LMFDB - Embedded newform 690.2.w.a.373.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			373.8
Character	$\chi$	$=$	690.373
Dual form			690.2.w.a.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.877679 - 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-0.516511 + 2.17560i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-1.41675 + 3.79846i) q^{7} +(0.0713392 - 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +O(q^{10})$	\(q+(0.877679 - 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-0.516511 + 2.17560i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-1.41675 + 3.79846i) q^{7} +(0.0713392 - 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +(0.589321 + 2.15701i) q^{10} +(0.380664 + 1.29642i) q^{11} +(0.479249 - 0.877679i) q^{12} +(-3.10788 + 1.15918i) q^{13} +(0.576955 + 4.01281i) q^{14} +(-0.359989 + 2.20690i) q^{15} +(-0.415415 - 0.909632i) q^{16} +(1.22067 + 0.265541i) q^{17} +(0.800541 - 0.599278i) q^{18} +(6.03561 + 3.87885i) q^{19} +(1.55098 + 1.61073i) q^{20} +(-1.14216 + 3.88985i) q^{21} +(0.955409 + 0.955409i) q^{22} +(-1.15127 - 4.65560i) q^{23} -1.00000i q^{24} +(-4.46643 - 2.24744i) q^{25} +(-2.17219 + 2.50684i) q^{26} +(0.977147 - 0.212565i) q^{27} +(2.42951 + 3.24545i) q^{28} +(5.50536 + 8.56651i) q^{29} +(0.741699 + 2.10947i) q^{30} +(-4.64297 - 5.35827i) q^{31} +(-0.800541 - 0.599278i) q^{32} +(0.472179 + 1.26596i) q^{33} +(1.19862 - 0.351947i) q^{34} +(-7.53215 - 5.04423i) q^{35} +(0.415415 - 0.909632i) q^{36} +(4.71614 - 6.30002i) q^{37} +(7.15626 + 0.511826i) q^{38} +(-3.01727 + 1.37794i) q^{39} +(2.13321 + 0.670400i) q^{40} +(-0.384623 + 2.67511i) q^{41} +(0.861755 + 3.96142i) q^{42} +(0.0327711 + 0.458200i) q^{43} +(1.29642 + 0.380664i) q^{44} +(-0.201634 + 2.22696i) q^{45} +(-3.24163 - 3.53438i) q^{46} +(4.63739 - 4.63739i) q^{47} +(-0.479249 - 0.877679i) q^{48} +(-7.13087 - 6.17894i) q^{49} +(-4.99718 + 0.168005i) q^{50} +(1.23651 + 0.177783i) q^{51} +(-0.705083 + 3.24122i) q^{52} +(-0.204563 - 0.0762982i) q^{53} +(0.755750 - 0.654861i) q^{54} +(-3.01711 + 0.158555i) q^{55} +(3.68771 + 1.68412i) q^{56} +(6.29695 + 3.43839i) q^{57} +(8.93743 + 4.88021i) q^{58} +(7.48072 + 3.41633i) q^{59} +(1.66194 + 1.49598i) q^{60} +(8.31763 - 7.20727i) q^{61} +(-6.64298 - 2.47770i) q^{62} +(-0.861755 + 3.96142i) q^{63} +(-0.989821 - 0.142315i) q^{64} +(-0.916652 - 7.36022i) q^{65} +(1.02113 + 0.884817i) q^{66} +(-5.54092 - 10.1474i) q^{67} +(0.883334 - 0.883334i) q^{68} +(-1.48046 - 4.56161i) q^{69} +(-9.02825 - 0.817438i) q^{70} +(-3.52204 - 1.03416i) q^{71} +(-0.0713392 - 0.997452i) q^{72} +(-2.22874 - 10.2453i) q^{73} +(1.11998 - 7.78960i) q^{74} +(-4.61538 - 1.92308i) q^{75} +(6.52619 - 2.98041i) q^{76} +(-5.46371 - 0.390772i) q^{77} +(-1.98782 + 2.65541i) q^{78} +(-4.99225 + 10.9315i) q^{79} +(2.19356 - 0.433940i) q^{80} +(0.959493 - 0.281733i) q^{81} +(0.944469 + 2.53222i) q^{82} +(5.17838 + 3.87649i) q^{83} +(2.65485 + 3.06386i) q^{84} +(-1.20820 + 2.51854i) q^{85} +(0.248355 + 0.386447i) q^{86} +(6.10246 + 8.15193i) q^{87} +(1.32027 - 0.287208i) q^{88} +(8.78742 - 10.1412i) q^{89} +(0.890298 + 2.05119i) q^{90} -13.4474i q^{91} +(-4.53896 - 1.54850i) q^{92} +(-5.01339 - 5.01339i) q^{93} +(1.84767 - 6.29260i) q^{94} +(-11.5563 + 11.1276i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(-2.05711 + 1.53994i) q^{97} +(-9.21986 - 2.00566i) q^{98} +(0.561289 + 1.22905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{22}\right)$

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 $

$2$	0.877679	−	0.479249i	0.620613	−	0.338880i
$2$	0.877679	−	0.479249i	0.620613	−	0.338880i
$3$	0.997452	−	0.0713392i	0.575879	−	0.0411877i
$3$	0.997452	−	0.0713392i	0.575879	−	0.0411877i
$4$	0.540641	−	0.841254i	0.270320	−	0.420627i
$5$	−0.516511	+	2.17560i	−0.230991	+	0.972956i
$5$	−0.516511	+	2.17560i	−0.230991	+	0.972956i
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	−1.41675	+	3.79846i	−0.535482	+	1.43568i	0.334403	+	0.942430i	$0.391465\pi$
$7$	−1.41675	+	3.79846i	−0.535482	+	1.43568i	−0.869886	+	0.493253i	$0.835808\pi$
$8$	0.0713392	−	0.997452i	0.0252222	−	0.352653i
$9$	0.989821	−	0.142315i	0.329940	−	0.0474383i
$10$	0.589321	+	2.15701i	0.186360	+	0.682107i
$11$	0.380664	+	1.29642i	0.114774	+	0.390886i	0.996764	−	0.0803831i	$-0.0256144\pi$
$11$	0.380664	+	1.29642i	0.114774	+	0.390886i	−0.881990	+	0.471269i	$0.843796\pi$
$12$	0.479249	−	0.877679i	0.138347	−	0.253364i
$13$	−3.10788	+	1.15918i	−0.861971	+	0.321499i	−0.741284	−	0.671192i	$-0.765783\pi$
$13$	−3.10788	+	1.15918i	−0.861971	+	0.321499i	−0.120687	+	0.992691i	$0.538510\pi$
$14$	0.576955	+	4.01281i	0.154198	+	1.07247i
$15$	−0.359989	+	2.20690i	−0.0929489	+	0.569819i
$16$	−0.415415	−	0.909632i	−0.103854	−	0.227408i
$17$	1.22067	+	0.265541i	0.296057	+	0.0644032i	0.358140	−	0.933668i	$-0.383411\pi$
$17$	1.22067	+	0.265541i	0.296057	+	0.0644032i	−0.0620836	+	0.998071i	$0.519775\pi$
$18$	0.800541	−	0.599278i	0.188689	−	0.141251i
$19$	6.03561	+	3.87885i	1.38466	+	0.889869i	0.999457	−	0.0329607i	$-0.0104936\pi$
$19$	6.03561	+	3.87885i	1.38466	+	0.889869i	0.385207	+	0.922830i	$0.374130\pi$
