LMFDB - Embedded newform 990.2.bg.a.751.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(31,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 0, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,11,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			751.1
Character	$\chi$	$=$	990.751
Dual form			990.2.bg.a.961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.913545 + 0.406737i) q^{2} +(-1.73115 - 0.0557391i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.913545 - 0.406737i) q^{5} +(-1.55882 - 0.755044i) q^{6} +(-0.496763 + 0.105590i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.99379 + 0.192986i) q^{9} +1.00000 q^{10} +(-3.05356 + 1.29452i) q^{11} +(-1.11695 - 1.32379i) q^{12} +(-0.245329 - 2.33415i) q^{13} +(-0.496763 - 0.105590i) q^{14} +(-1.60416 + 0.653203i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(5.29765 + 3.84897i) q^{17} +(2.65647 + 1.39398i) q^{18} +(1.83102 + 5.63528i) q^{19} +(0.913545 + 0.406737i) q^{20} +(0.865858 - 0.155104i) q^{21} +(-3.31609 - 0.0593911i) q^{22} +(-0.795133 + 1.37721i) q^{23} +(-0.481945 - 1.66365i) q^{24} +(0.669131 - 0.743145i) q^{25} +(0.725266 - 2.23214i) q^{26} +(-5.17195 - 0.500959i) q^{27} +(-0.410868 - 0.298513i) q^{28} +(8.29637 - 1.76345i) q^{29} +(-1.73115 - 0.0557391i) q^{30} +(0.0231374 + 0.220138i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.35833 - 2.07081i) q^{33} +(3.27413 + 5.67095i) q^{34} +(-0.410868 + 0.298513i) q^{35} +(1.85982 + 2.35395i) q^{36} +(0.472527 - 1.45429i) q^{37} +(-0.619361 + 5.89283i) q^{38} +(0.294599 + 4.05445i) q^{39} +(0.669131 + 0.743145i) q^{40} +(2.58225 + 0.548874i) q^{41} +(0.854087 + 0.210482i) q^{42} +(3.92865 + 6.80462i) q^{43} +(-3.00525 - 1.40303i) q^{44} +(2.81345 - 1.04138i) q^{45} +(-1.28655 + 0.934735i) q^{46} +(-1.54407 + 1.71487i) q^{47} +(0.236389 - 1.71584i) q^{48} +(-6.15919 + 2.74225i) q^{49} +(0.913545 - 0.406737i) q^{50} +(-8.95650 - 6.95844i) q^{51} +(1.57046 - 1.74417i) q^{52} +(-7.86208 + 5.71214i) q^{53} +(-4.52105 - 2.56127i) q^{54} +(-2.26304 + 2.42460i) q^{55} +(-0.253930 - 0.439820i) q^{56} +(-2.85566 - 9.85760i) q^{57} +(8.29637 + 1.76345i) q^{58} +(3.93056 + 4.36533i) q^{59} +(-1.55882 - 0.755044i) q^{60} +(-1.49212 + 14.1966i) q^{61} +(-0.0684011 + 0.210517i) q^{62} +(-1.50758 + 0.220246i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.17350 - 2.03257i) q^{65} +(5.73736 + 0.287651i) q^{66} +(2.62010 - 4.53815i) q^{67} +(0.684479 + 6.51238i) q^{68} +(1.45326 - 2.33984i) q^{69} +(-0.496763 + 0.105590i) q^{70} +(7.01483 + 5.09657i) q^{71} +(0.741590 + 2.90690i) q^{72} +(2.54387 - 7.82923i) q^{73} +(1.02319 - 1.13636i) q^{74} +(-1.19979 + 1.24920i) q^{75} +(-2.96264 + 5.13145i) q^{76} +(1.38021 - 0.965495i) q^{77} +(-1.37996 + 3.82375i) q^{78} +(12.4757 + 5.55453i) q^{79} +(0.309017 + 0.951057i) q^{80} +(8.92551 + 1.15552i) q^{81} +(2.13576 + 1.55172i) q^{82} +(0.946408 - 9.00447i) q^{83} +(0.694637 + 0.539674i) q^{84} +(6.40516 + 1.36146i) q^{85} +(0.821311 + 7.81425i) q^{86} +(-14.4606 + 2.59037i) q^{87} +(-2.17476 - 2.50408i) q^{88} +10.3999 q^{89} +(2.99379 + 0.192986i) q^{90} +(0.368334 + 1.13362i) q^{91} +(-1.55552 + 0.330635i) q^{92} +(-0.0277841 - 0.382382i) q^{93} +(-2.10808 + 0.938578i) q^{94} +(3.96479 + 4.40335i) q^{95} +(0.913848 - 1.47135i) q^{96} +(-14.9964 - 6.67684i) q^{97} -6.74208 q^{98} +(-9.39153 + 3.28622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) $ 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$3$	−1.73115	−	0.0557391i	−0.999482	−	0.0321810i
$3$	−1.73115	−	0.0557391i	−0.999482	−	0.0321810i
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	0.913545	−	0.406737i	0.408550	−	0.181898i
$5$	0.913545	−	0.406737i	0.408550	−	0.181898i
$6$	−1.55882	−	0.755044i	−0.636384	−	0.308245i
$7$	−0.496763	+	0.105590i	−0.187759	+	0.0399093i	−0.300831	−	0.953677i	$-0.597264\pi$
$7$	−0.496763	+	0.105590i	−0.187759	+	0.0399093i	0.113073	+	0.993587i	$0.463931\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	2.99379	+	0.192986i	0.997929	+	0.0643287i
$10$	1.00000			0.316228
$11$	−3.05356	+	1.29452i	−0.920682	+	0.390312i
$11$	−3.05356	+	1.29452i	−0.920682	+	0.390312i
$12$	−1.11695	−	1.32379i	−0.322434	−	0.382147i
$13$	−0.245329	−	2.33415i	−0.0680421	−	0.647377i	−0.974393	−	0.224851i	$-0.927810\pi$
$13$	−0.245329	−	2.33415i	−0.0680421	−	0.647377i	0.906351	−	0.422526i	$-0.138856\pi$
$14$	−0.496763	−	0.105590i	−0.132765	−	0.0282202i
$15$	−1.60416	+	0.653203i	−0.414192	+	0.168656i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	5.29765	+	3.84897i	1.28487	+	0.933511i	0.999688	−	0.0249627i	$-0.00794671\pi$
$17$	5.29765	+	3.84897i	1.28487	+	0.933511i	0.285180	+	0.958474i	$0.407947\pi$
$18$	2.65647	+	1.39398i	0.626135	+	0.328565i
$19$	1.83102	+	5.63528i	0.420064	+	1.29282i	0.907643	+	0.419744i	$0.137880\pi$
$19$	1.83102	+	5.63528i	0.420064	+	1.29282i	−0.487579	+	0.873079i	$0.662120\pi$
$20$	0.913545	+	0.406737i	0.204275	+	0.0909491i
$21$	0.865858	−	0.155104i	0.188946	−	0.0338464i
$22$	−3.31609	−	0.0593911i	−0.706993	−	0.0126622i
$23$	−0.795133	+	1.37721i	−0.165797	+	0.287168i	−0.936938	−	0.349496i	$-0.886353\pi$
$23$	−0.795133	+	1.37721i	−0.165797	+	0.287168i	0.771141	+	0.636664i	$0.219686\pi$
$24$	−0.481945	−	1.66365i	−0.0983766	−	0.339591i
$25$	0.669131	−	0.743145i	0.133826	−	0.148629i
$26$	0.725266	−	2.23214i	0.142236	−	0.437758i
$27$	−5.17195	−	0.500959i	−0.995342	−	0.0964097i
$28$	−0.410868	−	0.298513i	−0.0776468	−	0.0564137i
$29$	8.29637	−	1.76345i	1.54060	−	0.327464i	0.642162	−	0.766569i	$-0.278038\pi$
$29$	8.29637	−	1.76345i	1.54060	−	0.327464i	0.898436	+	0.439105i	$0.144704\pi$
$30$	−1.73115	−	0.0557391i	−0.316064	−	0.0101765i
$31$	0.0231374	+	0.220138i	0.00415560	+	0.0395379i	0.996403	−	0.0847388i	$-0.0270056\pi$
$31$	0.0231374	+	0.220138i	0.00415560	+	0.0395379i	−0.992248	+	0.124277i	$0.960339\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	5.35833	−	2.07081i	0.932766	−	0.360482i
$34$	3.27413	+	5.67095i	0.561508	+	0.972560i
$35$	−0.410868	+	0.298513i	−0.0694494	+	0.0504579i
$36$	1.85982	+	2.35395i	0.309970	+	0.392325i
$37$	0.472527	−	1.45429i	0.0776829	−	0.239083i	−0.904672	−	0.426108i	$-0.859884\pi$
$37$	0.472527	−	1.45429i	0.0776829	−	0.239083i	0.982355	+	0.187025i	$0.0598844\pi$
$38$	−0.619361	+	5.89283i	−0.100474	+	0.955943i
$39$	0.294599	+	4.05445i	0.0471736	+	0.649232i
$40$	0.669131	+	0.743145i	0.105799	+	0.117502i
$41$	2.58225	+	0.548874i	0.403280	+	0.0857198i	0.405086	−	0.914279i	$-0.367242\pi$
$41$	2.58225	+	0.548874i	0.403280	+	0.0857198i	−0.00180611	+	0.999998i	$0.500575\pi$
$42$	0.854087	+	0.210482i	0.131789	+	0.0324781i
$43$	3.92865	+	6.80462i	0.599113	+	1.03769i	0.992952	+	0.118515i	$0.0378134\pi$
$43$	3.92865	+	6.80462i	0.599113	+	1.03769i	−0.393839	+	0.919179i	$0.628853\pi$
$44$	−3.00525	−	1.40303i	−0.453058	−	0.211515i
$45$	2.81345	−	1.04138i	0.419405	−	0.155240i
$46$	−1.28655	+	0.934735i	−0.189692	+	0.137819i
$47$	−1.54407	+	1.71487i	−0.225226	+	0.250139i	−0.845158	−	0.534517i	$-0.820494\pi$
$47$	−1.54407	+	1.71487i	−0.225226	+	0.250139i	0.619932	+	0.784656i	$0.287160\pi$
$48$	0.236389	−	1.71584i	0.0341198	−	0.247661i
$49$	−6.15919	+	2.74225i	−0.879885	+	0.391750i
$50$	0.913545	−	0.406737i	0.129195	−	0.0575212i
$51$	−8.95650	−	6.95844i	−1.25416	−	0.974376i
$52$	1.57046	−	1.74417i	0.217783	−	0.241872i
$53$	−7.86208	+	5.71214i	−1.07994	+	0.784622i	−0.977672	−	0.210135i	$-0.932610\pi$
$53$	−7.86208	+	5.71214i	−1.07994	+	0.784622i	−0.102267	+	0.994757i	$0.532610\pi$
$54$	−4.52105	−	2.56127i	−0.615237	−	0.348545i
$55$	−2.26304	+	2.42460i	−0.305148	+	0.326933i
$56$	−0.253930	−	0.439820i	−0.0339329	−	0.0587735i
$57$	−2.85566	−	9.85760i	−0.378242	−	1.30567i
$58$	8.29637	+	1.76345i	1.08937	+	0.231552i
$59$	3.93056	+	4.36533i	0.511716	+	0.568318i	0.942530	−	0.334123i	$-0.108440\pi$
$59$	3.93056	+	4.36533i	0.511716	+	0.568318i	−0.430814	+	0.902441i	$0.641773\pi$
$60$	−1.55882	−	0.755044i	−0.201242	−	0.0974757i
$61$	−1.49212	+	14.1966i	−0.191046	+	1.81768i	0.308308	+	0.951286i	$0.400237\pi$
$61$	−1.49212	+	14.1966i	−0.191046	+	1.81768i	−0.499355	+	0.866398i	$0.666429\pi$
$62$	−0.0684011	+	0.210517i	−0.00868694	+	0.0267357i
$63$	−1.50758	+	0.220246i	−0.189937	+	0.0277484i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.17350	−	2.03257i	−0.145555	−	0.252109i
$66$	5.73736	+	0.287651i	0.706220	+	0.0354074i
$67$	2.62010	−	4.53815i	0.320096	−	0.554423i	−0.660411	−	0.750904i	$-0.729618\pi$
$67$	2.62010	−	4.53815i	0.320096	−	0.554423i	0.980508	+	0.196481i	$0.0629513\pi$
$68$	0.684479	+	6.51238i	0.0830052	+	0.789742i
$69$	1.45326	−	2.33984i	0.174952	−	0.281684i
$70$	−0.496763	+	0.105590i	−0.0593745	+	0.0126204i
$71$	7.01483	+	5.09657i	0.832507	+	0.604852i	0.920267	−	0.391290i	$-0.127971\pi$
$71$	7.01483	+	5.09657i	0.832507	+	0.604852i	−0.0877606	+	0.996142i	$0.527971\pi$
$72$	0.741590	+	2.90690i	0.0873973	+	0.342581i
$73$	2.54387	−	7.82923i	0.297737	−	0.916342i	−0.684551	−	0.728965i	$-0.740002\pi$
$73$	2.54387	−	7.82923i	0.297737	−	0.916342i	0.982288	−	0.187376i	$-0.0599984\pi$
$74$	1.02319	−	1.13636i	0.118943	−	0.132100i
$75$	−1.19979	+	1.24920i	−0.138540	+	0.144245i
$76$	−2.96264	+	5.13145i	−0.339839	+	0.588618i
$77$	1.38021	−	0.965495i	0.157289	−	0.110028i
$78$	−1.37996	+	3.82375i	−0.156250	+	0.432954i
