LMFDB - Embedded newform 756.2.bp.a.193.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(193,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 12]))

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

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

chi := DirichletCharacter("756.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bp (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.17
Character	$\chi$	$=$	756.193
Dual form			756.2.bp.a.709.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.963882 + 1.43907i) q^{3} +(-0.981872 + 0.357372i) q^{5} +(0.459325 - 2.60557i) q^{7} +(-1.14186 + 2.77419i) q^{9} +O(q^{10})$	\(q+(0.963882 + 1.43907i) q^{3} +(-0.981872 + 0.357372i) q^{5} +(0.459325 - 2.60557i) q^{7} +(-1.14186 + 2.77419i) q^{9} +(4.11203 + 1.49665i) q^{11} +(2.26426 - 0.824123i) q^{13} +(-1.46069 - 1.06852i) q^{15} +(1.67980 + 2.90949i) q^{17} +(-1.10258 + 1.90972i) q^{19} +(4.19235 - 1.85047i) q^{21} +(-0.274350 + 1.55592i) q^{23} +(-2.99386 + 2.51215i) q^{25} +(-5.09289 + 1.03077i) q^{27} +(9.47940 + 3.45022i) q^{29} +(6.01934 - 2.19086i) q^{31} +(1.80971 + 7.36010i) q^{33} +(0.480162 + 2.72249i) q^{35} -5.88632 q^{37} +(3.36845 + 2.46408i) q^{39} +(1.95781 - 0.712584i) q^{41} +(0.727841 + 4.12779i) q^{43} +(0.129742 - 3.13197i) q^{45} +(-7.33846 - 2.67098i) q^{47} +(-6.57804 - 2.39361i) q^{49} +(-2.56785 + 5.22176i) q^{51} +(2.84430 - 4.92648i) q^{53} -4.57235 q^{55} +(-3.81098 + 0.254056i) q^{57} +(3.93783 + 3.30423i) q^{59} +(-3.43555 - 1.25044i) q^{61} +(6.70388 + 4.24946i) q^{63} +(-1.92870 + 1.61837i) q^{65} +(1.01172 - 5.73775i) q^{67} +(-2.50352 + 1.10491i) q^{69} +(-1.66736 + 2.88795i) q^{71} -9.33431 q^{73} +(-6.50090 - 1.88697i) q^{75} +(5.78840 - 10.0267i) q^{77} +(2.00454 + 11.3683i) q^{79} +(-6.39230 - 6.33549i) q^{81} +(0.482130 + 0.175481i) q^{83} +(-2.68912 - 2.25644i) q^{85} +(4.17191 + 16.9671i) q^{87} +(5.77894 - 10.0094i) q^{89} +(-1.10728 - 6.27824i) q^{91} +(8.95475 + 6.55054i) q^{93} +(0.400109 - 2.26913i) q^{95} +(-2.60776 - 14.7893i) q^{97} +(-8.84737 + 9.69858i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.963882	+	1.43907i	0.556498	+	0.830849i
$3$	0.963882	+	1.43907i	0.556498	+	0.830849i
$4$		0			0
$5$	−0.981872	+	0.357372i	−0.439107	+	0.159822i	−0.552107	−	0.833773i	$-0.686176\pi$
$5$	−0.981872	+	0.357372i	−0.439107	+	0.159822i	0.113000	+	0.993595i	$0.463954\pi$
$6$		0			0
$7$	0.459325	−	2.60557i	0.173609	−	0.984815i
$7$	0.459325	−	2.60557i	0.173609	−	0.984815i
$8$		0			0
$9$	−1.14186	+	2.77419i	−0.380621	+	0.924731i
$10$		0			0
$11$	4.11203	+	1.49665i	1.23982	+	0.451258i	0.876951	−	0.480581i	$-0.159574\pi$
$11$	4.11203	+	1.49665i	1.23982	+	0.451258i	0.362872	+	0.931839i	$0.381796\pi$
$12$		0			0
$13$	2.26426	−	0.824123i	0.627993	−	0.228571i	−0.00836466	−	0.999965i	$-0.502663\pi$
$13$	2.26426	−	0.824123i	0.627993	−	0.228571i	0.636357	+	0.771394i	$0.280440\pi$
$14$		0			0
$15$	−1.46069	−	1.06852i	−0.377150	−	0.275891i
$16$		0			0
$17$	1.67980	+	2.90949i	0.407410	+	0.705656i	0.994599	−	0.103795i	$-0.0330985\pi$
$17$	1.67980	+	2.90949i	0.407410	+	0.705656i	−0.587188	+	0.809450i	$0.699765\pi$
$18$		0			0
$19$	−1.10258	+	1.90972i	−0.252948	+	0.438119i	−0.964336	−	0.264680i	$-0.914734\pi$
$19$	−1.10258	+	1.90972i	−0.252948	+	0.438119i	0.711388	+	0.702800i	$0.248067\pi$
$20$		0			0
$21$	4.19235	−	1.85047i	0.914845	−	0.403805i
$22$		0			0
$23$	−0.274350	+	1.55592i	−0.0572060	+	0.324432i	−0.999959	−	0.00906049i	$-0.997116\pi$
$23$	−0.274350	+	1.55592i	−0.0572060	+	0.324432i	0.942753	+	0.333492i	$0.108227\pi$
$24$		0			0
$25$	−2.99386	+	2.51215i	−0.598773	+	0.502430i
$26$		0			0
$27$	−5.09289	+	1.03077i	−0.980127	+	0.198373i
$28$		0			0
$29$	9.47940	+	3.45022i	1.76028	+	0.640689i	0.999961	−	0.00886019i	$-0.00282032\pi$
$29$	9.47940	+	3.45022i	1.76028	+	0.640689i	0.760319	+	0.649550i	$0.225043\pi$
$30$		0			0
$31$	6.01934	−	2.19086i	1.08111	−	0.393490i	0.260787	−	0.965396i	$-0.416018\pi$
$31$	6.01934	−	2.19086i	1.08111	−	0.393490i	0.820319	+	0.571906i	$0.193796\pi$
$32$		0			0
$33$	1.80971	+	7.36010i	0.315031	+	1.28123i
$34$		0			0
$35$	0.480162	+	2.72249i	0.0811621	+	0.460185i
$36$		0			0
$37$	−5.88632			−0.967704			−0.483852	−	0.875150i	$-0.660763\pi$
$37$	−5.88632			−0.967704			−0.483852	+	0.875150i	$0.660763\pi$
$38$		0			0
$39$	3.36845	+	2.46408i	0.539384	+	0.394568i
$40$		0			0
$41$	1.95781	−	0.712584i	0.305758	−	0.111287i	−0.184584	−	0.982817i	$-0.559094\pi$
$41$	1.95781	−	0.712584i	0.305758	−	0.111287i	0.490343	+	0.871530i	$0.336872\pi$
$42$		0			0
$43$	0.727841	+	4.12779i	0.110995	+	0.629482i	0.988656	+	0.150200i	$0.0479918\pi$
$43$	0.727841	+	4.12779i	0.110995	+	0.629482i	−0.877661	+	0.479282i	$0.840897\pi$
$44$		0			0
$45$	0.129742	−	3.13197i	0.0193408	−	0.466887i
$46$		0			0
$47$	−7.33846	−	2.67098i	−1.07042	−	0.389603i	−0.254089	−	0.967181i	$-0.581776\pi$
$47$	−7.33846	−	2.67098i	−1.07042	−	0.389603i	−0.816335	+	0.577578i	$0.803998\pi$
$48$		0			0
$49$	−6.57804	−	2.39361i	−0.939720	−	0.341945i
$50$		0			0
$51$	−2.56785	+	5.22176i	−0.359570	+	0.731192i
$52$		0			0
$53$	2.84430	−	4.92648i	0.390695	−	0.676704i	−0.601846	−	0.798612i	$-0.705568\pi$
$53$	2.84430	−	4.92648i	0.390695	−	0.676704i	0.992541	+	0.121908i	$0.0389014\pi$
$54$		0			0
$55$	−4.57235			−0.616535
$56$		0			0
$57$	−3.81098	+	0.254056i	−0.504776	+	0.0336505i
$58$		0			0
$59$	3.93783	+	3.30423i	0.512662	+	0.430174i	0.862065	−	0.506798i	$-0.169171\pi$
$59$	3.93783	+	3.30423i	0.512662	+	0.430174i	−0.349403	+	0.936973i	$0.613616\pi$
$60$		0			0
$61$	−3.43555	−	1.25044i	−0.439877	−	0.160102i	0.112581	−	0.993643i	$-0.464088\pi$
$61$	−3.43555	−	1.25044i	−0.439877	−	0.160102i	−0.552459	+	0.833540i	$0.686310\pi$
$62$		0			0
$63$	6.70388	+	4.24946i	0.844610	+	0.535382i
$64$		0			0
$65$	−1.92870	+	1.61837i	−0.239225	+	0.200734i
$66$		0			0
$67$	1.01172	−	5.73775i	0.123601	−	0.700978i	−0.858527	−	0.512768i	$-0.828620\pi$
$67$	1.01172	−	5.73775i	0.123601	−	0.700978i	0.982129	−	0.188210i	$-0.0602687\pi$
$68$		0			0
$69$	−2.50352	+	1.10491i	−0.301389	+	0.133016i
$70$		0			0
$71$	−1.66736	+	2.88795i	−0.197879	+	0.342737i	−0.947841	−	0.318745i	$-0.896739\pi$
$71$	−1.66736	+	2.88795i	−0.197879	+	0.342737i	0.749961	+	0.661482i	$0.230072\pi$
$72$		0			0
$73$	−9.33431			−1.09250			−0.546249	−	0.837623i	$-0.683945\pi$
$73$	−9.33431			−1.09250			−0.546249	+	0.837623i	$0.683945\pi$
$74$		0			0
$75$	−6.50090	−	1.88697i	−0.750659	−	0.217889i
$76$		0			0
$77$	5.78840	−	10.0267i	0.659650	−	1.14265i
$78$		0			0
$79$	2.00454	+	11.3683i	0.225528	+	1.27903i	0.861673	+	0.507463i	$0.169417\pi$
$79$	2.00454	+	11.3683i	0.225528	+	1.27903i	−0.636146	+	0.771569i	$0.719472\pi$
$80$		0			0
$81$	−6.39230	−	6.33549i	−0.710256	−	0.703943i
