i) q^{3} +(-1.87825 - 0.687161i) q^{4} +(-0.359364 + 1.80664i) q^{5} +(-2.03245 - 1.36716i) q^{6} +(-3.05294 - 1.26457i) q^{7} +(1.42031 - 2.44596i) q^{8} +(-2.01673 - 2.22099i) q^{9} +O(q^{10})$	\(q+(-0.246732 + 1.39252i) q^{2} +(-0.701166 + 1.58378i) q^{3} +(-1.87825 - 0.687161i) q^{4} +(-0.359364 + 1.80664i) q^{5} +(-2.03245 - 1.36716i) q^{6} +(-3.05294 - 1.26457i) q^{7} +(1.42031 - 2.44596i) q^{8} +(-2.01673 - 2.22099i) q^{9} +(-2.42713 - 0.946180i) q^{10} +(2.05692 + 3.07840i) q^{11} +(2.40528 - 2.49292i) q^{12} +(0.534830 - 0.106384i) q^{13} +(2.51420 - 3.93929i) q^{14} +(-2.60936 - 1.83591i) q^{15} +(3.05562 + 2.58132i) q^{16} +(0.827691 + 0.827691i) q^{17} +(3.59037 - 2.26036i) q^{18} +(-6.44815 + 1.28262i) q^{19} +(1.91643 - 3.14638i) q^{20} +(4.14342 - 3.94852i) q^{21} +(-4.79426 + 2.10477i) q^{22} +(-7.47552 + 3.09646i) q^{23} +(2.87799 + 3.96449i) q^{24} +(1.48458 + 0.614932i) q^{25} +(0.0161829 + 0.771012i) q^{26} +(4.93163 - 1.63679i) q^{27} +(4.86522 + 4.47304i) q^{28} +(0.420063 + 0.280677i) q^{29} +(3.20036 - 3.18061i) q^{30} +2.79490 q^{31} +(-4.34846 + 3.61813i) q^{32} +(-6.31776 + 1.09925i) q^{33} +(-1.35680 + 0.948362i) q^{34} +(3.38175 - 5.06114i) q^{35} +(2.26175 + 5.55738i) q^{36} +(-0.213702 + 1.07435i) q^{37} +(-0.195109 - 9.29567i) q^{38} +(-0.206515 + 0.921647i) q^{39} +(3.90857 + 3.44499i) q^{40} +(3.82720 + 9.23967i) q^{41} +(4.47610 + 6.74405i) q^{42} +(3.05140 + 4.56674i) q^{43} +(-1.74805 - 7.19543i) q^{44} +(4.73728 - 2.84538i) q^{45} +(-2.46745 - 11.1738i) q^{46} +(-7.47207 + 7.47207i) q^{47} +(-6.23074 + 3.02951i) q^{48} +(2.77158 + 2.77158i) q^{49} +(-1.22260 + 1.91559i) q^{50} +(-1.89123 + 0.730534i) q^{51} +(-1.07765 - 0.167698i) q^{52} +(2.02433 - 1.35261i) q^{53} +(1.06247 + 7.27126i) q^{54} +(-6.30076 + 2.60986i) q^{55} +(-7.42922 + 5.67129i) q^{56} +(2.48984 - 11.1118i) q^{57} +(-0.494492 + 0.515695i) q^{58} +(10.5918 + 2.10685i) q^{59} +(3.63945 + 5.24134i) q^{60} +(0.153998 + 0.102898i) q^{61} +(-0.689591 + 3.89196i) q^{62} +(3.34838 + 9.33085i) q^{63} +(-3.96543 - 6.94805i) q^{64} +1.00448i q^{65} +(0.0280666 - 9.06886i) q^{66} +(1.39419 - 2.08655i) q^{67} +(-0.985851 - 2.12337i) q^{68} +(0.337457 - 14.0107i) q^{69} +(6.21338 + 5.95791i) q^{70} +(5.26483 - 12.7104i) q^{71} +(-8.29683 + 1.77835i) q^{72} +(-3.57907 - 8.64064i) q^{73} +(-1.44333 - 0.562662i) q^{74} +(-2.01485 + 1.92008i) q^{75} +(12.9926 + 2.02185i) q^{76} +(-2.38681 - 11.9993i) q^{77} +(-1.23246 - 0.514977i) q^{78} +(9.99933 - 9.99933i) q^{79} +(-5.76160 + 4.59279i) q^{80} +(-0.865574 + 8.95828i) q^{81} +(-13.8108 + 3.04974i) q^{82} +(1.76923 + 8.89454i) q^{83} +(-10.4956 + 4.56910i) q^{84} +(-1.79279 + 1.19790i) q^{85} +(-7.11217 + 3.12238i) q^{86} +(-0.739064 + 0.468487i) q^{87} +(10.4511 - 0.658856i) q^{88} +(4.17398 - 10.0769i) q^{89} +(2.79342 + 7.29882i) q^{90} +(-1.76734 - 0.351545i) q^{91} +(16.1686 - 0.679033i) q^{92} +(-1.95969 + 4.42651i) q^{93} +(-8.56143 - 12.2486i) q^{94} -12.1104i q^{95} +(-2.68134 - 9.42393i) q^{96} +15.1389i q^{97} +(-4.54333 + 3.17565i) q^{98} +(2.68883 - 10.7767i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	−0.246732	+	1.39252i	−0.174466	+	0.984663i
$2$	−0.246732	+	1.39252i	−0.174466	+	0.984663i
$3$	−0.701166	+	1.58378i	−0.404818	+	0.914397i
$3$	−0.701166	+	1.58378i	−0.404818	+	0.914397i
$4$	−1.87825	−	0.687161i	−0.939123	−	0.343580i
$5$	−0.359364	+	1.80664i	−0.160712	+	0.807956i	0.813367	+	0.581751i	$0.197632\pi$
$5$	−0.359364	+	1.80664i	−0.160712	+	0.807956i	−0.974080	+	0.226205i	$0.927368\pi$
$6$	−2.03245	−	1.36716i	−0.829746	−	0.558141i
$7$	−3.05294	−	1.26457i	−1.15390	−	0.477963i	−0.278063	−	0.960563i	$-0.589693\pi$
$7$	−3.05294	−	1.26457i	−1.15390	−	0.477963i	−0.875841	+	0.482600i	$0.839693\pi$
$8$	1.42031	−	2.44596i	0.502156	−	0.864777i
$9$	−2.01673	−	2.22099i	−0.672244	−	0.740329i
$10$	−2.42713	−	0.946180i	−0.767525	−	0.299208i
$11$	2.05692	+	3.07840i	0.620185	+	0.928173i	0.999995	+	0.00310847i	$0.000989458\pi$
$11$	2.05692	+	3.07840i	0.620185	+	0.928173i	−0.379810	+	0.925065i	$0.624011\pi$
$12$	2.40528	−	2.49292i	0.694343	−	0.719644i
$13$	0.534830	−	0.106384i	0.148335	−	0.0295057i	−0.120364	−	0.992730i	$-0.538406\pi$
$13$	0.534830	−	0.106384i	0.148335	−	0.0295057i	0.268699	+	0.963224i	$0.413406\pi$
$14$	2.51420	−	3.93929i	0.671949	−	1.05282i
$15$	−2.60936	−	1.83591i	−0.673733	−	0.474030i
$16$	3.05562	+	2.58132i	0.763905	+	0.645329i
$17$	0.827691	+	0.827691i	0.200745	+	0.200745i	0.800319	−	0.599574i	$-0.204663\pi$
$17$	0.827691	+	0.827691i	0.200745	+	0.200745i	−0.599574	+	0.800319i	$0.704663\pi$
$18$	3.59037	−	2.26036i	0.846259	−	0.532772i
$19$	−6.44815	+	1.28262i	−1.47931	+	0.294253i	−0.867771	−	0.496964i	$-0.834448\pi$
$19$	−6.44815	+	1.28262i	−1.47931	+	0.294253i	−0.611536	+	0.791216i	$0.709448\pi$
$20$	1.91643	−	3.14638i	0.428527	−	0.703552i
$21$	4.14342	−	3.94852i	0.904169	−	0.861639i
$22$	−4.79426	+	2.10477i	−1.02214	+	0.448739i
$23$	−7.47552	+	3.09646i	−1.55875	+	0.645657i	−0.984872	−	0.173281i	$-0.944563\pi$
$23$	−7.47552	+	3.09646i	−1.55875	+	0.645657i	−0.573882	+	0.818938i	$0.694563\pi$
$24$	2.87799	+	3.96449i	0.587468	+	0.809248i
$25$	1.48458	+	0.614932i	0.296916	+	0.122986i
$26$	0.0161829	+	0.771012i	0.00317373	+	0.151208i
$27$	4.93163	−	1.63679i	0.949092	−	0.315000i
$28$	4.86522	+	4.47304i	0.919440	+	0.845325i
$29$	0.420063	+	0.280677i	0.0780037	+	0.0521204i	0.593961	−	0.804494i	$-0.297564\pi$
$29$	0.420063	+	0.280677i	0.0780037	+	0.0521204i	−0.515957	+	0.856615i	$0.672564\pi$
$30$	3.20036	−	3.18061i	0.584304	−	0.580698i
$31$	2.79490			0.501978			0.250989	−	0.967990i	$-0.419244\pi$
$31$	2.79490			0.501978			0.250989	+	0.967990i	$0.419244\pi$
$32$	−4.34846	+	3.61813i	−0.768707	+	0.639601i
$33$	−6.31776	+	1.09925i	−1.09978	+	0.191354i
$34$	−1.35680	+	0.948362i	−0.232689	+	0.162643i
$35$	3.38175	−	5.06114i	0.571619	−	0.855489i
$36$	2.26175	+	5.55738i	0.376958	+	0.926230i
$37$	−0.213702	+	1.07435i	−0.0351323	+	0.176622i	−0.994368	−	0.105987i	$-0.966200\pi$
$37$	−0.213702	+	1.07435i	−0.0351323	+	0.176622i	0.959235	+	0.282609i	$0.0911999\pi$
$38$	−0.195109	−	9.29567i	−0.0316508	−	1.50796i
$39$	−0.206515	+	0.921647i	−0.0330688	+	0.147582i
$40$	3.90857	+	3.44499i	0.617999	+	0.544700i
$41$	3.82720	+	9.23967i	0.597708	+	1.44299i	0.875911	+	0.482472i	$0.160261\pi$
$41$	3.82720	+	9.23967i	0.597708	+	1.44299i	−0.278204	+	0.960522i	$0.589739\pi$
$42$	4.47610	+	6.74405i	0.690677	+	1.04063i
$43$	3.05140	+	4.56674i	0.465334	+	0.696421i	0.987711	−	0.156293i	$-0.0499546\pi$
$43$	3.05140	+	4.56674i	0.465334	+	0.696421i	−0.522377	+	0.852715i	$0.674955\pi$
$44$	−1.74805	−	7.19543i	−0.263528	−	1.08475i
$45$	4.73728	−	2.84538i	0.706191	−	0.424164i
$46$	−2.46745	−	11.1738i	−0.363805	−	1.64749i
$47$	−7.47207	+	7.47207i	−1.08991	+	1.08991i	−0.0943761	+	0.995537i	$0.530086\pi$
$47$	−7.47207	+	7.47207i	−1.08991	+	1.08991i	−0.995537	+	0.0943761i	$0.969914\pi$
$48$	−6.23074	+	3.02951i	−0.899329	+	0.437272i
$49$	2.77158	+	2.77158i	0.395940	+	0.395940i
$50$	−1.22260	+	1.91559i	−0.172902	+	0.270905i
$51$	−1.89123	+	0.730534i	−0.264825	+	0.102295i
$52$	−1.07765	−	0.167698i	−0.149443	−	0.0232556i
$53$	2.02433	−	1.35261i	0.278063	−	0.185796i	−0.408717	−	0.912661i	$-0.634024\pi$
$53$	2.02433	−	1.35261i	0.278063	−	0.185796i	0.686780	+	0.726866i	$0.259024\pi$
$54$	1.06247	+	7.27126i	0.144584	+	0.989492i
$55$	−6.30076	+	2.60986i	−0.849594	+	0.351913i
$56$	−7.42922	+	5.67129i	−0.992771	+	0.757858i
$57$	2.48984	−	11.1118i	0.329787	−	1.47179i
$58$	−0.494492	+	0.515695i	−0.0649300	+	0.0677141i
$59$	10.5918	+	2.10685i	1.37894	+	0.274288i	0.828220	−	0.560403i	$-0.189354\pi$
$59$	10.5918	+	2.10685i	1.37894	+	0.274288i	0.550719	+	0.834691i	$0.314354\pi$
$60$	3.63945	+	5.24134i	0.469851	+	0.676654i
$61$	0.153998	+	0.102898i	0.0197175	+	0.0131748i	0.565390	−	0.824824i	$-0.308726\pi$
$61$	0.153998	+	0.102898i	0.0197175	+	0.0131748i	−0.545672	+	0.837999i	$0.683726\pi$
$62$	−0.689591	+	3.89196i	−0.0875782	+	0.494280i
$63$	3.34838	+	9.33085i	0.421856	+	1.17558i
$64$	−3.96543	−	6.94805i	−0.495678	−	0.868506i
$65$			1.00448i			0.124590i
$66$	0.0280666	−	9.06886i	0.00345476	−	1.11630i
$67$	1.39419	−	2.08655i	0.170327	−	0.254913i	−0.736479	−	0.676460i	$-0.763513\pi$
$67$	1.39419	−	2.08655i	0.170327	−	0.254913i	0.906806	+	0.421548i	$0.138513\pi$
$68$	−0.985851	−	2.12337i	−0.119552	−	0.257496i
$69$	0.337457	−	14.0107i	0.0406251	−	1.68669i
$70$	6.21338	+	5.95791i	0.742640	+	0.712106i
$71$	5.26483	−	12.7104i	0.624820	−	1.50845i	−0.221161	−	0.975237i	$-0.570985\pi$
$71$	5.26483	−	12.7104i	0.624820	−	1.50845i	0.845981	−	0.533213i	$-0.179015\pi$
$72$	−8.29683	+	1.77835i	−0.977791	+	0.209581i
$73$	−3.57907	−	8.64064i	−0.418899	−	1.01131i	−0.982667	−	0.185378i	$-0.940649\pi$
$73$	−3.57907	−	8.64064i	−0.418899	−	1.01131i	0.563769	−	0.825933i	$-0.309351\pi$
$74$	−1.44333	−	0.562662i	−0.167784	−	0.0654081i
$75$	−2.01485	+	1.92008i	−0.232655	+	0.221712i
$76$	12.9926	+	2.02185i	1.49035	+	0.231922i
$77$	−2.38681	−	11.9993i	−0.272002	−	1.36745i
$78$	−1.23246	−	0.514977i	−0.139549	−	0.0583097i
$79$	9.99933	−	9.99933i	1.12501	−	1.12501i	0.134036	−	0.990976i	$-0.457206\pi$
$79$	9.99933	−	9.99933i	1.12501	−	1.12501i	0.990976	−	0.134036i	$-0.0427939\pi$