$79$	12.4757	+	5.55453i	1.40362	+	0.624934i	0.962195	−	0.272362i	$-0.0878048\pi$
$79$	12.4757	+	5.55453i	1.40362	+	0.624934i	0.441430	+	0.897296i	$0.354471\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	8.92551	+	1.15552i	0.991724	+	0.128391i
$82$	2.13576	+	1.55172i	0.235855	+	0.171359i
$83$	0.946408	−	9.00447i	0.103882	−	0.988369i	−0.811109	−	0.584895i	$-0.801136\pi$
$83$	0.946408	−	9.00447i	0.103882	−	0.988369i	0.914991	−	0.403474i	$-0.132197\pi$
$84$	0.694637	+	0.539674i	0.0757911	+	0.0588832i
$85$	6.40516	+	1.36146i	0.694737	+	0.147671i
$86$	0.821311	+	7.81425i	0.0885642	+	0.842632i
$87$	−14.4606	+	2.59037i	−1.55034	+	0.277717i
$88$	−2.17476	−	2.50408i	−0.231831	−	0.266936i
$89$	10.3999			1.10239			0.551194	−	0.834377i	$-0.314172\pi$
$89$	10.3999			1.10239			0.551194	+	0.834377i	$0.314172\pi$
$90$	2.99379	+	0.192986i	0.315573	+	0.0203425i
$91$	0.368334	+	1.13362i	0.0386119	+	0.118835i
$92$	−1.55552	+	0.330635i	−0.162174	+	0.0344711i
$93$	−0.0277841	−	0.382382i	−0.00288108	−	0.0396512i
$94$	−2.10808	+	0.938578i	−0.217432	+	0.0968069i
$95$	3.96479	+	4.40335i	0.406779	+	0.451774i
$96$	0.913848	−	1.47135i	0.0932693	−	0.150169i
$97$	−14.9964	−	6.67684i	−1.52266	−	0.677930i	−0.536523	−	0.843886i	$-0.680263\pi$
$97$	−14.9964	−	6.67684i	−1.52266	−	0.677930i	−0.986133	+	0.165955i	$0.946929\pi$
$98$	−6.74208			−0.681053
$99$	−9.39153	+	3.28622i	−0.943884	+	0.330278i
$100$	1.00000			0.100000
$101$	−6.04810	−	2.69279i	−0.601808	−	0.267942i	0.0831353	−	0.996538i	$-0.473507\pi$
$101$	−6.04810	−	2.69279i	−0.601808	−	0.267942i	−0.684944	+	0.728596i	$0.740173\pi$
$102$	−5.35192	−	9.99979i	−0.529919	−	0.990126i
$103$	−1.23396	−	1.37046i	−0.121586	−	0.135035i	0.679278	−	0.733881i	$-0.262293\pi$
$103$	−1.23396	−	1.37046i	−0.121586	−	0.135035i	−0.800864	+	0.598846i	$0.795626\pi$
$104$	2.14410	−	0.954614i	0.210246	−	0.0936076i
$105$	0.727915	−	0.493871i	0.0710372	−	0.0481968i
$106$	−9.50570	+	2.02050i	−0.923275	+	0.196248i
$107$	−3.84829	−	11.8438i	−0.372029	−	1.14499i	−0.945462	−	0.325734i	$-0.894389\pi$
$107$	−3.84829	−	11.8438i	−0.372029	−	1.14499i	0.573433	−	0.819252i	$-0.305611\pi$
$108$	−3.08842	−	4.17871i	−0.297184	−	0.402097i
$109$	−18.5602			−1.77775			−0.888874	−	0.458151i	$-0.848512\pi$
$109$	−18.5602			−1.77775			−0.888874	+	0.458151i	$0.848512\pi$
$110$	−3.05356	+	1.29452i	−0.291145	+	0.123428i
$111$	−0.899077	+	2.49126i	−0.0853366	+	0.236460i
$112$	−0.0530859	−	0.505079i	−0.00501615	−	0.0477255i
$113$	19.8943	+	4.22867i	1.87150	+	0.397800i	0.996299	−	0.0859557i	$-0.0273944\pi$
$113$	19.8943	+	4.22867i	1.87150	+	0.397800i	0.875203	+	0.483756i	$0.160728\pi$
$114$	1.40067	−	10.1669i	0.131185	−	0.952215i
$115$	−0.166228	+	1.58156i	−0.0155009	+	0.147481i
$116$	6.86186	+	4.98543i	0.637107	+	0.462886i
$117$	−0.284005	−	7.03530i	−0.0262562	−	0.650413i
$118$	1.81521	+	5.58663i	0.167103	+	0.514291i
$119$	−3.03809	−	1.35264i	−0.278501	−	0.123997i
$120$	−1.11695	−	1.32379i	−0.101963	−	0.120845i
$121$	7.64844	−	7.90578i	0.695312	−	0.718708i
$122$	−7.13738	+	12.3623i	−0.646188	+	1.11923i
$123$	−4.43968	−	1.09412i	−0.400312	−	0.0986533i
$124$	−0.148112	+	0.164495i	−0.0133009	+	0.0147721i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−1.46682	−	0.411983i	−0.130675	−	0.0367023i
$127$	−12.8997	−	9.37221i	−1.14467	−	0.831649i	−0.156904	−	0.987614i	$-0.550151\pi$
$127$	−12.8997	−	9.37221i	−1.14467	−	0.831649i	−0.987763	+	0.155965i	$0.950151\pi$
$128$	−0.978148	+	0.207912i	−0.0864569	+	0.0183770i
$129$	−6.42181	−	11.9988i	−0.565409	−	1.05644i
$130$	−0.245329	−	2.33415i	−0.0215168	−	0.204719i
$131$	−0.0182633	+	0.0316330i	−0.00159567	+	0.00276379i	−0.866822	−	0.498617i	$-0.833841\pi$
$131$	−0.0182633	+	0.0316330i	−0.00159567	+	0.00276379i	0.865226	+	0.501381i	$0.167175\pi$
$132$	5.12434	+	2.59638i	0.446016	+	0.225985i
$133$	−1.50461	−	2.60606i	−0.130466	−	0.225974i
$134$	4.23942	−	3.08012i	0.366230	−	0.266081i
$135$	−4.92857	+	1.64597i	−0.424184	+	0.141663i
$136$	−2.02352	+	6.22776i	−0.173516	+	0.534026i
$137$	1.97263	−	18.7684i	0.168533	−	1.60349i	−0.504189	−	0.863594i	$-0.668208\pi$
$137$	1.97263	−	18.7684i	0.168533	−	1.60349i	0.672722	−	0.739895i	$-0.265125\pi$
$138$	2.27932	−	1.54646i	0.194029	−	0.131643i
$139$	−11.9089	−	13.2262i	−1.01010	−	1.12183i	−0.992532	−	0.121988i	$-0.961073\pi$
$139$	−11.9089	−	13.2262i	−1.01010	−	1.12183i	−0.0175715	−	0.999846i	$-0.505593\pi$
$140$	−0.496763	−	0.105590i	−0.0419841	−	0.00892400i
$141$	2.76861	−	2.88263i	0.233159	−	0.242761i
$142$	4.33540	+	7.50914i	0.363819	+	0.630153i
$143$	3.77073	+	6.80988i	0.315325	+	0.569471i
$144$	−0.504865	+	2.95721i	−0.0420721	+	0.246434i
$145$	6.86186	−	4.98543i	0.569846	−	0.414017i
$146$	5.50837	−	6.11767i	0.455876	−	0.506302i
$147$	10.8154	−	4.40395i	0.892036	−	0.363232i
$148$	1.39693	−	0.621952i	0.114827	−	0.0511242i
$149$	−2.31582	+	1.03107i	−0.189719	+	0.0844684i	−0.499398	−	0.866373i	$-0.666445\pi$
$149$	−2.31582	+	1.03107i	−0.189719	+	0.0844684i	0.309678	+	0.950841i	$0.399779\pi$
$150$	−1.60416	+	0.653203i	−0.130979	+	0.0533338i
$151$	−6.07753	+	6.74978i	−0.494583	+	0.549290i	−0.937823	−	0.347113i	$-0.887162\pi$
$151$	−6.07753	+	6.74978i	−0.494583	+	0.549290i	0.443241	+	0.896403i	$0.353829\pi$
$152$	−4.79366	+	3.48280i	−0.388817	+	0.282492i
$153$	15.1172	+	12.5454i	1.22216	+	1.01423i
$154$	1.65358	−	0.320644i	0.133250	−	0.0258382i
$155$	0.110675	+	0.191695i	0.00888965	+	0.0153973i
$156$	−2.81592	+	2.93189i	−0.225454	+	0.234739i
$157$	−9.37792	−	1.99334i	−0.748440	−	0.159086i	−0.182126	−	0.983275i	$-0.558298\pi$
$157$	−9.37792	−	1.99334i	−0.748440	−	0.159086i	−0.566314	+	0.824189i	$0.691631\pi$
$158$	9.13788	+	10.1486i	0.726970	+	0.807382i
$159$	13.9289	−	9.45036i	1.10463	−	0.749462i
$160$	−0.104528	+	0.994522i	−0.00826370	+	0.0786239i
$161$	0.249573	−	0.768106i	0.0196691	−	0.0605352i
$162$	7.68387	+	4.68595i	0.603702	+	0.368163i
$163$	−5.11356	+	3.71522i	−0.400525	+	0.290999i	−0.769755	−	0.638340i	$-0.779622\pi$
$163$	−5.11356	+	3.71522i	−0.400525	+	0.290999i	0.369230	+	0.929338i	$0.379622\pi$
$164$	1.31997	+	2.28626i	0.103072	+	0.178527i
$165$	4.05281	−	4.07121i	0.315511	−	0.316943i
$166$	4.52703	−	7.84105i	0.351366	−	0.608584i
$167$	−1.20700	−	11.4838i	−0.0934002	−	0.888644i	−0.936448	−	0.350805i	$-0.885908\pi$
$167$	−1.20700	−	11.4838i	−0.0934002	−	0.888644i	0.843048	−	0.537838i	$-0.180759\pi$
$168$	0.415077	+	0.775551i	0.0320239	+	0.0598350i
$169$	7.32784	−	1.55758i	0.563680	−	0.119814i
$170$	5.29765	+	3.84897i	0.406311	+	0.295202i
$171$	4.39414	+	17.2242i	0.336028	+	1.31717i
$172$	−2.42804	+	7.47273i	−0.185136	+	0.569790i
$173$	6.67148	−	7.40943i	0.507223	−	0.563328i	−0.434087	−	0.900871i	$-0.642929\pi$
$173$	6.67148	−	7.40943i	0.507223	−	0.563328i	0.941310	+	0.337542i	$0.109596\pi$
$174$	−14.2640	−	3.51523i	−1.08135	−	0.266489i
$175$	−0.253930	+	0.439820i	−0.0191953	+	0.0332473i
$176$	−0.968245	−	3.17214i	−0.0729842	−	0.239109i
$177$	−6.56109	−	7.77615i	−0.493162	−	0.584491i
$178$	9.50080	+	4.23003i	0.712115	+	0.317054i
$179$	1.98308	+	6.10330i	0.148222	+	0.456182i	0.997411	−	0.0719075i	$-0.0229086\pi$
$179$	1.98308	+	6.10330i	0.148222	+	0.456182i	−0.849189	+	0.528089i	$0.822909\pi$
$180$	2.65647	+	1.39398i	0.198001	+	0.103901i
$181$	−1.89912	−	1.37979i	−0.141160	−	0.102559i	0.514964	−	0.857212i	$-0.327805\pi$
$181$	−1.89912	−	1.37979i	−0.141160	−	0.102559i	−0.656124	+	0.754653i	$0.727805\pi$
$182$	−0.124593	+	1.18542i	−0.00923546	+	0.0878695i
$183$	3.37439	−	24.4933i	0.249442	−	1.81059i
$184$	−1.55552	−	0.330635i	−0.114674	−	0.0243747i
$185$	−0.159837	−	1.52075i	−0.0117515	−	0.111808i
$186$	0.130147	−	0.360624i	0.00954282	−	0.0264423i
$187$	−21.1592	−	4.89513i	−1.54732	−	0.357967i
$188$	−2.30758			−0.168298
$189$	2.62213	−	0.297249i	0.190732	−	0.0216217i
$190$	1.83102	+	5.63528i	0.132836	+	0.408827i
$191$	19.7440	−	4.19672i	1.42863	−	0.303664i	0.572276	−	0.820061i	$-0.306060\pi$
$191$	19.7440	−	4.19672i	1.42863	−	0.303664i	0.856349	+	0.516397i	$0.172727\pi$
$192$	1.43330	−	0.972453i	0.103439	−	0.0701807i
$193$	7.71907	−	3.43675i	0.555631	−	0.247383i	−0.109657	−	0.993969i	$-0.534975\pi$
$193$	7.71907	−	3.43675i	0.555631	−	0.247383i	0.665288	+	0.746587i	$0.268309\pi$
$194$	−10.9842	−	12.1992i	−0.788620	−	0.875851i
$195$	1.91822	+	3.58410i	0.137367	+	0.256663i
$196$	−6.15919	−	2.74225i	−0.439942	−	0.195875i
$197$	−9.97957			−0.711015			−0.355507	−	0.934673i	$-0.615692\pi$
$197$	−9.97957			−0.711015			−0.355507	+	0.934673i	$0.615692\pi$
$198$	−9.91621	−	0.817764i	−0.704715	−	0.0581159i
$199$	−9.26656			−0.656889			−0.328445	−	0.944523i	$-0.606524\pi$
$199$	−9.26656			−0.656889			−0.328445	+	0.944523i	$0.606524\pi$
$200$	0.913545	+	0.406737i	0.0645974	+	0.0287606i
$201$	−4.78875	+	7.71019i	−0.337773	+	0.543835i
$202$	−4.42996	−	4.91997i	−0.311691	−	0.346168i
$203$	−3.93513	+	1.75203i	−0.276192	+	0.122969i
$204$	−0.821943	−	11.3121i	−0.0575476	−	0.792004i
$205$	2.58225	−	0.548874i	0.180352	−	0.0383351i
$206$	−0.569868	−	1.75387i	−0.0397046	−	0.122198i
$207$	−2.64624	+	3.96963i	−0.183927	+	0.275908i
$208$	2.34701			0.162736
$209$	−12.8861	−	14.8374i	−0.891350	−	1.02632i
$210$	0.865858	−	0.155104i	0.0597499	−	0.0107032i
$211$	−2.91023	−	27.6890i	−0.200349	−	1.90619i	−0.384222	−	0.923241i	$-0.625530\pi$