$20$	1.55098	+	1.61073i	0.346810	+	0.360171i
$21$	−1.14216	+	3.88985i	−0.249241	+	0.848836i
$22$	0.955409	+	0.955409i	0.203694	+	0.203694i
$23$	−1.15127	−	4.65560i	−0.240056	−	0.970759i
$23$	−1.15127	−	4.65560i	−0.240056	−	0.970759i
$24$		−	1.00000i		−	0.204124i
$25$	−4.46643	−	2.24744i	−0.893287	−	0.449487i
$26$	−2.17219	+	2.50684i	−0.426001	+	0.491631i
$27$	0.977147	−	0.212565i	0.188052	−	0.0409082i
$28$	2.42951	+	3.24545i	0.459135	+	0.613333i
$29$	5.50536	+	8.56651i	1.02232	+	1.59076i	0.785163	+	0.619289i	$0.212579\pi$
$29$	5.50536	+	8.56651i	1.02232	+	1.59076i	0.237157	+	0.971471i	$0.423785\pi$
$30$	0.741699	+	2.10947i	0.135415	+	0.385136i
$31$	−4.64297	−	5.35827i	−0.833902	−	0.962374i	0.165815	−	0.986157i	$-0.446974\pi$
$31$	−4.64297	−	5.35827i	−0.833902	−	0.962374i	−0.999717	+	0.0237829i	$0.992429\pi$
$32$	−0.800541	−	0.599278i	−0.141517	−	0.105938i
$33$	0.472179	+	1.26596i	0.0821959	+	0.220376i
$34$	1.19862	−	0.351947i	0.205562	−	0.0603583i
$35$	−7.53215	−	5.04423i	−1.27317	−	0.852630i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	4.71614	−	6.30002i	0.775328	−	1.03572i	−0.222819	−	0.974860i	$-0.571526\pi$
$37$	4.71614	−	6.30002i	0.775328	−	1.03572i	0.998147	−	0.0608568i	$-0.0193833\pi$
$38$	7.15626	+	0.511826i	1.16090	+	0.0830291i
$39$	−3.01727	+	1.37794i	−0.483149	+	0.220647i
$40$	2.13321	+	0.670400i	0.337289	+	0.106000i
$41$	−0.384623	+	2.67511i	−0.0600680	+	0.417782i	0.937494	+	0.348001i	$0.113139\pi$
$41$	−0.384623	+	2.67511i	−0.0600680	+	0.417782i	−0.997562	+	0.0697816i	$0.977770\pi$
$42$	0.861755	+	3.96142i	0.132972	+	0.611261i
$43$	0.0327711	+	0.458200i	0.00499755	+	0.0698749i	0.999339	−	0.0363580i	$-0.0115756\pi$
$43$	0.0327711	+	0.458200i	0.00499755	+	0.0698749i	−0.994341	+	0.106233i	$0.966121\pi$
$44$	1.29642	+	0.380664i	0.195443	+	0.0573872i
$45$	−0.201634	+	2.22696i	−0.0300578	+	0.331975i
$46$	−3.24163	−	3.53438i	−0.477953	−	0.521115i
$47$	4.63739	−	4.63739i	0.676433	−	0.676433i	−0.282759	−	0.959191i	$-0.591250\pi$
$47$	4.63739	−	4.63739i	0.676433	−	0.676433i	0.959191	+	0.282759i	$0.0912495\pi$
$48$	−0.479249	−	0.877679i	−0.0691736	−	0.126682i
$49$	−7.13087	−	6.17894i	−1.01870	−	0.882705i
$50$	−4.99718	+	0.168005i	−0.706707	+	0.0237596i
$51$	1.23651	+	0.177783i	0.173146	+	0.0248946i
$52$	−0.705083	+	3.24122i	−0.0977775	+	0.449476i
$53$	−0.204563	−	0.0762982i	−0.0280989	−	0.0104804i	0.335375	−	0.942085i	$-0.391137\pi$
$53$	−0.204563	−	0.0762982i	−0.0280989	−	0.0104804i	−0.363474	+	0.931604i	$0.618410\pi$
$54$	0.755750	−	0.654861i	0.102844	−	0.0891153i
$55$	−3.01711	+	0.158555i	−0.406826	+	0.0213795i
$56$	3.68771	+	1.68412i	0.492791	+	0.225050i
$57$	6.29695	+	3.43839i	0.834051	+	0.455426i
$58$	8.93743	+	4.88021i	1.17354	+	0.640802i
$59$	7.48072	+	3.41633i	0.973907	+	0.444769i	0.837831	−	0.545930i	$-0.183823\pi$
$59$	7.48072	+	3.41633i	0.973907	+	0.444769i	0.136076	+	0.990698i	$0.456551\pi$
$60$	1.66194	+	1.49598i	0.214555	+	0.193131i
$61$	8.31763	−	7.20727i	1.06496	−	0.922796i	0.0677725	−	0.997701i	$-0.478411\pi$
$61$	8.31763	−	7.20727i	1.06496	−	0.922796i	0.997191	+	0.0749049i	$0.0238653\pi$
$62$	−6.64298	−	2.47770i	−0.843660	−	0.314669i
$63$	−0.861755	+	3.96142i	−0.108571	+	0.499092i
$64$	−0.989821	−	0.142315i	−0.123728	−	0.0177894i
$65$	−0.916652	−	7.36022i	−0.113697	−	0.912923i
$66$	1.02113	+	0.884817i	0.125693	+	0.108913i
$67$	−5.54092	−	10.1474i	−0.676932	−	1.23971i	−0.959837	−	0.280560i	$-0.909480\pi$
$67$	−5.54092	−	10.1474i	−0.676932	−	1.23971i	0.282905	−	0.959148i	$-0.408702\pi$
$68$	0.883334	−	0.883334i	0.107120	−	0.107120i
$69$	−1.48046	−	4.56161i	−0.178226	−	0.549153i
$70$	−9.02825	−	0.817438i	−1.07908	−	0.0977025i
$71$	−3.52204	−	1.03416i	−0.417989	−	0.122733i	0.0659734	−	0.997821i	$-0.478985\pi$
$71$	−3.52204	−	1.03416i	−0.417989	−	0.122733i	−0.483963	+	0.875089i	$0.660803\pi$
$72$	−0.0713392	−	0.997452i	−0.00840740	−	0.117551i
$73$	−2.22874	−	10.2453i	−0.260854	−	1.19913i	−0.902010	−	0.431715i	$-0.857908\pi$
$73$	−2.22874	−	10.2453i	−0.260854	−	1.19913i	0.641156	−	0.767411i	$-0.278455\pi$
$74$	1.11998	−	7.78960i	0.130194	−	0.905522i
$75$	−4.61538	−	1.92308i	−0.532939	−	0.222058i
$76$	6.52619	−	2.98041i	0.748606	−	0.341877i
$77$	−5.46371	−	0.390772i	−0.622648	−	0.0445326i
$78$	−1.98782	+	2.65541i	−0.225076	+	0.300666i
$79$	−4.99225	+	10.9315i	−0.561672	+	1.22989i	0.389443	+	0.921051i	$0.372668\pi$
$79$	−4.99225	+	10.9315i	−0.561672	+	1.22989i	−0.951114	+	0.308839i	$0.900060\pi$
$80$	2.19356	−	0.433940i	0.245247	−	0.0485160i
$81$	0.959493	−	0.281733i	0.106610	−	0.0313036i
$82$	0.944469	+	2.53222i	0.104299	+	0.279637i
$83$	5.17838	+	3.87649i	0.568401	+	0.425500i	0.844443	−	0.535646i	$-0.179932\pi$
$83$	5.17838	+	3.87649i	0.568401	+	0.425500i	−0.276041	+	0.961146i	$0.589023\pi$
$84$	2.65485	+	3.06386i	0.289668	+	0.334295i
$85$	−1.20820	+	2.51854i	−0.131048	+	0.273174i
$86$	0.248355	+	0.386447i	0.0267808	+	0.0416717i
$87$	6.10246	+	8.15193i	0.654252	+	0.873979i
$88$	1.32027	−	0.287208i	0.140742	−	0.0306165i
$89$	8.78742	−	10.1412i	0.931464	−	1.07497i	−0.0655578	−	0.997849i	$-0.520883\pi$
$89$	8.78742	−	10.1412i	0.931464	−	1.07497i	0.997022	−	0.0771181i	$-0.0245719\pi$