$80$	−5.76160	+	4.59279i	−0.644166	+	0.513489i
$81$	−0.865574	+	8.95828i	−0.0961749	+	0.995364i
$82$	−13.8108	+	3.04974i	−1.52514	+	0.336787i
$83$	1.76923	+	8.89454i	0.194199	+	0.976302i	0.947775	+	0.318941i	$0.103327\pi$
$83$	1.76923	+	8.89454i	0.194199	+	0.976302i	−0.753576	+	0.657361i	$0.771673\pi$
$84$	−10.4956	+	4.56910i	−1.14517	+	0.498530i
$85$	−1.79279	+	1.19790i	−0.194455	+	0.129931i
$86$	−7.11217	+	3.12238i	−0.766925	+	0.336695i
$87$	−0.739064	+	0.468487i	−0.0792360	+	0.0502270i
$88$	10.4511	−	0.658856i	1.11409	−	0.0702343i
$89$	4.17398	−	10.0769i	0.442441	−	1.06815i	−0.532649	−	0.846336i	$-0.678803\pi$
$89$	4.17398	−	10.0769i	0.442441	−	1.06815i	0.975090	−	0.221810i	$-0.0711965\pi$
$90$	2.79342	+	7.29882i	0.294452	+	0.769363i
$91$	−1.76734	−	0.351545i	−0.185267	−	0.0368519i
$92$	16.1686	−	0.679033i	1.68570	−	0.0707941i
$93$	−1.95969	+	4.42651i	−0.203210	+	0.459008i
$94$	−8.56143	−	12.2486i	−0.883044	−	1.26335i
$95$		−	12.1104i		−	1.24250i
$96$	−2.68134	−	9.42393i	−0.273663	−	0.961826i
$97$			15.1389i			1.53712i	0.639777	+	0.768561i	$0.279027\pi$
$97$			15.1389i			1.53712i	−0.639777	+	0.768561i	$0.720973\pi$
$98$	−4.54333	+	3.17565i	−0.458945	+	0.320789i
$99$	2.68883	−	10.7767i	0.270238	−	1.08310i
$100$	−2.36585	−	2.17514i	−0.236585	−	0.217514i
$101$	−4.20479	−	0.836385i	−0.418392	−	0.0832234i	−0.0185952	−	0.999827i	$-0.505919\pi$
$101$	−4.20479	−	0.836385i	−0.418392	−	0.0832234i	−0.399797	+	0.916604i	$0.630919\pi$
$102$	−0.550659	−	2.81383i	−0.0545233	−	0.278611i
$103$	−3.14426	+	7.59092i	−0.309813	+	0.747956i	0.689897	+	0.723907i	$0.257656\pi$
$103$	−3.14426	+	7.59092i	−0.309813	+	0.747956i	−0.999711	+	0.0240486i	$0.992344\pi$
$104$	0.499414	−	1.45927i	0.0489716	−	0.143093i
$105$	5.64458	+	8.90465i	0.550855	+	0.869005i
$106$	1.38408	+	3.15266i	0.134434	+	0.306213i
$107$	−2.57078	+	1.71774i	−0.248527	+	0.166060i	−0.673594	−	0.739101i	$-0.735250\pi$
$107$	−2.57078	+	1.71774i	−0.248527	+	0.166060i	0.425067	+	0.905162i	$0.360250\pi$
$108$	−10.3875	−	0.314533i	−0.999542	−	0.0302660i
$109$	−0.569133	−	2.86122i	−0.0545130	−	0.274056i	0.943909	−	0.330205i	$-0.107118\pi$
$109$	−0.569133	−	2.86122i	−0.0545130	−	0.274056i	−0.998422	+	0.0561491i	$0.982118\pi$
$110$	−2.07969	−	9.41790i	−0.198291	−	0.897961i
$111$	−1.55170	−	1.09175i	−0.147281	−	0.103625i
$112$	−6.06438	−	11.7447i	−0.573030	−	1.10977i
$113$	−5.94703	+	5.94703i	−0.559449	+	0.559449i	−0.929151	−	0.369701i	$-0.879460\pi$
$113$	−5.94703	+	5.94703i	−0.559449	+	0.559449i	0.369701	+	0.929151i	$0.379460\pi$
$114$	14.8591	+	6.20879i	1.39168	+	0.581507i
$115$	−2.90777	−	14.6184i	−0.271151	−	1.36317i
$116$	−0.596111	−	0.815831i	−0.0553475	−	0.0757480i
$117$	−1.31489	−	0.973302i	−0.121561	−	0.0899818i
$118$	−5.54718	+	14.2295i	−0.510659	+	1.30994i
$119$	−1.48022	−	3.57357i	−0.135692	−	0.327589i
$120$	−8.19666	+	3.77481i	−0.748250	+	0.344592i
$121$	−1.03611	+	2.50139i	−0.0941919	+	0.227399i
$122$	−0.181285	+	0.189058i	−0.0164128	+	0.0171165i
$123$	−17.3171	−	0.417093i	−1.56143	−	0.0376080i
$124$	−5.24951	−	1.92054i	−0.471420	−	0.172470i
$125$	−6.76137	+	10.1191i	−0.604756	+	0.905081i
$126$	−13.8196	+	2.36047i	−1.23115	+	0.210288i
$127$		−	22.0807i		−	1.95935i	−0.200602	−	0.979673i	$-0.564290\pi$
$127$		−	22.0807i		−	1.95935i	0.200602	−	0.979673i	$-0.435710\pi$
$128$	10.6537	−	3.80765i	0.941665	−	0.336552i
$129$	−9.37226	+	1.63071i	−0.825181	+	0.143576i
$130$	−1.39876	−	0.247837i	−0.122679	−	0.0217367i
$131$	11.6039	+	7.75347i	1.01384	+	0.677423i	0.947296	−	0.320360i	$-0.103804\pi$
$131$	11.6039	+	7.75347i	1.01384	+	0.677423i	0.0665400	+	0.997784i	$0.478804\pi$
$132$	12.6217	+	2.27666i	1.09858	+	0.198158i
$133$	21.3078	+	4.23839i	1.84762	+	0.367515i
$134$	2.56158	+	2.45626i	0.221287	+	0.212188i
$135$	1.18484	+	9.49789i	0.101975	+	0.817449i
$136$	3.20008	−	0.848919i	0.274404	−	0.0727942i
$137$	−8.78236	+	3.63777i	−0.750328	+	0.310796i	−0.724875	−	0.688880i	$-0.758103\pi$
$137$	−8.78236	+	3.63777i	−0.750328	+	0.310796i	−0.0254526	+	0.999676i	$0.508103\pi$
$138$	19.4270	+	3.92682i	1.65374	+	0.334273i
$139$	9.49037	−	6.34126i	0.804963	−	0.537859i	−0.0836617	−	0.996494i	$-0.526662\pi$
$139$	9.49037	−	6.34126i	0.804963	−	0.537859i	0.888625	+	0.458635i	$0.151662\pi$
$140$	−9.82957	+	7.18227i	−0.830750	+	0.607012i
$141$	−6.59497	−	17.0733i	−0.555397	−	1.43783i
$142$	16.4006	+	10.4675i	1.37631	+	0.878411i
$143$	1.42760	+	1.42760i	0.119382	+	0.119382i
$144$	−0.429299	−	11.9923i	−0.0357749	−	0.999360i
$145$	−0.658038	+	0.658038i	−0.0546471	+	0.0546471i
$146$	12.9154	−	2.85202i	1.06888	−	0.236035i
$147$	−6.33291	+	2.44624i	−0.522330	+	0.201763i
$148$	1.13964	−	1.87105i	0.0936775	−	0.153799i
$149$	4.81608	+	7.20777i	0.394548	+	0.590484i	0.974561	−	0.224124i	$-0.0719522\pi$
$149$	4.81608	+	7.20777i	0.394548	+	0.590484i	−0.580012	+	0.814608i	$0.696952\pi$
$150$	−2.17663	−	3.27948i	−0.177721	−	0.267768i
$151$	1.60104	+	3.86526i	0.130291	+	0.314551i	0.975540	−	0.219822i	$-0.0705478\pi$
$151$	1.60104	+	3.86526i	0.130291	+	0.314551i	−0.845249	+	0.534373i	$0.820548\pi$
$152$	−6.02116	+	17.5936i	−0.488380	+	1.42703i
$153$	0.169060	−	3.50752i	0.0136677	−	0.283567i
$154$	17.2982	−	0.363076i	1.39393	−	0.0292575i
$155$	−1.00438	+	5.04938i	−0.0806741	+	0.405576i
$156$	1.02121	−	1.58917i	0.0817619	−	0.127236i
$157$	−5.75579	+	8.61415i	−0.459362	+	0.687484i	−0.986770	−	0.162128i	$-0.948164\pi$
$157$	−5.75579	+	8.61415i	−0.459362	+	0.687484i	0.527407	+	0.849613i	$0.323164\pi$
$158$	11.4572	+	16.3915i	0.911482	+	1.30404i
$159$	0.722854	+	4.15450i	0.0573261	+	0.329473i
$160$	−4.97399	−	9.15635i	−0.393229	−	0.723873i
$161$	26.7381			2.10725
$162$	−12.2611	−	3.41563i	−0.963319	−	0.268357i
$163$	0.602415	+	0.402521i	0.0471847	+	0.0315278i	0.578939	−	0.815371i	$-0.303467\pi$
$163$	0.602415	+	0.402521i	0.0471847	+	0.0315278i	−0.531754	+	0.846899i	$0.678467\pi$
$164$	−0.839278	−	19.9843i	−0.0655366	−	1.56051i
$165$	0.284426	−	11.8090i	0.0221426	−	0.919328i
$166$	−12.8224	+	0.269132i	−0.995210	+	0.0208887i
$167$	−3.14806	−	1.30397i	−0.243604	−	0.100904i	0.257541	−	0.966267i	$-0.417088\pi$
$167$	−3.14806	−	1.30397i	−0.243604	−	0.100904i	−0.501145	+	0.865363i	$0.667088\pi$
$168$	−3.77297	−	15.7428i	−0.291091	−	1.21458i
$169$	−11.7357	+	4.86109i	−0.902747	+	0.373930i
$170$	−1.22577	−	2.79206i	−0.0940121	−	0.214141i
$171$	15.8529	+	11.7346i	1.21230	+	0.897365i
$172$	−2.59319	−	10.6743i	−0.197729	−	0.813905i
$173$	0.0807891	−	0.0160700i	0.00614228	−	0.00122178i	−0.192018	−	0.981391i	$-0.561503\pi$
$173$	0.0807891	−	0.0160700i	0.00614228	−	0.00122178i	0.198161	+	0.980170i	$0.436503\pi$
$174$	−0.470028	−	1.14476i	−0.0356327	−	0.0867837i
$175$	−3.75471	−	3.75471i	−0.283829	−	0.283829i
$176$	−1.66115	+	14.7160i	−0.125214	+	1.10926i
$177$	−10.7634	+	15.2979i	−0.809028	+	1.14986i
$178$	13.0024	+	8.29865i	0.974573	+	0.622010i
$179$	−15.2598	+	3.03535i	−1.14057	+	0.226873i	−0.729005	−	0.684508i	$-0.760017\pi$
$179$	−15.2598	+	3.03535i	−1.14057	+	0.226873i	−0.411563	+	0.911381i	$0.635017\pi$
$180$	−10.8530	+	2.08905i	−0.808935	+	0.155708i
$181$	9.09877	+	13.6173i	0.676306	+	1.01216i	0.997867	+	0.0652752i	$0.0207925\pi$
$181$	9.09877	+	13.6173i	0.676306	+	1.01216i	−0.321561	+	0.946889i	$0.604207\pi$
$182$	0.925594	−	2.37432i	0.0686096	−	0.175996i
$183$	−0.270947	+	0.171751i	−0.0200290	+	0.0126962i
$184$	−3.04376	+	22.6828i	−0.224389	+	1.67220i
$185$	−1.86417	−	0.772166i	−0.137057	−	0.0567708i
$186$	−5.68050	−	3.82107i	−0.416515	−	0.280175i
$187$	−0.845470	+	4.25046i	−0.0618269	+	0.310825i
$188$	19.1689	−	8.89987i	1.39804	−	0.649090i
$189$	−17.1258	−	1.23937i	−1.24572	−	0.0901512i
$190$	16.8641	+	2.98804i	1.22345	+	0.216775i
$191$	1.98808			0.143852			0.0719260	−	0.997410i	$-0.477085\pi$
$191$	1.98808			0.143852			0.0719260	+	0.997410i	$0.477085\pi$
$192$	13.7846	−	1.40864i	0.994819	−	0.101660i
$193$	11.9983			0.863656			0.431828	−	0.901956i	$-0.357869\pi$
$193$	11.9983			0.863656			0.431828	+	0.901956i	$0.357869\pi$
$194$	−21.0813	−	3.73525i	−1.51355	−	0.268175i
$195$	−1.59087	−	0.704306i	−0.113925	−	0.0504364i
$196$	−3.30119	−	7.11023i	−0.235799	−	0.507873i
$197$	−0.501219	+	2.51980i	−0.0357103	+	0.179528i	−0.994524	−	0.104508i	$-0.966673\pi$
$197$	−0.501219	+	2.51980i	−0.0357103	+	0.179528i	0.958814	+	0.284036i	$0.0916734\pi$
$198$	14.3434	+	6.40322i	1.01934	+	0.455057i
$199$	1.03878	+	0.430275i	0.0736368	+	0.0305014i	0.419198	−	0.907895i	$-0.362311\pi$
$199$	1.03878	+	0.430275i	0.0736368	+	0.0305014i	−0.345561	+	0.938396i	$0.612311\pi$
$200$	3.61266	−	2.75782i	0.255454	−	0.195007i
$201$	2.32708	+	3.67111i	0.164140	+	0.258940i
$202$	2.20214	−	5.64891i	0.154942	−	0.397456i
$203$	−0.927492	−	1.38809i	−0.0650972	−	0.0974248i
$204$	4.05419	−	0.0725425i	0.283850	−	0.00507899i
$205$	−18.0682	+	3.59398i	−1.26193	+	0.251014i
$206$	−9.79475	−	6.25139i	−0.682433	−	0.435555i
$207$	21.9533	+	10.3583i	1.52586	+	0.719952i
$208$	1.90885	+	1.05549i	0.132355	+	0.0731854i
$209$	−17.2118	−	17.2118i	−1.19056	−	1.19056i
$210$	−13.7926	+	5.66315i	−0.951782	+	0.390795i
$211$	14.1029	−	2.80524i	0.970885	−	0.193121i	0.315924	−	0.948784i	$-0.397685\pi$
$211$	14.1029	−	2.80524i	0.970885	−	0.193121i	0.654960	+	0.755663i	$0.272685\pi$
$212$	−4.73165	+	1.14950i	−0.324971	+	0.0789480i