$211$	−2.91023	−	27.6890i	−0.200349	−	1.90619i	0.183874	−	0.982950i	$-0.441136\pi$
$212$	−9.50570	−	2.02050i	−0.652854	−	0.138768i
$213$	−11.8597	−	9.21395i	−0.812611	−	0.631329i
$214$	1.30173	−	12.3851i	0.0889843	−	0.846629i
$215$	6.35668	+	4.61840i	0.433522	+	0.314972i
$216$	−1.12178	−	5.07362i	−0.0763274	−	0.345216i
$217$	−0.0347382	−	0.106913i	−0.00235818	−	0.00725774i
$218$	−16.9556	−	7.54913i	−1.14838	−	0.511292i
$219$	−4.84022	+	13.4118i	−0.327072	+	0.906286i
$220$	−3.31609	−	0.0593911i	−0.223571	−	0.00400415i
$221$	7.68440	−	13.3098i	0.516909	−	0.895312i
$222$	−1.83463	+	1.91019i	−0.123132	+	0.128203i
$223$	−5.08909	+	5.65201i	−0.340791	+	0.378486i	−0.889041	−	0.457828i	$-0.848628\pi$
$223$	−5.08909	+	5.65201i	−0.340791	+	0.378486i	0.548250	+	0.836314i	$0.315294\pi$
$224$	0.156938	−	0.483004i	0.0104858	−	0.0322721i
$225$	2.14665	−	2.09568i	0.143110	−	0.139712i
$226$	16.4544	+	11.9548i	1.09453	+	0.795224i
$227$	12.9697	−	2.75680i	0.860832	−	0.182976i	0.243715	−	0.969847i	$-0.421634\pi$
$227$	12.9697	−	2.75680i	0.860832	−	0.182976i	0.617117	+	0.786871i	$0.288300\pi$
$228$	5.41482	−	8.71820i	0.358605	−	0.577377i
$229$	1.30562	+	12.4221i	0.0862778	+	0.820878i	0.949016	+	0.315228i	$0.102081\pi$
$229$	1.30562	+	12.4221i	0.0862778	+	0.820878i	−0.862738	+	0.505651i	$0.831252\pi$
$230$	−0.795133	+	1.37721i	−0.0524295	+	0.0908106i
$231$	−2.44316	+	1.59449i	−0.160748	+	0.104910i
$232$	4.24086	+	7.34539i	0.278426	+	0.482248i
$233$	−7.08965	+	5.15093i	−0.464458	+	0.337449i	−0.795278	−	0.606245i	$-0.792675\pi$
$233$	−7.08965	+	5.15093i	−0.464458	+	0.337449i	0.330819	+	0.943694i	$0.392675\pi$
$234$	2.60206	−	6.54258i	0.170102	−	0.427702i
$235$	−0.713082	+	2.19464i	−0.0465163	+	0.143163i
$236$	−0.614014	+	5.84196i	−0.0399689	+	0.380279i
$237$	−21.2877	−	10.3111i	−1.38279	−	0.669780i
$238$	−2.22526	−	2.47140i	−0.144242	−	0.160197i
$239$	9.16546	+	1.94818i	0.592865	+	0.126017i	0.494567	−	0.869140i	$-0.335327\pi$
$239$	9.16546	+	1.94818i	0.592865	+	0.126017i	0.0982981	+	0.995157i	$0.468660\pi$
$240$	−0.481945	−	1.66365i	−0.0311094	−	0.107388i
$241$	−4.71451	−	8.16576i	−0.303688	−	0.526003i	0.673280	−	0.739387i	$-0.264885\pi$
$241$	−4.71451	−	8.16576i	−0.303688	−	0.526003i	−0.976968	+	0.213384i	$0.931551\pi$
$242$	10.2028	−	4.11139i	0.655859	−	0.264290i
$243$	−15.3870	−	2.49788i	−0.987078	−	0.160239i
$244$	−11.5485	+	8.39050i	−0.739319	+	0.537147i
$245$	−4.51133	+	5.01034i	−0.288218	+	0.320099i
$246$	−3.61083	−	2.80531i	−0.230218	−	0.178860i
$247$	12.7044	−	5.65637i	0.808362	−	0.359906i
$248$	−0.202214	+	0.0900313i	−0.0128406	+	0.00571700i
$249$	−2.14028	+	15.5354i	−0.135635	+	0.984514i
$250$	0.669131	−	0.743145i	0.0423195	−	0.0470006i
$251$	5.10232	−	3.70705i	0.322055	−	0.233987i	−0.414997	−	0.909823i	$-0.636217\pi$
$251$	5.10232	−	3.70705i	0.322055	−	0.233987i	0.737052	+	0.675836i	$0.236217\pi$
$252$	−1.17244	−	0.972976i	−0.0738569	−	0.0612917i
$253$	0.645158	−	5.23471i	0.0405608	−	0.329104i
$254$	−7.97248	−	13.8087i	−0.500238	−	0.866437i
$255$	−11.0124	−	2.71391i	−0.689625	−	0.169952i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	10.2281	+	11.3594i	0.638009	+	0.708580i	0.972260	−	0.233904i	$-0.0751501\pi$
$257$	10.2281	+	11.3594i	0.638009	+	0.708580i	−0.334251	+	0.942484i	$0.608483\pi$
$258$	−0.986256	−	13.5734i	−0.0614016	−	0.845046i
$259$	−0.0811752	+	0.772330i	−0.00504398	+	0.0479903i
$260$	0.725266	−	2.23214i	0.0449791	−	0.138431i
$261$	25.1779	−	3.67831i	1.55847	−	0.227681i
$262$	−0.0295507	+	0.0214698i	−0.00182565	+	0.00132641i
$263$	3.63305	+	6.29263i	0.224024	+	0.388020i	0.956026	−	0.293282i	$-0.0947474\pi$
$263$	3.63305	+	6.29263i	0.224024	+	0.388020i	−0.732002	+	0.681302i	$0.761414\pi$
$264$	3.62527	+	4.45616i	0.223120	+	0.274258i
$265$	−4.85903	+	8.41609i	−0.298488	+	0.516996i
$266$	−0.314549	−	2.99274i	−0.0192863	−	0.183497i
$267$	−18.0039	−	0.579682i	−1.10182	−	0.0354760i
$268$	5.12569	−	1.08950i	0.313102	−	0.0665518i
$269$	2.47016	+	1.79468i	0.150608	+	0.109423i	0.660538	−	0.750793i	$-0.270328\pi$
$269$	2.47016	+	1.79468i	0.150608	+	0.109423i	−0.509929	+	0.860216i	$0.670328\pi$
$270$	−5.17195	−	0.500959i	−0.314755	−	0.0304874i
$271$	−6.61004	+	20.3436i	−0.401532	+	1.23579i	0.522225	+	0.852808i	$0.325102\pi$
$271$	−6.61004	+	20.3436i	−0.401532	+	1.23579i	−0.923757	+	0.382979i	$0.874898\pi$
$272$	−4.38164	+	4.86630i	−0.265676	+	0.295063i
$273$	−0.574456	−	1.98299i	−0.0347677	−	0.120016i
$274$	9.43587	−	16.3434i	0.570042	−	0.987341i
$275$	−1.08121	+	3.13544i	−0.0651996	+	0.189074i
$276$	2.71127	−	0.485677i	0.163199	−	0.0292343i
$277$	27.1035	+	12.0673i	1.62849	+	0.725051i	0.998663	−	0.0516842i	$-0.0164589\pi$
$277$	27.1035	+	12.0673i	1.62849	+	0.725051i	0.629827	+	0.776735i	$0.283126\pi$
$278$	−5.49977	−	16.9266i	−0.329854	−	1.01519i
$279$	0.0267850	+	0.663511i	0.00160357	+	0.0397234i
$280$	−0.410868	−	0.298513i	−0.0245541	−	0.0178396i
$281$	−0.728545	+	6.93164i	−0.0434614	+	0.413507i	0.951063	+	0.308998i	$0.0999937\pi$
$281$	−0.728545	+	6.93164i	−0.0434614	+	0.413507i	−0.994524	+	0.104509i	$0.966673\pi$
$282$	3.70173	−	1.50732i	0.220435	−	0.0897596i
$283$	−4.17251	−	0.886894i	−0.248030	−	0.0527204i	0.0822189	−	0.996614i	$-0.473799\pi$
$283$	−4.17251	−	0.886894i	−0.248030	−	0.0527204i	−0.330249	+	0.943894i	$0.607133\pi$
$284$	0.906346	+	8.62330i	0.0537817	+	0.511699i
$285$	−6.61823	−	7.84387i	−0.392030	−	0.464631i
$286$	0.674907	+	7.75483i	0.0399081	+	0.458553i
$287$	−1.34072			−0.0791403
$288$	−1.66402	+	2.49620i	−0.0980535	+	0.147090i
$289$	7.99724	+	24.6130i	0.470426	+	1.44782i
$290$	8.29637	−	1.76345i	0.487180	−	0.103553i
$291$	25.5890	+	12.3945i	1.50005	+	0.726580i
$292$	7.52043	−	3.34831i	0.440100	−	0.195945i
$293$	−6.42472	−	7.13537i	−0.375336	−	0.416853i	0.525650	−	0.850701i	$-0.323822\pi$
$293$	−6.42472	−	7.13537i	−0.375336	−	0.416853i	−0.900986	+	0.433848i	$0.857155\pi$
$294$	11.6716	+	0.375797i	0.680700	+	0.0219170i
$295$	5.36629	+	2.38923i	0.312437	+	0.139106i
$296$	1.52913			0.0888788
$297$	16.4413	−	5.16548i	0.954024	−	0.299732i
$298$	−2.53498			−0.146847
$299$	3.40969	+	1.51809i	0.197187	+	0.0877935i
$300$	−1.73115	−	0.0557391i	−0.0999482	−	0.00321810i
$301$	−2.67011	−	2.96545i	−0.153902	−	0.170926i
$302$	−8.29749	+	3.69428i	−0.477467	+	0.212582i
$303$	10.3201	+	4.99875i	0.592874	+	0.287170i
$304$	−5.79581	+	1.23194i	−0.332412	+	0.0706564i
$305$	4.41115	+	13.5761i	0.252581	+	0.777366i
$306$	8.70762	+	17.6095i	0.497781	+	1.00667i
$307$	−15.6455			−0.892937			−0.446468	−	0.894799i	$-0.647318\pi$
$307$	−15.6455			−0.892937			−0.446468	+	0.894799i	$0.647318\pi$
$308$	1.64104	+	0.379650i	0.0935070	+	0.0216326i
$309$	2.05979	+	2.44125i	0.117178	+	0.138878i
$310$	0.0231374	+	0.220138i	0.00131412	+	0.0125030i
$311$	−23.4660	−	4.98785i	−1.33063	−	0.282835i	−0.512908	−	0.858443i	$-0.671432\pi$
$311$	−23.4660	−	4.98785i	−1.33063	−	0.282835i	−0.817725	+	0.575609i	$0.804765\pi$
$312$	−3.76497	+	1.53307i	−0.213150	+	0.0867932i
$313$	2.16413	−	20.5904i	0.122324	−	1.16384i	−0.745340	−	0.666685i	$-0.767713\pi$
$313$	2.16413	−	20.5904i	0.122324	−	1.16384i	0.867664	−	0.497151i	$-0.165621\pi$
$314$	−7.75640	−	5.63535i	−0.437719	−	0.318021i
$315$	−1.28766	+	0.814393i	−0.0725514	+	0.0458858i
$316$	4.22004	+	12.9880i	0.237396	+	0.730629i
$317$	9.87195	+	4.39528i	0.554464	+	0.246863i	0.664788	−	0.747032i	$-0.268522\pi$
$317$	9.87195	+	4.39528i	0.554464	+	0.246863i	−0.110324	+	0.993896i	$0.535189\pi$
$318$	16.5685	−	2.96796i	0.929113	−	0.166435i
$319$	−23.0506	+	16.1246i	−1.29059	+	0.902805i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	6.00182	+	20.7180i	0.334989	+	1.15637i
$322$	0.540413	−	0.600189i	0.0301160	−	0.0334472i
$323$	−11.9899	+	36.9013i	−0.667139	+	2.05324i
$324$	5.11362	+	7.40614i	0.284090	+	0.411452i
$325$	−1.89877	−	1.37954i	−0.105325	−	0.0765230i
$326$	−6.18259	+	1.31415i	−0.342422	+	0.0727840i
$327$	32.1306	+	1.03453i	1.77683	+	0.0572097i
$328$	0.275949	+	2.62548i	0.0152367	+	0.144968i
$329$	0.585965	−	1.01492i	0.0323053	−	0.0559544i
$330$	5.35833	−	2.07081i	0.294967	−	0.113994i
$331$	−2.50934	−	4.34631i	−0.137926	−	0.238895i	0.788785	−	0.614669i	$-0.210710\pi$
$331$	−2.50934	−	4.34631i	−0.137926	−	0.238895i	−0.926711	+	0.375774i	$0.877377\pi$
$332$	7.32489	−	5.32185i	0.402006	−	0.292074i
$333$	1.69530	−	4.26263i	0.0929019	−	0.233591i
$334$	3.56824	−	10.9819i	0.195245	−	0.600903i
$335$	0.547751	−	5.21150i	0.0299268	−	0.284735i
$336$	0.0637472	+	0.877328i	0.00347770	+	0.0478622i
$337$	−1.87894	−	2.08678i	−0.102353	−	0.113674i	0.689792	−	0.724008i	$-0.257702\pi$
$337$	−1.87894	−	2.08678i	−0.102353	−	0.113674i	−0.792144	+	0.610334i	$0.791035\pi$
$338$	7.32784	+	1.55758i	0.398582	+	0.0847212i
$339$	−34.2045	−	8.42937i	−1.85773	−	0.457821i
$340$	3.27413	+	5.67095i	0.177564	+	0.307551i
$341$	−0.355624	−	0.642252i	−0.0192581	−	0.0347799i
$342$	−2.99147	+	17.5223i	−0.161760	+	0.947500i
$343$	5.64618	−	4.10219i	0.304865	−	0.221497i
$344$	−5.25756	+	5.83911i	−0.283468	+	0.314824i
$345$	0.375921	−	2.72865i	0.0202389	−	0.146906i
$346$	9.10839	−	4.05531i	0.489670	−	0.218015i
$347$	20.0138	−	8.91073i	1.07440	−	0.478353i	0.208217	−	0.978083i	$-0.433234\pi$
$347$	20.0138	−	8.91073i	1.07440	−	0.478353i	0.866182	+	0.499729i	$0.166567\pi$
$348$	−11.6010	−	9.01302i	−0.621881	−	0.483149i