$90$	0.890298	+	2.05119i	0.0938456	+	0.216214i
$91$		−	13.4474i		−	1.40967i
$92$	−4.53896	−	1.54850i	−0.473219	−	0.161442i
$93$	−5.01339	−	5.01339i	−0.519865	−	0.519865i
$94$	1.84767	−	6.29260i	0.190573	−	0.649032i
$95$	−11.5563	+	11.1276i	−1.18565	+	1.14167i
$96$	−0.841254	−	0.540641i	−0.0858601	−	0.0551789i
$97$	−2.05711	+	1.53994i	−0.208868	+	0.156357i	−0.698591	−	0.715522i	$-0.746189\pi$
$97$	−2.05711	+	1.53994i	−0.208868	+	0.156357i	0.489722	+	0.871878i	$0.337098\pi$
$98$	−9.21986	−	2.00566i	−0.931347	−	0.202602i
$99$	0.561289	+	1.22905i	0.0564117	+	0.123524i
$100$	−4.30540	+	2.54235i	−0.430540	+	0.254235i
$101$	1.25693	+	8.74215i	0.125069	+	0.869876i	0.951678	+	0.307099i	$0.0993582\pi$
$101$	1.25693	+	8.74215i	0.125069	+	0.869876i	−0.826608	+	0.562778i	$0.809733\pi$
$102$	1.17046	−	0.436558i	0.115893	−	0.0432257i
$103$	−7.20394	+	13.1930i	−0.709825	+	1.29995i	0.234880	+	0.972024i	$0.424530\pi$
$103$	−7.20394	+	13.1930i	−0.709825	+	1.29995i	−0.944705	+	0.327923i	$0.893651\pi$
$104$	0.934512	+	3.18266i	0.0916365	+	0.312085i
$105$	−7.87281	−	4.49404i	−0.768307	−	0.438573i
$106$	−0.216107	+	0.0310715i	−0.0209901	+	0.00301793i
$107$	−0.276704	+	3.86882i	−0.0267500	+	0.374013i	0.966390	+	0.257081i	$0.0827607\pi$
$107$	−0.276704	+	3.86882i	−0.0267500	+	0.374013i	−0.993140	+	0.116933i	$0.962694\pi$
$108$	0.349464	−	0.936950i	0.0336272	−	0.0901580i
$109$	−16.1864	+	10.4024i	−1.55038	+	0.996367i	−0.565176	+	0.824971i	$0.691192\pi$
$109$	−16.1864	+	10.4024i	−1.55038	+	0.996367i	−0.985202	+	0.171397i	$0.945172\pi$
$110$	−2.57206	+	1.58510i	−0.245237	+	0.151134i
$111$	4.25468	−	6.62041i	0.403836	−	0.628382i
$112$	4.04374	−	0.289214i	0.382098	−	0.0273282i
$113$	15.1432	−	8.26880i	1.42455	−	0.777863i	0.432254	−	0.901752i	$-0.357718\pi$
$113$	15.1432	−	8.26880i	1.42455	−	0.777863i	0.992296	+	0.123889i	$0.0395366\pi$
$114$	7.17454			0.671958
$115$	10.7233	−	0.100023i	0.999957	−	0.00932721i
$116$	10.1830			0.945470
$117$	−2.91128	+	1.58968i	−0.269148	+	0.146966i
$118$	8.20295	−	0.586686i	0.755143	−	0.0540089i
$119$	−2.73804	+	4.26048i	−0.250996	+	0.390557i
$120$	2.17560	+	0.516511i	0.198604	+	0.0471508i
$121$	7.71799	−	4.96005i	0.701635	−	0.450913i
$122$	3.84613	−	10.3119i	0.348213	−	0.933594i
$123$	−0.192803	+	2.69573i	−0.0173844	+	0.243066i
$124$	−7.01784	+	1.00901i	−0.630221	+	0.0906121i
$125$	7.19647	−	8.55633i	0.643672	−	0.765301i
$126$	1.14216	+	3.88985i	0.101752	+	0.346536i
$127$	−4.88465	+	8.94557i	−0.433442	+	0.793791i	−0.999533	−	0.0305523i	$-0.990273\pi$
$127$	−4.88465	+	8.94557i	−0.433442	+	0.793791i	0.566091	+	0.824343i	$0.308455\pi$
$128$	−0.936950	+	0.349464i	−0.0828154	+	0.0308886i
$129$	0.0653753	+	0.454695i	0.00575597	+	0.0400337i
$130$	−4.33191	−	6.02061i	−0.379933	−	0.528042i
$131$	0.800808	+	1.75352i	0.0699669	+	0.153206i	0.941384	−	0.337336i	$-0.109526\pi$
$131$	0.800808	+	1.75352i	0.0699669	+	0.153206i	−0.871417	+	0.490542i	$0.836799\pi$
$132$	1.32027	+	0.287208i	0.114915	+	0.0249983i
$133$	−23.2846	+	17.4307i	−2.01903	+	1.51143i
$134$	−9.72630	−	6.25072i	−0.840225	−	0.539980i
$135$	−0.0422507	+	2.23567i	−0.00363636	+	0.192416i
$136$	0.351947	−	1.19862i	0.0301792	−	0.102781i
$137$	0.655626	+	0.655626i	0.0560139	+	0.0560139i	0.734559	−	0.678545i	$-0.237389\pi$
$137$	0.655626	+	0.655626i	0.0560139	+	0.0560139i	−0.678545	+	0.734559i	$0.737389\pi$
$138$	−3.48551	−	3.29412i	−0.296707	−	0.280414i
$139$		−	15.5586i		−	1.31967i	−0.751412	−	0.659833i	$-0.770627\pi$
$139$		−	15.5586i		−	1.31967i	0.751412	−	0.659833i	$-0.229373\pi$
$140$	−8.31566	+	3.60933i	−0.702802	+	0.305044i
$141$	4.29474	−	4.95640i	0.361683	−	0.417404i
$142$	−3.58684	+	0.780270i	−0.301001	+	0.0654788i
$143$	−2.68584	−	3.58786i	−0.224601	−	0.300032i
$144$	−0.540641	−	0.841254i	−0.0450534	−	0.0701045i
$145$	−21.4808	+	7.55274i	−1.78389	+	0.627221i
$146$	−6.86618	−	7.92400i	−0.568249	−	0.655795i
$147$	−7.55350	−	5.65448i	−0.623002	−	0.466374i
$148$	−2.75018	−	7.37351i	−0.226063	−	0.606099i
$149$	−0.442108	+	0.129815i	−0.0362189	+	0.0106348i	−0.299792	−	0.954005i	$-0.596917\pi$
$149$	−0.442108	+	0.129815i	−0.0362189	+	0.0106348i	0.263573	+	0.964639i	$0.415099\pi$
$150$	−4.97246	+	0.524072i	−0.406000	+	0.0427903i
$151$	1.65445	−	3.62274i	0.134637	−	0.294814i	−0.830290	−	0.557331i	$-0.811825\pi$
$151$	1.65445	−	3.62274i	0.134637	−	0.294814i	0.964927	+	0.262517i	$0.0845526\pi$
$152$	4.29954	−	5.74352i	0.348739	−	0.465861i
$153$	1.24604	+	0.0891185i	0.100736	+	0.00720480i
$154$	−4.98266	+	2.27551i	−0.401514	+	0.183365i
$155$	14.0556	−	7.33362i	1.12897	−	0.589050i
$156$	−0.472061	+	3.28326i	−0.0377951	+	0.262871i
$157$	−3.34623	−	15.3824i	−0.267058	−	1.22765i	−0.893817	−	0.448432i	$-0.851982\pi$
$157$	−3.34623	−	15.3824i	−0.267058	−	1.22765i	0.626759	−	0.779213i	$-0.284381\pi$
$158$	0.857318	+	11.9869i	0.0682046	+	0.953625i
$159$	−0.209485	−	0.0615104i	−0.0166132	−	0.00487809i
$160$	1.71727	−	1.43212i	0.135762	−	0.113219i
$161$	19.3152	+	2.22279i	1.52225	+	0.175181i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−6.00597	−	10.9991i	−0.470424	−	0.861517i	−0.999913	−	0.0132000i	$-0.995798\pi$