$82$		0			0
$83$	0.482130	+	0.175481i	0.0529206	+	0.0192615i	0.368345	−	0.929689i	$-0.379925\pi$
$83$	0.482130	+	0.175481i	0.0529206	+	0.0192615i	−0.315424	+	0.948951i	$0.602147\pi$
$84$		0			0
$85$	−2.68912	−	2.25644i	−0.291676	−	0.244745i
$86$		0			0
$87$	4.17191	+	16.9671i	0.447275	+	1.81907i
$88$		0			0
$89$	5.77894	−	10.0094i	0.612566	−	1.06100i	−0.378240	−	0.925707i	$-0.623471\pi$
$89$	5.77894	−	10.0094i	0.612566	−	1.06100i	0.990806	−	0.135288i	$-0.0431959\pi$
$90$		0			0
$91$	−1.10728	−	6.27824i	−0.116075	−	0.658138i
$92$		0			0
$93$	8.95475	+	6.55054i	0.928564	+	0.679259i
$94$		0			0
$95$	0.400109	−	2.26913i	0.0410503	−	0.232808i
$96$		0			0
$97$	−2.60776	−	14.7893i	−0.264778	−	1.50163i	−0.769668	−	0.638444i	$-0.779578\pi$
$97$	−2.60776	−	14.7893i	−0.264778	−	1.50163i	0.504890	−	0.863183i	$-0.331533\pi$
$98$		0			0
$99$	−8.84737	+	9.69858i	−0.889195	+	0.974744i
$100$		0			0
$101$	−0.220963	−	1.25314i	−0.0219866	−	0.124692i	0.971839	−	0.235646i	$-0.0757206\pi$
$101$	−0.220963	−	1.25314i	−0.0219866	−	0.124692i	−0.993826	+	0.110954i	$0.964609\pi$
$102$		0			0
$103$	16.7384	−	6.09227i	1.64928	−	0.600290i	0.660657	−	0.750688i	$-0.270278\pi$
$103$	16.7384	−	6.09227i	1.64928	−	0.600290i	0.988625	+	0.150399i	$0.0480557\pi$
$104$		0			0
$105$	−3.45505	+	3.31515i	−0.337178	+	0.323525i
$106$		0			0
$107$	6.12057	+	10.6011i	0.591698	+	1.02485i	0.994004	+	0.109345i	$0.0348754\pi$
$107$	6.12057	+	10.6011i	0.591698	+	1.02485i	−0.402306	+	0.915505i	$0.631791\pi$
$108$		0			0
$109$	9.14741	−	15.8438i	0.876163	−	1.51756i	0.0206435	−	0.999787i	$-0.493428\pi$
$109$	9.14741	−	15.8438i	0.876163	−	1.51756i	0.855519	−	0.517771i	$-0.173238\pi$
$110$		0			0
$111$	−5.67372	−	8.47084i	−0.538525	−	0.804016i
$112$		0			0
$113$	−0.103370	+	0.586238i	−0.00972419	+	0.0551486i	−0.989284	−	0.146006i	$-0.953358\pi$
$113$	−0.103370	+	0.586238i	−0.00972419	+	0.0551486i	0.979560	+	0.201154i	$0.0644693\pi$
$114$		0			0
$115$	−0.286665	−	1.62576i	−0.0267317	−	0.151603i
$116$		0			0
$117$	−0.299194	+	7.22253i	−0.0276605	+	0.667723i
$118$		0			0
$119$	8.35247	−	3.04043i	0.765670	−	0.278716i
$120$		0			0
$121$	6.24229	+	5.23790i	0.567481	+	0.476173i
$122$		0			0
$123$	2.91256	+	2.13058i	0.262616	+	0.192108i
$124$		0			0
$125$	4.65404	−	8.06103i	0.416270	−	0.721000i
$126$		0			0
$127$	2.68124	+	4.64404i	0.237921	+	0.412092i	0.960118	−	0.279596i	$-0.0902007\pi$
$127$	2.68124	+	4.64404i	0.237921	+	0.412092i	−0.722196	+	0.691688i	$0.756867\pi$
$128$		0			0
$129$	−5.23864	+	5.02612i	−0.461237	+	0.442525i
$130$		0			0
$131$	3.19668	−	18.1293i	0.279295	−	1.58396i	−0.445682	−	0.895191i	$-0.647039\pi$
$131$	3.19668	−	18.1293i	0.279295	−	1.58396i	0.724978	−	0.688772i	$-0.241850\pi$
$132$		0			0
$133$	4.46947	+	3.75003i	0.387552	+	0.325169i
$134$		0			0
$135$	4.63220	−	2.83215i	0.398676	−	0.243752i
$136$		0			0
$137$	−7.45326	+	6.25402i	−0.636775	+	0.534317i	−0.903026	−	0.429586i	$-0.858659\pi$
$137$	−7.45326	+	6.25402i	−0.636775	+	0.534317i	0.266251	+	0.963904i	$0.414215\pi$
$138$		0			0
$139$	−12.3553	−	10.3673i	−1.04796	−	0.879345i	−0.0550844	−	0.998482i	$-0.517543\pi$
$139$	−12.3553	−	10.3673i	−1.04796	−	0.879345i	−0.992878	+	0.119137i	$0.961987\pi$
$140$		0			0
$141$	−3.22968	−	13.1351i	−0.271988	−	1.10617i
$142$		0			0
$143$	10.5441			0.881744
$144$		0			0
$145$	−10.5406			−0.875347
$146$		0			0
$147$	−2.89587	−	11.7734i	−0.238848	−	0.971057i
$148$		0			0
$149$	−7.07352	−	5.93539i	−0.579486	−	0.486246i	0.305293	−	0.952259i	$-0.401246\pi$
$149$	−7.07352	−	5.93539i	−0.579486	−	0.486246i	−0.884778	+	0.466012i	$0.845690\pi$
$150$		0			0
$151$	−7.28121	−	2.65014i	−0.592536	−	0.215666i	0.0283083	−	0.999599i	$-0.490988\pi$
$151$	−7.28121	−	2.65014i	−0.592536	−	0.215666i	−0.620845	+	0.783934i	$0.713210\pi$
$152$		0			0
$153$	−9.98959	+	1.33784i	−0.807611	+	0.108158i
$154$		0			0
$155$	−5.12727	+	4.30229i	−0.411833	+	0.345569i
$156$		0			0
$157$	−3.24131	−	2.71978i	−0.258684	−	0.217062i	0.504217	−	0.863577i	$-0.331781\pi$
$157$	−3.24131	−	2.71978i	−0.258684	−	0.217062i	−0.762901	+	0.646515i	$0.776226\pi$
$158$		0			0
$159$	9.83113	−	0.655385i	0.779660	−	0.0519754i
$160$		0			0
$161$	3.92805	+	1.42951i	0.309573	+	0.112661i
$162$		0			0
$163$	−4.11630	−	7.12964i	−0.322413	−	0.558437i	0.658572	−	0.752518i	$-0.271161\pi$
$163$	−4.11630	−	7.12964i	−0.322413	−	0.558437i	−0.980985	+	0.194081i	$0.937827\pi$
$164$		0			0
$165$	−4.40720	−	6.57994i	−0.343100	−	0.512248i
$166$		0			0
$167$	−1.98329	+	11.2478i	−0.153472	+	0.870381i	0.806698	+	0.590964i	$0.201252\pi$
$167$	−1.98329	+	11.2478i	−0.153472	+	0.870381i	−0.960170	+	0.279417i	$0.909859\pi$
$168$		0			0
$169$	−5.51088	+	4.62418i	−0.423914	+	0.355706i
$170$		0			0
$171$	−4.03894	−	5.23939i	−0.308865	−	0.400667i
$172$		0			0
$173$	−11.9132	+	9.99638i	−0.905746	+	0.760011i	−0.971305	−	0.237838i	$-0.923561\pi$
$173$	−11.9132	+	9.99638i	−0.905746	+	0.760011i	0.0655593	+	0.997849i	$0.479117\pi$
$174$		0			0
$175$	5.17044	+	8.95463i	0.390848	+	0.676906i
$176$		0			0
$177$	−0.959426	+	8.85172i	−0.0721149	+	0.665336i
$178$		0			0
$179$	7.51543	+	13.0171i	0.561730	+	0.972945i	0.997346	+	0.0728119i	$0.0231973\pi$
$179$	7.51543	+	13.0171i	0.561730	+	0.972945i	−0.435616	+	0.900133i	$0.643469\pi$
$180$		0			0
$181$	−8.94771	−	15.4979i	−0.665078	−	1.15195i	−0.979264	−	0.202587i	$-0.935065\pi$
$181$	−8.94771	−	15.4979i	−0.665078	−	1.15195i	0.314187	−	0.949361i	$-0.398268\pi$
$182$		0			0
$183$	−1.51200	−	6.14929i	−0.111770	−	0.454568i
$184$		0			0
$185$	5.77961	−	2.10361i	0.424925	−	0.154660i
$186$		0			0
$187$	2.55286	+	14.4780i	0.186684	+	1.05874i
$188$		0			0
$189$	0.346468	+	13.7434i	0.0252018	+	0.999682i
$190$		0			0
$191$	3.07563	+	17.4428i	0.222545	+	1.26212i	0.867323	+	0.497746i	$0.165839\pi$
$191$	3.07563	+	17.4428i	0.222545	+	1.26212i	−0.644778	+	0.764370i	$0.723050\pi$
$192$		0			0
$193$	0.198495	−	0.0722461i	0.0142880	−	0.00520039i	−0.334866	−	0.942266i	$-0.608691\pi$
$193$	0.198495	−	0.0722461i	0.0142880	−	0.00520039i	0.349154	+	0.937065i	$0.386469\pi$
$194$		0			0
$195$	−4.18798	−	1.21562i	−0.299908	−	0.0870522i
$196$		0			0
$197$	−8.28841	−	14.3560i	−0.590525	−	1.02282i	−0.994162	−	0.107900i	$-0.965587\pi$
$197$	−8.28841	−	14.3560i	−0.590525	−	1.02282i	0.403637	−	0.914919i	$-0.367746\pi$
$198$		0			0
$199$	−0.600332	−	1.03981i	−0.0425564	−	0.0737099i	0.843963	−	0.536402i	$-0.180217\pi$
$199$	−0.600332	−	1.03981i	−0.0425564	−	0.0737099i	−0.886519	+	0.462692i	$0.846884\pi$
$200$		0			0
$201$	9.23223	−	4.07458i	0.651191	−	0.287399i
$202$		0			0
$203$	13.3439	−	23.1145i	0.936560	−	1.62232i
$204$		0			0
$205$	−1.66766	+	1.39933i	−0.116474	+	0.0977337i
$206$		0			0
$207$	−4.00315	−	2.53775i	−0.278238	−	0.176386i