$349$	−8.63568	+	9.59090i	−0.462258	+	0.513389i	−0.928533	−	0.371251i	$-0.878929\pi$
$349$	−8.63568	+	9.59090i	−0.462258	+	0.513389i	0.466275	+	0.884640i	$0.345596\pi$
$350$	−0.410868	+	0.298513i	−0.0219618	+	0.0159562i
$351$	0.0995146	+	12.1950i	0.00531169	+	0.650921i
$352$	0.405692	−	3.29172i	0.0216234	−	0.175449i
$353$	4.94852	+	8.57108i	0.263383	+	0.456193i	0.967139	−	0.254249i	$-0.0818284\pi$
$353$	4.94852	+	8.57108i	0.263383	+	0.456193i	−0.703756	+	0.710442i	$0.748495\pi$
$354$	−2.83101	−	9.77250i	−0.150466	−	0.519403i
$355$	8.48133	+	1.80276i	0.450142	+	0.0956806i
$356$	6.95890	+	7.72864i	0.368821	+	0.409617i
$357$	5.18400	+	2.51097i	0.274366	+	0.132895i
$358$	−0.670799	+	6.38223i	−0.0354529	+	0.337311i
$359$	7.53542	−	23.1916i	0.397704	−	1.22401i	−0.529131	−	0.848540i	$-0.677482\pi$
$359$	7.53542	−	23.1916i	0.397704	−	1.22401i	0.926835	−	0.375468i	$-0.122518\pi$
$360$	1.85982	+	2.35395i	0.0980210	+	0.124064i
$361$	−13.0325	+	9.46866i	−0.685921	+	0.498351i
$362$	−1.17372	−	2.03294i	−0.0616893	−	0.106849i
$363$	−13.6813	+	13.2598i	−0.718081	+	0.695960i
$364$	−0.595977	+	1.03226i	−0.0312377	+	0.0541052i
$365$	−0.860493	−	8.18704i	−0.0450402	−	0.428529i
$366$	13.0450	−	21.0032i	0.681872	−	1.09786i
$367$	−12.8547	+	2.73234i	−0.671008	+	0.142627i	−0.530803	−	0.847495i	$-0.678110\pi$
$367$	−12.8547	+	2.73234i	−0.671008	+	0.142627i	−0.140205	+	0.990122i	$0.544776\pi$
$368$	−1.28655	−	0.934735i	−0.0670662	−	0.0487265i
$369$	7.62478	+	2.14155i	0.396930	+	0.111485i
$370$	0.472527	−	1.45429i	0.0245655	−	0.0756048i
$371$	3.30244	−	3.66774i	0.171454	−	0.190419i
$372$	0.265574	−	0.276511i	0.0137694	−	0.0143364i
$373$	−12.7103	+	22.0149i	−0.658116	+	1.13989i	0.322987	+	0.946403i	$0.395313\pi$
$373$	−12.7103	+	22.0149i	−0.658116	+	1.13989i	−0.981103	+	0.193487i	$0.938020\pi$
$374$	−17.3389	−	13.0782i	−0.896573	−	0.676256i
$375$	−0.587967	+	1.62920i	−0.0303625	+	0.0841316i
$376$	−2.10808	−	0.938578i	−0.108716	−	0.0484034i
$377$	−6.15150	−	18.9324i	−0.316818	−	0.975067i
$378$	2.51634	+	0.794965i	0.129426	+	0.0408886i
$379$	9.78131	+	7.10653i	0.502432	+	0.365038i	0.809945	−	0.586506i	$-0.199497\pi$
$379$	9.78131	+	7.10653i	0.502432	+	0.365038i	−0.307513	+	0.951544i	$0.599497\pi$
$380$	−0.619361	+	5.89283i	−0.0317726	+	0.302296i
$381$	21.8090	+	16.9438i	1.11731	+	0.868055i
$382$	19.7440	+	4.19672i	1.01019	+	0.214723i
$383$	2.11902	+	20.1611i	0.108277	+	1.03018i	0.904876	+	0.425676i	$0.139964\pi$
$383$	2.11902	+	20.1611i	0.108277	+	1.03018i	−0.796599	+	0.604508i	$0.793370\pi$
$384$	1.70491	−	0.305406i	0.0870035	−	0.0155852i
$385$	0.868178	−	1.44340i	0.0442465	−	0.0735627i
$386$	8.44958			0.430072
$387$	10.4483	+	21.1297i	0.531119	+	1.07409i
$388$	−5.07271	−	15.6122i	−0.257528	−	0.792589i
$389$	22.1028	−	4.69810i	1.12066	−	0.238203i	0.389912	−	0.920852i	$-0.372506\pi$
$389$	22.1028	−	4.69810i	1.12066	−	0.238203i	0.730746	+	0.682649i	$0.239172\pi$
$390$	0.294599	+	4.05445i	0.0149176	+	0.205305i
$391$	−9.51318	+	4.23554i	−0.481102	+	0.214200i
$392$	−4.51133	−	5.01034i	−0.227857	−	0.253060i
$393$	0.0333798	−	0.0537436i	0.00168379	−	0.00271101i
$394$	−9.11679	−	4.05906i	−0.459297	−	0.204492i
$395$	13.6563			0.687125
$396$	−8.72630	−	4.78035i	−0.438513	−	0.240222i
$397$	−31.7559			−1.59378			−0.796892	−	0.604122i	$-0.793524\pi$
$397$	−31.7559			−1.59378			−0.796892	+	0.604122i	$0.793524\pi$
$398$	−8.46542	−	3.76905i	−0.424333	−	0.188925i
$399$	2.45945	+	4.59536i	0.123127	+	0.230056i
$400$	0.669131	+	0.743145i	0.0334565	+	0.0371572i
$401$	−4.24494	+	1.88997i	−0.211982	+	0.0943806i	−0.509981	−	0.860186i	$-0.670348\pi$
$401$	−4.24494	+	1.88997i	−0.211982	+	0.0943806i	0.297999	+	0.954566i	$0.403681\pi$
$402$	−7.51076	+	5.09585i	−0.374603	+	0.254158i
$403$	0.508159	−	0.108013i	0.0253132	−	0.00538049i
$404$	−2.04584	−	6.29644i	−0.101784	−	0.313260i
$405$	8.62385	−	2.57472i	0.428523	−	0.127939i
$406$	−4.30753			−0.213779
$407$	0.439717	+	5.05245i	0.0217959	+	0.250440i
$408$	3.85016	−	10.6684i	0.190611	−	0.528165i
$409$	0.991678	+	9.43518i	0.0490353	+	0.466540i	0.991295	+	0.131657i	$0.0420299\pi$
$409$	0.991678	+	9.43518i	0.0490353	+	0.466540i	−0.942260	+	0.334882i	$0.891303\pi$
$410$	2.58225	+	0.548874i	0.127528	+	0.0271070i
$411$	−4.46106	+	32.3810i	−0.220048	+	1.59723i
$412$	0.192764	−	1.83403i	0.00949681	−	0.0903561i
$413$	−2.41349	−	1.75351i	−0.118760	−	0.0862844i
$414$	−4.03206	+	2.55011i	−0.198165	+	0.125331i
$415$	−2.79786	−	8.61093i	−0.137342	−	0.422694i
$416$	2.14410	+	0.954614i	0.105123	+	0.0468038i
$417$	19.8790	+	23.5604i	0.973478	+	1.15376i
$418$	−5.73713	−	18.7959i	−0.280612	−	0.919336i
$419$	4.58994	−	7.95002i	0.224233	−	0.388384i	−0.731856	−	0.681460i	$-0.761346\pi$
$419$	4.58994	−	7.95002i	0.224233	−	0.388384i	0.956089	+	0.293076i	$0.0946789\pi$
$420$	0.854087	+	0.210482i	0.0416752	+	0.0102705i
$421$	14.5515	−	16.1611i	0.709196	−	0.787642i	−0.275616	−	0.961268i	$-0.588882\pi$
$421$	14.5515	−	16.1611i	0.709196	−	0.787642i	0.984812	+	0.173626i	$0.0555484\pi$
$422$	8.60351	−	26.4789i	0.418812	−	1.28897i
$423$	−4.95357	+	4.83596i	−0.240851	+	0.235132i
$424$	−7.86208	−	5.71214i	−0.381816	−	0.277406i
$425$	6.40516	−	1.36146i	0.310696	−	0.0660404i
$426$	−7.08669	−	13.2411i	−0.343351	−	0.641534i
$427$	−0.757789	−	7.20988i	−0.0366720	−	0.348911i
$428$	6.22667	−	10.7849i	0.300977	−	0.521308i
$429$	−6.14814	−	11.9991i	−0.296835	−	0.579324i
$430$	3.92865	+	6.80462i	0.189456	+	0.328148i
$431$	5.66991	−	4.11943i	0.273110	−	0.198426i	−0.442797	−	0.896622i	$-0.646014\pi$
$431$	5.66991	−	4.11943i	0.273110	−	0.198426i	0.715907	+	0.698196i	$0.246014\pi$
$432$	1.03883	−	5.09125i	0.0499808	−	0.244953i
$433$	8.82483	−	27.1600i	0.424094	−	1.30523i	−0.479764	−	0.877397i	$-0.659278\pi$
$433$	8.82483	−	27.1600i	0.424094	−	1.30523i	0.903859	−	0.427831i	$-0.140722\pi$
$434$	0.0117506	−	0.111799i	0.000564046	−	0.00536654i
$435$	−12.1568	+	8.24807i	−0.582874	+	0.395465i
$436$	−12.4192	−	13.7929i	−0.594773	−	0.660562i
$437$	−9.21688	−	1.95911i	−0.440903	−	0.0937169i
$438$	−9.87684	+	10.2836i	−0.471933	+	0.491369i
$439$	0.483001	+	0.836582i	0.0230524	+	0.0399279i	0.877321	−	0.479903i	$-0.159328\pi$
$439$	0.483001	+	0.836582i	0.0230524	+	0.0399279i	−0.854269	+	0.519831i	$0.825995\pi$
$440$	−3.00525	−	1.40303i	−0.143269	−	0.0668870i
$441$	−18.9685	+	7.02107i	−0.903263	+	0.334337i
$442$	12.4336	−	9.03356i	0.591407	−	0.429682i
$443$	−20.0488	+	22.2664i	−0.952545	+	1.05791i	0.0457155	+	0.998955i	$0.485443\pi$
$443$	−20.0488	+	22.2664i	−0.952545	+	1.05791i	−0.998261	+	0.0589541i	$0.981223\pi$
$444$	−2.45296	+	0.998832i	−0.116413	+	0.0474025i
$445$	9.50080	−	4.23003i	0.450381	−	0.200523i
$446$	−6.94800	+	3.09345i	−0.328997	+	0.146479i
$447$	4.06650	−	1.65586i	0.192339	−	0.0783193i
$448$	0.339825	−	0.377414i	0.0160552	−	0.0178311i
$449$	20.2041	−	14.6791i	0.953488	−	0.692750i	0.00185895	−	0.999998i	$-0.499408\pi$
$449$	20.2041	−	14.6791i	0.953488	−	0.692750i	0.951629	+	0.307248i	$0.0994083\pi$
$450$	2.81345	−	1.04138i	0.132628	−	0.0490912i
$451$	−8.59558	+	1.66676i	−0.404750	+	0.0784845i
$452$	10.1694	+	17.6139i	0.478328	+	0.828489i
$453$	10.8974	−	11.3462i	0.512003	−	0.533089i
$454$	12.9697	+	2.75680i	0.608700	+	0.129383i
$455$	0.797573	+	0.885794i	0.0373908	+	0.0415267i
$456$	8.49269	−	5.76206i	0.397707	−	0.269833i
$457$	−1.22955	+	11.6984i	−0.0575158	+	0.547226i	0.927385	+	0.374108i	$0.122051\pi$
$457$	−1.22955	+	11.6984i	−0.0575158	+	0.547226i	−0.984901	+	0.173119i	$0.944616\pi$
$458$	−3.85980	+	11.8792i	−0.180357	+	0.555080i
$459$	−25.4710	−	22.5606i	−1.18888	−	1.05304i
$460$	−1.28655	+	0.934735i	−0.0599858	+	0.0435823i
$461$	−8.76830	−	15.1871i	−0.408380	−	0.707336i	0.586328	−	0.810074i	$-0.300573\pi$
$461$	−8.76830	−	15.1871i	−0.408380	−	0.707336i	−0.994708	+	0.102738i	$0.967240\pi$
$462$	−2.88048	+	0.462914i	−0.134012	+	0.0215367i
$463$	5.91683	−	10.2482i	0.274978	−	0.476276i	−0.695151	−	0.718863i	$-0.744663\pi$
$463$	5.91683	−	10.2482i	0.274978	−	0.476276i	0.970130	+	0.242587i	$0.0779960\pi$
$464$	0.886581	+	8.43526i	0.0411585	+	0.391597i
$465$	−0.180911	−	0.338023i	−0.00838954	−	0.0156754i
$466$	−8.57179	+	1.82199i	−0.397080	+	0.0844020i
$467$	−2.93155	−	2.12990i	−0.135656	−	0.0985598i	0.517888	−	0.855449i	$-0.326718\pi$
$467$	−2.93155	−	2.12990i	−0.135656	−	0.0985598i	−0.653544	+	0.756889i	$0.726718\pi$
$468$	5.03821	−	4.91859i	0.232891	−	0.227362i
$469$	−0.822385	+	2.53104i	−0.0379742	+	0.116873i
$470$	−1.54407	+	1.71487i	−0.0712228	+	0.0791009i
$471$	16.1235	+	3.97349i	0.742933	+	0.183089i
$472$	−2.93707	+	5.08715i	−0.135189	+	0.234155i
$473$	−20.8051	−	15.6926i	−0.956618	−	0.721546i
$474$	−15.2534	−	18.0782i	−0.700611	−	0.830359i
$475$	5.41302	+	2.41003i	0.248366	+	0.110580i
$476$	−1.02767	−	3.16283i	−0.0471030	−	0.144968i
$477$	−24.6398	+	15.5836i	−1.12818	+	0.713526i
$478$	7.58067	+	5.50768i	0.346732	+	0.251915i
$479$	1.56644	−	14.9037i	0.0715725	−	0.680967i	−0.898636	−	0.438695i	$-0.855441\pi$
$479$	1.56644	−	14.9037i	0.0715725	−	0.680967i	0.970208	−	0.242272i	$-0.0778925\pi$
$480$	0.236389	−	1.71584i	0.0107896	−	0.0783172i
$481$	−3.51045	−	0.746169i	−0.160063	−	0.0340224i
$482$	−0.985600	−	9.37736i	−0.0448929	−	0.427127i
$483$	−0.474862	+	1.31580i	−0.0216070	+	0.0598709i
$484$	10.9929	+	0.393893i	0.499679	+	0.0179042i