$163$	−6.00597	−	10.9991i	−0.470424	−	0.861517i	0.529489	−	0.848317i	$-0.322384\pi$
$164$	2.04250	+	1.76984i	0.159493	+	0.138201i
$165$	−2.99811	+	0.373389i	−0.233402	+	0.0290683i
$166$	6.40276	+	0.920578i	0.496951	+	0.0714507i
$167$	−2.15623	+	9.91203i	−0.166854	+	0.767016i	0.815315	+	0.579017i	$0.196564\pi$
$167$	−2.15623	+	9.91203i	−0.166854	+	0.767016i	−0.982169	+	0.187999i	$0.939800\pi$
$168$	3.79846	+	1.41675i	0.293058	+	0.109305i
$169$	−1.50952	+	1.30801i	−0.116117	+	0.100616i
$170$	0.146593	+	2.78950i	0.0112432	+	0.213945i
$171$	6.52619	+	2.98041i	0.499071	+	0.227918i
$172$	0.403180	+	0.220153i	0.0307422	+	0.0167865i
$173$	−0.940615	−	0.513615i	−0.0715136	−	0.0390494i	0.443094	−	0.896475i	$-0.353881\pi$
$173$	−0.940615	−	0.513615i	−0.0715136	−	0.0390494i	−0.514608	+	0.857426i	$0.672063\pi$
$174$	9.26281	+	4.23018i	0.702212	+	0.320689i
$175$	14.8646	−	13.7815i	1.12366	−	1.04178i
$176$	1.02113	−	0.884817i	0.0769708	−	0.0666956i
$177$	7.70538	+	2.87396i	0.579172	+	0.216020i
$178$	2.85236	−	13.1121i	0.213794	−	0.982793i
$179$	8.36854	+	1.20321i	0.625494	+	0.0899324i	0.447771	−	0.894148i	$-0.352218\pi$
$179$	8.36854	+	1.20321i	0.625494	+	0.0899324i	0.177723	+	0.984081i	$0.443127\pi$
$180$	1.76443	+	1.37361i	0.131512	+	0.102383i
$181$	−2.11421	−	1.83198i	−0.157148	−	0.136170i	0.572738	−	0.819739i	$-0.305881\pi$
$181$	−2.11421	−	1.83198i	−0.157148	−	0.136170i	−0.729886	+	0.683569i	$0.760427\pi$
$182$	−6.44467	−	11.8025i	−0.477711	−	0.874862i
$183$	7.78228	−	7.78228i	0.575282	−	0.575282i
$184$	−4.72587	+	0.816206i	−0.348395	+	0.0601715i
$185$	11.2704	+	13.5144i	0.828613	+	0.993601i
$186$	−6.80281	−	1.99749i	−0.498807	−	0.146463i
$187$	0.120413	+	1.68359i	0.00880545	+	0.123116i
$188$	−1.39406	−	6.40838i	−0.101672	−	0.467379i
$189$	−0.576955	+	4.01281i	−0.0419673	+	0.291889i
$190$	−4.80981	+	15.3048i	−0.348941	+	1.11032i
$191$	−9.33107	+	4.26136i	−0.675172	+	0.308341i	−0.723334	−	0.690499i	$-0.757391\pi$
$191$	−9.33107	+	4.26136i	−0.675172	+	0.308341i	0.0481613	+	0.998840i	$0.484664\pi$
$192$	−0.997452	−	0.0713392i	−0.0719849	−	0.00514846i
$193$	4.65283	−	6.21546i	0.334918	−	0.447398i	−0.601192	−	0.799104i	$-0.705307\pi$
$193$	4.65283	−	6.21546i	0.334918	−	0.447398i	0.936110	+	0.351706i	$0.114398\pi$
$194$	−1.06747	+	2.33744i	−0.0766401	+	0.167818i
$195$	−1.43939	−	7.27607i	−0.103077	−	0.521051i
$196$	−9.05329	+	2.65829i	−0.646664	+	0.189878i
$197$	−1.78616	−	4.78888i	−0.127259	−	0.341194i	0.857659	−	0.514220i	$-0.171918\pi$
$197$	−1.78616	−	4.78888i	−0.127259	−	0.341194i	−0.984917	+	0.173026i	$0.944646\pi$
$198$	1.08165	+	0.809715i	0.0768697	+	0.0575440i
$199$	14.9576	+	17.2620i	1.06032	+	1.22367i	0.973797	+	0.227419i	$0.0730288\pi$
$199$	14.9576	+	17.2620i	1.06032	+	1.22367i	0.0865187	+	0.996250i	$0.472426\pi$
$200$	−2.56034	+	4.29472i	−0.181044	+	0.303683i
$201$	−6.25072	−	9.72630i	−0.440892	−	0.686041i
$202$	5.29285	+	7.07042i	0.372404	+	0.497473i
$203$	−40.3393	+	8.77527i	−2.83126	+	0.615903i
$204$	0.818067	−	0.944099i	0.0572761	−	0.0661002i
$205$	−5.62130	−	2.21851i	−0.392609	−	0.154947i
$206$			15.0317i			1.04731i
$207$	−1.80211	−	4.44437i	−0.125255	−	0.308905i
$208$	2.34549	+	2.34549i	0.162630	+	0.162630i
$209$	−2.73109	+	9.30123i	−0.188913	+	0.643379i
$210$	−9.06356	−	0.171287i	−0.625445	−	0.0118199i
$211$	−15.8774	−	10.2038i	−1.09304	−	0.702456i	−0.135508	−	0.990776i	$-0.543267\pi$
$211$	−15.8774	−	10.2038i	−1.09304	−	0.702456i	−0.957534	+	0.288321i	$0.906903\pi$
$212$	−0.174781	+	0.130840i	−0.0120040	+	0.00898611i
$213$	−3.58684	−	0.780270i	−0.245766	−	0.0534632i
$214$	1.61127	+	3.52820i	0.110144	+	0.241183i
$215$	−1.01379	−	0.165369i	−0.0691396	−	0.0112781i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	26.9311	−	10.0448i	1.82820	−	0.681885i
$218$	−9.22115	+	16.8873i	−0.624535	+	1.14375i
$219$	−2.95395	−	10.0602i	−0.199610	−	0.679808i
$220$	−1.49779	+	2.62387i	−0.100981	+	0.176901i
$221$	−4.10152	+	0.589709i	−0.275898	+	0.0396681i
$222$	0.561418	−	7.84965i	0.0376799	−	0.526834i
$223$	1.52135	−	4.07890i	0.101877	−	0.273144i	−0.876004	−	0.482304i	$-0.839800\pi$
$223$	1.52135	−	4.07890i	0.101877	−	0.273144i	0.977881	+	0.209160i	$0.0670729\pi$
$224$	3.41050	−	2.19180i	0.227874	−	0.146446i
$225$	−4.74082	−	1.58892i	−0.316054	−	0.105928i
$226$	9.32803	−	14.5147i	0.620491	−	0.965504i
$227$	−18.9136	+	1.35273i	−1.25534	+	0.0897838i	−0.683115	−	0.730311i	$-0.739375\pi$
$227$	−18.9136	+	1.35273i	−1.25534	+	0.0897838i	−0.572227	+	0.820095i	$0.693921\pi$
$228$	6.29695	−	3.43839i	0.417025	−	0.227713i
$229$	24.0345			1.58824			0.794122	−	0.607758i	$-0.207931\pi$
$229$	24.0345			1.58824			0.794122	+	0.607758i	$0.207931\pi$
$230$	9.36371	−	5.22694i	0.617425	−	0.344654i
$231$	−5.47767			−0.360404
$232$	8.93743	−	4.88021i	0.586771	−	0.320401i
$233$	−15.0105	+	1.07357i	−0.983369	+	0.0703319i	−0.553754	−	0.832680i	$-0.686805\pi$
$233$	−15.0105	+	1.07357i	−0.983369	+	0.0703319i	−0.429615	+	0.903012i	$0.641351\pi$
$234$	−1.79332	+	2.79045i	−0.117233	+	0.182418i
$235$	7.69382	+	12.4843i	0.501889	+	0.814389i
$236$	6.91839	−	4.44618i	0.450349	−	0.289421i
$237$	−4.19968	+	11.2598i	−0.272799	+	0.731402i
$238$	−0.361293	+	5.05153i	−0.0234191	+	0.327442i