$213$	16.4390	+	17.2505i	1.12638	+	1.18198i
$214$	−1.75770	−	4.00370i	−0.120154	−	0.273687i
$215$	−9.34703	+	3.87167i	−0.637462	+	0.264046i
$216$	3.00094	−	14.3873i	0.204188	−	0.978932i
$217$	−8.53266	−	3.53434i	−0.579235	−	0.239927i
$218$	4.12475	−	0.0865751i	0.279363	−	0.00586361i
$219$	16.1944	+	0.390052i	1.09432	+	0.0263573i
$220$	13.6278	−	0.572324i	0.918784	−	0.0385861i
$221$	0.530727	+	0.354621i	0.0357006	+	0.0238544i
$222$	1.90315	−	1.89141i	0.127731	−	0.126943i
$223$	17.0025			1.13857			0.569286	−	0.822140i	$-0.307220\pi$
$223$	17.0025			1.13857			0.569286	+	0.822140i	$0.307220\pi$
$224$	17.8510	−	5.54701i	1.19272	−	0.370625i
$225$	−1.62824	−	4.53738i	−0.108549	−	0.302492i
$226$	−6.81406	−	9.74870i	−0.453264	−	0.648474i
$227$	9.29893	−	13.9168i	0.617192	−	0.923693i	−0.382808	−	0.923828i	$-0.625043\pi$
$227$	9.29893	−	13.9168i	0.617192	−	0.923693i	1.00000		0.000135074i	$4.29954e-5\pi$
$228$	−12.3121	+	19.1598i	−0.815390	+	1.26889i
$229$	−1.72964	+	8.69549i	−0.114298	+	0.574614i	0.880611	+	0.473839i	$0.157132\pi$
$229$	−1.72964	+	8.69549i	−0.114298	+	0.574614i	−0.994909	+	0.100775i	$0.967868\pi$
$230$	21.0739	−	0.442324i	1.38957	−	0.0291660i
$231$	20.6778	+	4.63332i	1.36050	+	0.304850i
$232$	1.28314	−	0.628807i	0.0842425	−	0.0412832i
$233$	−4.61203	−	11.1344i	−0.302144	−	0.729441i	−0.999914	−	0.0131185i	$-0.995824\pi$
$233$	−4.61203	−	11.1344i	−0.302144	−	0.729441i	0.697770	−	0.716322i	$-0.254176\pi$
$234$	1.67977	−	1.59087i	0.109810	−	0.103998i
$235$	−10.8142	−	16.1846i	−0.705439	−	1.05576i
$236$	−18.4463	−	11.2355i	−1.20075	−	0.731367i
$237$	8.82558	+	22.8480i	0.573283	+	1.48413i
$238$	5.34150	−	1.17953i	0.346238	−	0.0764575i
$239$	−12.7729	+	12.7729i	−0.826209	+	0.826209i	−0.986990	−	0.160781i	$-0.948599\pi$
$239$	−12.7729	+	12.7729i	−0.826209	+	0.826209i	0.160781	+	0.986990i	$0.448599\pi$
$240$	−3.23414	−	12.3454i	−0.208763	−	0.796893i
$241$	−1.12018	−	1.12018i	−0.0721574	−	0.0721574i	0.670107	−	0.742264i	$-0.266248\pi$
$241$	−1.12018	−	1.12018i	−0.0721574	−	0.0721574i	−0.742264	+	0.670107i	$0.766248\pi$
$242$	−3.22761	−	2.05998i	−0.207478	−	0.132421i
$243$	−13.5811	−	7.65212i	−0.871225	−	0.490884i
$244$	−0.218539	−	0.299090i	−0.0139905	−	0.0191473i
$245$	−6.00326	+	4.01125i	−0.383534	+	0.256269i
$246$	4.85351	−	24.0116i	0.309448	−	1.53092i
$247$	−3.31221	+	1.37196i	−0.210751	+	0.0872960i
$248$	3.96963	−	6.83620i	0.252072	−	0.434099i
$249$	−15.3275	−	3.43446i	−0.971343	−	0.217650i
$250$	−12.4229	−	11.9121i	−0.785691	−	0.753387i
$251$	−4.95413	−	0.985437i	−0.312702	−	0.0622002i	0.0362446	−	0.999343i	$-0.488460\pi$
$251$	−4.95413	−	0.985437i	−0.312702	−	0.0622002i	−0.348946	+	0.937143i	$0.613460\pi$
$252$	0.122721	−	19.8265i	0.00773069	−	1.24895i
$253$	−24.9087	−	16.6435i	−1.56600	−	1.04637i
$254$	30.7479	+	5.44802i	1.92930	+	0.341839i
$255$	−0.640175	−	3.67931i	−0.0400893	−	0.230407i
$256$	2.67362	+	15.7750i	0.167101	+	0.985940i
$257$		−	21.3362i		−	1.33092i	−0.746435	−	0.665458i	$-0.768236\pi$
$257$		−	21.3362i		−	1.33092i	0.746435	−	0.665458i	$-0.231764\pi$
$258$	0.0416362	−	13.4534i	0.00259216	−	0.837575i
$259$	2.01101	−	3.00969i	0.124958	−	0.187013i
$260$	0.690238	−	1.88666i	0.0428068	−	0.117006i
$261$	−0.223774	−	1.49900i	−0.0138513	−	0.0927860i
$262$	−13.6599	+	14.2457i	−0.843914	+	0.880099i
$263$	−1.14122	+	2.75514i	−0.0703705	+	0.169889i	−0.955151	−	0.296118i	$-0.904308\pi$
$263$	−1.14122	+	2.75514i	−0.0703705	+	0.169889i	0.884781	+	0.466007i	$0.154308\pi$
$264$	−6.28448	+	17.0143i	−0.386783	+	1.04716i
$265$	1.71622	+	4.14332i	0.105426	+	0.254522i
$266$	−11.1594	+	28.6259i	−0.684225	+	1.75517i
$267$	13.0329	+	13.6762i	0.797602	+	0.836972i
$268$	−4.05242	+	2.96102i	−0.247541	+	0.180873i
$269$	2.86161	+	14.3863i	0.174476	+	0.877148i	0.964502	+	0.264075i	$0.0850668\pi$
$269$	2.86161	+	14.3863i	0.174476	+	0.877148i	−0.790026	+	0.613073i	$0.789933\pi$
$270$	−13.5184	−	0.693516i	−0.822703	−	0.0422060i
$271$	−14.9476	+	14.9476i	−0.907999	+	0.907999i	−0.996111	−	0.0881113i	$-0.971917\pi$
$271$	−14.9476	+	14.9476i	−0.907999	+	0.907999i	0.0881113	+	0.996111i	$0.471917\pi$
$272$	0.392577	+	4.66564i	0.0238035	+	0.282896i
$273$	1.79597	−	2.55258i	0.108697	−	0.154489i
$274$	−2.89880	−	13.1272i	−0.175123	−	0.793044i
$275$	1.16065	+	5.83499i	0.0699900	+	0.351863i
$276$	−10.2615	+	26.0837i	−0.617667	+	1.57006i
$277$	0.819369	−	0.547485i	0.0492311	−	0.0328952i	−0.530711	−	0.847553i	$-0.678075\pi$
$277$	0.819369	−	0.547485i	0.0492311	−	0.0328952i	0.579942	+	0.814658i	$0.303075\pi$
$278$	6.48878	+	14.7802i	0.389171	+	0.886456i
$279$	−5.63656	−	6.20743i	−0.337452	−	0.371629i
$280$	−7.57621	−	15.4600i	−0.452765	−	0.923912i
$281$	5.35268	−	12.9225i	0.319314	−	0.770893i	−0.679976	−	0.733234i	$-0.738010\pi$
$281$	5.35268	−	12.9225i	0.319314	−	0.770893i	0.999291	−	0.0376590i	$-0.0119901\pi$
$282$	25.4021	−	4.97113i	1.51268	−	0.296026i
$283$	−2.79329	−	0.555619i	−0.166044	−	0.0330281i	0.111368	−	0.993779i	$-0.464477\pi$
$283$	−2.79329	−	0.555619i	−0.166044	−	0.0330281i	−0.277412	+	0.960751i	$0.589477\pi$
$284$	−18.6228	+	20.2555i	−1.10506	+	1.20194i
$285$	19.1803	+	8.49143i	1.13614	+	0.502989i
$286$	−2.34020	+	1.63573i	−0.138379	+	0.0967227i
$287$		−	33.0480i		−	1.95076i
$288$	16.8055	+	2.36108i	0.990274	+	0.139128i
$289$		−	15.6299i		−	0.919403i
$290$	−0.753975	−	1.07869i	−0.0442749	−	0.0633431i
$291$	−23.9767	−	10.6149i	−1.40554	−	0.622255i
$292$	0.784866	+	18.6887i	0.0459308	+	1.09367i
$293$	−28.5066	−	5.67031i	−1.66537	−	0.331263i	−0.729602	−	0.683872i	$-0.760294\pi$
$293$	−28.5066	−	5.67031i	−1.66537	−	0.331263i	−0.935771	+	0.352609i	$0.885294\pi$
$294$	−1.84392	−	9.42230i	−0.107539	−	0.549520i
$295$	−7.61264	+	18.3785i	−0.443225	+	1.07004i
$296$	2.32429	+	2.04862i	0.135097	+	0.119074i
$297$	15.1827	+	11.8148i	0.880987	+	0.685563i
$298$	−11.2253	+	4.92812i	−0.650263	+	0.285478i
$299$	−3.66872	+	2.45136i	−0.212168	+	0.141766i
$300$	5.10379	−	2.22185i	0.294668	−	0.128279i
$301$	−3.54078	−	17.8007i	−0.204087	−	1.02602i
$302$	−5.77750	+	1.27581i	−0.332458	+	0.0734145i
$303$	4.27291	−	6.07303i	0.245472	−	0.348886i
$304$	−23.0139	−	12.7255i	−1.31994	−	0.729859i
$305$	−0.241242	+	0.241242i	−0.0138135	+	0.0138135i
$306$	4.84260	+	1.10084i	0.276833	+	0.0629308i
$307$	2.86761	+	14.4164i	0.163663	+	0.822790i	0.972165	+	0.234296i	$0.0752786\pi$
$307$	2.86761	+	14.4164i	0.163663	+	0.822790i	−0.808502	+	0.588493i	$0.799721\pi$
$308$	−3.76244	+	24.1778i	−0.214385	+	1.37766i
$309$	−9.81772	−	10.3023i	−0.558510	−	0.586079i
$310$	−6.78357	−	2.64448i	−0.385281	−	0.150196i
$311$	−1.95981	−	4.73141i	−0.111131	−	0.268294i	0.858523	−	0.512775i	$-0.171382\pi$
$311$	−1.95981	−	4.73141i	−0.111131	−	0.268294i	−0.969654	+	0.244481i	$0.921382\pi$
$312$	1.96100	+	1.81415i	0.111020	+	0.102706i
$313$	−0.752332	+	1.81629i	−0.0425243	+	0.102663i	−0.943715	−	0.330761i	$-0.892695\pi$
$313$	−0.752332	+	1.81629i	−0.0425243	+	0.102663i	0.901190	+	0.433424i	$0.142695\pi$
$314$	−10.5753	−	10.1405i	−0.596797	−	0.572260i
$315$	−18.0608	+	2.69615i	−1.01761	+	0.151911i
$316$	−25.6524	+	11.9101i	−1.44306	+	0.669993i
$317$	−6.37904	+	9.54690i	−0.358282	+	0.536208i	−0.966200	−	0.257792i	$-0.917005\pi$
$317$	−6.37904	+	9.54690i	−0.358282	+	0.536208i	0.607918	+	0.794000i	$0.292005\pi$
$318$	−5.96359	−	0.0184563i	−0.334422	−	0.00103498i
$319$			1.87045i			0.104725i
$320$	13.9777	−	4.66724i	0.781376	−	0.260907i
$321$	−0.917985	−	5.27598i	−0.0512369	−	0.294477i
$322$	−6.59714	+	37.2334i	−0.367644	+	2.07494i
$323$	−6.39869	−	4.27547i	−0.356033	−	0.237893i
$324$	7.78154	−	16.2311i	0.432308	−	0.901726i
$325$	0.859416	+	0.170948i	0.0476718	+	0.00948251i
$326$	−0.709155	+	0.739562i	−0.0392764	+	0.0409605i
$327$	4.93061	+	1.10481i	0.272663	+	0.0610961i
$328$	28.0357	+	3.76205i	1.54801	+	0.207724i
$329$	32.2607	−	13.3628i	1.77859	−	0.736717i
$330$	16.3741	+	3.30973i	0.901365	+	0.182194i
$331$	−28.1107	+	18.7830i	−1.54510	+	1.03240i	−0.567141	+	0.823621i	$0.691950\pi$
$331$	−28.1107	+	18.7830i	−1.54510	+	1.03240i	−0.977962	+	0.208784i	$0.933050\pi$
$332$	2.78892	−	17.9219i	0.153062	−	0.983591i
$333$	2.81710	−	1.69205i	0.154376	−	0.0927238i
$334$	2.59254	−	4.06202i	0.141857	−	0.222264i
$335$	3.26863	+	3.26863i	0.178584	+	0.178584i
$336$	22.8531	−	1.36970i	1.24674	−	0.0747235i
$337$	−2.58232	+	2.58232i	−0.140668	+	0.140668i	−0.773934	−	0.633266i	$-0.781714\pi$
$337$	−2.58232	+	2.58232i	−0.140668	+	0.140668i	0.633266	+	0.773934i	$0.281714\pi$
$338$	−3.87361	−	17.5416i	−0.210696	−	0.954140i
$339$	−5.24895	−	13.5887i	−0.285084	−	0.738034i
$340$	4.19044	−	1.01802i	0.227259	−	0.0552099i
$341$	5.74889	+	8.60382i	0.311320	+	0.465923i
$342$	−20.2521	+	19.1802i	−1.09511	+	1.03715i
$343$	3.89538	+	9.40427i	0.210331	+	0.507783i
$344$	15.5040	−	0.977398i	0.835919	−	0.0526978i
$345$	25.1911	+	5.64462i	1.35625	+	0.303896i
$346$	0.00244452	+	0.116466i	0.000131418	+	0.00626124i
$347$	5.96824	−	30.0043i	0.320392	−	1.61072i	−0.399569	−	0.916703i	$-0.630840\pi$
$347$	5.96824	−	30.0043i	0.320392	−	1.61072i	0.719961	−	0.694015i	$-0.244160\pi$
$348$	1.71007	−	0.372077i	0.0916694	−	0.0199454i
$349$	6.31423	−	9.44991i	0.337993	−	0.505842i	−0.623072	−	0.782164i	$-0.714116\pi$
$349$	6.31423	−	9.44991i	0.337993	−	0.505842i	0.961065	+	0.276322i	$0.0891157\pi$