$485$	−16.4156			−0.745395
$486$	−13.0408	−	8.54039i	−0.591541	−	0.387400i
$487$	2.88808	+	8.88860i	0.130871	+	0.402781i	0.994925	−	0.100619i	$-0.0320823\pi$
$487$	2.88808	+	8.88860i	0.130871	+	0.402781i	−0.864054	+	0.503400i	$0.832082\pi$
$488$	−13.9628	+	2.96789i	−0.632068	+	0.134350i
$489$	9.05945	−	6.14659i	0.409682	−	0.277959i
$490$	−6.15919	+	2.74225i	−0.278244	+	0.123882i
$491$	−20.1651	−	22.3956i	−0.910036	−	1.01070i	−0.999891	−	0.0147426i	$-0.995307\pi$
$491$	−20.1651	−	22.3956i	−0.910036	−	1.01070i	0.0898553	−	0.995955i	$-0.471360\pi$
$492$	−2.15764	−	4.03143i	−0.0972738	−	0.181751i
$493$	50.7387	+	22.5903i	2.28516	+	1.01742i
$494$	13.9067			0.625692
$495$	−7.24296	+	6.82199i	−0.325547	+	0.306626i
$496$	−0.221350			−0.00993893
$497$	−4.02285	−	1.79109i	−0.180450	−	0.0803414i
$498$	−8.27404	+	13.3217i	−0.370769	+	0.596961i
$499$	−1.00363	−	1.11465i	−0.0449287	−	0.0498984i	0.720262	−	0.693703i	$-0.244022\pi$
$499$	−1.00363	−	1.11465i	−0.0449287	−	0.0498984i	−0.765190	+	0.643804i	$0.777355\pi$
$500$	0.913545	−	0.406737i	0.0408550	−	0.0181898i
$501$	1.44940	+	19.9475i	0.0647544	+	0.891189i
$502$	6.16899	−	1.31126i	0.275336	−	0.0585244i
$503$	3.68755	+	11.3491i	0.164420	+	0.506033i	0.998993	−	0.0448646i	$-0.0142857\pi$
$503$	3.68755	+	11.3491i	0.164420	+	0.506033i	−0.834573	+	0.550897i	$0.814286\pi$
$504$	−0.675334	−	1.36573i	−0.0300818	−	0.0608346i
$505$	−6.62047			−0.294607
$506$	2.71853	−	4.51974i	0.120853	−	0.200927i
$507$	−12.7724	+	2.28796i	−0.567244	+	0.101612i
$508$	−1.66670	−	15.8576i	−0.0739479	−	0.703568i
$509$	−25.7809	−	5.47991i	−1.14272	−	0.242893i	−0.402606	−	0.915374i	$-0.631895\pi$
$509$	−25.7809	−	5.47991i	−1.14272	−	0.242893i	−0.740115	+	0.672481i	$0.765229\pi$
$510$	−8.95650	−	6.95844i	−0.396601	−	0.308125i
$511$	−0.437010	+	4.15788i	−0.0193322	+	0.183934i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−6.64686	−	30.0627i	−0.293466	−	1.32730i
$514$	4.72351	+	14.5375i	0.208345	+	0.641220i
$515$	−1.68470	−	0.750076i	−0.0742367	−	0.0330523i
$516$	4.61983	−	12.8011i	0.203377	−	0.563537i
$517$	2.49499	−	7.23528i	0.109729	−	0.318207i
$518$	−0.388292	+	0.672542i	−0.0170606	+	0.0295498i
$519$	−11.9624	+	12.4550i	−0.525089	+	0.546714i
$520$	1.57046	−	1.74417i	0.0688690	−	0.0764868i
$521$	−4.01406	+	12.3540i	−0.175859	+	0.541239i	−0.999672	−	0.0256232i	$-0.991843\pi$
$521$	−4.01406	+	12.3540i	−0.175859	+	0.541239i	0.823812	+	0.566863i	$0.191843\pi$
$522$	24.4973	+	6.88047i	1.07222	+	0.301150i
$523$	−5.31776	−	3.86358i	−0.232529	−	0.168942i	0.465419	−	0.885090i	$-0.345904\pi$
$523$	−5.31776	−	3.86358i	−0.232529	−	0.168942i	−0.697949	+	0.716148i	$0.745904\pi$
$524$	−0.0357284	+	0.00759431i	−0.00156080	+	0.000331759i
$525$	0.464108	−	0.747243i	0.0202553	−	0.0326124i
$526$	0.759515	+	7.22630i	0.0331164	+	0.315082i
$527$	−0.724729	+	1.25527i	−0.0315697	+	0.0546803i
$528$	1.49937	+	5.54544i	0.0652516	+	0.241334i
$529$	10.2355	+	17.7285i	0.445023	+	0.770802i
$530$	−7.86208	+	5.71214i	−0.341507	+	0.248119i
$531$	10.9248	+	13.8274i	0.474097	+	0.600059i
$532$	0.929901	−	2.86194i	0.0403163	−	0.124081i
$533$	0.647655	−	6.16202i	0.0280530	−	0.266907i
$534$	−16.2116	−	7.85239i	−0.701543	−	0.339806i
$535$	−8.33291	−	9.25463i	−0.360263	−	0.400113i
$536$	5.12569	+	1.08950i	0.221396	+	0.0470592i
$537$	−3.09283	−	10.6763i	−0.133465	−	0.460715i
$538$	1.52664	+	2.64422i	0.0658183	+	0.114001i
$539$	15.2576	−	16.3468i	0.657190	−	0.704107i
$540$	−4.52105	−	2.56127i	−0.194555	−	0.110219i
$541$	−6.58074	+	4.78119i	−0.282928	+	0.205559i	−0.720194	−	0.693773i	$-0.755947\pi$
$541$	−6.58074	+	4.78119i	−0.282928	+	0.205559i	0.437266	+	0.899332i	$0.355947\pi$
$542$	−14.3131	+	15.8963i	−0.614799	+	0.682804i
$543$	3.21076	+	2.49448i	0.137787	+	0.107048i
$544$	−5.98213	+	2.66341i	−0.256482	+	0.114193i
$545$	−16.9556	+	7.54913i	−0.726299	+	0.323369i
$546$	0.281764	−	2.04521i	0.0120584	−	0.0875268i
$547$	12.4759	−	13.8559i	0.533430	−	0.592434i	−0.414842	−	0.909894i	$-0.636163\pi$
$547$	12.4759	−	13.8559i	0.533430	−	0.592434i	0.948272	+	0.317459i	$0.102830\pi$
$548$	15.2676	−	11.0925i	0.652198	−	0.473849i
$549$	−7.20683	+	42.2135i	−0.307580	+	1.80163i
$550$	−2.26304	+	2.42460i	−0.0964962	+	0.103385i
$551$	25.1283	+	43.5235i	1.07050	+	1.85416i
$552$	2.67441	+	0.659083i	0.113830	+	0.0280524i
$553$	−6.78396	−	1.44198i	−0.288483	−	0.0613191i
$554$	19.8521	+	22.0480i	0.843434	+	0.936728i
$555$	0.191938	+	2.64156i	0.00814730	+	0.112128i
$556$	1.86036	−	17.7001i	0.0788968	−	0.750653i
$557$	−8.63311	+	26.5700i	−0.365797	+	1.12581i	0.583684	+	0.811981i	$0.301611\pi$
$557$	−8.63311	+	26.5700i	−0.365797	+	1.12581i	−0.949481	+	0.313825i	$0.898389\pi$
$558$	−0.245405	+	0.617042i	−0.0103888	+	0.0261215i
$559$	14.9192	−	10.8394i	0.631015	−	0.458459i
$560$	−0.253930	−	0.439820i	−0.0107305	−	0.0185858i
$561$	36.3570	+	9.65362i	1.53500	+	0.407576i
$562$	−3.48491	+	6.03604i	−0.147002	+	0.254615i
$563$	0.160306	+	1.52521i	0.00675609	+	0.0642799i	0.997380	−	0.0723339i	$-0.0230447\pi$
$563$	0.160306	+	1.52521i	0.00675609	+	0.0642799i	−0.990624	+	0.136614i	$0.956378\pi$
$564$	3.99478	+	0.128623i	0.168210	+	0.00541599i
$565$	19.8943	−	4.22867i	0.836961	−	0.177902i
$566$	−3.45104	−	2.50733i	−0.145058	−	0.105391i
$567$	−4.55587	+	0.368429i	−0.191329	+	0.0154725i
$568$	−2.67943	+	8.24642i	−0.112426	+	0.346012i
$569$	−24.9975	+	27.7625i	−1.04795	+	1.16387i	−0.0617862	+	0.998089i	$0.519680\pi$
$569$	−24.9975	+	27.7625i	−1.04795	+	1.16387i	−0.986163	+	0.165776i	$0.946987\pi$
$570$	−2.85566	−	9.85760i	−0.119611	−	0.412890i
$571$	−7.86088	+	13.6154i	−0.328968	+	0.569788i	−0.982307	−	0.187276i	$-0.940034\pi$
$571$	−7.86088	+	13.6154i	−0.328968	+	0.569788i	0.653340	+	0.757065i	$0.273367\pi$
$572$	−2.53762	+	7.35890i	−0.106103	+	0.307691i
$573$	−34.4138	+	6.16465i	−1.43766	+	0.257532i
$574$	−1.22481	−	0.545321i	−0.0511226	−	0.0227613i
$575$	0.491420	+	1.51243i	0.0204936	+	0.0630728i
$576$	−2.53546	+	1.60357i	−0.105644	+	0.0668156i
$577$	7.43741	+	5.40360i	0.309624	+	0.224955i	0.731735	−	0.681589i	$-0.238711\pi$
$577$	7.43741	+	5.40360i	0.309624	+	0.224955i	−0.422111	+	0.906544i	$0.638711\pi$
$578$	−2.70515	+	25.7378i	−0.112520	+	1.07055i
$579$	−13.5545	+	5.51929i	−0.563304	+	0.229374i
$580$	8.29637	+	1.76345i	0.344488	+	0.0732232i
$581$	0.480643	+	4.57302i	0.0199404	+	0.189721i
$582$	18.3354	+	21.7309i	0.760025	+	0.900776i
$583$	16.6128	−	27.6200i	0.688034	−	1.14390i
$584$	8.23214			0.340648
$585$	−3.12096	−	6.31155i	−0.129036	−	0.260950i
$586$	−2.96705	−	9.13165i	−0.122568	−	0.377225i
$587$	−12.1989	+	2.59295i	−0.503500	+	0.107022i	−0.452658	−	0.891684i	$-0.649524\pi$
$587$	−12.1989	+	2.59295i	−0.503500	+	0.107022i	−0.0508427	+	0.998707i	$0.516191\pi$
$588$	10.5097	+	5.09056i	0.433411	+	0.209931i
$589$	−1.19817	+	0.533462i	−0.0493699	+	0.0219809i
$590$	3.93056	+	4.36533i	0.161819	+	0.179718i
$591$	17.2762	+	0.556252i	0.710646	+	0.0228812i
$592$	1.39693	+	0.621952i	0.0574134	+	0.0255621i
$593$	−42.9148			−1.76230			−0.881149	−	0.472838i	$-0.843229\pi$
$593$	−42.9148			−1.76230			−0.881149	+	0.472838i	$0.843229\pi$
$594$	17.1209	+	1.96840i	0.702479	+	0.0807643i
$595$	−3.32560			−0.136336
$596$	−2.31582	−	1.03107i	−0.0948595	−	0.0422342i
$597$	16.0418	+	0.516510i	0.656549	+	0.0211393i
$598$	2.49744	+	2.77369i	0.102128	+	0.113425i
$599$	−14.5469	+	6.47669i	−0.594370	+	0.264631i	−0.681798	−	0.731540i	$-0.738802\pi$
$599$	−14.5469	+	6.47669i	−0.594370	+	0.264631i	0.0874283	+	0.996171i	$0.472135\pi$
$600$	−1.55882	−	0.755044i	−0.0636384	−	0.0308245i
$601$	22.5152	−	4.78576i	0.918414	−	0.195215i	0.275632	−	0.961263i	$-0.411113\pi$
$601$	22.5152	−	4.78576i	0.918414	−	0.195215i	0.642783	+	0.766048i	$0.277780\pi$
$602$	−1.23311	−	3.79511i	−0.0502576	−	0.154677i
$603$	8.71983	−	13.0806i	0.355099	−	0.532684i
$604$	−9.08273			−0.369571
$605$	3.77162	−	10.3332i	0.153338	−	0.420104i
$606$	7.39471	+	8.76414i	0.300389	+	0.356019i
$607$	−4.95098	−	47.1055i	−0.200954	−	1.91195i	−0.374675	−	0.927156i	$-0.622246\pi$
$607$	−4.95098	−	47.1055i	−0.200954	−	1.91195i	0.173721	−	0.984795i	$-0.444421\pi$
$608$	−5.79581	−	1.23194i	−0.235051	−	0.0499616i
$609$	6.90997	−	2.81370i	0.280006	−	0.114017i
$610$	−1.49212	+	14.1966i	−0.0604141	+	0.574802i
$611$	4.38156	+	3.18339i	0.177259	+	0.128786i
$612$	0.792385	+	19.6288i	0.0320303	+	0.793446i
$613$	−2.91471	−	8.97057i	−0.117724	−	0.362318i	0.874781	−	0.484518i	$-0.161005\pi$
$613$	−2.91471	−	8.97057i	−0.117724	−	0.362318i	−0.992505	+	0.122200i	$0.961005\pi$
$614$	−14.2929	−	6.36361i	−0.576814	−	0.256814i
$615$	−4.50087	+	0.806254i	−0.181493	+	0.0325113i
$616$	1.34475	+	1.01430i	0.0541814	+	0.0408673i
$617$	−6.70370	+	11.6111i	−0.269881	+	0.467447i	−0.968831	−	0.247723i	$-0.920318\pi$
$617$	−6.70370	+	11.6111i	−0.269881	+	0.467447i	0.698950	+	0.715170i	$0.253651\pi$
$618$	0.888770	+	3.06799i	0.0357516	+	0.123413i
$619$	25.2603	−	28.0544i	1.01530	−	1.12760i	0.0235059	−	0.999724i	$-0.492517\pi$
$619$	25.2603	−	28.0544i	1.01530	−	1.12760i	0.991790	−	0.127877i	$-0.0408162\pi$
$620$	−0.0684011	+	0.210517i	−0.00274705	+	0.00845456i
$621$	4.80232	−	6.72454i	0.192710	−	0.269846i
$622$	−19.4085	−	14.1011i	−0.778210	−	0.565403i
$623$	−5.16629	+	1.09813i	−0.206983	+	0.0439956i
$624$	−4.06303	−	0.130820i	−0.162651	−	0.00523700i