$239$	−6.31714	+	0.908268i	−0.408622	+	0.0587510i	−0.343561	−	0.939130i	$-0.611633\pi$
$239$	−6.31714	+	0.908268i	−0.408622	+	0.0587510i	−0.0650608	+	0.997881i	$0.520724\pi$
$240$	2.15701	−	0.589321i	0.139235	−	0.0380405i
$241$	−4.67069	−	15.9069i	−0.300865	−	1.02465i	−0.961696	−	0.274118i	$-0.911614\pi$
$241$	−4.67069	−	15.9069i	−0.300865	−	1.02465i	0.660831	−	0.750535i	$-0.270204\pi$
$242$	4.39682	−	8.05217i	0.282638	−	0.517613i
$243$	0.936950	−	0.349464i	0.0601054	−	0.0224181i
$244$	−1.56629	−	10.8938i	−0.100271	−	0.697403i
$245$	17.1260	−	12.3224i	1.09414	−	0.787250i
$246$	1.12271	+	2.45839i	0.0715813	+	0.156741i
$247$	−23.2542	−	5.05865i	−1.47963	−	0.321874i
$248$	−5.67584	+	4.24888i	−0.360417	+	0.269804i
$249$	5.44173	+	3.49719i	0.344856	+	0.221625i
$250$	2.21558	−	10.9586i	0.140126	−	0.693084i
$251$	−4.73664	+	16.1315i	−0.298974	+	1.01821i	0.663801	+	0.747909i	$0.268942\pi$
$251$	−4.73664	+	16.1315i	−0.298974	+	1.01821i	−0.962775	+	0.270303i	$0.912876\pi$
$252$	2.86666	+	2.86666i	0.180583	+	0.180583i
$253$	5.59737	−	3.26474i	0.351904	−	0.205253i
$254$			10.1923i			0.639522i
$255$	−1.02545	+	2.59831i	−0.0642163	+	0.162713i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	18.5700	−	4.03966i	1.15837	−	0.251987i	0.407983	−	0.912990i	$-0.366232\pi$
$257$	18.5700	−	4.03966i	1.15837	−	0.251987i	0.750384	+	0.661002i	$0.229869\pi$
$258$	0.275291	+	0.367745i	0.0171389	+	0.0228948i
$259$	17.2488	+	26.8396i	1.07179	+	1.66773i
$260$	−6.68739	−	3.20810i	−0.414734	−	0.198958i
$261$	6.66846	+	7.69582i	0.412768	+	0.476359i
$262$	1.54323	+	1.15525i	0.0953409	+	0.0713713i
$263$	5.27210	+	14.1351i	0.325092	+	0.871605i	0.991974	+	0.126442i	$0.0403556\pi$
$263$	5.27210	+	14.1351i	0.325092	+	0.871605i	−0.666882	+	0.745163i	$0.732372\pi$
$264$	1.29642	−	0.380664i	0.0797892	−	0.0234282i
$265$	0.271653	−	0.405638i	0.0166875	−	0.0249182i
$266$	−12.0828	+	26.4577i	−0.740844	+	1.62222i
$267$	8.04156	−	10.7423i	0.492135	−	0.657416i
$268$	−11.5322	−	0.824801i	−0.704443	−	0.0503827i
$269$	13.7734	−	6.29008i	0.839776	−	0.383513i	0.0513789	−	0.998679i	$-0.483638\pi$
$269$	13.7734	−	6.29008i	0.839776	−	0.383513i	0.788397	+	0.615166i	$0.210911\pi$
$270$	1.03436	+	1.98245i	0.0629491	+	0.120648i
$271$	−0.131221	+	0.912665i	−0.00797113	+	0.0554404i	−0.993419	−	0.114539i	$-0.963461\pi$
$271$	−0.131221	+	0.912665i	−0.00797113	+	0.0554404i	0.985448	+	0.169979i	$0.0543701\pi$
$272$	−0.265541	−	1.22067i	−0.0161008	−	0.0740142i
$273$	−0.959329	−	13.4132i	−0.0580612	−	0.811802i
$274$	0.889637	+	0.261221i	0.0537449	+	0.0157809i
$275$	1.21342	−	6.64590i	0.0731717	−	0.400763i
$276$	−4.63786	−	1.22075i	−0.279167	−	0.0734804i
$277$	8.26888	−	8.26888i	0.496829	−	0.496829i	−0.413621	−	0.910449i	$-0.635736\pi$
$277$	8.26888	−	8.26888i	0.496829	−	0.496829i	0.910449	+	0.413621i	$0.135736\pi$
$278$	−7.45646	−	13.6555i	−0.447209	−	0.819002i
$279$	−5.35827	−	4.64297i	−0.320791	−	0.277967i
$280$	−5.56871	+	7.15311i	−0.332794	+	0.427480i
$281$	24.3223	+	3.49702i	1.45095	+	0.208615i	0.822290	−	0.569069i	$-0.192696\pi$
$281$	24.3223	+	3.49702i	1.45095	+	0.208615i	0.628656	+	0.777684i	$0.283605\pi$
$282$	1.39406	−	6.40838i	0.0830149	−	0.381613i
$283$	−9.39274	−	3.50331i	−0.558341	−	0.208250i	0.0544211	−	0.998518i	$-0.482669\pi$
$283$	−9.39274	−	3.50331i	−0.558341	−	0.208250i	−0.612762	+	0.790268i	$0.709941\pi$
$284$	−2.77415	+	2.40382i	−0.164616	+	0.142640i
$285$	−10.7330	+	11.9236i	−0.635768	+	0.706296i
$286$	−4.07679	−	1.86181i	−0.241066	−	0.110091i
$287$	−9.61639	−	5.25095i	−0.567638	−	0.309954i
$288$	−0.877679	−	0.479249i	−0.0517177	−	0.0282400i
$289$	−14.0442	−	6.41378i	−0.826130	−	0.377281i
$290$	−15.2336	+	16.9236i	−0.894550	+	0.993785i
$291$	−1.94201	+	1.68277i	−0.113843	+	0.0986455i
$292$	−9.82387	−	3.66412i	−0.574899	−	0.214426i
$293$	3.49851	−	16.0824i	0.204385	−	0.939544i	−0.754621	−	0.656161i	$-0.772179\pi$
$293$	3.49851	−	16.0824i	0.204385	−	0.939544i	0.959007	−	0.283384i	$-0.0914570\pi$
$294$	−9.33946	−	1.34281i	−0.544688	−	0.0783143i
$295$	−11.2964	+	14.5105i	−0.657704	+	0.844832i
$296$	−5.94752	−	5.15356i	−0.345693	−	0.299544i
$297$	0.647538	+	1.18588i	0.0375740	+	0.0688116i
$298$	−0.325816	+	0.325816i	−0.0188740	+	0.0188740i
$299$	8.97467	+	13.1345i	0.519019	+	0.759589i
$300$	−4.11306	+	2.84301i	−0.237468	+	0.164141i
$301$	−1.78689	−	0.524677i	−0.102994	−	0.0302419i
$302$	−0.284118	−	3.97250i	−0.0163492	−	0.228591i
$303$	1.87739	+	8.63021i	0.107853	+	0.495792i
$304$	1.02104	−	7.10152i	0.0585609	−	0.407300i
$305$	11.3840	+	21.8184i	0.651843	+	1.24932i
$306$	1.13633	−	0.518946i	0.0649598	−	0.0296662i
$307$	18.5737	+	1.32842i	1.06006	+	0.0758170i	0.590464	−	0.807064i	$-0.298945\pi$
$307$	18.5737	+	1.32842i	1.06006	+	0.0758170i	0.469596	+	0.882881i	$0.344399\pi$
$308$	−3.28264	+	4.38510i	−0.187046	+	0.249864i
$309$	−6.24440	+	13.6733i	−0.355232	+	0.777849i
$310$	8.82165	−	13.1727i	0.501036	−	0.748158i
$311$	22.3717	−	6.56892i	1.26858	−	0.372489i	0.422900	−	0.906176i	$-0.361012\pi$
$311$	22.3717	−	6.56892i	1.26858	−	0.372489i	0.845682	+	0.533687i	$0.179194\pi$
$312$	1.15918	+	3.10788i	0.0656256	+	0.175949i