$208$		0			0
$209$	−7.39201	+	6.20263i	−0.511316	+	0.429045i
$210$		0			0
$211$	2.59468	−	14.7152i	0.178625	−	1.01303i	−0.755251	−	0.655436i	$-0.772485\pi$
$211$	2.59468	−	14.7152i	0.178625	−	1.01303i	0.933876	−	0.357597i	$-0.116404\pi$
$212$		0			0
$213$	−5.76312	+	0.384194i	−0.394882	+	0.0263245i
$214$		0			0
$215$	−2.18981	−	3.79285i	−0.149344	−	0.258671i
$216$		0			0
$217$	−2.94362	−	16.6902i	−0.199826	−	1.13300i
$218$		0			0
$219$	−8.99717	−	13.4327i	−0.607973	−	0.907701i
$220$		0			0
$221$	6.20128	+	5.20349i	0.417143	+	0.350025i
$222$		0			0
$223$	7.37865	−	6.19142i	0.494111	−	0.414608i	−0.361386	−	0.932416i	$-0.617696\pi$
$223$	7.37865	−	6.19142i	0.494111	−	0.414608i	0.855497	+	0.517808i	$0.173252\pi$
$224$		0			0
$225$	−3.55061	−	11.1741i	−0.236708	−	0.744939i
$226$		0			0
$227$	−20.9667	−	7.63124i	−1.39161	−	0.506503i	−0.465931	−	0.884821i	$-0.654280\pi$
$227$	−20.9667	−	7.63124i	−1.39161	−	0.506503i	−0.925676	+	0.378318i	$0.876503\pi$
$228$		0			0
$229$	−21.1639	−	17.7586i	−1.39855	−	1.17352i	−0.961738	−	0.273971i	$-0.911663\pi$
$229$	−21.1639	−	17.7586i	−1.39855	−	1.17352i	−0.436813	−	0.899552i	$-0.643893\pi$
$230$		0			0
$231$	20.0085	−	1.33466i	1.31647	−	0.0878143i
$232$		0			0
$233$	26.1106			1.71056			0.855282	−	0.518164i	$-0.173384\pi$
$233$	26.1106			1.71056			0.855282	+	0.518164i	$0.173384\pi$
$234$		0			0
$235$	8.15997			0.532297
$236$		0			0
$237$	−14.4277	+	13.8424i	−0.937177	+	0.899158i
$238$		0			0
$239$	−7.29574	−	6.12186i	−0.471922	−	0.395990i	0.375573	−	0.926793i	$-0.377446\pi$
$239$	−7.29574	−	6.12186i	−0.471922	−	0.395990i	−0.847495	+	0.530803i	$0.821890\pi$
$240$		0			0
$241$	−0.363599	+	0.305096i	−0.0234215	+	0.0196530i	−0.654423	−	0.756128i	$-0.727089\pi$
$241$	−0.363599	+	0.305096i	−0.0234215	+	0.0196530i	0.631002	+	0.775781i	$0.282644\pi$
$242$		0			0
$243$	2.95580	−	15.3057i	0.189615	−	0.981859i
$244$		0			0
$245$	7.31421		0.000587571i	0.467288		3.75385e-5i
$246$		0			0
$247$	−0.922676	+	5.23276i	−0.0587085	+	0.332952i
$248$		0			0
$249$	0.212187	+	0.862963i	0.0134468	+	0.0546880i
$250$		0			0
$251$	7.99107	+	13.8409i	0.504392	+	0.873632i	0.999987	+	0.00507870i	$0.00161661\pi$
$251$	7.99107	+	13.8409i	0.504392	+	0.873632i	−0.495595	+	0.868554i	$0.665050\pi$
$252$		0			0
$253$	−3.45681	+	5.98737i	−0.217328	+	0.376423i
$254$		0			0
$255$	0.655185	−	6.04478i	0.0410293	−	0.378539i
$256$		0			0
$257$	−8.67806	−	7.28176i	−0.541323	−	0.454224i	0.330667	−	0.943747i	$-0.392726\pi$
$257$	−8.67806	−	7.28176i	−0.541323	−	0.454224i	−0.871990	+	0.489524i	$0.837171\pi$
$258$		0			0
$259$	−2.70373	+	15.3372i	−0.168002	+	0.953010i
$260$		0			0
$261$	−20.3957	+	22.3580i	−1.26246	+	1.38393i
$262$		0			0
$263$	−2.80194	−	15.8906i	−0.172775	−	0.979857i	−0.940680	−	0.339294i	$-0.889812\pi$
$263$	−2.80194	−	15.8906i	−0.172775	−	0.979857i	0.767905	−	0.640564i	$-0.221299\pi$
$264$		0			0
$265$	−1.03216	+	5.85365i	−0.0634048	+	0.359587i
$266$		0			0
$267$	19.9745	−	1.33158i	1.22242	−	0.0814916i
$268$		0			0
$269$	−8.78113	+	15.2094i	−0.535395	+	0.927332i	0.463749	+	0.885967i	$0.346504\pi$
$269$	−8.78113	+	15.2094i	−0.535395	+	0.927332i	−0.999144	+	0.0413651i	$0.986829\pi$
$270$		0			0
$271$	0.433086	+	0.750128i	0.0263081	+	0.0455670i	0.878880	−	0.477043i	$-0.158292\pi$
$271$	0.433086	+	0.750128i	0.0263081	+	0.0455670i	−0.852572	+	0.522610i	$0.824958\pi$
$272$		0			0
$273$	7.96755	−	7.64495i	0.482218	−	0.462693i
$274$		0			0
$275$	−16.0707	+	5.84924i	−0.969098	+	0.352723i
$276$		0			0
$277$	−2.23305	−	12.6643i	−0.134171	−	0.760923i	−0.975433	−	0.220295i	$-0.929298\pi$
$277$	−2.23305	−	12.6643i	−0.134171	−	0.760923i	0.841262	−	0.540628i	$-0.181813\pi$
$278$		0			0
$279$	−0.795382	+	19.2005i	−0.0476183	+	1.14950i
$280$		0			0
$281$	−0.508316	−	2.88280i	−0.0303236	−	0.171974i	0.965885	−	0.258972i	$-0.0833837\pi$
$281$	−0.508316	−	2.88280i	−0.0303236	−	0.171974i	−0.996208	+	0.0869982i	$0.972273\pi$
$282$		0			0
$283$	−4.13169	+	23.4320i	−0.245603	+	1.39289i	0.573484	+	0.819217i	$0.305591\pi$
$283$	−4.13169	+	23.4320i	−0.245603	+	1.39289i	−0.819087	+	0.573669i	$0.805520\pi$
$284$		0			0
$285$	3.65110	−	1.61139i	0.216273	−	0.0954504i
$286$		0			0
$287$	−0.957420	−	5.42852i	−0.0565147	−	0.320436i
$288$		0			0
$289$	2.85657	−	4.94772i	0.168033	−	0.291042i
$290$		0			0
$291$	18.7693	−	18.0079i	1.10028	−	1.05564i
$292$		0			0
$293$	−21.8544	−	18.3380i	−1.27675	−	1.07132i	−0.993684	−	0.112215i	$-0.964205\pi$
$293$	−21.8544	−	18.3380i	−1.27675	−	1.07132i	−0.283062	−	0.959102i	$-0.591350\pi$
$294$		0			0
$295$	−5.04729	−	1.83706i	−0.293864	−	0.106958i
$296$		0			0
$297$	−22.4848	−	3.38372i	−1.30470	−	0.196344i
$298$		0			0
$299$	0.661068	+	3.74910i	0.0382306	+	0.216816i
$300$		0			0
$301$	11.0896		0.000445429i	0.639193		2.56741e-5i
$302$		0			0
$303$	1.59038	−	1.52586i	0.0913649	−	0.0876585i
$304$		0			0
$305$	3.82015			0.218741
$306$		0			0
$307$	−3.81811	+	6.61316i	−0.217911	+	0.377433i	−0.954169	−	0.299268i	$-0.903258\pi$
$307$	−3.81811	+	6.61316i	−0.217911	+	0.377433i	0.736258	+	0.676701i	$0.236591\pi$
$308$		0			0
$309$	24.9011	+	18.2155i	1.41657	+	1.03624i
$310$		0			0
$311$	0.347845	−	1.97273i	0.0197245	−	0.111863i	−0.973356	−	0.229299i	$-0.926357\pi$
$311$	0.347845	−	1.97273i	0.0197245	−	0.111863i	0.993080	+	0.117436i	$0.0374676\pi$
$312$		0			0
$313$	−24.0504	+	20.1807i	−1.35941	+	1.14068i	−0.383248	+	0.923646i	$0.625194\pi$
$313$	−24.0504	+	20.1807i	−1.35941	+	1.14068i	−0.976164	+	0.217036i	$0.930361\pi$
$314$		0			0
$315$	−8.10100	−	1.77665i	−0.456440	−	0.100103i
$316$		0			0
$317$	18.1343	+	6.60036i	1.01853	+	0.370713i	0.796701	−	0.604373i	$-0.206576\pi$
$317$	18.1343	+	6.60036i	1.01853	+	0.370713i	0.221825	+	0.975087i	$0.428799\pi$
$318$		0			0
$319$	33.8157	+	28.3748i	1.89332	+	1.58868i
$320$		0			0
$321$	−9.35630	+	19.0262i	−0.522218	+	1.06194i
$322$		0			0
$323$	−7.40842			−0.412215
$324$		0			0
$325$	−4.70857	+	8.15547i	−0.261184	+	0.452384i
$326$		0			0
$327$	31.6174	−	2.10775i	1.74844	−	0.116559i
$328$		0			0
$329$	−10.3302	+	17.8941i	−0.569521	+	0.986531i
$330$		0			0
$331$	27.0582	+	9.84836i	1.48725	+	0.541315i	0.952724	−	0.303837i	$-0.0982677\pi$
$331$	27.0582	+	9.84836i	1.48725	+	0.541315i	0.534527	+	0.845152i	$0.320490\pi$
$332$		0			0
$333$	6.72136	−	16.3298i	0.368328	−	0.894867i
$334$		0			0
$335$	1.05713	+	5.99530i	0.0577574	+	0.327558i
$336$		0			0
$337$	19.8619	−	7.22914i	1.08195	−	0.393796i	0.261315	−	0.965254i	$-0.415844\pi$
$337$	19.8619	−	7.22914i	1.08195	−	0.393796i	0.820632	+	0.571457i	$0.193622\pi$
$338$		0			0
$339$	−0.943275	+	0.416308i	−0.0512317	+	0.0226108i
$340$		0			0
$341$	28.0307			1.51795
$342$		0			0
$343$	−9.25820	+	16.0401i	−0.499896	+	0.866086i
$344$		0			0