$350$	6.15493	−	4.30211i	0.328995	−	0.229958i
$351$	2.46345	−	1.40005i	0.131489	−	0.0747291i
$352$	−20.0825	−	5.94411i	−1.07040	−	0.316822i
$353$	18.7391			0.997379			0.498690	−	0.866781i	$-0.333815\pi$
$353$	18.7391			0.997379			0.498690	+	0.866781i	$0.333815\pi$
$354$	−18.6470	−	18.7628i	−0.991078	−	0.997231i
$355$	21.0712	+	14.0793i	1.11834	+	0.747254i
$356$	−14.7642	+	16.0587i	−0.782500	+	0.851107i
$357$	6.69764	+	0.161317i	0.354476	+	0.00853778i
$358$	−0.461731	−	21.9985i	−0.0244032	−	1.16266i
$359$	18.0775	+	7.48794i	0.954094	+	0.395199i	0.804768	−	0.593590i	$-0.202290\pi$
$359$	18.0775	+	7.48794i	0.954094	+	0.395199i	0.149326	+	0.988788i	$0.452290\pi$
$360$	−0.231263	−	15.6285i	−0.0121887	−	0.823694i
$361$	22.3798	−	9.27003i	1.17789	−	0.487896i
$362$	−21.2073	+	9.31044i	−1.11463	+	0.489346i
$363$	−3.23518	−	3.39486i	−0.169803	−	0.178184i
$364$	3.07793	+	1.87473i	0.161327	+	0.0982627i
$365$	16.8968	−	3.36097i	0.884417	−	0.175921i
$366$	−0.172316	−	0.419677i	−0.00900711	−	0.0219369i
$367$	−1.66204	−	1.66204i	−0.0867576	−	0.0867576i	0.662396	−	0.749154i	$-0.269540\pi$
$367$	−1.66204	−	1.66204i	−0.0867576	−	0.0867576i	−0.749154	+	0.662396i	$0.769540\pi$
$368$	−30.8353	−	9.83507i	−1.60740	−	0.512689i
$369$	12.8028	−	27.1341i	0.666485	−	1.41255i
$370$	1.53521	−	2.40539i	0.0798118	−	0.125050i
$371$	−7.89063	+	1.56954i	−0.409661	+	0.0814867i
$372$	6.72250	−	6.96745i	0.348545	−	0.361246i
$373$	3.60356	+	5.39311i	0.186585	+	0.279245i	0.912956	−	0.408059i	$-0.133794\pi$
$373$	3.60356	+	5.39311i	0.186585	+	0.279245i	−0.726370	+	0.687304i	$0.758794\pi$
$374$	−5.71027	−	2.22606i	−0.295271	−	0.115107i
$375$	−11.2856	−	17.8037i	−0.582787	−	0.919380i
$376$	7.66370	+	28.8890i	0.395225	+	1.48984i
$377$	0.254522	+	0.105426i	0.0131085	+	0.00542973i
$378$	5.95135	−	23.5423i	0.306104	−	1.21089i
$379$	0.395416	−	1.98789i	0.0203112	−	0.102111i	−0.969300	−	0.245881i	$-0.920923\pi$
$379$	0.395416	−	1.98789i	0.0203112	−	0.102111i	0.989611	+	0.143770i	$0.0459226\pi$
$380$	−8.32182	+	22.7464i	−0.426900	+	1.16687i
$381$	34.9710	+	15.4822i	1.79162	+	0.793179i
$382$	−0.490522	+	2.76844i	−0.0250973	+	0.141646i
$383$	24.1070			1.23181			0.615905	−	0.787821i	$-0.288791\pi$
$383$	24.1070			1.23181			0.615905	+	0.787821i	$0.288791\pi$
$384$	−1.43954	+	19.5430i	−0.0734614	+	0.997298i
$385$	22.5362			1.14855
$386$	−2.96037	+	16.7079i	−0.150679	+	0.850410i
$387$	3.98882	−	15.9870i	0.202763	−	0.812666i
$388$	10.4029	−	28.4346i	0.528125	−	1.44355i
$389$	−7.20317	+	36.2128i	−0.365215	+	1.83606i	0.162587	+	0.986694i	$0.448016\pi$
$389$	−7.20317	+	36.2128i	−0.365215	+	1.83606i	−0.527802	+	0.849367i	$0.676984\pi$
$390$	1.37328	−	2.04156i	0.0695389	−	0.103378i
$391$	−8.75034	−	3.62451i	−0.442524	−	0.183299i
$392$	10.7157	−	2.84266i	0.541223	−	0.143576i
$393$	−20.4160	+	12.9416i	−1.02985	+	0.652815i
$394$	−3.38521	−	1.31967i	−0.170544	−	0.0664842i
$395$	14.4718	+	21.6586i	0.728157	+	1.08976i
$396$	−12.4556	+	18.3937i	−0.625919	+	0.924317i
$397$	30.1732	−	6.00182i	1.51435	−	0.301223i	0.633173	−	0.774011i	$-0.281752\pi$
$397$	30.1732	−	6.00182i	1.51435	−	0.301223i	0.881176	+	0.472788i	$0.156752\pi$
$398$	−0.855467	+	1.34036i	−0.0428807	+	0.0671860i
$399$	−21.6530	+	30.7751i	−1.08400	+	1.54068i
$400$	2.94897	+	5.71116i	0.147449	+	0.285558i
$401$	−9.14394	−	9.14394i	−0.456626	−	0.456626i	0.440920	−	0.897546i	$-0.354652\pi$
$401$	−9.14394	−	9.14394i	−0.456626	−	0.456626i	−0.897546	+	0.440920i	$0.854652\pi$
$402$	−5.68627	+	2.33474i	−0.283605	+	0.116446i
$403$	1.49479	−	0.297333i	0.0744610	−	0.0148112i
$404$	7.32290	+	4.46030i	0.364328	+	0.221908i
$405$	−15.8734	−	4.78307i	−0.788754	−	0.237672i
$406$	2.16179	−	0.949068i	0.107288	−	0.0471015i
$407$	−3.74685	+	1.55200i	−0.185725	+	0.0769296i
$408$	−0.899283	+	5.66346i	−0.0445211	+	0.280383i
$409$	−25.5396	−	10.5789i	−1.26285	−	0.523091i	−0.352069	−	0.935974i	$-0.614522\pi$
$409$	−25.5396	−	10.5789i	−1.26285	−	0.523091i	−0.910784	+	0.412883i	$0.864522\pi$
$410$	−0.546708	−	26.0471i	−0.0270000	−	1.28637i
$411$	0.396450	−	16.4600i	0.0195554	−	0.811914i
$412$	11.1219	−	12.0970i	0.547936	−	0.595977i
$413$	−29.6720	−	19.8262i	−1.46006	−	0.975583i
$414$	−19.8408	+	28.0148i	−0.975122	+	1.37685i
$415$	−16.7051			−0.820019
$416$	−1.94078	+	2.39769i	−0.0951544	+	0.117557i
$417$	3.38886	+	19.4770i	0.165953	+	0.953791i
$418$	28.2145	−	19.7211i	1.38002	−	0.964590i
$419$	10.6745	−	15.9755i	0.521484	−	0.780455i	−0.473468	−	0.880811i	$-0.656998\pi$
$419$	10.6745	−	15.9755i	0.521484	−	0.780455i	0.994952	+	0.100356i	$0.0319981\pi$
$420$	−4.48299	−	20.6039i	−0.218747	−	1.00537i
$421$	4.39818	−	22.1111i	0.214354	−	1.07763i	−0.712346	−	0.701829i	$-0.752367\pi$
$421$	4.39818	−	22.1111i	0.214354	−	1.07763i	0.926700	−	0.375802i	$-0.122633\pi$
$422$	0.426727	+	20.3308i	0.0207727	+	0.989687i
$423$	31.6645	+	1.52620i	1.53958	+	0.0742066i
$424$	−0.433257	−	6.87255i	−0.0210408	−	0.333761i
$425$	0.719798	+	1.73775i	0.0349153	+	0.0842931i
$426$	−28.0777	+	18.6355i	−1.36037	+	0.902893i
$427$	−0.340026	−	0.508885i	−0.0164550	−	0.0246267i
$428$	6.00893	−	1.45980i	0.290453	−	0.0705622i
$429$	−3.26199	+	1.26002i	−0.157490	+	0.0608344i
$430$	−3.08518	−	13.9712i	−0.148780	−	0.673753i
$431$	10.8612	−	10.8612i	0.523167	−	0.523167i	−0.395359	−	0.918527i	$-0.629380\pi$
$431$	10.8612	−	10.8612i	0.523167	−	0.523167i	0.918527	+	0.395359i	$0.129380\pi$
$432$	19.2942	+	7.72869i	0.928294	+	0.371847i
$433$	6.03352	+	6.03352i	0.289952	+	0.289952i	0.837061	−	0.547109i	$-0.184272\pi$
$433$	6.03352	+	6.03352i	0.289952	+	0.289952i	−0.547109	+	0.837061i	$0.684272\pi$
$434$	7.02694	−	11.0099i	0.337304	−	0.528492i
$435$	−0.580796	−	1.50358i	−0.0278470	−	0.0720913i
$436$	−0.897150	+	5.76517i	−0.0429657	+	0.276102i
$437$	44.2317	−	29.5547i	2.11589	−	1.41379i
$438$	−4.53884	+	22.4549i	−0.216874	+	1.07294i
$439$	12.3126	−	5.10006i	0.587650	−	0.243412i	−0.0689894	−	0.997617i	$-0.521977\pi$
$439$	12.3126	−	5.10006i	0.587650	−	0.243412i	0.656639	+	0.754205i	$0.271977\pi$
$440$	−2.56543	+	19.1182i	−0.122302	+	0.911425i
$441$	0.566108	−	11.7452i	0.0269575	−	0.559294i
$442$	−0.624766	+	0.651554i	−0.0297171	+	0.0309913i
$443$	−39.4508	−	7.84725i	−1.87436	−	0.372834i	−0.879658	−	0.475607i	$-0.842228\pi$
$443$	−39.4508	−	7.84725i	−1.87436	−	0.372834i	−0.994705	+	0.102774i	$0.967228\pi$
$444$	2.16426	+	3.11685i	0.102711	+	0.147919i
$445$	16.7053	+	11.1622i	0.791909	+	0.529137i
$446$	−4.19506	+	23.6764i	−0.198642	+	1.12111i
$447$	−14.7924	+	2.57378i	−0.699657	+	0.121736i
$448$	3.31993	+	26.2266i	0.156852	+	1.23909i
$449$			6.27965i			0.296355i	0.988961	+	0.148178i	$0.0473407\pi$
$449$			6.27965i			0.296355i	−0.988961	+	0.148178i	$0.952659\pi$
$450$	6.72015	−	1.14785i	0.316791	−	0.0541099i
$451$	−20.5712	+	30.7869i	−0.968659	+	1.44970i
$452$	15.2565	−	7.08342i	0.717608	−	0.333176i
$453$	−7.24433	−	0.174484i	−0.340368	−	0.00819798i
$454$	17.0852	+	16.3827i	0.801847	+	0.768879i
$455$	1.27023	−	3.06662i	0.0595495	−	0.143765i
$456$	−23.6426	−	21.8723i	−1.10717	−	1.02426i
$457$	−3.03960	−	7.33824i	−0.142186	−	0.343268i	0.836704	−	0.547656i	$-0.184480\pi$
$457$	−3.03960	−	7.33824i	−0.142186	−	0.343268i	−0.978890	+	0.204388i	$0.934480\pi$
$458$	−11.6819	−	4.55402i	−0.545860	−	0.212795i
$459$	5.43662	+	2.72711i	0.253760	+	0.127291i
$460$	−4.58366	+	29.4550i	−0.213714	+	1.37335i
$461$	4.23707	+	21.3012i	0.197340	+	0.992096i	0.944765	+	0.327749i	$0.106290\pi$
$461$	4.23707	+	21.3012i	0.197340	+	0.992096i	−0.747425	+	0.664347i	$0.768710\pi$
$462$	−11.5539	+	27.6512i	−0.537536	+	1.28645i
$463$	24.9132	−	24.9132i	1.15781	−	1.15781i	0.172869	−	0.984945i	$-0.444696\pi$
$463$	24.9132	−	24.9132i	1.15781	−	1.15781i	0.984945	−	0.172869i	$-0.0553036\pi$
$464$	0.559036	+	1.94196i	0.0259526	+	0.0901530i
$465$	−7.29289	−	5.13118i	−0.338199	−	0.237953i
$466$	16.6429	−	3.67514i	0.770967	−	0.170248i
$467$	4.59236	+	23.0874i	0.212509	+	1.06836i	0.928808	+	0.370562i	$0.120835\pi$
$467$	4.59236	+	23.0874i	0.212509	+	1.06836i	−0.716299	+	0.697794i	$0.754165\pi$
$468$	1.80087	+	2.73164i	0.0832451	+	0.126270i
$469$	−6.89497	+	4.60707i	−0.318380	+	0.212735i
$470$	25.2056	−	11.0657i	1.16265	−	0.510425i
$471$	−9.60718	−	15.1559i	−0.442675	−	0.698346i
$472$	20.1970	−	22.9148i	0.929640	−	1.05474i
$473$	−7.78177	+	18.7869i	−0.357806	+	0.863821i
$474$	−33.9939	+	6.65250i	−1.56139	+	0.305560i
$475$	−10.3615	−	2.06103i	−0.475418	−	0.0945666i
$476$	0.324602	+	7.72919i	0.0148781	+	0.354267i
$477$	−7.08666	−	1.76815i	−0.324476	−	0.0809579i
$478$	−14.6351	−	20.9380i	−0.669392	−	0.957683i
$479$			16.8605i			0.770374i	0.922838	+	0.385187i	$0.125863\pi$
$479$			16.8605i			0.770374i	−0.922838	+	0.385187i	$0.874137\pi$
$480$	17.9893	−	1.45760i	0.821094	−	0.0665302i
$481$			0.597330i			0.0272359i
$482$	1.83627	−	1.28350i	0.0836397	−	0.0584617i
$483$	−18.7478	+	42.3473i	−0.853055	+	1.92687i
$484$	3.66493	−	3.98626i	0.166588	−	0.181194i
$485$	−27.3506	−	5.44037i	−1.24193	−	0.247034i
$486$	14.0066	−	17.0239i	0.635354	−	0.772221i
$487$	−5.51670	+	13.3185i	−0.249986	+	0.603519i	−0.998202	−	0.0599357i	$-0.980910\pi$
$487$	−5.51670	+	13.3185i	−0.249986	+	0.603519i	0.748216	+	0.663455i	$0.230910\pi$
$488$	0.470411	−	0.230526i	0.0212945	−	0.0104354i
$489$	−1.05990	+	0.671860i	−0.0479302	+	0.0303826i