$313$	4.26102	+	3.18976i	0.240847	+	0.180296i	0.712882	−	0.701284i	$-0.247389\pi$
$313$	4.26102	+	3.18976i	0.240847	+	0.180296i	−0.472035	+	0.881580i	$0.656480\pi$
$314$	−10.3089	−	11.8971i	−0.581764	−	0.671392i
$315$	−8.17335	−	3.92095i	−0.460516	−	0.220920i
$316$	6.49715	+	10.1098i	0.365493	+	0.568718i
$317$	−3.91709	−	5.23262i	−0.220006	−	0.293893i	0.676936	−	0.736042i	$-0.263307\pi$
$317$	−3.91709	−	5.23262i	−0.220006	−	0.293893i	−0.896942	+	0.442148i	$0.854216\pi$
$318$	−0.213339	+	0.0464092i	−0.0119635	+	0.00260250i
$319$	−9.01011	+	10.3982i	−0.504469	+	0.582189i
$320$	0.820873	−	2.07994i	0.0458882	−	0.116272i
$321$			3.87871i			0.216488i
$322$	18.0178	−	7.30588i	1.00409	−	0.407141i
$323$	6.33752	+	6.33752i	0.352629	+	0.352629i
$324$	0.281733	−	0.959493i	0.0156518	−	0.0533052i
$325$	16.4863	+	1.80737i	0.914497	+	0.100255i
$326$	−10.5426	−	6.77533i	−0.583902	−	0.375251i
$327$	−15.4031	+	11.5306i	−0.851792	+	0.637644i
$328$	2.64086	+	0.574483i	0.145817	+	0.0317205i
$329$	11.0449	+	24.1850i	0.608925	+	1.33336i
$330$	−2.45243	+	1.76455i	−0.135002	+	0.0971355i
$331$	0.184112	+	1.28053i	0.0101197	+	0.0703841i	0.994255	−	0.107033i	$-0.0341350\pi$
$331$	0.184112	+	1.28053i	0.0101197	+	0.0703841i	−0.984136	+	0.177417i	$0.943226\pi$
$332$	6.06075	−	2.26054i	0.332627	−	0.124064i
$333$	3.77155	−	6.90707i	0.206679	−	0.378505i
$334$	2.85785	+	9.73295i	0.156375	+	0.532563i
$335$	24.9387	−	6.81355i	1.36255	−	0.372264i
$336$	4.01281	−	0.576955i	0.218917	−	0.0314754i
$337$	−1.09607	+	15.3251i	−0.0597068	+	0.834811i	0.876062	+	0.482198i	$0.160161\pi$
$337$	−1.09607	+	15.3251i	−0.0597068	+	0.834811i	−0.935769	+	0.352613i	$0.885293\pi$
$338$	−0.698012	+	1.87144i	−0.0379669	+	0.101793i
$339$	14.5147	−	9.32803i	0.788330	−	0.506629i
$340$	1.46553	+	2.37803i	0.0794793	+	0.128967i
$341$	5.17917	−	8.05894i	0.280468	−	0.436416i
$342$	7.15626	−	0.511826i	0.386966	−	0.0276764i
$343$	8.66591	−	4.73195i	0.467915	−	0.255501i
$344$	0.459371			0.0247676
$345$	10.6889	−	0.864763i	0.575470	−	0.0465573i
$346$	−1.07171			−0.0576153
$347$	−18.2708	+	9.97659i	−0.980826	+	0.535572i	−0.887868	−	0.460098i	$-0.847814\pi$
$347$	−18.2708	+	9.97659i	−0.980826	+	0.535572i	−0.0929581	+	0.995670i	$0.529632\pi$
$348$	10.1571	−	0.726449i	0.544477	−	0.0389417i
$349$	−10.3926	+	16.1711i	−0.556301	+	0.865621i	−0.999526	−	0.0307891i	$-0.990198\pi$
$349$	−10.3926	+	16.1711i	−0.556301	+	0.865621i	0.443225	+	0.896411i	$0.353834\pi$
$350$	6.44160	−	19.2196i	0.344318	−	1.02733i
$351$	−2.79045	+	1.79332i	−0.148943	+	0.0957201i
$352$	0.472179	−	1.26596i	0.0251672	−	0.0674760i
$353$	1.90416	−	26.6237i	0.101348	−	1.41704i	−0.651404	−	0.758731i	$-0.725820\pi$
$353$	1.90416	−	26.6237i	0.101348	−	1.41704i	0.752752	−	0.658304i	$-0.228726\pi$
$354$	8.14019	−	1.17038i	0.432646	−	0.0622052i
$355$	4.06909	−	7.12838i	0.215965	−	0.378335i
$356$	−3.78050	−	12.8752i	−0.200366	−	0.682384i
$357$	−2.42713	+	4.44495i	−0.128457	+	0.235252i
$358$	7.92153	−	2.95458i	0.418666	−	0.156154i
$359$	2.04591	+	14.2296i	0.107979	+	0.751009i	0.969818	+	0.243828i	$0.0784033\pi$
$359$	2.04591	+	14.2296i	0.107979	+	0.751009i	−0.861840	+	0.507181i	$0.830688\pi$
$360$	2.20690	+	0.359989i	0.116314	+	0.0189731i
$361$	13.4902	+	29.5395i	0.710011	+	1.55471i
$362$	−2.73357	−	0.594652i	−0.143673	−	0.0312542i
$363$	7.34448	−	5.49801i	0.385485	−	0.288570i
$364$	−11.3127	−	7.27023i	−0.592947	−	0.381064i
$365$	23.4409	+	0.442996i	1.22695	+	0.0231875i
$366$	3.10069	−	10.5600i	0.162076	−	0.551979i
$367$	2.15200	+	2.15200i	0.112334	+	0.112334i	0.761039	−	0.648706i	$-0.224689\pi$
$367$	2.15200	+	2.15200i	0.112334	+	0.112334i	−0.648706	+	0.761039i	$0.724689\pi$
$368$	−3.75663	+	2.98123i	−0.195828	+	0.155408i
$369$			2.70262i			0.140693i
$370$	16.3685	+	6.46002i	0.850960	+	0.335841i
$371$	0.579631	−	0.668930i	0.0300929	−	0.0347291i
$372$	−6.92798	+	1.50709i	−0.359199	+	0.0781390i
$373$	0.714741	+	0.954782i	0.0370079	+	0.0494367i	0.818663	−	0.574274i	$-0.194715\pi$
$373$	0.714741	+	0.954782i	0.0370079	+	0.0494367i	−0.781656	+	0.623710i	$0.785625\pi$
$374$	0.912542	+	1.41994i	0.0471864	+	0.0734235i
$375$	6.56774	−	9.04792i	0.339157	−	0.467232i
$376$	−4.29474	−	4.95640i	−0.221485	−	0.255607i
$377$	−27.0401	−	20.2420i	−1.39264	−	1.04252i
$378$	1.41675	+	3.79846i	0.0728699	+	0.195372i
$379$	−2.93663	+	0.862272i	−0.150844	+	0.0442919i	−0.356283	−	0.934378i	$-0.615956\pi$
$379$	−2.93663	+	0.862272i	−0.150844	+	0.0442919i	0.205439	+	0.978670i	$0.434138\pi$
$380$	3.11332	+	15.7378i	0.159710	+	0.807331i
$381$	−4.23403	+	9.27124i	−0.216916	+	0.474980i
$382$	−6.14743	+	8.21201i	−0.314530	+	0.420163i
$383$	−14.0122	−	1.00217i	−0.715988	−	0.0512085i	−0.291408	−	0.956599i	$-0.594124\pi$
$383$	−14.0122	−	1.00217i	−0.715988	−	0.0512085i	−0.424580	+	0.905390i	$0.639578\pi$
$384$	−0.909632	+	0.415415i	−0.0464195	+	0.0211991i
$385$	3.67223	−	11.6850i	0.187154	−	0.595522i
$386$	1.10494	−	7.68504i	0.0562401	−	0.391158i
$387$	0.0976463	+	0.448873i	0.00496364	+	0.0228175i
$388$	0.183317	+	2.56311i	0.00930651	+	0.130122i
$389$	17.1829	+	5.04535i	0.871207	+	0.255809i	0.686629	−	0.727008i	$-0.259090\pi$