$345$	2.06327	−	1.97957i	0.111083	−	0.106577i
$346$		0			0
$347$	−24.6596	+	8.97536i	−1.32380	+	0.481822i	−0.904673	−	0.426107i	$-0.859885\pi$
$347$	−24.6596	+	8.97536i	−1.32380	+	0.481822i	−0.419123	+	0.907929i	$0.637662\pi$
$348$		0			0
$349$	−5.29808	−	1.92835i	−0.283600	−	0.103222i	0.196304	−	0.980543i	$-0.437106\pi$
$349$	−5.29808	−	1.92835i	−0.283600	−	0.103222i	−0.479904	+	0.877321i	$0.659328\pi$
$350$		0			0
$351$	−10.6821	+	6.53111i	−0.570170	+	0.348605i
$352$		0			0
$353$	−9.13705	+	7.66690i	−0.486316	+	0.408068i	−0.852704	−	0.522395i	$-0.825039\pi$
$353$	−9.13705	+	7.66690i	−0.486316	+	0.408068i	0.366388	+	0.930462i	$0.380594\pi$
$354$		0			0
$355$	0.605061	−	3.43147i	0.0321133	−	0.182124i
$356$		0			0
$357$	12.4262	+	9.08920i	0.657665	+	0.481052i
$358$		0			0
$359$	−9.55303	+	16.5463i	−0.504190	+	0.873282i	0.495799	+	0.868437i	$0.334875\pi$
$359$	−9.55303	+	16.5463i	−0.504190	+	0.873282i	−0.999988	+	0.00484440i	$0.998458\pi$
$360$		0			0
$361$	7.06865	+	12.2433i	0.372034	+	0.644382i
$362$		0			0
$363$	−1.52089	+	14.0318i	−0.0798261	+	0.736480i
$364$		0			0
$365$	9.16510	−	3.33582i	0.479723	−	0.174605i
$366$		0			0
$367$	−5.69494	−	2.07279i	−0.297274	−	0.108199i	0.189078	−	0.981962i	$-0.439450\pi$
$367$	−5.69494	−	2.07279i	−0.297274	−	0.108199i	−0.486351	+	0.873763i	$0.661672\pi$
$368$		0			0
$369$	−0.258700	+	6.24501i	−0.0134674	+	0.325102i
$370$		0			0
$371$	−11.5298	−	9.67390i	−0.598600	−	0.502244i
$372$		0			0
$373$	33.6882	−	12.2615i	1.74431	−	0.634876i	0.744832	−	0.667252i	$-0.232530\pi$
$373$	33.6882	−	12.2615i	1.74431	−	0.634876i	0.999476	+	0.0323758i	$0.0103073\pi$
$374$		0			0
$375$	16.0863	−	1.07238i	0.830695	−	0.0553777i
$376$		0			0
$377$	24.3072			1.25189
$378$		0			0
$379$	−9.21008			−0.473090			−0.236545	−	0.971621i	$-0.576015\pi$
$379$	−9.21008			−0.473090			−0.236545	+	0.971621i	$0.576015\pi$
$380$		0			0
$381$	−4.09871	+	8.33480i	−0.209983	+	0.427005i
$382$		0			0
$383$	−0.969570	+	0.352895i	−0.0495427	+	0.0180321i	−0.366673	−	0.930350i	$-0.619503\pi$
$383$	−0.969570	+	0.352895i	−0.0495427	+	0.0180321i	0.317130	+	0.948382i	$0.397281\pi$
$384$		0			0
$385$	−2.10019	+	11.9136i	−0.107036	+	0.607173i
$386$		0			0
$387$	−12.2824	−	2.69420i	−0.624349	−	0.136954i
$388$		0			0
$389$	−0.106033	−	0.0385927i	−0.00537607	−	0.00195673i	0.339331	−	0.940667i	$-0.389799\pi$
$389$	−0.106033	−	0.0385927i	−0.00537607	−	0.00195673i	−0.344707	+	0.938710i	$0.612022\pi$
$390$		0			0
$391$	−4.98779	+	1.81541i	−0.252243	+	0.0918090i
$392$		0			0
$393$	29.1706	−	12.8742i	1.47146	−	0.649420i
$394$		0			0
$395$	−6.03091	−	10.4458i	−0.303448	−	0.525587i
$396$		0			0
$397$	−1.14471	+	1.98270i	−0.0574514	+	0.0995087i	−0.893321	−	0.449420i	$-0.851631\pi$
$397$	−1.14471	+	1.98270i	−0.0574514	+	0.0995087i	0.835869	+	0.548929i	$0.184964\pi$
$398$		0			0
$399$	−1.08852	+	10.0465i	−0.0544940	+	0.502953i
$400$		0			0
$401$	4.20335	−	23.8384i	0.209905	−	1.19043i	−0.679626	−	0.733558i	$-0.737858\pi$
$401$	4.20335	−	23.8384i	0.209905	−	1.19043i	0.889532	−	0.456873i	$-0.151031\pi$
$402$		0			0
$403$	11.8238	−	9.92136i	0.588986	−	0.494218i
$404$		0			0
$405$	8.54056	+	3.93621i	0.424384	+	0.195592i
$406$		0			0
$407$	−24.2047	−	8.80978i	−1.19978	−	0.436685i
$408$		0			0
$409$	34.3378	−	12.4979i	1.69789	−	0.617982i	0.702310	−	0.711871i	$-0.252152\pi$
$409$	34.3378	−	12.4979i	1.69789	−	0.617982i	0.995583	+	0.0938890i	$0.0299299\pi$
$410$		0			0
$411$	−16.1841	−	4.69763i	−0.798301	−	0.231717i
$412$		0			0
$413$	10.4182	−	8.74260i	0.512645	−	0.430195i
$414$		0			0
$415$	−0.536102			−0.0263162
$416$		0			0
$417$	3.01028	−	27.7730i	0.147414	−	1.36005i
$418$		0			0
$419$	14.7578	−	5.37140i	0.720966	−	0.262410i	0.0446303	−	0.999004i	$-0.485789\pi$
$419$	14.7578	−	5.37140i	0.720966	−	0.262410i	0.676336	+	0.736593i	$0.263567\pi$
$420$		0			0
$421$	6.07862	+	34.4735i	0.296254	+	1.68014i	0.662063	+	0.749448i	$0.269681\pi$
$421$	6.07862	+	34.4735i	0.296254	+	1.68014i	−0.365809	+	0.930690i	$0.619208\pi$
$422$		0			0
$423$	15.7893	−	17.3084i	0.767703	−	0.841564i
$424$		0			0
$425$	−12.3382	−	4.49072i	−0.598489	−	0.217832i
$426$		0			0
$427$	−4.83615	+	8.37723i	−0.234038	+	0.405403i
$428$		0			0
$429$	10.1633	+	15.1738i	0.490688	+	0.732596i
$430$		0			0
$431$	−8.11724	+	14.0595i	−0.390993	+	0.677221i	−0.992581	−	0.121586i	$-0.961202\pi$
$431$	−8.11724	+	14.0595i	−0.390993	+	0.677221i	0.601587	+	0.798807i	$0.294535\pi$
$432$		0			0
$433$	−3.67578			−0.176647			−0.0883234	−	0.996092i	$-0.528151\pi$
$433$	−3.67578			−0.176647			−0.0883234	+	0.996092i	$0.528151\pi$
$434$		0			0
$435$	−10.1599	−	15.1686i	−0.487128	−	0.727281i
$436$		0			0
$437$	−2.66887	−	2.23945i	−0.127670	−	0.107127i
$438$		0			0
$439$	34.1027	+	12.4124i	1.62764	+	0.592411i	0.984815	−	0.173606i	$-0.0555420\pi$
$439$	34.1027	+	12.4124i	1.62764	+	0.592411i	0.642820	+	0.766017i	$0.277764\pi$
$440$		0			0
$441$	14.1516	−	15.5156i	0.673884	−	0.738837i
$442$		0			0
$443$	−28.4100	+	23.8388i	−1.34980	+	1.13262i	−0.370811	+	0.928708i	$0.620920\pi$
$443$	−28.4100	+	23.8388i	−1.34980	+	1.13262i	−0.978990	+	0.203909i	$0.934635\pi$
$444$		0			0
$445$	−2.09709	+	11.8932i	−0.0994116	+	0.563791i
$446$		0			0
$447$	1.72342	−	15.9003i	0.0815148	−	0.752060i
$448$		0			0
$449$	−9.54785	+	16.5374i	−0.450591	+	0.780446i	−0.998423	−	0.0561422i	$-0.982120\pi$
$449$	−9.54785	+	16.5374i	−0.450591	+	0.780446i	0.547832	+	0.836588i	$0.315453\pi$
$450$		0			0
$451$	9.11705			0.429305
$452$		0			0
$453$	−3.20448	−	13.0326i	−0.150560	−	0.612326i
$454$		0			0
$455$	3.33088	+	5.76872i	0.156154	+	0.270442i
$456$		0			0
$457$	1.29113	+	7.32236i	0.0603965	+	0.342525i	1.00000		0.000260519i	$8.29259e-5\pi$
$457$	1.29113	+	7.32236i	0.0603965	+	0.342525i	−0.939603	+	0.342265i	$0.888806\pi$
$458$		0			0
$459$	−11.5540	−	13.0862i	−0.539297	−	0.610813i
$460$		0			0
$461$	31.7221	+	11.5459i	1.47744	+	0.537746i	0.950111	−	0.311913i	$-0.100970\pi$
$461$	31.7221	+	11.5459i	1.47744	+	0.537746i	0.527333	+	0.849658i	$0.323192\pi$
$462$		0			0
$463$	3.23819	+	2.71716i	0.150491	+	0.126277i	0.714925	−	0.699201i	$-0.246461\pi$
$463$	3.23819	+	2.71716i	0.150491	+	0.126277i	−0.564433	+	0.825479i	$0.690905\pi$
$464$		0			0
$465$	−11.1334	−	3.23162i	−0.516299	−	0.149863i
$466$		0			0
$467$	0.0795140	−	0.137722i	0.00367947	−	0.00637303i	−0.864180	−	0.503183i	$-0.832162\pi$
$467$	0.0795140	−	0.137722i	0.00367947	−	0.00637303i	0.867859	+	0.496810i	$0.165495\pi$
$468$		0			0
$469$	−14.4854	−	5.27161i	−0.668876	−	0.243420i
$470$		0			0
$471$	0.789722	−	7.28602i	0.0363885	−	0.335722i
$472$		0			0
$473$	−3.18498	+	18.0629i	−0.146445	+	0.830534i
$474$		0			0
$475$	−1.49654	−	8.48727i	−0.0686658	−	0.389423i
$476$		0			0