$490$	−4.10457	−	9.34939i	−0.185425	−	0.422362i
$491$	−8.17112	+	5.45977i	−0.368758	+	0.246396i	−0.726117	−	0.687571i	$-0.758677\pi$
$491$	−8.17112	+	5.45977i	−0.368758	+	0.246396i	0.357360	+	0.933967i	$0.383677\pi$
$492$	32.2392	+	12.6831i	1.45346	+	0.571796i
$493$	0.115368	+	0.579996i	0.00519593	+	0.0261217i
$494$	−1.09326	−	4.95085i	−0.0491882	−	0.222749i
$495$	18.5034	+	8.73052i	0.831667	+	0.392408i
$496$	8.54014	+	7.21451i	0.383464	+	0.323941i
$497$	−32.1465	+	32.1465i	−1.44197	+	1.44197i
$498$	8.56437	−	20.4966i	0.383779	−	0.918473i
$499$	3.78425	+	19.0247i	0.169407	+	0.851664i	0.968223	+	0.250089i	$0.0804599\pi$
$499$	3.78425	+	19.0247i	0.169407	+	0.851664i	−0.798816	+	0.601575i	$0.794540\pi$
$500$	19.6530	−	14.3600i	0.878908	−	0.642200i
$501$	4.27252	−	4.07155i	0.190882	−	0.181903i
$502$	2.59459	−	6.65560i	0.115802	−	0.297054i
$503$	4.59413	+	11.0912i	0.204842	+	0.494532i	0.992597	−	0.121457i	$-0.0387566\pi$
$503$	4.59413	+	11.0912i	0.204842	+	0.494532i	−0.787755	+	0.615989i	$0.788757\pi$
$504$	27.5786	+	5.06273i	1.22845	+	0.225512i
$505$	3.02210	−	7.29599i	0.134482	−	0.324667i
$506$	29.3222	−	30.5795i	1.30353	−	1.35943i
$507$	0.529769	−	21.9952i	0.0235278	−	0.976843i
$508$	−15.1730	+	41.4730i	−0.673193	+	1.84007i
$509$	−13.6072	+	20.3646i	−0.603129	+	0.902647i	−0.999883	−	0.0152784i	$-0.995137\pi$
$509$	−13.6072	+	20.3646i	−0.603129	+	0.902647i	0.396754	+	0.917925i	$0.370137\pi$
$510$	5.28148	+	0.0163453i	0.233868	+	0.000723783i
$511$			30.9054i			1.36717i
$512$	−22.6268	−	0.169126i	−0.999972	−	0.00747439i
$513$	−29.7005	+	16.8796i	−1.31131	+	0.745254i
$514$	29.7112	+	5.26433i	1.31050	+	0.232200i
$515$	−12.5842	−	8.40847i	−0.554524	−	0.370521i
$516$	18.7240	+	3.37738i	0.824277	+	0.148681i
$517$	−38.3715	−	7.63256i	−1.68758	−	0.335680i
$518$	3.69489	+	3.54297i	0.162344	+	0.155669i
$519$	−0.0311953	+	0.139220i	−0.00136932	+	0.00611108i
$520$	2.45691	+	1.42667i	0.107743	+	0.0625637i
$521$	9.74629	−	4.03705i	0.426993	−	0.176866i	−0.158829	−	0.987306i	$-0.550772\pi$
$521$	9.74629	−	4.03705i	0.426993	−	0.176866i	0.585822	+	0.810440i	$0.300772\pi$
$522$	2.14261	+	0.0582415i	0.0937796	+	0.00254916i
$523$	8.73360	−	5.83560i	0.381894	−	0.255173i	−0.349775	−	0.936834i	$-0.613742\pi$
$523$	8.73360	−	5.83560i	0.381894	−	0.255173i	0.731669	+	0.681661i	$0.238742\pi$
$524$	−16.4671	−	22.5367i	−0.719367	−	0.984518i
$525$	8.57931	−	3.31397i	0.374432	−	0.144633i
$526$	−3.55503	−	2.26896i	−0.155007	−	0.0989312i
$527$	2.31331	+	2.31331i	0.100769	+	0.100769i
$528$	−22.1422	−	12.9493i	−0.963615	−	0.563544i
$529$	30.0319	−	30.0319i	1.30574	−	1.30574i
$530$	−6.19312	+	1.36759i	−0.269012	+	0.0594041i
$531$	−16.6816	−	27.7733i	−0.723920	−	1.20526i
$532$	−37.1089	−	22.6026i	−1.60887	−	0.979948i
$533$	3.02986	+	4.53450i	0.131238	+	0.196411i
$534$	−22.2601	+	14.7743i	−0.963289	+	0.639346i
$535$	−2.17950	−	5.26178i	−0.0942281	−	0.227487i
$536$	−3.12343	−	6.37368i	−0.134912	−	0.275301i
$537$	5.89228	−	26.2964i	0.254271	−	1.13477i
$538$	−20.7393	+	0.435302i	−0.894136	+	0.0187672i
$539$	−2.83111	+	14.2330i	−0.121945	+	0.613057i
$540$	4.30116	−	18.6536i	0.185092	−	0.802721i
$541$	22.1758	−	33.1885i	0.953413	−	1.42688i	0.0496911	−	0.998765i	$-0.484176\pi$
$541$	22.1758	−	33.1885i	0.953413	−	1.42688i	0.903722	−	0.428119i	$-0.140824\pi$
$542$	−17.1268	−	24.5029i	−0.735658	−	1.05249i
$543$	−27.9465	+	4.86251i	−1.19930	+	0.208670i
$544$	−6.59388	−	0.604490i	−0.282710	−	0.0259173i
$545$	5.37374			0.230186
$546$	3.11141	+	3.13073i	0.133156	+	0.133983i
$547$	−0.839814	−	0.561146i	−0.0359079	−	0.0239929i	0.537487	−	0.843272i	$-0.319374\pi$
$547$	−0.839814	−	0.561146i	−0.0359079	−	0.0239929i	−0.573395	+	0.819279i	$0.694374\pi$
$548$	18.9952	−	0.797739i	0.811434	−	0.0340777i
$549$	−0.0820375	−	0.549547i	−0.00350128	−	0.0234541i
$550$	−8.41174	+	0.176556i	−0.358678	+	0.00752836i
$551$	−3.06863	−	1.27107i	−0.130728	−	0.0541493i
$552$	−33.7904	−	20.7250i	−1.43821	−	0.882116i
$553$	−43.1723	+	17.8825i	−1.83587	+	0.760443i
$554$	0.560221	+	1.27607i	0.0238015	+	0.0542152i
$555$	2.53004	−	2.41103i	0.107394	−	0.102342i
$556$	−22.1827	+	5.38904i	−0.940757	+	0.228546i
$557$	31.2872	−	6.22341i	1.32568	−	0.263694i	0.519047	−	0.854746i	$-0.326287\pi$
$557$	31.2872	−	6.22341i	1.32568	−	0.263694i	0.806634	+	0.591052i	$0.201287\pi$
$558$	10.0347	−	6.31747i	0.424804	−	0.267440i
$559$	2.11781	+	2.11781i	0.0895738	+	0.0895738i
$560$	23.3977	−	6.73557i	0.988735	−	0.284630i
$561$	−6.13899	−	4.31932i	−0.259189	−	0.182362i
$562$	16.6742	+	10.6421i	0.703361	+	0.448912i
$563$	−0.331921	+	0.0660232i	−0.0139888	+	0.00278255i	−0.202080	−	0.979369i	$-0.564770\pi$
$563$	−0.331921	+	0.0660232i	−0.0139888	+	0.00278255i	0.188091	+	0.982152i	$0.439770\pi$
$564$	0.654885	+	36.5996i	0.0275756	+	1.54112i
$565$	−8.60702	−	12.8813i	−0.362100	−	0.541921i
$566$	1.46291	−	3.75263i	0.0614905	−	0.157735i
$567$	13.9709	−	26.2545i	0.586724	−	1.10259i
$568$	−23.6115	−	30.9303i	−0.990715	−	1.29781i
$569$	−4.20099	−	1.74011i	−0.176115	−	0.0729491i	0.292884	−	0.956148i	$-0.405385\pi$
$569$	−4.20099	−	1.74011i	−0.176115	−	0.0729491i	−0.468999	+	0.883199i	$0.655385\pi$
$570$	−16.5569	+	24.6139i	−0.693493	+	1.03096i
$571$	6.40640	−	32.2071i	0.268099	−	1.34783i	−0.578537	−	0.815656i	$-0.696376\pi$
$571$	6.40640	−	32.2071i	0.268099	−	1.34783i	0.846637	−	0.532171i	$-0.178624\pi$
$572$	−1.70039	−	3.66237i	−0.0710969	−	0.153131i
$573$	−1.39397	+	3.14868i	−0.0582339	+	0.131538i
$574$	46.0201	+	8.15399i	1.92084	+	0.340341i
$575$	−13.0021			−0.542226
$576$	−7.43432	+	22.8195i	−0.309763	+	0.950814i
$577$	−29.0303			−1.20855			−0.604274	−	0.796777i	$-0.706537\pi$
$577$	−29.0303			−1.20855			−0.604274	+	0.796777i	$0.706537\pi$
$578$	21.7649	+	3.85639i	0.905302	+	0.160405i
$579$	−8.41279	+	19.0027i	−0.349624	+	0.789725i
$580$	1.68814	−	0.783780i	0.0700961	−	0.0325447i
$581$	5.84640	−	29.3918i	0.242550	−	1.21938i
$582$	20.6973	−	30.7691i	0.857930	−	1.27542i
$583$	8.32777	+	3.44947i	0.344901	+	0.142863i
$584$	−26.2181	−	3.51815i	−1.08491	−	0.145582i
$585$	2.23093	−	2.02576i	0.0922378	−	0.0837550i
$586$	14.9295	−	38.2971i	0.616733	−	1.58204i
$587$	6.76560	+	10.1254i	0.279246	+	0.417922i	0.944407	−	0.328779i	$-0.106637\pi$
$587$	6.76560	+	10.1254i	0.279246	+	0.417922i	−0.665161	+	0.746700i	$0.731637\pi$
$588$	13.5757	−	0.242913i	0.559854	−	0.0100176i
$589$	−18.0219	+	3.58478i	−0.742580	+	0.147708i
$590$	−23.7143	−	15.1354i	−0.976301	−	0.623113i
$591$	−3.63937	−	2.56062i	−0.149704	−	0.105330i
$592$	−3.42623	+	2.73118i	−0.140817	+	0.112251i
$593$	13.3642	+	13.3642i	0.548802	+	0.548802i	0.926094	−	0.377292i	$-0.123145\pi$
$593$	13.3642	+	13.3642i	0.548802	+	0.548802i	−0.377292	+	0.926094i	$0.623145\pi$
$594$	−20.1984	+	18.2271i	−0.828751	+	0.747868i
$595$	6.98810	−	1.39002i	0.286484	−	0.0569853i
$596$	−4.09288	−	16.8474i	−0.167651	−	0.690096i
$597$	−1.40982	+	1.34350i	−0.0576999	+	0.0549858i
$598$	−2.50839	−	5.71361i	−0.102576	−	0.233647i
$599$	6.94122	−	2.87515i	0.283610	−	0.117475i	−0.236344	−	0.971670i	$-0.575949\pi$
$599$	6.94122	−	2.87515i	0.283610	−	0.117475i	0.519954	+	0.854194i	$0.325949\pi$
$600$	1.83471	+	7.65536i	0.0749018	+	0.312529i
$601$	32.8120	+	13.5912i	1.33843	+	0.554395i	0.933048	−	0.359753i	$-0.117139\pi$
$601$	32.8120	+	13.5912i	1.33843	+	0.554395i	0.405381	+	0.914148i	$0.367139\pi$
$602$	25.6615	−	0.538615i	1.04589	−	0.0219523i
$603$	−7.44591	+	1.11154i	−0.303221	+	0.0452654i
$604$	−0.351098	−	8.36009i	−0.0142860	−	0.340167i
$605$	−4.14679	−	2.77079i	−0.168591	−	0.112649i
$606$	7.40257	+	7.44853i	0.300709	+	0.302576i
$607$	17.6571			0.716678			0.358339	−	0.933592i	$-0.383343\pi$
$607$	17.6571			0.716678			0.358339	+	0.933592i	$0.383343\pi$
$608$	23.3989	−	28.9077i	0.948950	−	1.17236i
$609$	2.84876	−	0.495664i	0.115437	−	0.0200853i
$610$	−0.276414	−	0.395458i	−0.0111917	−	0.0160116i
$611$	−3.20137	+	4.79120i	−0.129514	+	0.193831i
$612$	−2.72777	+	6.47182i	−0.110264	+	0.261608i
$613$	−4.92328	+	24.7510i	−0.198849	+	0.999683i	0.744434	+	0.667696i	$0.232719\pi$
$613$	−4.92328	+	24.7510i	−0.198849	+	0.999683i	−0.943284	+	0.331987i	$0.892281\pi$
$614$	−20.7828	+	0.436214i	−0.838724	+	0.0176042i
$615$	6.97669	−	31.1360i	0.281327	−	1.25552i
$616$	−32.7398	−	11.2047i	−1.31913	−	0.451451i
$617$	−4.75928	−	11.4899i	−0.191602	−	0.462567i	0.798661	−	0.601782i	$-0.205542\pi$
$617$	−4.75928	−	11.4899i	−0.191602	−	0.462567i	−0.990262	+	0.139215i	$0.955542\pi$
$618$	16.7686	−	11.1295i	0.674531	−	0.447694i
$619$	−1.24045	−	1.85647i	−0.0498579	−	0.0746176i	0.805703	−	0.592319i	$-0.201788\pi$
$619$	−1.24045	−	1.85647i	−0.0498579	−	0.0746176i	−0.855561	+	0.517702i	$0.826788\pi$
$620$	5.35622	−	8.79381i	0.215111	−	0.353168i
$621$	−31.7982	+	27.5064i	−1.27602	+	1.10380i
$622$	7.07215	−	1.56170i	0.283567	−	0.0626183i
$623$	−25.4858	+	25.4858i	−1.02107	+	1.02107i
$624$	−3.01009	+	2.28312i	−0.120500	+	0.0913981i
$625$	−10.1706	−	10.1706i	−0.406824	−	0.406824i
$626$	−2.34360	−	1.49578i	−0.0936693	−	0.0597833i
$627$	39.3280	−	15.1914i	1.57061	−	0.606685i
$628$	16.7301	−	12.2243i	0.667604	−	0.487805i
$629$	−1.06611	+	0.712352i	−0.0425086	+	0.0284033i
$630$	0.701725	−	25.8153i	0.0279574	−	1.02851i
$631$	−3.29336	+	1.36415i	−0.131106	+	0.0543061i	−0.447272	−	0.894398i	$-0.647604\pi$