$625$	−0.104528	−	0.994522i	−0.00418114	−	0.0397809i
$626$	10.3519	−	17.9300i	0.413745	−	0.716627i
$627$	21.4808	+	26.4041i	0.857860	+	1.05448i
$628$	−4.79372	−	8.30296i	−0.191290	−	0.331324i
$629$	8.10078	−	5.88556i	0.322999	−	0.234673i
$630$	−1.50758	+	0.220246i	−0.0600634	+	0.00877482i
$631$	3.12065	−	9.60438i	0.124231	−	0.382344i	−0.869529	−	0.493882i	$-0.835578\pi$
$631$	3.12065	−	9.60438i	0.124231	−	0.382344i	0.993760	+	0.111537i	$0.0355775\pi$
$632$	−1.42748	+	13.5815i	−0.0567820	+	0.540244i
$633$	3.49470	+	48.0962i	0.138902	+	1.91165i
$634$	7.23076	+	8.03057i	0.287170	+	0.318935i
$635$	−15.5965	−	3.31514i	−0.618929	−	0.131557i
$636$	16.3432	+	4.02763i	0.648050	+	0.159706i
$637$	7.91186	+	13.7037i	0.313479	+	0.542962i
$638$	−27.6163	+	5.35503i	−1.09334	+	0.212008i
$639$	20.0173	+	16.6118i	0.791873	+	0.657153i
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	21.6696	−	24.0665i	0.855897	−	0.950570i	−0.143338	−	0.989674i	$-0.545784\pi$
$641$	21.6696	−	24.0665i	0.855897	−	0.950570i	0.999235	+	0.0391035i	$0.0124502\pi$
$642$	−2.94383	+	21.3680i	−0.116184	+	0.843327i
$643$	11.7831	−	5.24615i	0.464678	−	0.206888i	−0.161023	−	0.986951i	$-0.551479\pi$
$643$	11.7831	−	5.24615i	0.464678	−	0.206888i	0.625702	+	0.780063i	$0.284813\pi$
$644$	0.737811	−	0.328494i	0.0290738	−	0.0129445i
$645$	−10.7470	−	8.34948i	−0.423162	−	0.328760i
$646$	−25.9625	+	28.8342i	−1.02148	+	1.13447i
$647$	11.7999	−	8.57313i	0.463902	−	0.337045i	−0.331158	−	0.943575i	$-0.607439\pi$
$647$	11.7999	−	8.57313i	0.463902	−	0.337045i	0.795060	+	0.606531i	$0.207439\pi$
$648$	1.65917	+	8.84574i	0.0651785	+	0.347494i
$649$	−17.6532	−	8.24161i	−0.692949	−	0.323511i
$650$	−1.17350	−	2.03257i	−0.0460286	−	0.0797239i
$651$	0.0541779	+	0.187020i	0.00212340	+	0.00732987i
$652$	−6.18259	−	1.31415i	−0.242129	−	0.0514661i
$653$	32.7531	+	36.3760i	1.28173	+	1.42350i	0.854579	+	0.519322i	$0.173816\pi$
$653$	32.7531	+	36.3760i	1.28173	+	1.42350i	0.427149	+	0.904181i	$0.359518\pi$
$654$	28.9320	+	14.0138i	1.13133	+	0.547983i
$655$	−0.00381807	+	0.0363265i	−0.000149184	+	0.00141940i
$656$	−0.815786	+	2.51073i	−0.0318511	+	0.0980276i
$657$	9.12673	−	22.9481i	0.356068	−	0.895291i
$658$	0.948111	−	0.688843i	0.0369612	−	0.0268539i
$659$	12.6154	+	21.8505i	0.491425	+	0.851173i	0.999951	−	0.00987361i	$-0.00314292\pi$
$659$	12.6154	+	21.8505i	0.491425	+	0.851173i	−0.508526	+	0.861046i	$0.669810\pi$
$660$	5.73736	+	0.287651i	0.223326	+	0.0111968i
$661$	3.81166	−	6.60200i	0.148257	−	0.256788i	−0.782327	−	0.622868i	$-0.785967\pi$
$661$	3.81166	−	6.60200i	0.148257	−	0.256788i	0.930583	+	0.366081i	$0.119301\pi$
$662$	−0.524596	−	4.99119i	−0.0203890	−	0.193988i
$663$	−14.0448	+	22.6129i	−0.545453	+	0.878214i
$664$	8.85621	−	1.88245i	0.343688	−	0.0730531i
$665$	−2.43451	−	1.76878i	−0.0944063	−	0.0685902i
$666$	3.28250	−	3.20457i	0.127194	−	0.124175i
$667$	−4.16808	+	12.8280i	−0.161389	+	0.496704i
$668$	7.72649	−	8.58114i	0.298947	−	0.332014i
$669$	9.12504	−	9.50083i	0.352794	−	0.367323i
$670$	2.62010	−	4.53815i	0.101223	−	0.175324i
$671$	−13.8215	−	45.2816i	−0.533572	−	1.74808i
$672$	−0.298605	+	0.827407i	−0.0115190	+	0.0319179i
$673$	13.9066	+	6.19163i	0.536061	+	0.238670i	0.656867	−	0.754006i	$-0.271881\pi$
$673$	13.9066	+	6.19163i	0.536061	+	0.238670i	−0.120806	+	0.992676i	$0.538548\pi$
$674$	−0.867731	−	2.67060i	−0.0334238	−	0.102868i
$675$	−3.83299	+	3.50830i	−0.147532	+	0.135034i
$676$	6.06079	+	4.40342i	0.233107	+	0.169362i
$677$	5.21479	−	49.6154i	0.200421	−	1.90687i	−0.182687	−	0.983171i	$-0.558480\pi$
$677$	5.21479	−	49.6154i	0.200421	−	1.90687i	0.383108	−	0.923704i	$-0.374854\pi$
$678$	−27.8188	−	21.6128i	−1.06837	−	0.830035i
$679$	8.15468	+	1.73333i	0.312948	+	0.0665191i
$680$	0.684479	+	6.51238i	0.0262486	+	0.249738i
$681$	−22.6063	+	4.04953i	−0.866275	+	0.155178i
$682$	−0.0636516	−	0.731372i	−0.00243735	−	0.0280057i
$683$	−47.5460			−1.81930			−0.909648	−	0.415380i	$-0.863649\pi$
$683$	−47.5460			−1.81930			−0.909648	+	0.415380i	$0.863649\pi$
$684$	−9.85982	+	14.7907i	−0.377000	+	0.565537i
$685$	−5.83169	−	17.9481i	−0.222817	−	0.685761i
$686$	6.82655	−	1.45103i	0.260639	−	0.0554005i
$687$	−1.56783	−	21.5774i	−0.0598164	−	0.823230i
$688$	−7.17800	+	3.19585i	−0.273659	+	0.121841i
$689$	15.2618	+	16.9499i	0.581428	+	0.645741i
$690$	1.45326	−	2.33984i	0.0553248	−	0.0890764i
$691$	0.772398	+	0.343894i	0.0293834	+	0.0130823i	0.421376	−	0.906886i	$-0.361547\pi$
$691$	0.772398	+	0.343894i	0.0293834	+	0.0130823i	−0.391992	+	0.919968i	$0.628214\pi$
$692$	9.97037			0.379017
$693$	4.31837	−	2.62413i	0.164041	−	0.0996823i
$694$	21.9079			0.831611
$695$	−16.2589	−	7.23895i	−0.616737	−	0.274589i
$696$	−6.93216	−	12.9524i	−0.262763	−	0.490958i
$697$	11.5673	+	12.8467i	0.438141	+	0.486605i
$698$	−11.7901	+	5.24927i	−0.446260	+	0.198688i
$699$	12.5604	−	8.52188i	0.475077	−	0.322327i
$700$	−0.496763	+	0.105590i	−0.0187759	+	0.00399093i
$701$	−10.4294	−	32.0984i	−0.393913	−	1.21234i	−0.929804	−	0.368054i	$-0.880024\pi$
$701$	−10.4294	−	32.0984i	−0.393913	−	1.21234i	0.535891	−	0.844287i	$-0.319976\pi$
$702$	−4.86925	+	11.1812i	−0.183778	+	0.422006i
$703$	9.06053			0.341724
$704$	1.70948	−	2.84213i	0.0644285	−	0.107117i
$705$	1.35678	−	3.75951i	0.0510993	−	0.141591i
$706$	1.03452	+	9.84282i	0.0389347	+	0.370439i
$707$	3.28880	+	0.699057i	0.123688	+	0.0262907i
$708$	1.38858	−	10.0791i	0.0521860	−	0.378796i
$709$	2.44662	−	23.2780i	0.0918847	−	0.874224i	−0.847370	−	0.531003i	$-0.821815\pi$
$709$	2.44662	−	23.2780i	0.0918847	−	0.874224i	0.939255	−	0.343221i	$-0.111518\pi$
$710$	7.01483	+	5.09657i	0.263262	+	0.191271i
$711$	36.2776	+	19.0367i	1.36052	+	0.713933i
$712$	3.21375	+	9.89091i	0.120440	+	0.370677i
$713$	−0.321574	−	0.143174i	−0.0120430	−	0.00536190i
$714$	3.71452	+	4.40241i	0.139012	+	0.164756i
$715$	6.21457	+	4.68744i	0.232412	+	0.175300i
$716$	−3.20869	+	5.55762i	−0.119914	+	0.207698i
$717$	−15.7582	−	3.88347i	−0.588502	−	0.145031i
$718$	16.3168	−	18.1217i	0.608939	−	0.676295i
$719$	−12.8706	+	39.6117i	−0.479994	+	1.47727i	0.359109	+	0.933296i	$0.383081\pi$
$719$	−12.8706	+	39.6117i	−0.479994	+	1.47727i	−0.839103	+	0.543973i	$0.816919\pi$
$720$	0.741590	+	2.90690i	0.0276374	+	0.108334i
$721$	0.757695	+	0.550497i	0.0282180	+	0.0205016i
$722$	−15.7570	+	3.34926i	−0.586416	+	0.124647i
$723$	7.70638	+	14.3990i	0.286603	+	0.535504i
$724$	−0.245374	−	2.33458i	−0.00911926	−	0.0867639i
$725$	4.24086	−	7.34539i	0.157502	−	0.272801i
$726$	−17.8917	+	6.54876i	−0.664024	+	0.243047i
$727$	16.8336	+	29.1567i	0.624324	+	1.08136i	0.988671	+	0.150097i	$0.0479587\pi$
$727$	16.8336	+	29.1567i	0.624324	+	1.08136i	−0.364348	+	0.931263i	$0.618708\pi$
$728$	−0.964311	+	0.700613i	−0.0357397	+	0.0259664i
$729$	26.4981	+	5.18187i	0.981410	+	0.191921i
$730$	2.54387	−	7.82923i	0.0941529	−	0.289773i
$731$	−5.37815	+	51.1697i	−0.198918	+	1.89258i
$732$	20.4600	−	13.8815i	0.756222	−	0.513076i
$733$	−5.79495	−	6.43595i	−0.214041	−	0.237717i	0.626557	−	0.779375i	$-0.284463\pi$
$733$	−5.79495	−	6.43595i	−0.214041	−	0.237717i	−0.840599	+	0.541658i	$0.817797\pi$
$734$	−12.8547	−	2.73234i	−0.474475	−	0.100853i
$735$	8.08908	−	8.42221i	0.298370	−	0.310658i
$736$	−0.795133	−	1.37721i	−0.0293090	−	0.0507647i
$737$	−2.12591	+	17.2493i	−0.0783089	+	0.635386i
$738$	6.09454	+	5.05768i	0.224343	+	0.186176i
$739$	43.2373	−	31.4137i	1.59051	−	1.15557i	0.687300	−	0.726374i	$-0.258796\pi$
$739$	43.2373	−	31.4137i	1.59051	−	1.15557i	0.903210	−	0.429199i	$-0.141204\pi$
$740$	1.02319	−	1.13636i	0.0376131	−	0.0417736i
$741$	−22.3086	+	9.08391i	−0.819526	+	0.333706i
$742$	4.50874	−	2.00742i	0.165521	−	0.0736946i
$743$	23.7967	−	10.5950i	0.873017	−	0.388692i	0.0792074	−	0.996858i	$-0.474761\pi$
$743$	23.7967	−	10.5950i	0.873017	−	0.388692i	0.793810	+	0.608166i	$0.208094\pi$
$744$	0.355081	−	0.144587i	0.0130179	−	0.00530081i
$745$	−1.69623	+	1.88385i	−0.0621451	+	0.0690191i
$746$	−20.5657	+	14.9419i	−0.752966	+	0.547061i
$747$	4.57108	−	26.7748i	0.167247	−	0.979639i
$748$	−10.5205	−	18.9999i	−0.384668	−	0.694704i
$749$	3.16228	+	5.47723i	0.115547	+	0.200134i
$750$	−1.19979	+	1.24920i	−0.0438101	+	0.0456144i
$751$	25.4098	+	5.40101i	0.927216	+	0.197086i	0.646683	−	0.762759i	$-0.276156\pi$
$751$	25.4098	+	5.40101i	0.927216	+	0.197086i	0.280532	+	0.959845i	$0.409489\pi$
$752$	−1.54407	−	1.71487i	−0.0563065	−	0.0625348i
$753$	−9.03952	+	6.13307i	−0.329418	+	0.223502i
$754$	2.08081	−	19.7976i	0.0757788	−	0.720987i
$755$	−2.80672	+	8.63819i	−0.102147	+	0.314376i
$756$	1.97545	+	1.74972i	0.0718462	+	0.0636368i
$757$	−27.1184	+	19.7027i	−0.985636	+	0.716107i	−0.958961	−	0.283537i	$-0.908492\pi$
$757$	−27.1184	+	19.7027i	−0.985636	+	0.716107i	−0.0266752	+	0.999644i	$0.508492\pi$
$758$	6.04518	+	10.4706i	0.219571	+	0.380308i
$759$	−1.40865	+	9.02613i	−0.0511306	+	0.327628i
$760$	−2.96264	+	5.13145i	−0.107466	+	0.186137i
$761$	−3.57146	−	33.9802i	−0.129465	−	1.23178i	−0.845599	−	0.533818i	$-0.820757\pi$
$761$	−3.57146	−	33.9802i	−0.129465	−	1.23178i	0.716134	−	0.697963i	$-0.245910\pi$
$762$	13.0319	+	24.3494i	0.472096	+	0.882087i
$763$	9.22004	−	1.95978i	0.333788	−	0.0709488i
$764$	16.3301	+	11.8645i	0.590802	+	0.429243i
$765$	18.9129	+	5.31202i	0.683798	+	0.192056i
$766$	−6.26444	+	19.2800i	−0.226343	+	0.696613i