$477$	10.4192	+	13.5160i	0.477062	+	0.618855i
$478$		0			0
$479$	1.25986	+	7.14504i	0.0575646	+	0.326465i	0.999968	−	0.00801366i	$-0.00255085\pi$
$479$	1.25986	+	7.14504i	0.0575646	+	0.326465i	−0.942403	+	0.334479i	$0.891440\pi$
$480$		0			0
$481$	−13.3282	+	4.85105i	−0.607711	+	0.221189i
$482$		0			0
$483$	1.72900	+	7.03063i	0.0786723	+	0.319905i
$484$		0			0
$485$	7.84578	+	13.5893i	0.356258	+	0.617058i
$486$		0			0
$487$	6.25963	−	10.8420i	0.283651	−	0.491298i	−0.688630	−	0.725113i	$-0.741788\pi$
$487$	6.25963	−	10.8420i	0.283651	−	0.491298i	0.972281	+	0.233815i	$0.0751210\pi$
$488$		0			0
$489$	6.29244	−	12.7958i	0.284554	−	0.578646i
$490$		0			0
$491$	−3.70258	+	20.9983i	−0.167095	+	0.947642i	0.779783	+	0.626050i	$0.215329\pi$
$491$	−3.70258	+	20.9983i	−0.167095	+	0.947642i	−0.946878	+	0.321593i	$0.895782\pi$
$492$		0			0
$493$	5.88507	+	33.3759i	0.265050	+	1.50318i
$494$		0			0
$495$	5.22099	−	12.6846i	0.234666	−	0.570129i
$496$		0			0
$497$	6.75892	+	5.67094i	0.303179	+	0.254377i
$498$		0			0
$499$	−11.8497	−	9.94308i	−0.530466	−	0.445113i	0.337797	−	0.941219i	$-0.390318\pi$
$499$	−11.8497	−	9.94308i	−0.530466	−	0.445113i	−0.868262	+	0.496106i	$0.834763\pi$
$500$		0			0
$501$	−18.0981	+	7.98746i	−0.808562	+	0.356853i
$502$		0			0
$503$	6.86671	−	11.8935i	0.306172	−	0.530305i	−0.671350	−	0.741141i	$-0.734285\pi$
$503$	6.86671	−	11.8935i	0.306172	−	0.530305i	0.977522	+	0.210836i	$0.0676185\pi$
$504$		0			0
$505$	0.664795	+	1.15146i	0.0295830	+	0.0512392i
$506$		0			0
$507$	−11.9664	−	3.47340i	−0.531445	−	0.154259i
$508$		0			0
$509$	4.40817	−	25.0000i	0.195389	−	1.10810i	−0.716475	−	0.697612i	$-0.754246\pi$
$509$	4.40817	−	25.0000i	0.195389	−	1.10810i	0.911864	−	0.410492i	$-0.134643\pi$
$510$		0			0
$511$	−4.28748	+	24.3212i	−0.189667	+	1.07591i
$512$		0			0
$513$	3.64681	−	10.8625i	0.161011	−	0.479591i
$514$		0			0
$515$	−14.2577	+	11.9637i	−0.628271	+	0.527182i
$516$		0			0
$517$	−26.1784	−	21.9663i	−1.15132	−	0.966076i
$518$		0			0
$519$	−25.8685	−	7.50866i	−1.13550	−	0.329594i
$520$		0			0
$521$	−35.4194			−1.55175			−0.775876	−	0.630885i	$-0.782692\pi$
$521$	−35.4194			−1.55175			−0.775876	+	0.630885i	$0.782692\pi$
$522$		0			0
$523$	−22.2117			−0.971249			−0.485624	−	0.874168i	$-0.661408\pi$
$523$	−22.2117			−0.971249			−0.485624	+	0.874168i	$0.661408\pi$
$524$		0			0
$525$	−7.90267	+	16.0718i	−0.344901	+	0.701433i
$526$		0			0
$527$	16.4856	+	13.8330i	0.718123	+	0.602576i
$528$		0			0
$529$	19.2673	+	7.01273i	0.837709	+	0.304901i
$530$		0			0
$531$	−13.6630	+	7.15133i	−0.592925	+	0.310341i
$532$		0			0
$533$	3.84573	−	3.22695i	0.166577	−	0.139775i
$534$		0			0
$535$	−9.79817	−	8.22164i	−0.423612	−	0.355453i
$536$		0			0
$537$	−11.4886	+	23.3622i	−0.495769	+	1.00815i
$538$		0			0
$539$	−23.4667	−	19.6877i	−1.01078	−	0.848007i
$540$		0			0
$541$	−3.77393	−	6.53664i	−0.162254	−	0.281032i	0.773423	−	0.633891i	$-0.218543\pi$
$541$	−3.77393	−	6.53664i	−0.162254	−	0.281032i	−0.935677	+	0.352858i	$0.885210\pi$
$542$		0			0
$543$	13.6780	−	27.8145i	0.586981	−	1.19364i
$544$		0			0
$545$	−3.31946	+	18.8256i	−0.142190	+	0.806400i
$546$		0			0
$547$	−0.823105	+	0.690667i	−0.0351934	+	0.0295308i	−0.660215	−	0.751077i	$-0.729535\pi$
$547$	−0.823105	+	0.690667i	−0.0351934	+	0.0295308i	0.625021	+	0.780608i	$0.285090\pi$
$548$		0			0
$549$	7.39189	−	8.10306i	0.315478	−	0.345830i
$550$		0			0
$551$	−17.0407	+	14.2988i	−0.725958	+	0.609151i
$552$		0			0
$553$	30.5417	−	0.00122675i	1.29876	−	5.21667e-5i
$554$		0			0
$555$	8.59811	+	6.28965i	0.364969	+	0.266981i
$556$		0			0
$557$	−15.5515	−	26.9360i	−0.658939	−	1.14132i	−0.980891	−	0.194560i	$-0.937672\pi$
$557$	−15.5515	−	26.9360i	−0.658939	−	1.14132i	0.321951	−	0.946756i	$-0.395661\pi$
$558$		0			0
$559$	5.04983	+	8.74656i	0.213585	+	0.369940i
$560$		0			0
$561$	−18.3742	+	17.6288i	−0.775760	+	0.744290i
$562$		0			0
$563$	0.0285096	−	0.0103766i	0.00120153	−	0.000437323i	−0.341419	−	0.939911i	$-0.610908\pi$
$563$	0.0285096	−	0.0103766i	0.00120153	−	0.000437323i	0.342621	+	0.939474i	$0.388685\pi$
$564$		0			0
$565$	−0.108009	−	0.612552i	−0.00454399	−	0.0257703i
$566$		0			0
$567$	−19.4437	+	13.7456i	−0.816560	+	0.577260i
$568$		0			0
$569$	−1.98432	−	11.2536i	−0.0831871	−	0.471777i	−0.997733	−	0.0672954i	$-0.978563\pi$
$569$	−1.98432	−	11.2536i	−0.0831871	−	0.471777i	0.914546	−	0.404482i	$-0.132548\pi$
$570$		0			0
$571$	13.9243	−	5.06802i	0.582713	−	0.212090i	−0.0338085	−	0.999428i	$-0.510764\pi$
$571$	13.9243	−	5.06802i	0.582713	−	0.212090i	0.616521	+	0.787338i	$0.288541\pi$
$572$		0			0
$573$	−22.1369	+	21.2389i	−0.924782	+	0.887266i
$574$		0			0
$575$	−3.08733	−	5.34742i	−0.128751	−	0.223003i
$576$		0			0
$577$	−8.14704	−	14.1111i	−0.339166	−	0.587453i	0.645110	−	0.764090i	$-0.276811\pi$
$577$	−8.14704	−	14.1111i	−0.339166	−	0.587453i	−0.984276	+	0.176637i	$0.943478\pi$
$578$		0			0
$579$	0.295293	+	0.216011i	0.0122720	+	0.00897713i
$580$		0			0
$581$	0.678683	−	1.17562i	0.0281565	−	0.0487730i
$582$		0			0
$583$	19.0691	−	16.0009i	0.789761	−	0.662688i
$584$		0			0
$585$	−2.28736	−	7.19853i	−0.0945708	−	0.297622i
$586$		0			0
$587$	19.6726	−	16.5073i	0.811977	−	0.681330i	−0.139102	−	0.990278i	$-0.544421\pi$
$587$	19.6726	−	16.5073i	0.811977	−	0.681330i	0.951079	+	0.308948i	$0.0999770\pi$
$588$		0			0
$589$	−2.45286	+	13.9108i	−0.101068	+	0.573186i
$590$		0			0
$591$	12.6702	−	25.7651i	0.521183	−	1.05983i
$592$		0			0
$593$	2.65668	+	4.60151i	0.109097	+	0.188961i	0.915405	−	0.402535i	$-0.131871\pi$
$593$	2.65668	+	4.60151i	0.109097	+	0.188961i	−0.806308	+	0.591496i	$0.798537\pi$
$594$		0			0
$595$	−7.11450	+	5.97026i	−0.291666	+	0.244757i
$596$		0			0
$597$	0.917707	−	1.86617i	0.0375592	−	0.0763773i
$598$		0			0
$599$	−13.2128	−	11.0868i	−0.539859	−	0.452995i	0.331631	−	0.943409i	$-0.392401\pi$
$599$	−13.2128	−	11.0868i	−0.539859	−	0.452995i	−0.871490	+	0.490414i	$0.836846\pi$
$600$		0			0
$601$	−13.9417	+	11.6985i	−0.568694	+	0.477191i	−0.881212	−	0.472721i	$-0.843272\pi$
$601$	−13.9417	+	11.6985i	−0.568694	+	0.477191i	0.312518	+	0.949912i	$0.398827\pi$
$602$		0			0
$603$	14.7624	+	9.35843i	0.601171	+	0.381105i
$604$		0			0
$605$	−8.00101	−	2.91213i	−0.325287	−	0.118395i
$606$		0			0
$607$	−1.11057	−	0.931883i	−0.0450768	−	0.0378239i	0.619971	−	0.784625i	$-0.287144\pi$
$607$	−1.11057	−	0.931883i	−0.0450768	−	0.0378239i	−0.665048	+	0.746801i	$0.731589\pi$
$608$		0			0
$609$	46.1254	−	3.07678i	1.86910	−	0.124677i
$610$		0			0
$611$	−18.8174			−0.761271
$612$		0			0
$613$	30.7129			1.24048			0.620242	−	0.784411i	$-0.287034\pi$
$613$	30.7129			1.24048			0.620242	+	0.784411i	$0.287034\pi$
$614$		0			0
$615$	−3.62117	−	1.05109i	−0.146020	−	0.0423841i
$616$		0			0