$389$	17.1829	+	5.04535i	0.871207	+	0.255809i	0.184578	+	0.982818i	$0.440908\pi$
$390$	−4.75037	−	5.69623i	−0.240544	−	0.288440i
$391$	−0.169067	−	5.98867i	−0.00855006	−	0.302860i
$392$	−6.67190	+	6.67190i	−0.336982	+	0.336982i
$393$	0.923863	+	1.69193i	0.0466027	+	0.0853465i
$394$	−3.86274	−	3.34709i	−0.194602	−	0.168624i
$395$	−21.2040	−	16.5073i	−1.06689	−	0.830575i
$396$	1.33740	+	0.192289i	0.0672069	+	0.00966289i
$397$	−2.85173	+	13.1092i	−0.143124	+	0.657931i	0.848545	+	0.529123i	$0.177479\pi$
$397$	−2.85173	+	13.1092i	−0.143124	+	0.657931i	−0.991670	+	0.128808i	$0.958885\pi$
$398$	21.4008	+	7.98207i	1.07272	+	0.400105i
$399$	−21.9818	+	19.0474i	−1.10047	+	0.953560i
$400$	−0.188917	+	4.99643i	−0.00944585	+	0.249821i
$401$	13.3342	+	6.08951i	0.665876	+	0.304095i	0.719527	−	0.694464i	$-0.244359\pi$
$401$	13.3342	+	6.08951i	0.665876	+	0.304095i	−0.0536510	+	0.998560i	$0.517086\pi$
$402$	−10.1474	−	5.54092i	−0.506108	−	0.276356i
$403$	20.6410	+	11.2708i	1.02820	+	0.561440i
$404$	8.03391	+	3.66896i	0.399702	+	0.182538i
$405$	0.117348	+	2.23299i	0.00583106	+	0.110958i
$406$	−31.1994	+	27.0344i	−1.54840	+	1.34170i
$407$	9.96274	+	3.71591i	0.493835	+	0.184191i
$408$	0.265541	−	1.22067i	0.0131463	−	0.0604324i
$409$	12.6277	+	1.81559i	0.624400	+	0.0897752i	0.447251	−	0.894409i	$-0.352403\pi$
$409$	12.6277	+	1.81559i	0.624400	+	0.0897752i	0.177150	+	0.984184i	$0.443312\pi$
$410$	−5.99691	+	0.746864i	−0.296167	+	0.0368850i
$411$	0.700727	+	0.607183i	0.0345643	+	0.0299501i
$412$	7.20394	+	13.1930i	0.354912	+	0.649974i
$413$	−23.5751	+	23.5751i	−1.16006	+	1.16006i
$414$	−3.71163	−	3.03707i	−0.182417	−	0.149264i
$415$	−11.1084	+	9.26382i	−0.545288	+	0.454743i
$416$	3.18266	+	0.934512i	0.156043	+	0.0458182i
$417$	−1.10994	−	15.5190i	−0.0543540	−	0.759969i
$418$	2.06059	+	9.47236i	0.100787	+	0.463308i
$419$	2.80524	−	19.5109i	0.137045	−	0.953169i	−0.799011	−	0.601317i	$-0.794643\pi$
$419$	2.80524	−	19.5109i	0.137045	−	0.953169i	0.936056	−	0.351852i	$-0.114448\pi$
$420$	−8.03699	+	4.19337i	−0.392165	+	0.204615i
$421$	14.8632	−	6.78779i	0.724388	−	0.330817i	−0.0188701	−	0.999822i	$-0.506007\pi$
$421$	14.8632	−	6.78779i	0.724388	−	0.330817i	0.743258	+	0.669005i	$0.233280\pi$
$422$	−18.8254	−	1.34642i	−0.916404	−	0.0655425i
$423$	3.93022	−	5.25015i	0.191094	−	0.255271i
$424$	−0.0906971	+	0.198599i	−0.00440464	+	0.00964482i
$425$	−4.85527	−	3.92941i	−0.235515	−	0.190604i
$426$	−3.52204	+	1.03416i	−0.170643	+	0.0501054i
$427$	15.5925	+	41.8051i	0.754574	+	2.02309i
$428$	3.10507	+	2.32442i	0.150089	+	0.112355i
$429$	−2.93495	−	3.38712i	−0.141701	−	0.163532i
$430$	−0.969031	+	0.340715i	−0.0467308	+	0.0164307i
$431$	−21.7183	−	33.7943i	−1.04613	−	1.62782i	−0.735814	−	0.677183i	$-0.763200\pi$
$431$	−21.7183	−	33.7943i	−1.04613	−	1.62782i	−0.310319	−	0.950632i	$-0.600436\pi$
$432$	−0.599278	−	0.800541i	−0.0288328	−	0.0385161i
$433$	15.2933	−	3.32684i	0.734947	−	0.159878i	0.170512	−	0.985356i	$-0.445458\pi$
$433$	15.2933	−	3.32684i	0.734947	−	0.159878i	0.564435	+	0.825478i	$0.309094\pi$
$434$	18.8229	−	21.7228i	0.903529	−	1.04273i
$435$	−20.8873	+	9.06593i	−1.00147	+	0.434678i
$436$			19.2408i			0.921469i
$437$	11.1098	−	32.5650i	0.531453	−	1.55779i
$438$	−7.41398	−	7.41398i	−0.354254	−	0.354254i
$439$	2.29784	−	7.82571i	0.109670	−	0.373501i	−0.886309	−	0.463095i	$-0.846739\pi$
$439$	2.29784	−	7.82571i	0.109670	−	0.373501i	0.995978	+	0.0895943i	$0.0285571\pi$
$440$	−0.0570871	+	3.02073i	−0.00272152	+	0.144008i
$441$	−7.93764	−	5.10121i	−0.377983	−	0.242915i
$442$	−3.31720	+	2.48322i	−0.157783	+	0.118115i
$443$	−5.39408	−	1.17341i	−0.256280	−	0.0557504i	0.0825894	−	0.996584i	$-0.473681\pi$
$443$	−5.39408	−	1.17341i	−0.256280	−	0.0557504i	−0.338870	+	0.940833i	$0.610045\pi$
$444$	−3.26919	−	7.15853i	−0.155149	−	0.339729i
$445$	17.5244	+	24.3559i	0.830736	+	1.15458i
$446$	−0.619551	−	4.30908i	−0.0293366	−	0.204041i
$447$	−0.431721	+	0.161024i	−0.0204197	+	0.00761615i
$448$	1.94291	−	3.55817i	0.0917939	−	0.168108i
$449$	−2.14503	−	7.30531i	−0.101230	−	0.344759i	0.893266	−	0.449528i	$-0.148408\pi$
$449$	−2.14503	−	7.30531i	−0.101230	−	0.344759i	−0.994497	+	0.104769i	$0.966590\pi$
$450$	−4.92240	+	0.877468i	−0.232044	+	0.0413642i
$451$	−3.61448	+	0.519684i	−0.170199	+	0.0244710i
$452$	1.23086	−	17.2097i	0.0578949	−	0.809476i
$453$	1.39179	−	3.73154i	0.0653920	−	0.175323i
$454$	−15.9518	+	10.2516i	−0.748655	+	0.481132i
$455$	29.2562	+	6.94574i	1.37155	+	0.325622i
$456$	3.87885	−	6.03561i	0.181644	−	0.282643i
$457$	18.8301	−	1.34675i	0.880834	−	0.0629985i	0.376408	−	0.926454i	$-0.377159\pi$
$457$	18.8301	−	1.34675i	0.880834	−	0.0629985i	0.504425	+	0.863455i	$0.331704\pi$
$458$	21.0946	−	11.5185i	0.985684	−	0.538224i
$459$	1.24922			0.0583087
$460$	5.71333	−	9.07512i	0.266385	−	0.423130i
$461$	6.49620			0.302558			0.151279	−	0.988491i	$-0.451661\pi$
$461$	6.49620			0.302558			0.151279	+	0.988491i	$0.451661\pi$
$462$	−4.80763	+	2.62517i	−0.223671	+	0.122134i
$463$	−34.0013	+	2.43182i	−1.58018	+	0.113016i	−0.833632	−	0.552320i	$-0.813743\pi$
$463$	−34.0013	+	2.43182i	−1.58018	+	0.113016i	−0.746544	+	0.665336i	$0.768288\pi$
$464$	5.50536	−	8.56651i	0.255580	−	0.397690i