$631$	−3.29336	+	1.36415i	−0.131106	+	0.0543061i	0.316166	+	0.948704i	$0.397604\pi$
$632$	−10.2558	−	38.6601i	−0.407953	−	1.53782i
$633$	−5.44558	+	24.3029i	−0.216443	+	0.965953i
$634$	−11.7204	−	11.2385i	−0.465476	−	0.446338i
$635$	39.8920	+	7.93501i	1.58306	+	0.314891i
$636$	1.49711	−	8.29989i	0.0593643	−	0.329112i
$637$	1.77718	+	1.18747i	0.0704143	+	0.0470493i
$638$	−2.60465	−	0.461501i	−0.103119	−	0.0182710i
$639$	−38.8475	+	13.9404i	−1.53678	+	0.551474i
$640$	3.05050	+	20.6158i	0.120581	+	0.814912i
$641$			5.80247i			0.229184i	0.993413	+	0.114592i	$0.0365560\pi$
$641$			5.80247i			0.229184i	−0.993413	+	0.114592i	$0.963444\pi$
$642$	7.57343	+	0.0234385i	0.298899	+	0.000925045i
$643$	20.9923	−	31.4171i	0.827854	−	1.23897i	−0.140672	−	0.990056i	$-0.544926\pi$
$643$	20.9923	−	31.4171i	0.827854	−	1.23897i	0.968525	−	0.248915i	$-0.0800738\pi$
$644$	−50.2207	−	18.3733i	−1.97897	−	0.724011i
$645$	0.421940	−	17.5184i	0.0166139	−	0.689784i
$646$	7.53245	−	7.85543i	0.296360	−	0.309068i
$647$	6.78354	−	16.3769i	0.266688	−	0.643843i	−0.732635	−	0.680622i	$-0.761710\pi$
$647$	6.78354	−	16.3769i	0.266688	−	0.643843i	0.999323	+	0.0367789i	$0.0117097\pi$
$648$	20.6822	+	14.8407i	0.812473	+	0.582998i
$649$	15.3009	+	36.9395i	0.600611	+	1.45000i
$650$	−0.450095	+	1.15458i	−0.0176542	+	0.0452863i
$651$	11.5804	−	11.0357i	0.453873	−	0.432524i
$652$	−0.854887	−	1.16999i	−0.0334799	−	0.0458203i
$653$	1.38945	+	6.98522i	0.0543733	+	0.273353i	0.998402	−	0.0565103i	$-0.0179974\pi$
$653$	1.38945	+	6.98522i	0.0543733	+	0.273353i	−0.944029	+	0.329863i	$0.892997\pi$
$654$	−2.75501	+	6.59340i	−0.107730	+	0.257823i
$655$	−18.1778	+	18.1778i	−0.710264	+	0.710264i
$656$	−12.1560	+	38.1121i	−0.474614	+	1.48803i
$657$	−11.9727	+	25.3749i	−0.467101	+	0.989971i
$658$	10.6483	+	48.2209i	0.415114	+	1.87985i
$659$	4.43616	+	22.3021i	0.172808	+	0.868765i	0.965751	+	0.259469i	$0.0835477\pi$
$659$	4.43616	+	22.3021i	0.172808	+	0.868765i	−0.792943	+	0.609296i	$0.791452\pi$
$660$	−8.64889	+	21.9847i	−0.336658	+	0.855754i
$661$	−19.0702	+	12.7423i	−0.741745	+	0.495618i	−0.868114	−	0.496365i	$-0.834668\pi$
$661$	−19.0702	+	12.7423i	−0.741745	+	0.495618i	0.126369	+	0.991983i	$0.459668\pi$
$662$	−19.2199	−	43.7792i	−0.747003	−	1.70153i
$663$	−0.933770	+	0.591909i	−0.0362646	+	0.0229878i
$664$	24.2685	+	8.30554i	0.941802	+	0.322318i
$665$	−15.3145	+	36.9725i	−0.593871	+	1.43373i
$666$	1.66115	+	4.34036i	0.0643683	+	0.168186i
$667$	−4.00929	−	0.797498i	−0.155240	−	0.0308792i
$668$	5.01680	+	4.61240i	0.194106	+	0.178459i
$669$	−11.9216	+	26.9283i	−0.460915	+	1.04111i
$670$	−5.35812	+	3.74517i	−0.207002	+	0.144689i
$671$			0.685723i			0.0264720i
$672$	−3.73125	+	32.1615i	−0.143936	+	1.24066i
$673$		−	23.4212i		−	0.902821i	−0.892316	−	0.451410i	$-0.850921\pi$
$673$		−	23.4212i		−	0.902821i	0.892316	−	0.451410i	$-0.149079\pi$
$674$	−2.95880	−	4.23309i	−0.113969	−	0.163052i
$675$	8.32789	+	0.602680i	0.320541	+	0.0231971i
$676$	25.3829	−	1.06600i	0.976266	−	0.0410001i
$677$	8.49094	+	1.68895i	0.326333	+	0.0649117i	0.355538	−	0.934662i	$-0.384298\pi$
$677$	8.49094	+	1.68895i	0.326333	+	0.0649117i	−0.0292050	+	0.999573i	$0.509298\pi$
$678$	20.2176	−	3.95653i	0.776452	−	0.151949i
$679$	19.1442	−	46.2182i	0.734687	−	1.77369i
$680$	0.383701	+	6.08647i	0.0147143	+	0.233406i
$681$	15.5211	+	24.4855i	0.594772	+	0.938286i
$682$	−13.3995	+	5.88262i	−0.513092	+	0.225257i
$683$	1.10592	−	0.738953i	0.0423169	−	0.0282753i	−0.534232	−	0.845338i	$-0.679399\pi$
$683$	1.10592	−	0.738953i	0.0423169	−	0.0282753i	0.576549	+	0.817063i	$0.304399\pi$
$684$	−21.7121	−	32.9339i	−0.830182	−	1.25926i
$685$	−3.41610	−	17.1739i	−0.130522	−	0.656181i
$686$	−14.0568	+	3.10407i	−0.536691	+	0.118514i
$687$	−12.5590	−	8.83635i	−0.479156	−	0.337128i
$688$	−2.46428	+	21.8308i	−0.0939500	+	0.832293i
$689$	0.938774	−	0.938774i	0.0357644	−	0.0357644i
$690$	−14.0757	+	33.6866i	−0.535854	+	1.28243i
$691$	5.02517	+	25.2633i	0.191167	+	0.961059i	0.950587	+	0.310459i	$0.100483\pi$
$691$	5.02517	+	25.2633i	0.191167	+	0.961059i	−0.759420	+	0.650600i	$0.774517\pi$
$692$	−0.162785	−	0.0253318i	−0.00618814	−	0.000962971i
$693$	−21.8368	+	29.5005i	−0.829510	+	1.12063i
$694$	40.3092	+	15.7139i	1.53012	+	0.596493i
$695$	8.04591	+	19.4245i	0.305199	+	0.736815i
$696$	0.0961969	+	2.47312i	0.00364633	+	0.0937433i
$697$	−4.47986	+	10.8153i	−0.169687	+	0.409660i
$698$	11.6013	+	11.1243i	0.439116	+	0.421061i
$699$	20.8683	+	0.502626i	0.789312	+	0.0190111i
$700$	4.47218	+	9.63235i	0.169032	+	0.364069i
$701$	8.51430	−	12.7425i	0.321581	−	0.481279i	−0.635096	−	0.772434i	$-0.719039\pi$
$701$	8.51430	−	12.7425i	0.321581	−	0.481279i	0.956676	+	0.291154i	$0.0940393\pi$
$702$	1.34179	+	3.77585i	0.0506426	+	0.142510i
$703$		−	7.20167i		−	0.271616i
$704$	13.2323	−	26.4988i	0.498711	−	0.998710i
$705$	33.2153	−	5.77924i	1.25096	−	0.217659i
$706$	−4.62353	+	26.0946i	−0.174009	+	0.982082i
$707$	11.7793	+	7.87069i	0.443007	+	0.296008i
$708$	30.7285	−	21.3370i	1.15485	−	0.801895i
$709$	−15.1060	−	3.00477i	−0.567317	−	0.112846i	−0.0969055	−	0.995294i	$-0.530894\pi$
$709$	−15.1060	−	3.00477i	−0.567317	−	0.112846i	−0.470411	+	0.882447i	$0.655894\pi$
$710$	−24.8048	+	25.8684i	−0.930906	+	0.970822i
$711$	−42.3744	−	2.04241i	−1.58916	−	0.0765964i
$712$	−18.7193	−	24.5217i	−0.701534	−	0.918989i
$713$	−20.8933	+	8.65430i	−0.782461	+	0.324106i
$714$	−1.87716	+	9.28682i	−0.0702509	+	0.347550i
$715$	−3.09219	+	2.06613i	−0.115641	+	0.0772690i
$716$	30.7474	+	4.78477i	1.14908	+	0.178815i
$717$	−11.2736	−	29.1854i	−0.421019	−	1.08995i
$718$	−14.8874	+	23.3258i	−0.555594	+	0.870512i
$719$	−10.7173	−	10.7173i	−0.399686	−	0.399686i	0.478436	−	0.878122i	$-0.341204\pi$
$719$	−10.7173	−	10.7173i	−0.399686	−	0.399686i	−0.878122	+	0.478436i	$0.841204\pi$
$720$	21.8201	+	3.53401i	0.813188	+	0.131705i
$721$	19.1985	−	19.1985i	0.714990	−	0.714990i
$722$	7.38692	+	33.4517i	0.274913	+	1.24494i
$723$	2.55956	−	0.988693i	0.0951911	−	0.0367699i
$724$	−7.73248	−	31.8289i	−0.287375	−	1.18291i
$725$	0.451018	+	0.674997i	0.0167504	+	0.0250687i
$726$	5.52565	−	3.66744i	0.205076	−	0.136111i
$727$	−1.37029	−	3.30817i	−0.0508212	−	0.122693i	0.896430	−	0.443185i	$-0.146152\pi$
$727$	−1.37029	−	3.30817i	−0.0508212	−	0.122693i	−0.947251	+	0.320492i	$0.896152\pi$
$728$	−3.37003	+	3.82353i	−0.124902	+	0.141709i
$729$	21.6419	−	16.1440i	0.801550	−	0.597927i
$730$	0.511263	+	24.3584i	0.0189227	+	0.901545i
$731$	−1.25424	+	6.30547i	−0.0463896	+	0.233216i
$732$	0.626926	−	0.136407i	0.0231719	−	0.00504173i
$733$	−4.88457	+	7.31028i	−0.180416	+	0.270011i	−0.910644	−	0.413192i	$-0.864414\pi$
$733$	−4.88457	+	7.31028i	−0.180416	+	0.270011i	0.730228	+	0.683204i	$0.239414\pi$
$734$	2.72450	−	1.90435i	0.100563	−	0.0702908i
$735$	−2.14367	−	12.3204i	−0.0790704	−	0.454445i
$736$	21.3036	−	40.5123i	0.785262	−	1.49330i
$737$	9.29098			0.342237
$738$	34.6260	+	24.5230i	1.27460	+	0.902704i
$739$	26.6757	+	17.8242i	0.981283	+	0.655673i	0.939174	−	0.343441i	$-0.111592\pi$
$739$	26.6757	+	17.8242i	0.981283	+	0.655673i	0.0421088	+	0.999113i	$0.486592\pi$
$740$	2.97077	+	2.73130i	0.109208	+	0.100405i
$741$	0.149519	−	6.20780i	0.00549270	−	0.228049i
$742$	−0.238755	−	11.3751i	−0.00876498	−	0.417595i
$743$	−40.3779	−	16.7251i	−1.48132	−	0.613583i	−0.511912	−	0.859038i	$-0.671063\pi$
$743$	−40.3779	−	16.7251i	−1.48132	−	0.613583i	−0.969408	+	0.245455i	$0.921063\pi$
$744$	8.04369	+	11.0803i	0.294896	+	0.406225i
$745$	−14.7526	+	6.11073i	−0.540493	+	0.223880i
$746$	−8.39916	+	3.68739i	−0.307515	+	0.135005i
$747$	16.1866	−	21.8673i	0.592236	−	0.800084i
$748$	4.50875	−	7.40244i	0.164856	−	0.270660i
$749$	10.0207	−	1.99323i	0.366147	−	0.0728312i
$750$	27.5766	−	11.3228i	1.00696	−	0.413449i
$751$	25.3960	+	25.3960i	0.926712	+	0.926712i	0.997492	−	0.0707803i	$-0.0225489\pi$
$751$	25.3960	+	25.3960i	0.926712	+	0.926712i	−0.0707803	+	0.997492i	$0.522549\pi$
$752$	−42.1195	+	3.54403i	−1.53594	+	0.129238i
$753$	5.03438	−	7.15531i	0.183463	−	0.260754i
$754$	−0.209607	+	0.328415i	−0.00763345	+	0.0119602i
$755$	−7.55851	+	1.50348i	−0.275082	+	0.0547173i
$756$	31.3148	+	14.0960i	1.13891	+	0.512668i
$757$	3.36700	+	5.03906i	0.122376	+	0.183148i	0.887599	−	0.460617i	$-0.152372\pi$
$757$	3.36700	+	5.03906i	0.122376	+	0.183148i	−0.765224	+	0.643764i	$0.777372\pi$
$758$	2.67063	+	1.04110i	0.0970015	+	0.0378146i
$759$	43.8248	−	27.7802i	1.59074	−	1.00836i
$760$	−29.6216	−	17.2006i	−1.07449	−	0.623931i
$761$	−2.07072	−	0.857719i	−0.0750635	−	0.0310923i	0.344836	−	0.938663i	$-0.387935\pi$
$761$	−2.07072	−	0.857719i	−0.0750635	−	0.0310923i	−0.419899	+	0.907571i	$0.637935\pi$
$762$	−30.1879	+	44.8780i	−1.09359	+	1.62576i
$763$	−1.88069	+	9.45486i	−0.0680855	+	0.342289i
$764$	−3.73410	−	1.36613i	−0.135095	−	0.0494248i
$765$	6.27609	+	1.56591i	0.226913	+	0.0566155i
$766$	−5.94797	+	33.5696i	−0.214909	+	1.21292i
$767$	5.88896			0.212638
$768$	−26.8589	−	6.82648i	−0.969186	−	0.246329i
$769$	7.95821			0.286981			0.143490	−	0.989652i	$-0.454167\pi$
$769$	7.95821			0.286981			0.143490	+	0.989652i	$0.454167\pi$
$770$	−5.56041	+	31.3822i	−0.200383	+	1.13094i
$771$	33.7919	+	14.9602i	1.21699	+	0.538779i
$772$	−22.5358	−	8.24476i	−0.811080	−	0.296735i