$617$	−30.5604	−	25.6432i	−1.23031	−	1.03236i	−0.998219	−	0.0596632i	$-0.980997\pi$
$617$	−30.5604	−	25.6432i	−1.23031	−	1.03236i	−0.232096	−	0.972693i	$-0.574558\pi$
$618$		0			0
$619$	6.75475	−	5.66791i	0.271496	−	0.227813i	−0.496866	−	0.867827i	$-0.665516\pi$
$619$	6.75475	−	5.66791i	0.271496	−	0.227813i	0.768363	+	0.640014i	$0.221072\pi$
$620$		0			0
$621$	−0.206565	−	8.20691i	−0.00828918	−	0.329332i
$622$		0			0
$623$	−23.4259	−	19.6550i	−0.938537	−	0.787462i
$624$		0			0
$625$	1.70439	−	9.66606i	0.0681755	−	0.386643i
$626$		0			0
$627$	−16.0511	−	4.65903i	−0.641018	−	0.186064i
$628$		0			0
$629$	−9.88781	−	17.1262i	−0.394253	−	0.682866i
$630$		0			0
$631$	2.52154	−	4.36743i	0.100381	−	0.173865i	−0.811461	−	0.584407i	$-0.801327\pi$
$631$	2.52154	−	4.36743i	0.100381	−	0.173865i	0.911842	+	0.410542i	$0.134661\pi$
$632$		0			0
$633$	23.6772	−	10.4497i	0.941082	−	0.415340i
$634$		0			0
$635$	−4.29228	−	3.60165i	−0.170334	−	0.142927i
$636$		0			0
$637$	−16.8670	+	0.00135498i	−0.668296	+	5.36861e-5i
$638$		0			0
$639$	−6.10785	−	7.92323i	−0.241623	−	0.313438i
$640$		0			0
$641$	8.10956	+	45.9916i	0.320308	+	1.81656i	0.540778	+	0.841165i	$0.318130\pi$
$641$	8.10956	+	45.9916i	0.320308	+	1.81656i	−0.220470	+	0.975394i	$0.570759\pi$
$642$		0			0
$643$	4.17632	−	23.6851i	0.164698	−	0.934048i	−0.784677	−	0.619904i	$-0.787171\pi$
$643$	4.17632	−	23.6851i	0.164698	−	0.934048i	0.949375	−	0.314144i	$-0.101717\pi$
$644$		0			0
$645$	3.34748	−	6.80716i	0.131807	−	0.268032i
$646$		0			0
$647$	−11.7454	+	20.3437i	−0.461760	+	0.799792i	−0.999049	−	0.0436066i	$-0.986115\pi$
$647$	−11.7454	+	20.3437i	−0.461760	+	0.799792i	0.537289	+	0.843398i	$0.319449\pi$
$648$		0			0
$649$	11.2472	+	19.4807i	0.441490	+	0.764683i
$650$		0			0
$651$	21.1811	−	20.3234i	0.830151	−	0.796538i
$652$		0			0
$653$	20.1824	−	7.34578i	0.789797	−	0.287463i	0.0845454	−	0.996420i	$-0.473056\pi$
$653$	20.1824	−	7.34578i	0.789797	−	0.287463i	0.705252	+	0.708957i	$0.250834\pi$
$654$		0			0
$655$	3.34017	+	18.9431i	0.130511	+	0.740166i
$656$		0			0
$657$	10.6585	−	25.8952i	0.415827	−	1.01027i
$658$		0			0
$659$	−4.78673	−	27.1469i	−0.186465	−	1.05749i	−0.924059	−	0.382249i	$-0.875150\pi$
$659$	−4.78673	−	27.1469i	−0.186465	−	1.05749i	0.737595	−	0.675244i	$-0.235962\pi$
$660$		0			0
$661$	−4.97361	+	28.2068i	−0.193451	+	1.09712i	0.721156	+	0.692773i	$0.243611\pi$
$661$	−4.97361	+	28.2068i	−0.193451	+	1.09712i	−0.914607	+	0.404343i	$0.867500\pi$
$662$		0			0
$663$	−1.51090	+	13.9396i	−0.0586785	+	0.541371i
$664$		0			0
$665$	−5.72861	−	2.08478i	−0.222146	−	0.0808444i
$666$		0			0
$667$	−7.96894	+	13.8026i	−0.308559	+	0.534439i
$668$		0			0
$669$	16.0221	+	4.65061i	0.619448	+	0.179803i
$670$		0			0
$671$	−12.2556	−	10.2837i	−0.473122	−	0.396997i
$672$		0			0
$673$	−5.50728	−	2.00448i	−0.212290	−	0.0772672i	0.233686	−	0.972312i	$-0.424921\pi$
$673$	−5.50728	−	2.00448i	−0.212290	−	0.0772672i	−0.445976	+	0.895045i	$0.647143\pi$
$674$		0			0
$675$	12.6580	−	15.8801i	0.487205	−	0.611225i
$676$		0			0
$677$	−2.69492	−	15.2837i	−0.103574	−	0.587399i	−0.991780	−	0.127953i	$-0.959159\pi$
$677$	−2.69492	−	15.2837i	−0.103574	−	0.587399i	0.888206	−	0.459446i	$-0.151952\pi$
$678$		0			0
$679$	−39.7325	+	0.00159591i	−1.52479	+	6.12454e-5i
$680$		0			0
$681$	−9.22749	−	37.5282i	−0.353598	−	1.43808i
$682$		0			0
$683$	−19.7937			−0.757384			−0.378692	−	0.925523i	$-0.623626\pi$
$683$	−19.7937			−0.757384			−0.378692	+	0.925523i	$0.623626\pi$
$684$		0			0
$685$	5.08313	−	8.80424i	0.194216	−	0.336393i
$686$		0			0
$687$	5.15644	−	47.5737i	0.196731	−	1.81505i
$688$		0			0
$689$	2.38022	−	13.4989i	0.0906790	−	0.514266i
$690$		0			0
$691$	20.2444	−	16.9871i	0.770135	−	0.646220i	−0.170609	−	0.985339i	$-0.554573\pi$
$691$	20.2444	−	16.9871i	0.770135	−	0.646220i	0.940744	+	0.339119i	$0.110129\pi$
$692$		0			0
$693$	21.2066	+	27.5073i	0.805571	+	1.04492i
$694$		0			0
$695$	15.8363	+	5.76395i	0.600706	+	0.218639i
$696$		0			0
$697$	5.36198	+	4.49923i	0.203099	+	0.170421i
$698$		0			0
$699$	25.1676	+	37.5751i	0.951924	+	1.42122i
$700$		0			0
$701$	16.9147			0.638860			0.319430	−	0.947610i	$-0.396509\pi$
$701$	16.9147			0.638860			0.319430	+	0.947610i	$0.396509\pi$
$702$		0			0
$703$	6.49011	−	11.2412i	0.244779	−	0.423970i
$704$		0			0
$705$	7.86525	+	11.7428i	0.296222	+	0.442259i
$706$		0			0
$707$	−3.36665		0.000135226i	−0.126616		5.08570e-6i
$708$		0			0
$709$	−34.7210	−	12.6374i	−1.30398	−	0.474608i	−0.405686	−	0.914012i	$-0.632967\pi$
$709$	−34.7210	−	12.6374i	−1.30398	−	0.474608i	−0.898289	+	0.439404i	$0.855190\pi$
$710$		0			0
$711$	−33.8267	−	7.42004i	−1.26860	−	0.278273i
$712$		0			0
$713$	1.75739	+	9.96667i	0.0658149	+	0.373255i
$714$		0			0
$715$	−10.3530	+	3.76818i	−0.387180	+	0.140922i
$716$		0			0
$717$	1.77756	−	16.3999i	0.0663841	−	0.612464i
$718$		0			0
$719$	30.3232			1.13087			0.565433	−	0.824794i	$-0.308709\pi$
$719$	30.3232			1.13087			0.565433	+	0.824794i	$0.308709\pi$
$720$		0			0
$721$	−8.18551	−	46.4114i	−0.304844	−	1.72845i
$722$		0			0
$723$	−0.789522	−	0.229169i	−0.0293626	−	0.00852289i
$724$		0			0
$725$	−37.0475	+	13.4842i	−1.37591	+	0.500790i
$726$		0			0
$727$	−10.1721	−	3.70235i	−0.377263	−	0.137313i	0.146427	−	0.989222i	$-0.453223\pi$
$727$	−10.1721	−	3.70235i	−0.377263	−	0.137313i	−0.523690	+	0.851909i	$0.675445\pi$
$728$		0			0
$729$	24.8750	−	10.4992i	0.921297	−	0.388861i
$730$		0			0
$731$	−10.7872	+	9.05150i	−0.398977	+	0.334782i
$732$		0			0
$733$	0.00697976	−	0.0395842i	0.000257803	−	0.00146207i	−0.984679	−	0.174379i	$-0.944208\pi$
$733$	0.00697976	−	0.0395842i	0.000257803	−	0.00146207i	0.984936	+	0.172917i	$0.0553193\pi$
$734$		0			0
$735$	7.05088	+	10.5251i	0.260076	+	0.388225i
$736$		0			0
$737$	12.7477	−	22.0796i	0.469566	−	0.813312i
$738$		0			0
$739$	25.5470	+	44.2487i	0.939762	+	1.62772i	0.765914	+	0.642943i	$0.222287\pi$
$739$	25.5470	+	44.2487i	0.939762	+	1.62772i	0.173848	+	0.984773i	$0.444380\pi$
$740$		0			0
$741$	−8.41967	+	3.71596i	−0.309304	+	0.136509i
$742$		0			0
$743$	35.6175	−	12.9637i	1.30668	−	0.475592i	0.407513	−	0.913200i	$-0.366396\pi$
$743$	35.6175	−	12.9637i	1.30668	−	0.475592i	0.899166	+	0.437607i	$0.144174\pi$
$744$		0			0
$745$	9.06644	+	3.29992i	0.332169	+	0.120900i
$746$		0			0
$747$	−1.03734	+	1.13715i	−0.0379544	+	0.0416060i
$748$		0			0
$749$	30.4334	−	11.0782i	1.11201	−	0.404790i
$750$		0			0
$751$	20.9564	−	7.62751i	0.764710	−	0.278332i	0.0699281	−	0.997552i	$-0.477723\pi$
$751$	20.9564	−	7.62751i	0.764710	−	0.278332i	0.694782	+	0.719220i	$0.255501\pi$
$752$		0			0
$753$	−12.2157	+	24.8408i	−0.445164	+	0.905248i
$754$		0			0
$755$	8.09630			0.294655
$756$		0			0
$757$	−45.8090			−1.66495			−0.832477	−	0.554059i	$-0.813078\pi$