$767$	9.22507	−	10.2455i	0.333098	−	0.369943i
$768$	1.68174	+	0.414448i	0.0606844	+	0.0149551i
$769$	−2.86826	+	4.96797i	−0.103432	+	0.179149i	−0.913096	−	0.407744i	$-0.866316\pi$
$769$	−2.86826	+	4.96797i	−0.103432	+	0.179149i	0.809665	+	0.586893i	$0.199649\pi$
$770$	1.38021	−	0.965495i	0.0497392	−	0.0347940i
$771$	−17.0732	−	20.2350i	−0.614875	−	0.728745i
$772$	7.71907	+	3.43675i	0.277816	+	0.123691i
$773$	12.0396	+	37.0541i	0.433035	+	1.33274i	0.895087	+	0.445892i	$0.147113\pi$
$773$	12.0396	+	37.0541i	0.433035	+	1.33274i	−0.462052	+	0.886853i	$0.652887\pi$
$774$	0.950788	+	23.5527i	0.0341754	+	0.846584i
$775$	0.179076	+	0.130107i	0.00643261	+	0.00467356i
$776$	1.71590	−	16.3257i	0.0615972	−	0.586059i
$777$	0.183576	−	1.33250i	0.00658574	−	0.0478031i
$778$	22.1028	+	4.69810i	0.792425	+	0.168435i
$779$	1.63508	+	15.5567i	0.0585827	+	0.557377i
$780$	−1.37996	+	3.82375i	−0.0494106	+	0.136912i
$781$	−28.0178	−	6.48184i	−1.00256	−	0.231938i
$782$	−10.4135			−0.372385
$783$	−43.7918	+	4.96432i	−1.56499	+	0.177410i
$784$	−2.08342	−	6.41210i	−0.0744077	−	0.229003i
$785$	−9.37792	+	1.99334i	−0.334712	+	0.0711453i
$786$	0.0523535	−	0.0355204i	0.00186739	−	0.00126697i
$787$	−22.9216	+	10.2053i	−0.817066	+	0.363781i	−0.772333	−	0.635218i	$-0.780910\pi$
$787$	−22.9216	+	10.2053i	−0.817066	+	0.363781i	−0.0447329	+	0.998999i	$0.514244\pi$
$788$	−6.67763	−	7.41626i	−0.237881	−	0.264193i
$789$	−5.93863	−	11.0960i	−0.211421	−	0.395029i
$790$	12.4757	+	5.55453i	0.443865	+	0.197621i
$791$	−10.3293			−0.367267
$792$	−6.02752	−	7.91637i	−0.214179	−	0.281296i
$793$	33.5030			1.18973
$794$	−29.0105	−	12.9163i	−1.02954	−	0.458382i
$795$	8.88084	−	14.2987i	0.314971	−	0.507123i
$796$	−6.20054	−	6.88640i	−0.219772	−	0.244082i
$797$	13.2939	−	5.91884i	0.470895	−	0.209656i	−0.157548	−	0.987511i	$-0.550359\pi$
$797$	13.2939	−	5.91884i	0.470895	−	0.209656i	0.628443	+	0.777855i	$0.283692\pi$
$798$	0.377721	+	5.19842i	0.0133712	+	0.184022i
$799$	−14.7804	+	3.14167i	−0.522894	+	0.111144i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	31.1351	+	2.00704i	1.10011	+	0.0709152i
$802$	−4.64667			−0.164080
$803$	2.36724	+	27.2001i	0.0835379	+	0.959870i
$804$	−8.93409	+	1.60039i	−0.315081	+	0.0564414i
$805$	−0.0844208	−	0.803210i	−0.00297544	−	0.0283094i
$806$	0.508159	+	0.108013i	0.0178991	+	0.00380458i
$807$	−4.17619	−	3.24455i	−0.147009	−	0.114213i
$808$	0.692028	−	6.58420i	0.0243454	−	0.231631i
$809$	38.9899	+	28.3278i	1.37081	+	0.995953i	0.997673	+	0.0681773i	$0.0217183\pi$
$809$	38.9899	+	28.3278i	1.37081	+	0.995953i	0.373138	+	0.927776i	$0.378282\pi$
$810$	8.92551	+	1.15552i	0.313611	+	0.0406007i
$811$	−9.00259	−	27.7071i	−0.316124	−	0.972929i	−0.975289	−	0.220931i	$-0.929090\pi$
$811$	−9.00259	−	27.7071i	−0.316124	−	0.972929i	0.659166	−	0.751998i	$-0.270910\pi$
$812$	−3.93513	−	1.75203i	−0.138096	−	0.0614843i
$813$	12.5769	−	34.8495i	0.441092	−	1.22223i
$814$	−1.65331	+	4.79449i	−0.0579486	+	0.168047i
$815$	−3.16036	+	5.47390i	−0.110702	+	0.191742i
$816$	7.85653	−	8.18008i	0.275033	−	0.286360i
$817$	−31.1525	+	34.5984i	−1.08989	+	1.21044i
$818$	−2.93169	+	9.02282i	−0.102504	+	0.315476i
$819$	0.883941	+	3.46489i	0.0308874	+	0.121073i
$820$	2.13576	+	1.55172i	0.0745839	+	0.0541883i
$821$	−22.3797	+	4.75695i	−0.781056	+	0.166019i	−0.581150	−	0.813797i	$-0.697397\pi$
$821$	−22.3797	+	4.75695i	−0.781056	+	0.166019i	−0.199906	+	0.979815i	$0.564064\pi$
$822$	−17.2459	+	27.7670i	−0.601520	+	0.968485i
$823$	−0.396662	−	3.77399i	−0.0138268	−	0.131553i	0.985431	−	0.170076i	$-0.0544013\pi$
$823$	−0.396662	−	3.77399i	−0.0138268	−	0.131553i	−0.999258	+	0.0385231i	$0.987735\pi$
$824$	0.922066	−	1.59706i	0.0321217	−	0.0556364i
$825$	2.04651	−	5.36766i	0.0712504	−	0.186878i
$826$	−1.49162	−	2.58356i	−0.0519002	−	0.0898937i
$827$	13.3905	−	9.72878i	0.465634	−	0.338303i	−0.330103	−	0.943945i	$-0.607084\pi$
$827$	13.3905	−	9.72878i	0.465634	−	0.338303i	0.795737	+	0.605642i	$0.207084\pi$
$828$	−4.72069	+	0.689658i	−0.164055	+	0.0239673i
$829$	−12.2809	+	37.7968i	−0.426534	+	1.31274i	0.474984	+	0.879995i	$0.342454\pi$
$829$	−12.2809	+	37.7968i	−0.426534	+	1.31274i	−0.901518	+	0.432742i	$0.857546\pi$
$830$	0.946408	−	9.00447i	0.0328503	−	0.312550i
$831$	−46.2477	−	22.4010i	−1.60431	−	0.777082i
$832$	1.57046	+	1.74417i	0.0544457	+	0.0604681i
$833$	−43.1841	−	9.17906i	−1.49624	−	0.318035i
$834$	8.57748	+	29.6090i	0.297014	+	1.02528i
$835$	−5.77353	−	10.0000i	−0.199801	−	0.346066i
$836$	2.40384	−	19.5044i	0.0831386	−	0.674573i
$837$	−0.00938539	−	1.15013i	−0.000324407	−	0.0397544i
$838$	7.42668	−	5.39580i	0.256551	−	0.186395i
$839$	−2.97414	+	3.30312i	−0.102679	+	0.114036i	−0.792294	−	0.610140i	$-0.791113\pi$
$839$	−2.97414	+	3.30312i	−0.102679	+	0.114036i	0.689615	+	0.724176i	$0.257780\pi$
$840$	0.694637	+	0.539674i	0.0239673	+	0.0186205i
$841$	39.2273	−	17.4651i	1.35266	−	0.602245i
$842$	19.8667	−	8.84524i	0.684653	−	0.304827i
$843$	1.64759	−	11.9591i	0.0567459	−	0.411894i
$844$	18.6296	−	20.6903i	0.641258	−	0.712189i
$845$	6.06079	−	4.40342i	0.208498	−	0.151482i
$846$	−6.49227	+	2.40307i	−0.223209	+	0.0826193i
$847$	−2.96469	+	4.73490i	−0.101868	+	0.162693i
$848$	−4.85903	−	8.41609i	−0.166860	−	0.289010i
$849$	7.17382	+	1.76792i	0.246205	+	0.0606749i
$850$	6.40516	+	1.36146i	0.219695	+	0.0466976i
$851$	1.62714	+	1.80712i	0.0557776	+	0.0619473i
$852$	−1.08837	−	14.9788i	−0.0372869	−	0.513165i
$853$	3.69661	−	35.1709i	0.126570	−	1.20423i	−0.728253	−	0.685309i	$-0.759667\pi$
$853$	3.69661	−	35.1709i	0.126570	−	1.20423i	0.854822	−	0.518921i	$-0.173666\pi$
$854$	2.24025	−	6.89477i	0.0766597	−	0.235934i
$855$	11.0200	+	13.9478i	0.376875	+	0.477006i
$856$	10.0750	−	7.31989i	0.344355	−	0.250189i
$857$	−4.36141	−	7.55419i	−0.148983	−	0.258046i	0.781869	−	0.623443i	$-0.214267\pi$
$857$	−4.36141	−	7.55419i	−0.148983	−	0.258046i	−0.930852	+	0.365397i	$0.880933\pi$
$858$	−0.736119	−	13.4624i	−0.0251307	−	0.459600i
$859$	20.1873	−	34.9654i	0.688782	−	1.19301i	−0.283450	−	0.958987i	$-0.591479\pi$
$859$	20.1873	−	34.9654i	0.688782	−	1.19301i	0.972232	−	0.234018i	$-0.0751876\pi$
$860$	0.821311	+	7.81425i	0.0280065	+	0.266464i
$861$	2.32100	+	0.0747307i	0.0790993	+	0.00254682i
$862$	6.85525	−	1.45713i	0.233491	−	0.0496300i
$863$	−1.89522	−	1.37696i	−0.0645142	−	0.0468723i	0.555061	−	0.831810i	$-0.312695\pi$
$863$	−1.89522	−	1.37696i	−0.0645142	−	0.0468723i	−0.619575	+	0.784938i	$0.712695\pi$
$864$	3.01982	−	4.22856i	0.102736	−	0.143858i
$865$	3.08101	−	9.48238i	0.104758	−	0.322411i
$866$	19.1089	−	21.2226i	0.649346	−	0.721172i
$867$	−12.4725	−	43.0546i	−0.423590	−	1.46221i
$868$	0.0562076	−	0.0973544i	0.00190781	−	0.00330443i
$869$	−45.2857	−	0.811066i	−1.53621	−	0.0275135i
$870$	−14.4606	+	2.59037i	−0.490260	+	0.0878217i
$871$	−11.2355	−	5.00238i	−0.380701	−	0.169499i
$872$	−5.73543	−	17.6518i	−0.194226	−	0.597767i
$873$	−43.6076	−	22.8831i	−1.47589	−	0.774477i
$874$	−7.62320	−	5.53858i	−0.257859	−	0.187345i
$875$	−0.0530859	+	0.505079i	−0.00179463	+	0.0170748i
$876$	−13.2057	+	5.37726i	−0.446178	+	0.181681i
$877$	37.8710	+	8.04972i	1.27881	+	0.271820i	0.796745	−	0.604315i	$-0.206553\pi$
$877$	37.8710	+	8.04972i	1.27881	+	0.271820i	0.482066	+	0.876135i	$0.339886\pi$
$878$	0.100975	+	0.960709i	0.00340773	+	0.0324224i
$879$	10.7245	+	12.7105i	0.361727	+	0.428716i
$880$	−2.17476	−	2.50408i	−0.0733112	−	0.0844124i
$881$	−22.4116			−0.755066			−0.377533	−	0.925996i	$-0.623227\pi$
$881$	−22.4116			−0.755066			−0.377533	+	0.925996i	$0.623227\pi$
$882$	−20.1843	−	1.30113i	−0.679642	−	0.0438112i
$883$	14.1316	+	43.4927i	0.475568	+	1.46365i	0.845190	+	0.534465i	$0.179487\pi$
$883$	14.1316	+	43.4927i	0.475568	+	1.46365i	−0.369623	+	0.929182i	$0.620513\pi$
$884$	15.0330	−	3.19535i	0.505613	−	0.107471i
$885$	−9.15670	−	4.43523i	−0.307799	−	0.149089i
$886$	−27.3720	+	12.1868i	−0.919581	+	0.409424i
$887$	−17.1615	−	19.0598i	−0.576227	−	0.639965i	0.382614	−	0.923908i	$-0.375024\pi$
$887$	−17.1615	−	19.0598i	−0.576227	−	0.639965i	−0.958841	+	0.283943i	$0.908357\pi$
$888$	−2.64716	−	0.0852323i	−0.0888327	−	0.00286021i
$889$	7.39773	+	3.29368i	0.248112	+	0.110466i
$890$	10.3999			0.348606
$891$	−28.7504	+	8.02581i	−0.963175	+	0.268875i
$892$	−7.60553			−0.254652
$893$	−12.4910	−	5.56134i	−0.417995	−	0.186103i
$894$	4.38843	+	0.141297i	0.146771	+	0.00472569i
$895$	4.29407	+	4.76905i	0.143535	+	0.159412i
$896$	0.463954	−	0.206566i	0.0154996	−	0.00690087i
$897$	−5.81808	−	2.81810i	−0.194260	−	0.0940937i
$898$	24.4279	−	5.19230i	0.815168	−	0.173269i
$899$	0.580159	+	1.78554i	0.0193494	+	0.0595512i
$900$	2.99379	+	0.192986i	0.0997929	+	0.00643287i
$901$	−63.6363			−2.12003
$902$	−8.53039	−	1.97348i	−0.284031	−	0.0657097i
$903$	4.45707	+	5.28249i	0.148322	+	0.175790i
$904$	2.12598	+	20.2274i	0.0707091	+	0.672752i
$905$	−2.29614	−	0.488060i	−0.0763263	−	0.0162237i
$906$	14.5701	−	5.93287i	0.484061	−	0.197106i
$907$	4.36055	−	41.4878i	0.144790	−	1.37758i	−0.644991	−	0.764190i	$-0.723139\pi$
$907$	4.36055	−	41.4878i	0.144790	−	1.37758i	0.789780	−	0.613390i	$-0.210195\pi$
$908$	10.7272	+	7.79374i	0.355993	+	0.258644i
$909$	−17.5871	−	9.22883i	−0.583326	−	0.306101i
$910$	0.368334	+	1.13362i	0.0122102	+	0.0375790i
$911$	14.8037	+	6.59105i	0.490469	+	0.218371i	0.637042	−	0.770829i	$-0.280158\pi$