$773$	3.37161	−	16.9502i	0.121268	−	0.609658i	−0.871578	−	0.490257i	$-0.836903\pi$
$773$	3.37161	−	16.9502i	0.121268	−	0.609658i	0.992846	−	0.119400i	$-0.0380972\pi$
$774$	21.2781	+	9.49904i	0.764827	+	0.341436i
$775$	4.14924	+	1.71867i	0.149045	+	0.0617365i
$776$	37.0291	+	21.5019i	1.32927	+	0.771875i
$777$	3.35664	+	5.29530i	0.120419	+	0.189968i
$778$	−48.6499	−	18.9655i	−1.74418	−	0.679944i
$779$	−36.5293	−	54.6700i	−1.30880	−	1.95875i
$780$	2.50408	+	2.41605i	0.0896606	+	0.0865083i
$781$	49.9571	−	9.93709i	1.78761	−	0.355577i
$782$	7.20621	−	11.2908i	0.257694	−	0.403757i
$783$	2.53100	+	0.696641i	0.0904505	+	0.0248959i
$784$	1.31457	+	15.6232i	0.0469490	+	0.557972i
$785$	−13.4943	−	13.4943i	−0.481632	−	0.481632i
$786$	−12.9841	−	31.6229i	−0.463129	−	1.12795i
$787$	6.03809	−	1.20105i	0.215235	−	0.0428128i	−0.0862951	−	0.996270i	$-0.527503\pi$
$787$	6.03809	−	1.20105i	0.215235	−	0.0428128i	0.301530	+	0.953457i	$0.402503\pi$
$788$	2.67292	−	4.38838i	0.0952187	−	0.156330i
$789$	−3.56337	−	3.73925i	−0.126859	−	0.133121i
$790$	−33.7308	+	14.8085i	−1.20009	+	0.526863i
$791$	25.6764	−	10.6355i	0.912947	−	0.378155i
$792$	−22.5404	−	21.8831i	−0.800939	−	0.777581i
$793$	0.0933098	+	0.0386502i	0.00331353	+	0.00137251i
$794$	0.912983	+	43.4977i	0.0324005	+	1.54368i
$795$	−7.76547	−	0.187036i	−0.275413	−	0.00663348i
$796$	−1.65541	−	1.52197i	−0.0586744	−	0.0539447i
$797$	7.45915	+	4.98405i	0.264217	+	0.176544i	0.680621	−	0.732635i	$-0.261710\pi$
$797$	7.45915	+	4.98405i	0.264217	+	0.176544i	−0.416404	+	0.909179i	$0.636710\pi$
$798$	−37.5126	−	37.7455i	−1.32793	−	1.33618i
$799$	−12.3691			−0.437588
$800$	−8.68054	+	2.69738i	−0.306903	+	0.0953670i
$801$	−30.7984	+	11.0520i	−1.08821	+	0.390504i
$802$	14.9893	−	10.4770i	0.529289	−	0.369957i
$803$	19.2375	−	28.7910i	0.678877	−	1.01601i
$804$	−1.84820	−	8.49433i	−0.0651808	−	0.299572i
$805$	−9.60869	+	48.3061i	−0.338662	+	1.70257i
$806$	0.0452296	+	2.15490i	0.00159315	+	0.0759031i
$807$	−24.7912	−	5.55501i	−0.872693	−	0.195546i
$808$	−8.01787	+	9.09681i	−0.282068	+	0.320025i
$809$	−9.87605	−	23.8429i	−0.347224	−	0.838272i	−0.996946	−	0.0781000i	$-0.975115\pi$
$809$	−9.87605	−	23.8429i	−0.347224	−	0.838272i	0.649722	−	0.760172i	$-0.274885\pi$
$810$	10.5770	−	20.9239i	0.371638	−	0.735191i
$811$	−9.69074	−	14.5032i	−0.340288	−	0.509277i	0.621374	−	0.783514i	$-0.286575\pi$
$811$	−9.69074	−	14.5032i	−0.340288	−	0.509277i	−0.961662	+	0.274237i	$0.911575\pi$
$812$	0.788217	+	3.24451i	0.0276610	+	0.113860i
$813$	−13.1930	−	34.1544i	−0.462697	−	1.19785i
$814$	−1.23672	−	5.60051i	−0.0433472	−	0.196298i
$815$	−0.943697	+	0.943697i	−0.0330563	+	0.0330563i
$816$	−7.66462	−	2.64963i	−0.268315	−	0.0927556i
$817$	−25.5333	−	25.5333i	−0.893295	−	0.893295i
$818$	21.0328	−	32.9544i	0.735393	−	1.15222i
$819$	2.78347	+	4.63421i	0.0972623	+	0.161932i
$820$	36.4061	+	5.66535i	1.27136	+	0.197843i
$821$	9.95404	−	6.65108i	0.347398	−	0.232124i	−0.369613	−	0.929186i	$-0.620510\pi$
$821$	9.95404	−	6.65108i	0.347398	−	0.232124i	0.717011	+	0.697062i	$0.245510\pi$
$822$	22.8232	+	4.61329i	0.796050	+	0.160907i
$823$	−25.2779	+	10.4704i	−0.881131	+	0.364976i	−0.776935	−	0.629581i	$-0.783227\pi$
$823$	−25.2779	+	10.4704i	−0.881131	+	0.364976i	−0.104195	+	0.994557i	$0.533227\pi$
$824$	14.1012	+	18.4722i	0.491240	+	0.643510i
$825$	−10.0552	−	2.25308i	−0.350076	−	0.0784421i
$826$	34.9295	−	36.4272i	1.21535	−	1.26746i
$827$	41.4125	+	8.23747i	1.44006	+	0.286445i	0.852495	−	0.522735i	$-0.175088\pi$
$827$	41.4125	+	8.23747i	1.44006	+	0.286445i	0.587560	+	0.809180i	$0.300088\pi$
$828$	−34.1160	−	34.5409i	−1.18561	−	1.20038i
$829$	13.6752	+	9.13744i	0.474958	+	0.317357i	0.769907	−	0.638156i	$-0.220303\pi$
$829$	13.6752	+	9.13744i	0.474958	+	0.317357i	−0.294949	+	0.955513i	$0.595303\pi$
$830$	4.12167	−	23.2622i	0.143065	−	0.807442i
$831$	0.292584	+	1.68158i	0.0101496	+	0.0583334i
$832$	−2.85999	−	3.29417i	−0.0991524	−	0.114205i
$833$			4.58802i			0.158966i
$834$	−27.9583	−	0.0865263i	−0.968116	−	0.00299616i
$835$	3.48711	−	5.21883i	0.120676	−	0.180605i
$836$	20.5007	+	44.1552i	0.709031	+	1.52714i
$837$	13.7834	−	4.57465i	0.476424	−	0.158123i
$838$	19.6126	+	18.8062i	0.677504	+	0.649649i
$839$	−17.8164	+	43.0125i	−0.615090	+	1.48496i	0.242254	+	0.970213i	$0.422113\pi$
$839$	−17.8164	+	43.0125i	−0.615090	+	1.48496i	−0.857343	+	0.514745i	$0.827887\pi$
$840$	29.7975	−	1.15903i	1.02811	−	0.0399904i
$841$	−11.0001	−	26.5567i	−0.379315	−	0.915748i
$842$	29.7051	+	11.5801i	1.02371	+	0.399076i
$843$	16.7133	+	17.5383i	0.575638	+	0.604052i
$844$	−28.4164	−	4.42203i	−0.978133	−	0.152213i
$845$	−4.56487	−	22.9491i	−0.157036	−	0.789475i
$846$	−9.93793	+	43.7171i	−0.341673	+	1.50302i
$847$	6.32638	−	6.32638i	0.217377	−	0.217377i
$848$	9.67709	+	1.09236i	0.332313	+	0.0375117i
$849$	2.83854	−	4.03438i	0.0974183	−	0.138459i
$850$	−2.59745	+	0.573578i	−0.0890918	+	0.0196736i
$851$	−1.72916	−	8.69306i	−0.0592747	−	0.297994i
$852$	−19.0227	−	43.6969i	−0.651707	−	1.49703i
$853$	7.94078	−	5.30586i	0.271887	−	0.181669i	−0.412151	−	0.911116i	$-0.635222\pi$
$853$	7.94078	−	5.30586i	0.271887	−	0.181669i	0.684038	+	0.729447i	$0.260222\pi$
$854$	0.792530	−	0.347936i	0.0271198	−	0.0119061i
$855$	−26.8971	+	24.4235i	−0.919863	+	0.835267i
$856$	0.550212	+	8.72776i	0.0188059	+	0.298309i
$857$	−18.5434	+	44.7677i	−0.633430	+	1.52923i	0.201854	+	0.979416i	$0.435303\pi$
$857$	−18.5434	+	44.7677i	−0.633430	+	1.52923i	−0.835284	+	0.549819i	$0.814697\pi$
$858$	−0.949773	−	4.85328i	−0.0324247	−	0.165688i
$859$	−18.8663	−	3.75274i	−0.643709	−	0.128042i	−0.137568	−	0.990492i	$-0.543929\pi$
$859$	−18.8663	−	3.75274i	−0.643709	−	0.128042i	−0.506141	+	0.862451i	$0.668929\pi$
$860$	20.2165	−	0.849030i	0.689377	−	0.0289517i
$861$	52.3408	+	23.1721i	1.78377	+	0.789703i
$862$	12.4447	+	17.8043i	0.423869	+	0.606418i
$863$			3.38582i			0.115255i	0.998338	+	0.0576274i	$0.0183535\pi$
$863$			3.38582i			0.115255i	−0.998338	+	0.0576274i	$0.981646\pi$
$864$	−15.5229	+	24.9608i	−0.528099	+	0.849183i
$865$			0.151732i			0.00515905i
$866$	−9.89048	+	6.91316i	−0.336092	+	0.234919i
$867$	24.7543	+	10.9591i	0.840700	+	0.372191i
$868$	13.5978	+	12.5017i	0.461539	+	0.424335i
$869$	51.3498	+	10.2141i	1.74192	+	0.346490i
$870$	2.23708	−	0.437789i	0.0758440	−	0.0148425i
$871$	0.523677	−	1.26427i	0.0177441	−	0.0428381i
$872$	−7.80678	−	2.67176i	−0.264371	−	0.0904771i
$873$	33.6233	−	30.5311i	1.13798	−	1.03332i
$874$	30.2422	+	68.8859i	1.02296	+	2.33010i
$875$	33.4384	−	22.3428i	1.13043	−	0.755326i
$876$	−30.1491	−	11.8608i	−1.01864	−	0.400739i
$877$	7.86570	+	39.5435i	0.265606	+	1.33529i	0.851266	+	0.524734i	$0.175835\pi$
$877$	7.86570	+	39.5435i	0.265606	+	1.33529i	−0.585660	+	0.810557i	$0.699165\pi$
$878$	4.06403	+	18.4040i	0.137154	+	0.621104i
$879$	28.9684	−	41.1724i	0.977079	−	1.38871i
$880$	−25.9896	−	8.28951i	−0.876109	−	0.279439i
$881$	5.13574	−	5.13574i	0.173028	−	0.173028i	−0.615281	−	0.788308i	$-0.710957\pi$
$881$	5.13574	−	5.13574i	0.173028	−	0.173028i	0.788308	+	0.615281i	$0.210957\pi$
$882$	16.2158	+	3.68623i	0.546013	+	0.124122i
$883$	−1.53900	−	7.73710i	−0.0517916	−	0.260374i	0.946211	−	0.323551i	$-0.104877\pi$
$883$	−1.53900	−	7.73710i	−0.0517916	−	0.260374i	−0.998002	+	0.0631770i	$0.979877\pi$
$884$	−0.753155	−	1.03076i	−0.0253314	−	0.0346682i
$885$	−23.7699	−	24.9432i	−0.799016	−	0.838455i
$886$	20.6613	−	53.0000i	0.694128	−	1.78057i
$887$	15.1105	+	36.4799i	0.507360	+	1.22488i	0.945397	+	0.325920i	$0.105674\pi$
$887$	15.1105	+	36.4799i	0.507360	+	1.22488i	−0.438037	+	0.898957i	$0.644326\pi$
$888$	−4.87428	+	2.24476i	−0.163570	+	0.0753291i
$889$	−27.9226	+	67.4111i	−0.936494	+	2.26090i
$890$	−19.6653	+	20.5085i	−0.659183	+	0.687447i
$891$	−29.3576	+	15.7619i	−0.983517	+	0.528044i
$892$	−31.9349	−	11.6835i	−1.06926	−	0.391191i
$893$	38.5972	−	57.7648i	1.29161	−	1.93303i
$894$	0.0657152	−	21.2338i	0.00219785	−	0.710165i
$895$		−	28.6597i		−	0.957990i
$896$	−37.3403	−	1.84786i	−1.24745	−	0.0617326i
$897$	−1.31004	−	7.52926i	−0.0437410	−	0.251395i
$898$	−8.74457	−	1.54939i	−0.291810	−	0.0517039i
$899$	1.17403	+	0.784463i	0.0391561	+	0.0261633i
$900$	−0.0596764	+	9.64119i	−0.00198921	+	0.321373i
$901$	2.79506	+	0.555973i	0.0931170	+	0.0185221i
$902$	−37.7960	−	36.2420i	−1.25847	−	1.20673i
$903$	30.6751	+	6.87342i	1.02080	+	0.228733i
$904$	6.09955	+	22.9928i	0.202868	+	0.764730i
$905$	−27.8713	+	11.5447i	−0.926475	+	0.383758i
$906$	2.03038	−	10.0449i	0.0674549	−	0.333718i
$907$	−30.0747	+	20.0953i	−0.998614	+	0.667252i	−0.943550	−	0.331230i	$-0.892536\pi$
$907$	−30.0747	+	20.0953i	−0.998614	+	0.667252i	−0.0550638	+	0.998483i	$0.517536\pi$
$908$	−27.0288	+	19.7494i	−0.896982	+	0.655406i
$909$	6.62234	+	11.0256i	0.219649	+	0.365694i
$910$	3.95693	+	2.52546i	0.131171	+	0.0837183i
$911$	−30.1032	−	30.1032i	−0.997363	−	0.997363i	0.00263353	−	0.999997i	$-0.499162\pi$
$911$	−30.1032	−	30.1032i	−0.997363	−	0.997363i	−0.999997	+	0.00263353i	$0.999162\pi$
$912$	36.2910	−	27.5264i	1.20172	−	0.911489i
$913$	−23.7418	+	23.7418i	−0.785738	+	0.785738i
$914$	10.9686	−	2.42213i	0.362810	−	0.0801171i
$915$	−0.212924	−	0.551226i	−0.00703907	−	0.0182230i
$916$	9.22389	−	15.1437i	0.304766	−	0.500363i
$917$	−25.6212	−	38.3448i	−0.846086	−	1.26626i