$757$	−45.8090			−1.66495			−0.832477	+	0.554059i	$0.813078\pi$
$758$		0			0
$759$	−11.9482	+	0.796519i	−0.433693	+	0.0289118i
$760$		0			0
$761$	−26.7755	+	9.74549i	−0.970611	+	0.353274i	−0.778183	−	0.628038i	$-0.783858\pi$
$761$	−26.7755	+	9.74549i	−0.970611	+	0.353274i	−0.192428	+	0.981311i	$0.561636\pi$
$762$		0			0
$763$	−37.0805	−	31.1117i	−1.34240	−	1.12632i
$764$		0			0
$765$	9.33040	−	4.88359i	0.337341	−	0.176567i
$766$		0			0
$767$	11.6394	+	4.23638i	0.420273	+	0.152967i
$768$		0			0
$769$	27.4378	−	9.98655i	0.989433	−	0.360124i	0.203932	−	0.978985i	$-0.434628\pi$
$769$	27.4378	−	9.98655i	0.989433	−	0.360124i	0.785501	+	0.618861i	$0.212406\pi$
$770$		0			0
$771$	2.11435	−	19.5071i	0.0761465	−	0.702532i
$772$		0			0
$773$	12.4991	+	21.6492i	0.449563	+	0.778666i	0.998358	−	0.0572913i	$-0.0182464\pi$
$773$	12.4991	+	21.6492i	0.449563	+	0.778666i	−0.548795	+	0.835957i	$0.684913\pi$
$774$		0			0
$775$	−12.5173	+	21.6806i	−0.449635	+	0.778791i
$776$		0			0
$777$	−24.6775	+	10.8924i	−0.885300	+	0.390763i
$778$		0			0
$779$	−0.797799	+	4.52454i	−0.0285841	+	0.162108i
$780$		0			0
$781$	−11.1785	+	9.37988i	−0.399998	+	0.335638i
$782$		0			0
$783$	−51.8339	−	7.80045i	−1.85239	−	0.278766i
$784$		0			0
$785$	4.15452	+	1.51212i	0.148281	+	0.0539700i
$786$		0			0
$787$	1.73257	−	0.630604i	0.0617595	−	0.0224786i	−0.310956	−	0.950424i	$-0.600649\pi$
$787$	1.73257	−	0.630604i	0.0617595	−	0.0224786i	0.372715	+	0.927946i	$0.378427\pi$
$788$		0			0
$789$	20.1670	−	19.3489i	0.717965	−	0.688839i
$790$		0			0
$791$	1.48001	+	0.538611i	0.0526230	+	0.0191508i
$792$		0			0
$793$	−8.80950			−0.312835
$794$		0			0
$795$	−9.41870	+	4.15688i	−0.334047	+	0.147429i
$796$		0			0
$797$	49.6051	−	18.0548i	1.75710	−	0.639533i	0.757197	−	0.653187i	$-0.226568\pi$
$797$	49.6051	−	18.0548i	1.75710	−	0.639533i	0.999907	+	0.0136531i	$0.00434605\pi$
$798$		0			0
$799$	−4.55592	−	25.8379i	−0.161177	−	0.914079i
$800$		0			0
$801$	21.1693	+	27.4612i	0.747980	+	0.970295i
$802$		0			0
$803$	−38.3829	−	13.9702i	−1.35450	−	0.492999i
$804$		0			0
$805$	−4.36771		0.000175435i	−0.153942		6.18328e-6i
$806$		0			0
$807$	−30.3514	+	2.02335i	−1.06842	+	0.0712254i
$808$		0			0
$809$	13.6876	−	23.7076i	0.481231	−	0.833516i	−0.518537	−	0.855055i	$-0.673523\pi$
$809$	13.6876	−	23.7076i	0.481231	−	0.833516i	0.999768	+	0.0215387i	$0.00685652\pi$
$810$		0			0
$811$	13.9976			0.491523			0.245762	−	0.969330i	$-0.420962\pi$
$811$	13.9976			0.491523			0.245762	+	0.969330i	$0.420962\pi$
$812$		0			0
$813$	−0.662044	+	1.34628i	−0.0232189	+	0.0472160i
$814$		0			0
$815$	6.58962	+	5.52934i	0.230824	+	0.193685i
$816$		0			0
$817$	−8.68542	−	3.16123i	−0.303864	−	0.110598i
$818$		0			0
$819$	18.6814	+	4.09706i	0.652782	+	0.143163i
$820$		0			0
$821$	−15.9552	+	13.3880i	−0.556839	+	0.467243i	−0.877249	−	0.480036i	$-0.840624\pi$
$821$	−15.9552	+	13.3880i	−0.556839	+	0.467243i	0.320410	+	0.947279i	$0.396179\pi$
$822$		0			0
$823$	−4.21899	+	23.9271i	−0.147065	+	0.834045i	0.818621	+	0.574333i	$0.194739\pi$
$823$	−4.21899	+	23.9271i	−0.147065	+	0.834045i	−0.965686	+	0.259712i	$0.916372\pi$
$824$		0			0
$825$	−23.9077	−	17.4889i	−0.832360	−	0.608885i
$826$		0			0
$827$	−19.3865	+	33.5784i	−0.674134	+	1.16763i	0.302588	+	0.953122i	$0.402149\pi$
$827$	−19.3865	+	33.5784i	−0.674134	+	1.16763i	−0.976721	+	0.214512i	$0.931184\pi$
$828$		0			0
$829$	9.56515			0.332211			0.166106	−	0.986108i	$-0.446881\pi$
$829$	9.56515			0.332211			0.166106	+	0.986108i	$0.446881\pi$
$830$		0			0
$831$	16.0724	−	15.4204i	0.557546	−	0.534928i
$832$		0			0
$833$	−4.08557	−	23.1595i	−0.141557	−	0.802431i
$834$		0			0
$835$	−2.07232	−	11.7527i	−0.0717154	−	0.406718i
$836$		0			0
$837$	−28.3976	+	17.3624i	−0.981563	+	0.600132i
$838$		0			0
$839$	13.7201	+	4.99370i	0.473669	+	0.172402i	0.567814	−	0.823157i	$-0.307789\pi$
$839$	13.7201	+	4.99370i	0.473669	+	0.172402i	−0.0941444	+	0.995559i	$0.530012\pi$
$840$		0			0
$841$	55.7397	+	46.7711i	1.92206	+	1.61280i
$842$		0			0
$843$	3.65861	−	3.51019i	0.126009	−	0.120897i
$844$		0			0
$845$	3.75843	−	6.50979i	0.129294	−	0.223944i
$846$		0			0
$847$	16.5150	−	13.8588i	0.567462	−	0.476196i
$848$		0			0
$849$	−37.7028	+	16.6399i	−1.29396	+	0.571078i
$850$		0			0
$851$	1.61491	−	9.15863i	0.0553585	−	0.313954i
$852$		0			0
$853$	−3.17248	−	17.9920i	−0.108624	−	0.616036i	−0.989711	−	0.143082i	$-0.954299\pi$
$853$	−3.17248	−	17.9920i	−0.108624	−	0.616036i	0.881087	−	0.472954i	$-0.156812\pi$
$854$		0			0
$855$	5.83814	+	3.70101i	0.199660	+	0.126572i
$856$		0			0
$857$	2.28520	+	12.9600i	0.0780609	+	0.442706i	0.998639	+	0.0521478i	$0.0166067\pi$
$857$	2.28520	+	12.9600i	0.0780609	+	0.442706i	−0.920578	+	0.390558i	$0.872282\pi$
$858$		0			0
$859$	−48.2104	+	17.5471i	−1.64492	+	0.598701i	−0.987889	−	0.155165i	$-0.950409\pi$
$859$	−48.2104	+	17.5471i	−1.64492	+	0.598701i	−0.657028	+	0.753866i	$0.728187\pi$
$860$		0			0
$861$	6.88920	−	6.61026i	0.234783	−	0.225277i
$862$		0			0
$863$	5.42579	+	9.39775i	0.184696	+	0.319903i	0.943474	−	0.331446i	$-0.107537\pi$
$863$	5.42579	+	9.39775i	0.184696	+	0.319903i	−0.758778	+	0.651349i	$0.774203\pi$
$864$		0			0
$865$	8.12483	−	14.0726i	0.276253	−	0.478484i
$866$		0			0
$867$	9.87352	−	0.658211i	0.335322	−	0.0223540i
$868$		0			0
$869$	−8.77170	+	49.7468i	−0.297560	+	1.68754i
$870$		0			0
$871$	−2.43782	−	13.8256i	−0.0826023	−	0.468461i
$872$		0			0
$873$	44.0061	+	9.65294i	1.48938	+	0.326702i
$874$		0			0
$875$	−18.8659	−	15.8291i	−0.637784	−	0.535120i
$876$		0			0
$877$	−35.4746	−	29.7667i	−1.19789	−	1.00515i	−0.999688	−	0.0249910i	$-0.992044\pi$
$877$	−35.4746	−	29.7667i	−1.19789	−	1.00515i	−0.198205	−	0.980161i	$-0.563511\pi$
$878$		0			0
$879$	5.32467	−	49.1257i	0.179597	−	1.65697i
$880$		0			0
$881$	−11.1094	+	19.2421i	−0.374286	+	0.648282i	−0.990220	−	0.139516i	$-0.955445\pi$
$881$	−11.1094	+	19.2421i	−0.374286	+	0.648282i	0.615934	+	0.787798i	$0.288779\pi$
$882$		0			0
$883$	−3.24883	−	5.62713i	−0.109332	−	0.189368i	0.806168	−	0.591687i	$-0.201538\pi$
$883$	−3.24883	−	5.62713i	−0.109332	−	0.189368i	−0.915500	+	0.402319i	$0.868204\pi$
$884$		0			0
$885$	−2.22132	−	9.03413i	−0.0746690	−	0.303679i
$886$		0			0
$887$	6.56052	−	37.2065i	0.220281	−	1.24927i	−0.651224	−	0.758886i	$-0.725744\pi$
$887$	6.56052	−	37.2065i	0.220281	−	1.24927i	0.871504	−	0.490388i	$-0.163145\pi$
$888$		0			0
$889$	13.3319	−	4.85304i	0.447139	−	0.162766i
$890$		0			0
$891$	−16.8033	−	35.6188i	−0.562931	−	1.19327i
$892$		0			0
$893$	13.1920	−	11.0694i	0.441455	−	0.370424i
$894$		0			0
$895$	−12.0312	−	10.0953i	−0.402157	−	0.337450i
$896$		0			0
$897$	−4.75804	+	4.56502i	−0.158866	+	0.152422i
$898$		0			0
$899$	64.6187			2.15515
$900$		0			0
$901$	19.1114			0.636693
$902$		0			0