$911$	14.8037	+	6.59105i	0.490469	+	0.218371i	−0.146573	+	0.989200i	$0.546824\pi$
$912$	10.1021	−	1.80962i	0.334514	−	0.0599225i
$913$	8.76655	+	28.7208i	0.290131	+	0.950520i
$914$	−5.88140	+	10.1869i	−0.194539	+	0.336952i
$915$	−6.87965	−	23.7482i	−0.227434	−	0.785091i
$916$	−8.35782	+	9.28230i	−0.276150	+	0.306696i
$917$	0.00573240	−	0.0176425i	0.000189301	−	0.000582607i
$918$	−14.0927	−	30.9701i	−0.465128	−	1.02216i
$919$	−6.10286	−	4.43398i	−0.201315	−	0.146264i	0.482561	−	0.875863i	$-0.339707\pi$
$919$	−6.10286	−	4.43398i	−0.201315	−	0.146264i	−0.683875	+	0.729599i	$0.739707\pi$
$920$	−1.55552	+	0.330635i	−0.0512838	+	0.0109007i
$921$	27.0848	+	0.872068i	0.892474	+	0.0287356i
$922$	−1.83307	−	17.4405i	−0.0603691	−	0.574373i
$923$	10.1752	−	17.6240i	0.334922	−	0.580101i
$924$	−2.81973	−	0.748703i	−0.0927624	−	0.0246305i
$925$	−0.764564	−	1.32426i	−0.0251387	−	0.0435415i
$926$	9.57363	−	6.95565i	0.314609	−	0.228577i
$927$	−3.42975	−	4.34099i	−0.112648	−	0.142577i
$928$	−2.62100	+	8.06660i	−0.0860384	+	0.264799i
$929$	2.38842	−	22.7243i	0.0783616	−	0.745561i	−0.882833	−	0.469688i	$-0.844366\pi$
$929$	2.38842	−	22.7243i	0.0783616	−	0.745561i	0.961194	−	0.275873i	$-0.0889668\pi$
$930$	−0.0277841	−	0.382382i	−0.000911078	−	0.0125388i
$931$	−26.7309	−	29.6877i	−0.876071	−	0.972975i
$932$	−8.57179	−	1.82199i	−0.280778	−	0.0596812i
$933$	40.3452	+	9.94270i	1.32084	+	0.325510i
$934$	−1.81180	−	3.13812i	−0.0592838	−	0.102683i
$935$	−21.3210	+	4.13431i	−0.697270	+	0.135206i
$936$	6.60320	−	2.44413i	0.215832	−	0.0798889i
$937$	7.37613	−	5.35907i	0.240968	−	0.175073i	−0.460747	−	0.887532i	$-0.652418\pi$
$937$	7.37613	−	5.35907i	0.240968	−	0.175073i	0.701714	+	0.712458i	$0.252418\pi$
$938$	−1.78075	+	1.97773i	−0.0581437	+	0.0645751i
$939$	−4.89414	+	35.5245i	−0.159714	+	1.15930i
$940$	−2.10808	+	0.938578i	−0.0687580	+	0.0306130i
$941$	24.8245	−	11.0526i	0.809256	−	0.360304i	0.0399635	−	0.999201i	$-0.487276\pi$
$941$	24.8245	−	11.0526i	0.809256	−	0.360304i	0.769292	+	0.638897i	$0.220609\pi$
$942$	13.1134	+	10.1880i	0.427258	+	0.331943i
$943$	−2.80915	+	3.11988i	−0.0914785	+	0.101597i
$944$	−4.75228	+	3.45273i	−0.154673	+	0.112377i
$945$	2.27453	−	1.33807i	0.0739905	−	0.0435273i
$946$	−12.6236	−	22.7981i	−0.410429	−	0.741229i
$947$	9.97819	+	17.2827i	0.324248	+	0.561613i	0.981360	−	0.192179i	$-0.0615555\pi$
$947$	9.97819	+	17.2827i	0.324248	+	0.561613i	−0.657112	+	0.753793i	$0.728222\pi$
$948$	−6.58160	−	22.7194i	−0.213761	−	0.737891i
$949$	−18.8987	−	4.01704i	−0.613477	−	0.130399i
$950$	3.96479	+	4.40335i	0.128635	+	0.142863i
$951$	−16.8449	−	8.15915i	−0.546233	−	0.264579i
$952$	0.347620	−	3.30738i	0.0112664	−	0.107193i
$953$	2.50651	−	7.71425i	0.0811939	−	0.249889i	−0.902217	−	0.431283i	$-0.858061\pi$
$953$	2.50651	−	7.71425i	0.0811939	−	0.249889i	0.983410	+	0.181394i	$0.0580610\pi$
$954$	−28.8480	+	4.21448i	−0.933988	+	0.136449i
$955$	16.3301	−	11.8645i	0.528429	−	0.383926i
$956$	4.68511	+	8.11485i	0.151527	+	0.262453i
$957$	40.8030	−	26.6294i	1.31897	−	0.860805i
$958$	7.49289	−	12.9781i	0.242084	−	0.419302i
$959$	1.00182	+	9.53171i	0.0323506	+	0.307795i
$960$	0.913848	−	1.47135i	0.0294943	−	0.0474877i
$961$	30.2747	−	6.43508i	0.976602	−	0.207583i
$962$	−2.90346	−	2.10949i	−0.0936114	−	0.0680127i
$963$	−9.23527	−	36.2006i	−0.297603	−	1.16655i
$964$	2.91372	−	8.96752i	0.0938448	−	0.288824i
$965$	5.65387	−	6.27926i	0.182005	−	0.202137i
$966$	−0.968992	+	1.00890i	−0.0311768	+	0.0324608i
$967$	9.98875	−	17.3010i	0.321216	−	0.556363i	−0.659523	−	0.751684i	$-0.729242\pi$
$967$	9.98875	−	17.3010i	0.321216	−	0.556363i	0.980739	+	0.195321i	$0.0625750\pi$
$968$	9.88234	+	4.83107i	0.317631	+	0.155277i
$969$	22.8133	−	63.2135i	0.732868	−	2.03071i
$970$	−14.9964	−	6.67684i	−0.481506	−	0.214380i
$971$	−18.2525	−	56.1753i	−0.585749	−	1.80275i	−0.596240	−	0.802806i	$-0.703340\pi$
$971$	−18.2525	−	56.1753i	−0.585749	−	1.80275i	0.0104912	−	0.999945i	$-0.496660\pi$
$972$	−8.43965	−	13.1062i	−0.270702	−	0.420381i
$973$	7.31248	+	5.31283i	0.234427	+	0.170321i
$974$	−0.976925	+	9.29482i	−0.0313027	+	0.297825i
$975$	3.21017	+	2.49403i	0.102808	+	0.0798728i
$976$	−13.9628	−	2.96789i	−0.446939	−	0.0949999i
$977$	−4.34785	−	41.3671i	−0.139100	−	1.32345i	−0.811974	−	0.583693i	$-0.801607\pi$
$977$	−4.34785	−	41.3671i	−0.139100	−	1.32345i	0.672874	−	0.739757i	$-0.265060\pi$
$978$	10.7763	−	1.93038i	0.344587	−	0.0617269i
$979$	−31.7568	+	13.4629i	−1.01495	+	0.430276i
$980$	−6.74208			−0.215368
$981$	−55.5654	−	3.58187i	−1.77407	−	0.114360i
$982$	−9.31260	−	28.6612i	−0.297177	−	0.914616i
$983$	49.0114	−	10.4177i	1.56322	−	0.332273i	0.656607	−	0.754233i	$-0.271991\pi$
$983$	49.0114	−	10.4177i	1.56322	−	0.332273i	0.906614	+	0.421960i	$0.138658\pi$
$984$	−0.331368	−	4.56049i	−0.0105636	−	0.145383i
$985$	−9.11679	+	4.05906i	−0.290485	+	0.129332i
$986$	37.1638	+	41.2746i	1.18354	+	1.31445i
$987$	−1.07097	+	1.72432i	−0.0340892	+	0.0548858i
$988$	12.7044	+	5.65637i	0.404181	+	0.179953i
$989$	−12.4952			−0.397324
$990$	−9.39153	+	3.28622i	−0.298482	+	0.104443i
$991$	44.3976			1.41033			0.705167	−	0.709041i	$-0.250872\pi$
$991$	44.3976			1.41033			0.705167	+	0.709041i	$0.250872\pi$
$992$	−0.202214	−	0.0900313i	−0.00642029	−	0.00285850i
$993$	4.10180	+	7.66400i	0.130167	+	0.243210i
$994$	−2.94656	−	3.27248i	−0.0934591	−	0.103797i
$995$	−8.46542	+	3.76905i	−0.268372	+	0.119487i
$996$	−12.9772	+	8.80465i	−0.411197	+	0.278986i
$997$	−54.2480	+	11.5308i	−1.71805	+	0.365183i	−0.958462	−	0.285219i	$-0.907934\pi$
$997$	−54.2480	+	11.5308i	−1.71805	+	0.365183i	−0.759590	+	0.650402i	$0.774600\pi$
$998$	−0.463496	−	1.42649i	−0.0146717	−	0.0451549i
$999$	−3.17242	+	7.28478i	−0.100371	+	0.230480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bg.a.751.1	yes	88
9.7	even	3	inner	990.2.bg.a.421.9	yes	88
11.4	even	5	inner	990.2.bg.a.301.9	✓	88
99.70	even	15	inner	990.2.bg.a.961.1	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bg.a.301.9	✓	88	11.4	even	5	inner
990.2.bg.a.421.9	yes	88	9.7	even	3	inner
990.2.bg.a.751.1	yes	88	1.1	even	1	trivial
990.2.bg.a.961.1	yes	88	99.70	even	15	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 + 0.406737i) q^{2} +(-1.73115 - 0.0557391i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.913545 - 0.406737i) q^{5} +(-1.55882 - 0.755044i) q^{6} +(-0.496763 + 0.105590i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.99379 + 0.192986i) q^{9} +1.00000 q^{10} +(-3.05356 + 1.29452i) q^{11} +(-1.11695 - 1.32379i) q^{12} +(-0.245329 - 2.33415i) q^{13} +(-0.496763 - 0.105590i) q^{14} +(-1.60416 + 0.653203i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(5.29765 + 3.84897i) q^{17} +(2.65647 + 1.39398i) q^{18} +(1.83102 + 5.63528i) q^{19} +(0.913545 + 0.406737i) q^{20} +(0.865858 - 0.155104i) q^{21} +(-3.31609 - 0.0593911i) q^{22} +(-0.795133 + 1.37721i) q^{23} +(-0.481945 - 1.66365i) q^{24} +(0.669131 - 0.743145i) q^{25} +(0.725266 - 2.23214i) q^{26} +(-5.17195 - 0.500959i) q^{27} +(-0.410868 - 0.298513i) q^{28} +(8.29637 - 1.76345i) q^{29} +(-1.73115 - 0.0557391i) q^{30} +(0.0231374 + 0.220138i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.35833 - 2.07081i) q^{33} +(3.27413 + 5.67095i) q^{34} +(-0.410868 + 0.298513i) q^{35} +(1.85982 + 2.35395i) q^{36} +(0.472527 - 1.45429i) q^{37} +(-0.619361 + 5.89283i) q^{38} +(0.294599 + 4.05445i) q^{39} +(0.669131 + 0.743145i) q^{40} +(2.58225 + 0.548874i) q^{41} +(0.854087 + 0.210482i) q^{42} +(3.92865 + 6.80462i) q^{43} +(-3.00525 - 1.40303i) q^{44} +(2.81345 - 1.04138i) q^{45} +(-1.28655 + 0.934735i) q^{46} +(-1.54407 + 1.71487i) q^{47} +(0.236389 - 1.71584i) q^{48} +(-6.15919 + 2.74225i) q^{49} +(0.913545 - 0.406737i) q^{50} +(-8.95650 - 6.95844i) q^{51} +(1.57046 - 1.74417i) q^{52} +(-7.86208 + 5.71214i) q^{53} +(-4.52105 - 2.56127i) q^{54} +(-2.26304 + 2.42460i) q^{55} +(-0.253930 - 0.439820i) q^{56} +(-2.85566 - 9.85760i) q^{57} +(8.29637 + 1.76345i) q^{58} +(3.93056 + 4.36533i) q^{59} +(-1.55882 - 0.755044i) q^{60} +(-1.49212 + 14.1966i) q^{61} +(-0.0684011 + 0.210517i) q^{62} +(-1.50758 + 0.220246i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.17350 - 2.03257i) q^{65} +(5.73736 + 0.287651i) q^{66} +(2.62010 - 4.53815i) q^{67} +(0.684479 + 6.51238i) q^{68} +(1.45326 - 2.33984i) q^{69} +(-0.496763 + 0.105590i) q^{70} +(7.01483 + 5.09657i) q^{71} +(0.741590 + 2.90690i) q^{72} +(2.54387 - 7.82923i) q^{73} +(1.02319 - 1.13636i) q^{74} +(-1.19979 + 1.24920i) q^{75} +(-2.96264 + 5.13145i) q^{76} +(1.38021 - 0.965495i) q^{77} +(-1.37996 + 3.82375i) q^{78} +(12.4757 + 5.55453i) q^{79} +(0.309017 + 0.951057i) q^{80} +(8.92551 + 1.15552i) q^{81} +(2.13576 + 1.55172i) q^{82} +(0.946408 - 9.00447i) q^{83} +(0.694637 + 0.539674i) q^{84} +(6.40516 + 1.36146i) q^{85} +(0.821311 + 7.81425i) q^{86} +(-14.4606 + 2.59037i) q^{87} +(-2.17476 - 2.50408i) q^{88} +10.3999 q^{89} +(2.99379 + 0.192986i) q^{90} +(0.368334 + 1.13362i) q^{91} +(-1.55552 + 0.330635i) q^{92} +(-0.0277841 - 0.382382i) q^{93} +(-2.10808 + 0.938578i) q^{94} +(3.96479 + 4.40335i) q^{95} +(0.913848 - 1.47135i) q^{96} +(-14.9964 - 6.67684i) q^{97} -6.74208 q^{98} +(-9.39153 + 3.28622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) \) 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more