$918$	−5.13895	+	6.89775i	−0.169611	+	0.227660i
$919$	2.76576	+	6.67714i	0.0912341	+	0.220259i	0.962909	−	0.269826i	$-0.0869660\pi$
$919$	2.76576	+	6.67714i	0.0912341	+	0.220259i	−0.871675	+	0.490084i	$0.836966\pi$
$920$	−39.8859	−	13.6503i	−1.31500	−	0.450039i
$921$	−24.8432	−	5.56665i	−0.818610	−	0.183427i
$922$	−30.7079	+	0.644533i	−1.01131	+	0.0212266i
$923$	1.46360	−	7.35801i	0.0481750	−	0.242192i
$924$	−35.6543	−	22.9115i	−1.17294	−	0.753734i
$925$	−0.977910	+	1.46355i	−0.0321535	+	0.0481211i
$926$	28.5453	+	40.8391i	0.938057	+	1.34206i
$927$	23.2005	−	8.32549i	0.762004	−	0.273445i
$928$	−2.84215	+	0.299328i	−0.0932982	+	0.00982593i
$929$	4.22030			0.138463			0.0692317	−	0.997601i	$-0.477945\pi$
$929$	4.22030			0.138463			0.0692317	+	0.997601i	$0.477945\pi$
$930$	8.94468	−	8.88949i	0.293308	−	0.291498i
$931$	−21.4264	−	14.3167i	−0.702223	−	0.469210i
$932$	1.01139	+	24.0824i	0.0331291	+	0.788846i
$933$	8.86768	+	0.213583i	0.290315	+	0.00699240i
$934$	−33.2828	+	0.698579i	−1.08905	+	0.0228582i
$935$	−7.37524	−	3.05493i	−0.241196	−	0.0999067i
$936$	−4.24821	+	1.83377i	−0.138857	+	0.0599386i
$937$	−15.9759	+	6.61744i	−0.521911	+	0.216182i	−0.628056	−	0.778168i	$-0.716149\pi$
$937$	−15.9759	+	6.61744i	−0.521911	+	0.216182i	0.106145	+	0.994351i	$0.466149\pi$
$938$	−4.71425	−	10.7381i	−0.153926	−	0.350612i
$939$	−2.34910	−	2.46505i	−0.0766600	−	0.0804439i
$940$	9.19029	+	37.8297i	0.299754	+	1.23387i
$941$	−15.5482	+	3.09272i	−0.506855	+	0.100820i	−0.441893	−	0.897068i	$-0.645693\pi$
$941$	−15.5482	+	3.09272i	−0.506855	+	0.100820i	−0.0649626	+	0.997888i	$0.520693\pi$
$942$	23.4753	−	9.63879i	0.764867	−	0.314049i
$943$	−57.2206	−	57.2206i	−1.86336	−	1.86336i
$944$	26.9262	+	33.7786i	0.876372	+	1.09940i
$945$	8.39350	−	30.4948i	0.273041	−	0.991998i
$946$	−24.2411	−	15.4716i	−0.788147	−	0.503026i
$947$	−18.2131	+	3.62281i	−0.591845	+	0.117725i	−0.481921	−	0.876215i	$-0.660061\pi$
$947$	−18.2131	+	3.62281i	−0.591845	+	0.117725i	−0.109924	+	0.993940i	$0.535061\pi$
$948$	−0.876385	−	48.9787i	−0.0284637	−	1.59075i
$949$	−2.83342	−	4.24052i	−0.0919768	−	0.137653i
$950$	5.42655	−	13.9201i	0.176061	−	0.451628i
$951$	−10.6475	−	16.7970i	−0.345267	−	0.544679i
$952$	−10.8432	−	1.45502i	−0.351429	−	0.0471576i
$953$	48.0723	+	19.9122i	1.55721	+	0.645019i	0.984602	−	0.174808i	$-0.0559306\pi$
$953$	48.0723	+	19.9122i	1.55721	+	0.645019i	0.572611	+	0.819827i	$0.305931\pi$
$954$	4.21070	−	9.43209i	0.136326	−	0.305375i
$955$	−0.714442	+	3.59174i	−0.0231188	+	0.116226i
$956$	32.7676	−	15.2136i	1.05978	−	0.492043i
$957$	−2.96239	−	1.31150i	−0.0957604	−	0.0423947i
$958$	−23.4786	−	4.16002i	−0.758559	−	0.134404i
$959$	31.4123			1.01436
$960$	−2.40878	+	25.4101i	−0.0777431	+	0.820108i
$961$	−23.1886			−0.748018
$962$	−0.831796	−	0.147380i	−0.0268182	−	0.00475174i
$963$	8.99967	+	2.24545i	0.290010	+	0.0723586i
$964$	1.33423	+	2.87373i	0.0429728	+	0.0925565i
$965$	−4.31175	+	21.6766i	−0.138800	+	0.697796i
$966$	−54.3439	−	36.5552i	−1.74849	−	1.17614i
$967$	34.7862	+	14.4089i	1.11865	+	0.463360i	0.863908	−	0.503650i	$-0.168010\pi$
$967$	34.7862	+	14.4089i	1.11865	+	0.463360i	0.254741	+	0.967009i	$0.418010\pi$
$968$	4.64670	+	6.08704i	0.149351	+	0.195645i
$969$	11.2580	−	7.13632i	0.361658	−	0.229252i
$970$	14.3241	−	36.7440i	0.459920	−	1.17978i
$971$	−19.1965	−	28.7296i	−0.616045	−	0.921976i	0.383954	−	0.923352i	$-0.374562\pi$
$971$	−19.1965	−	28.7296i	−0.616045	−	0.921976i	−0.999999	+	0.00137607i	$0.999562\pi$
$972$	20.2503	+	23.7049i	0.649530	+	0.760336i
$973$	−36.9926	+	7.35828i	−1.18593	+	0.235896i
$974$	−17.1852	−	10.9682i	−0.550649	−	0.351445i
$975$	−0.873338	+	1.24126i	−0.0279692	+	0.0397523i
$976$	0.204947	+	0.711937i	0.00656020	+	0.0227885i
$977$	22.5815	+	22.5815i	0.722445	+	0.722445i	0.969103	−	0.246658i	$-0.0793323\pi$
$977$	22.5815	+	22.5815i	0.722445	+	0.722445i	−0.246658	+	0.969103i	$0.579332\pi$
$978$	−0.674070	−	1.64170i	−0.0215544	−	0.0524958i
$979$	39.6062	−	7.87816i	1.26582	−	0.251787i
$980$	14.0320	−	3.40891i	0.448235	−	0.108894i
$981$	−5.20695	+	7.03436i	−0.166245	+	0.224590i
$982$	−5.58678	−	12.7256i	−0.178281	−	0.406090i
$983$	12.0098	−	4.97461i	0.383053	−	0.158666i	−0.182844	−	0.983142i	$-0.558530\pi$
$983$	12.0098	−	4.97461i	0.383053	−	0.158666i	0.565896	+	0.824476i	$0.308530\pi$
$984$	−25.6159	+	41.7646i	−0.816606	+	1.33141i
$985$	−4.37225	−	1.81105i	−0.139312	−	0.0577048i
$986$	−0.836123	+	0.0175496i	−0.0266276	+	0.000558892i
$987$	−1.45630	+	60.4636i	−0.0463546	+	1.92458i
$988$	7.16392	−	0.300862i	0.227915	−	0.00957170i
$989$	−36.9515	−	24.6902i	−1.17499	−	0.785104i
$990$	−16.7228	+	23.6124i	−0.531487	+	0.750450i
$991$	−39.8014			−1.26433			−0.632167	−	0.774832i	$-0.717834\pi$
$991$	−39.8014			−1.26433			−0.632167	+	0.774832i	$0.717834\pi$
$992$	−12.1535	+	10.1123i	−0.385874	+	0.321066i
$993$	−10.0379	−	57.6912i	−0.318542	−	1.83077i
$994$	−36.8332	−	52.6963i	−1.16828	−	1.67142i
$995$	−1.15065	+	1.72207i	−0.0364781	+	0.0545934i
$996$	26.4289	+	16.9833i	0.837430	+	0.538135i
$997$	7.72518	−	38.8371i	0.244659	−	1.22998i	−0.641689	−	0.766965i	$-0.721766\pi$
$997$	7.72518	−	38.8371i	0.244659	−	1.22998i	0.886348	−	0.463019i	$-0.153234\pi$
$998$	−27.4261	+	0.575652i	−0.868158	+	0.0182219i
$999$	0.704586	+	5.64808i	0.0222921	+	0.178697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.59.15	✓	240
3.2	odd	2	inner	192.2.s.a.59.16	yes	240
4.3	odd	2		768.2.s.a.143.19		240
12.11	even	2		768.2.s.a.143.23		240
64.13	even	16		768.2.s.a.623.23		240
64.51	odd	16	inner	192.2.s.a.179.16	yes	240
192.77	odd	16		768.2.s.a.623.19		240
192.179	even	16	inner	192.2.s.a.179.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.59.15	✓	240	1.1	even	1	trivial
192.2.s.a.59.16	yes	240	3.2	odd	2	inner
192.2.s.a.179.15	yes	240	192.179	even	16	inner
192.2.s.a.179.16	yes	240	64.51	odd	16	inner
768.2.s.a.143.19		240	4.3	odd	2
768.2.s.a.143.23		240	12.11	even	2
768.2.s.a.623.19		240	192.77	odd	16
768.2.s.a.623.23		240	64.13	even	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.246732 + 1.39252i) q^{2} +(-0.701166 + 1.58378i) q^{3} +(-1.87825 - 0.687161i) q^{4} +(-0.359364 + 1.80664i) q^{5} +(-2.03245 - 1.36716i) q^{6} +(-3.05294 - 1.26457i) q^{7} +(1.42031 - 2.44596i) q^{8} +(-2.01673 - 2.22099i) q^{9} +O(q^{10})\)	\(q+(-0.246732 + 1.39252i) q^{2} +(-0.701166 + 1.58378i) q^{3} +(-1.87825 - 0.687161i) q^{4} +(-0.359364 + 1.80664i) q^{5} +(-2.03245 - 1.36716i) q^{6} +(-3.05294 - 1.26457i) q^{7} +(1.42031 - 2.44596i) q^{8} +(-2.01673 - 2.22099i) q^{9} +(-2.42713 - 0.946180i) q^{10} +(2.05692 + 3.07840i) q^{11} +(2.40528 - 2.49292i) q^{12} +(0.534830 - 0.106384i) q^{13} +(2.51420 - 3.93929i) q^{14} +(-2.60936 - 1.83591i) q^{15} +(3.05562 + 2.58132i) q^{16} +(0.827691 + 0.827691i) q^{17} +(3.59037 - 2.26036i) q^{18} +(-6.44815 + 1.28262i) q^{19} +(1.91643 - 3.14638i) q^{20} +(4.14342 - 3.94852i) q^{21} +(-4.79426 + 2.10477i) q^{22} +(-7.47552 + 3.09646i) q^{23} +(2.87799 + 3.96449i) q^{24} +(1.48458 + 0.614932i) q^{25} +(0.0161829 + 0.771012i) q^{26} +(4.93163 - 1.63679i) q^{27} +(4.86522 + 4.47304i) q^{28} +(0.420063 + 0.280677i) q^{29} +(3.20036 - 3.18061i) q^{30} +2.79490 q^{31} +(-4.34846 + 3.61813i) q^{32} +(-6.31776 + 1.09925i) q^{33} +(-1.35680 + 0.948362i) q^{34} +(3.38175 - 5.06114i) q^{35} +(2.26175 + 5.55738i) q^{36} +(-0.213702 + 1.07435i) q^{37} +(-0.195109 - 9.29567i) q^{38} +(-0.206515 + 0.921647i) q^{39} +(3.90857 + 3.44499i) q^{40} +(3.82720 + 9.23967i) q^{41} +(4.47610 + 6.74405i) q^{42} +(3.05140 + 4.56674i) q^{43} +(-1.74805 - 7.19543i) q^{44} +(4.73728 - 2.84538i) q^{45} +(-2.46745 - 11.1738i) q^{46} +(-7.47207 + 7.47207i) q^{47} +(-6.23074 + 3.02951i) q^{48} +(2.77158 + 2.77158i) q^{49} +(-1.22260 + 1.91559i) q^{50} +(-1.89123 + 0.730534i) q^{51} +(-1.07765 - 0.167698i) q^{52} +(2.02433 - 1.35261i) q^{53} +(1.06247 + 7.27126i) q^{54} +(-6.30076 + 2.60986i) q^{55} +(-7.42922 + 5.67129i) q^{56} +(2.48984 - 11.1118i) q^{57} +(-0.494492 + 0.515695i) q^{58} +(10.5918 + 2.10685i) q^{59} +(3.63945 + 5.24134i) q^{60} +(0.153998 + 0.102898i) q^{61} +(-0.689591 + 3.89196i) q^{62} +(3.34838 + 9.33085i) q^{63} +(-3.96543 - 6.94805i) q^{64} +1.00448i q^{65} +(0.0280666 - 9.06886i) q^{66} +(1.39419 - 2.08655i) q^{67} +(-0.985851 - 2.12337i) q^{68} +(0.337457 - 14.0107i) q^{69} +(6.21338 + 5.95791i) q^{70} +(5.26483 - 12.7104i) q^{71} +(-8.29683 + 1.77835i) q^{72} +(-3.57907 - 8.64064i) q^{73} +(-1.44333 - 0.562662i) q^{74} +(-2.01485 + 1.92008i) q^{75} +(12.9926 + 2.02185i) q^{76} +(-2.38681 - 11.9993i) q^{77} +(-1.23246 - 0.514977i) q^{78} +(9.99933 - 9.99933i) q^{79} +(-5.76160 + 4.59279i) q^{80} +(-0.865574 + 8.95828i) q^{81} +(-13.8108 + 3.04974i) q^{82} +(1.76923 + 8.89454i) q^{83} +(-10.4956 + 4.56910i) q^{84} +(-1.79279 + 1.19790i) q^{85} +(-7.11217 + 3.12238i) q^{86} +(-0.739064 + 0.468487i) q^{87} +(10.4511 - 0.658856i) q^{88} +(4.17398 - 10.0769i) q^{89} +(2.79342 + 7.29882i) q^{90} +(-1.76734 - 0.351545i) q^{91} +(16.1686 - 0.679033i) q^{92} +(-1.95969 + 4.42651i) q^{93} +(-8.56143 - 12.2486i) q^{94} -12.1104i q^{95} +(-2.68134 - 9.42393i) q^{96} +15.1389i q^{97} +(-4.54333 + 3.17565i) q^{98} +(2.68883 - 10.7767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more