$903$	10.6897	+	15.9583i	0.355731	+	0.531059i
$904$		0			0
$905$	14.3240	+	12.0193i	0.476146	+	0.399534i
$906$		0			0
$907$	−45.0350	−	16.3914i	−1.49536	−	0.544268i	−0.540508	−	0.841339i	$-0.681768\pi$
$907$	−45.0350	−	16.3914i	−1.49536	−	0.544268i	−0.954855	+	0.297071i	$0.903990\pi$
$908$		0			0
$909$	3.72877	+	0.817921i	0.123675	+	0.0271287i
$910$		0			0
$911$	31.2624	−	26.2322i	1.03577	−	0.869113i	0.0442419	−	0.999021i	$-0.485913\pi$
$911$	31.2624	−	26.2322i	1.03577	−	0.869113i	0.991526	+	0.129908i	$0.0414683\pi$
$912$		0			0
$913$	1.71990	+	1.44316i	0.0569202	+	0.0477617i
$914$		0			0
$915$	3.68217	+	5.49747i	0.121729	+	0.181741i
$916$		0			0
$917$	−45.7689	−	16.6564i	−1.51142	−	0.550044i
$918$		0			0
$919$	19.9537	+	34.5607i	0.658210	+	1.14005i	0.981079	+	0.193610i	$0.0620195\pi$
$919$	19.9537	+	34.5607i	0.658210	+	1.14005i	−0.322868	+	0.946444i	$0.604647\pi$
$920$		0			0
$921$	−13.1970	+	0.879770i	−0.434857	+	0.0289894i
$922$		0			0
$923$	−1.39531	+	7.91319i	−0.0459272	+	0.260466i
$924$		0			0
$925$	17.6228	−	14.7873i	0.579435	−	0.486204i
$926$		0			0
$927$	−2.21177	+	53.3921i	−0.0726441	+	1.75363i
$928$		0			0
$929$	−1.30270	+	1.09309i	−0.0427401	+	0.0358632i	−0.663907	−	0.747815i	$-0.731103\pi$
$929$	−1.30270	+	1.09309i	−0.0427401	+	0.0358632i	0.621167	+	0.783678i	$0.286659\pi$
$930$		0			0
$931$	11.8239	−	9.92306i	0.387513	−	0.325215i
$932$		0			0
$933$	3.17418	−	1.40090i	0.103918	−	0.0458635i
$934$		0			0
$935$	−7.68061	−	13.3032i	−0.251183	−	0.435062i
$936$		0			0
$937$	−3.49529	−	6.05403i	−0.114186	−	0.197776i	0.803268	−	0.595618i	$-0.203093\pi$
$937$	−3.49529	−	6.05403i	−0.114186	−	0.197776i	−0.917454	+	0.397841i	$0.869759\pi$
$938$		0			0
$939$	−52.2233	−	15.1585i	−1.70424	−	0.494679i
$940$		0			0
$941$	−27.6525	+	10.0647i	−0.901447	+	0.328100i	−0.750832	−	0.660493i	$-0.770347\pi$
$941$	−27.6525	+	10.0647i	−0.901447	+	0.328100i	−0.150614	+	0.988593i	$0.548125\pi$
$942$		0			0
$943$	0.571597	+	3.24169i	0.0186138	+	0.105564i
$944$		0			0
$945$	−5.25168	−	13.3704i	−0.170837	−	0.434939i
$946$		0			0
$947$	−2.69051	−	15.2587i	−0.0874300	−	0.495840i	−0.996806	−	0.0798644i	$-0.974551\pi$
$947$	−2.69051	−	15.2587i	−0.0874300	−	0.495840i	0.909376	−	0.415976i	$-0.136560\pi$
$948$		0			0
$949$	−21.1353	+	7.69262i	−0.686081	+	0.249713i
$950$		0			0
$951$	7.98097	+	32.4586i	0.258801	+	1.05254i
$952$		0			0
$953$	13.6001	+	23.5561i	0.440550	+	0.763056i	0.997730	−	0.0673360i	$-0.0214500\pi$
$953$	13.6001	+	23.5561i	0.440550	+	0.763056i	−0.557180	+	0.830392i	$0.688117\pi$
$954$		0			0
$955$	−9.25345	−	16.0274i	−0.299435	−	0.518636i
$956$		0			0
$957$	−8.23897	+	76.0133i	−0.266328	+	2.45716i
$958$		0			0
$959$	12.8719	+	22.2926i	0.415654	+	0.719867i
$960$		0			0
$961$	7.68524	−	6.44868i	0.247911	−	0.208022i
$962$		0			0
$963$	−36.3985	+	4.87461i	−1.17292	+	0.157082i
$964$		0			0
$965$	−0.169078	+	0.141873i	−0.00544280	+	0.00456705i
$966$		0			0
$967$	1.01131	−	5.73541i	0.0325214	−	0.184438i	−0.964220	−	0.265104i	$-0.914594\pi$
$967$	1.01131	−	5.73541i	0.0325214	−	0.184438i	0.996741	+	0.0806660i	$0.0257047\pi$
$968$		0			0
$969$	−7.14084	−	10.6612i	−0.229397	−	0.342489i
$970$		0			0
$971$	−11.8942	−	20.6013i	−0.381703	−	0.661129i	0.609603	−	0.792707i	$-0.291329\pi$
$971$	−11.8942	−	20.6013i	−0.381703	−	0.661129i	−0.991306	+	0.131578i	$0.957996\pi$
$972$		0			0
$973$	−32.6879	+	27.4307i	−1.04793	+	0.879387i
$974$		0			0
$975$	−16.2748	+	1.08495i	−0.521212	+	0.0347462i
$976$		0			0
$977$	23.0096	+	19.3073i	0.736142	+	0.617696i	0.931798	−	0.362976i	$-0.118239\pi$
$977$	23.0096	+	19.3073i	0.736142	+	0.617696i	−0.195657	+	0.980672i	$0.562684\pi$
$978$		0			0
$979$	38.7438	−	32.5099i	1.23826	−	1.03902i
$980$		0			0
$981$	33.5086	+	43.4681i	1.06985	+	1.38783i
$982$		0			0
$983$	55.9367	+	20.3593i	1.78410	+	0.649361i	0.999571	+	0.0292738i	$0.00931946\pi$
$983$	55.9367	+	20.3593i	1.78410	+	0.649361i	0.784533	+	0.620087i	$0.212903\pi$
$984$		0			0
$985$	13.2686	+	11.1337i	0.422772	+	0.354748i
$986$		0			0
$987$	−35.7079	+	2.38188i	−1.13660	+	0.0758162i
$988$		0			0
$989$	−6.62219			−0.210574
$990$		0			0
$991$	52.1406			1.65630			0.828150	−	0.560507i	$-0.189394\pi$
$991$	52.1406			1.65630			0.828150	+	0.560507i	$0.189394\pi$
$992$		0			0
$993$	11.9084	+	48.4313i	0.377901	+	1.53692i
$994$		0			0
$995$	0.961047	+	0.806414i	0.0304672	+	0.0255651i
$996$		0			0
$997$	2.45563	−	2.06052i	0.0777706	−	0.0652573i	−0.603074	−	0.797686i	$-0.706057\pi$
$997$	2.45563	−	2.06052i	0.0777706	−	0.0652573i	0.680844	+	0.732428i	$0.261613\pi$
$998$		0			0
$999$	29.9783	−	6.06746i	0.948473	−	0.191966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bp.a.193.17	✓	144
7.2	even	3		756.2.bq.a.625.1	yes	144
27.7	even	9		756.2.bq.a.277.1	yes	144
189.142	even	9	inner	756.2.bp.a.709.17	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.193.17	✓	144	1.1	even	1	trivial
756.2.bp.a.709.17	yes	144	189.142	even	9	inner
756.2.bq.a.277.1	yes	144	27.7	even	9
756.2.bq.a.625.1	yes	144	7.2	even	3

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.963882 + 1.43907i) q^{3} +(-0.981872 + 0.357372i) q^{5} +(0.459325 - 2.60557i) q^{7} +(-1.14186 + 2.77419i) q^{9} +O(q^{10})\)	\(q+(0.963882 + 1.43907i) q^{3} +(-0.981872 + 0.357372i) q^{5} +(0.459325 - 2.60557i) q^{7} +(-1.14186 + 2.77419i) q^{9} +(4.11203 + 1.49665i) q^{11} +(2.26426 - 0.824123i) q^{13} +(-1.46069 - 1.06852i) q^{15} +(1.67980 + 2.90949i) q^{17} +(-1.10258 + 1.90972i) q^{19} +(4.19235 - 1.85047i) q^{21} +(-0.274350 + 1.55592i) q^{23} +(-2.99386 + 2.51215i) q^{25} +(-5.09289 + 1.03077i) q^{27} +(9.47940 + 3.45022i) q^{29} +(6.01934 - 2.19086i) q^{31} +(1.80971 + 7.36010i) q^{33} +(0.480162 + 2.72249i) q^{35} -5.88632 q^{37} +(3.36845 + 2.46408i) q^{39} +(1.95781 - 0.712584i) q^{41} +(0.727841 + 4.12779i) q^{43} +(0.129742 - 3.13197i) q^{45} +(-7.33846 - 2.67098i) q^{47} +(-6.57804 - 2.39361i) q^{49} +(-2.56785 + 5.22176i) q^{51} +(2.84430 - 4.92648i) q^{53} -4.57235 q^{55} +(-3.81098 + 0.254056i) q^{57} +(3.93783 + 3.30423i) q^{59} +(-3.43555 - 1.25044i) q^{61} +(6.70388 + 4.24946i) q^{63} +(-1.92870 + 1.61837i) q^{65} +(1.01172 - 5.73775i) q^{67} +(-2.50352 + 1.10491i) q^{69} +(-1.66736 + 2.88795i) q^{71} -9.33431 q^{73} +(-6.50090 - 1.88697i) q^{75} +(5.78840 - 10.0267i) q^{77} +(2.00454 + 11.3683i) q^{79} +(-6.39230 - 6.33549i) q^{81} +(0.482130 + 0.175481i) q^{83} +(-2.68912 - 2.25644i) q^{85} +(4.17191 + 16.9671i) q^{87} +(5.77894 - 10.0094i) q^{89} +(-1.10728 - 6.27824i) q^{91} +(8.95475 + 6.55054i) q^{93} +(0.400109 - 2.26913i) q^{95} +(-2.60776 - 14.7893i) q^{97} +(-8.84737 + 9.69858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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