$465$	13.4966	−	8.31765i	0.625889	−	0.385722i
$466$	−12.6599	+	8.13601i	−0.586457	+	0.376893i
$467$	−12.8690	+	34.5031i	−0.595506	+	1.59661i	0.192737	+	0.981250i	$0.438263\pi$
$467$	−12.8690	+	34.5031i	−0.595506	+	1.59661i	−0.788243	+	0.615363i	$0.789009\pi$
$468$	−0.236633	+	3.30857i	−0.0109384	+	0.152939i
$469$	46.3948	−	6.67056i	2.14231	−	0.308018i
$470$	12.7358	+	7.26999i	0.587459	+	0.335340i
$471$	−4.43507	−	15.1044i	−0.204357	−	0.695976i
$472$	3.94130	−	7.21795i	0.181413	−	0.332233i
$473$	−0.581546	+	0.216905i	−0.0267395	+	0.00997332i
$474$	1.71027	+	11.8952i	0.0785552	+	0.546363i
$475$	−18.2402	−	30.8893i	−0.836917	−	1.41730i
$476$	2.10384	+	4.60677i	0.0964295	+	0.211151i
$477$	−0.213339	−	0.0464092i	−0.00976814	−	0.00212493i
$478$	−5.10914	+	3.82465i	−0.233686	+	0.174935i
$479$	−0.924736	−	0.594292i	−0.0422523	−	0.0271539i	0.519344	−	0.854565i	$-0.326176\pi$
$479$	−0.924736	−	0.594292i	−0.0422523	−	0.0271539i	−0.561596	+	0.827411i	$0.689813\pi$
$480$	1.61073	−	1.55098i	0.0735195	−	0.0707923i
$481$	−7.35433	+	25.0466i	−0.335329	+	1.14202i
$482$	−11.7227	−	11.7227i	−0.533956	−	0.533956i
$483$	19.4245	+	0.839200i	0.883846	+	0.0381849i
$484$		−	9.17439i		−	0.417018i
$485$	−2.28776	−	5.27084i	−0.103882	−	0.239337i
$486$	0.654861	−	0.755750i	0.0297051	−	0.0342815i
$487$	−28.3659	+	6.17063i	−1.28538	+	0.279618i	−0.802808	−	0.596237i	$-0.796662\pi$
$487$	−28.3659	+	6.17063i	−1.28538	+	0.279618i	−0.482574	+	0.875855i	$0.660298\pi$
$488$	−6.59553	−	8.81060i	−0.298566	−	0.398837i
$489$	−6.77533	−	10.5426i	−0.306391	−	0.476754i
$490$	9.12566	−	19.0228i	0.412255	−	0.859360i
$491$	−7.84683	−	9.05573i	−0.354123	−	0.408679i	0.550539	−	0.834809i	$-0.314422\pi$
$491$	−7.84683	−	9.05573i	−0.354123	−	0.408679i	−0.904662	+	0.426130i	$0.859877\pi$
$492$	2.16356	+	1.61962i	0.0975408	+	0.0730181i
$493$	4.44549	+	11.9188i	0.200215	+	0.536796i
$494$	−22.8341	+	6.70470i	−1.02736	+	0.301659i
$495$	−2.96383	+	0.586320i	−0.133214	+	0.0263531i
$496$	−2.94530	+	6.44930i	−0.132248	+	0.289582i
$497$	8.91809	−	11.9132i	0.400031	−	0.534379i
$498$	6.45212	+	0.461465i	0.289126	+	0.0206787i
$499$	28.6690	−	13.0927i	1.28340	−	0.586109i	0.347270	−	0.937765i	$-0.387109\pi$
$499$	28.6690	−	13.0927i	1.28340	−	0.586109i	0.936129	+	0.351656i	$0.114381\pi$
$500$	−3.30733	−	10.6800i	−0.147908	−	0.477622i
$501$	−1.44362	+	10.0406i	−0.0644962	+	0.448581i
$502$	3.57376	+	16.4283i	0.159505	+	0.733232i
$503$	1.78254	+	24.9232i	0.0794795	+	1.11127i	0.868100	+	0.496389i	$0.165341\pi$
$503$	1.78254	+	24.9232i	0.0794795	+	1.11127i	−0.788621	+	0.614880i	$0.789205\pi$
$504$	3.88985	+	1.14216i	0.173268	+	0.0508760i
$505$	−19.6686	−	1.78084i	−0.875241	−	0.0792463i
$506$	3.34807	−	5.54793i	0.148840	−	0.246636i
$507$	−1.41236	+	1.41236i	−0.0627251	+	0.0627251i
$508$	4.88465	+	8.94557i	0.216721	+	0.396895i
$509$	−23.1827	−	20.0879i	−1.02755	−	0.890381i	−0.0335188	−	0.999438i	$-0.510671\pi$
$509$	−23.1827	−	20.0879i	−1.02755	−	0.890381i	−0.994035	+	0.109057i	$0.965217\pi$
$510$	0.345220	+	2.77193i	0.0152866	+	0.122743i
$511$	42.0741	+	6.04934i	1.86125	+	0.267607i
$512$	−0.212565	+	0.977147i	−0.00939415	+	0.0431842i
$513$	6.72219	+	2.50725i	0.296792	+	0.110698i
$514$	14.3625	−	12.4452i	0.633504	−	0.548934i
$515$	−24.9818	−	22.4872i	−1.10083	−	0.990904i
$516$	0.417858	+	0.190830i	0.0183952	+	0.00840080i
$517$	7.77729	+	4.24672i	0.342045	+	0.186771i
$518$	28.0018	+	15.2901i	1.23033	+	0.671809i
$519$	−0.974859	−	0.445203i	−0.0427916	−	0.0195423i
$520$	−7.40686	+	0.389245i	−0.324812	+	0.0170695i
$521$	−31.1675	+	27.0068i	−1.36547	+	1.18319i	−0.401921	+	0.915674i	$0.631657\pi$
$521$	−31.1675	+	27.0068i	−1.36547	+	1.18319i	−0.963553	+	0.267516i	$0.913797\pi$
$522$	9.54098	+	3.55860i	0.417598	+	0.155756i
$523$	−6.94219	+	31.9128i	−0.303561	+	1.39545i	0.532323	+	0.846541i	$0.321319\pi$
$523$	−6.94219	+	31.9128i	−0.303561	+	1.39545i	−0.835884	+	0.548906i	$0.815044\pi$
$524$	1.90811	+	0.274345i	0.0833561	+	0.0119848i
$525$	13.8436	−	14.8068i	0.604184	−	0.646223i
$526$	11.4014	+	9.87939i	0.497126	+	0.430762i
$527$	−4.24471	−	7.77360i	−0.184902	−	0.338623i
$528$	0.955409	−	0.955409i	0.0415788	−	0.0415788i
$529$	−20.3492	+	10.7197i	−0.884747	+	0.466072i
$530$	0.0440225	−	0.486210i	0.00191222	−	0.0211196i
$531$	7.89078	+	2.31694i	0.342430	+	0.100547i
$532$	2.07498	+	29.0120i	0.0899618	+	1.25783i
$533$	−1.90557	−	8.75978i	−0.0825395	−	0.379428i
$534$	1.90969	−	13.2822i	0.0826403	−	0.574776i
$535$	−8.27408	−	2.60029i	−0.357720	−	0.112420i
$536$	−10.5169	+	4.80290i	−0.454260	+	0.207453i
$537$	8.43305	+	0.603144i	0.363913	+	0.0260276i
$538$	9.07407	−	12.1215i	0.391211	−	0.522597i
$539$	5.29604	−	11.5967i	0.228117	−	0.499506i
$540$	1.85792	+	1.24424i	0.0799522	+	0.0535434i
$541$	−17.8215	+	5.23286i	−0.766205	+	0.224978i	−0.641404	−	0.767204i	$-0.721648\pi$
$541$	−17.8215	+	5.23286i	−0.766205	+	0.224978i	−0.124801	+	0.992182i	$0.539829\pi$
$542$	0.322223	+	0.863914i	0.0138407	+	0.0371083i
$543$	−2.23952	−	1.67648i	−0.0961069	−	0.0719447i
$544$	−0.818067	−	0.944099i	−0.0350743	−	0.0404779i
$545$	−14.2709	−	40.5880i	−0.611299	−	1.73860i
$546$	−7.27023	−	11.3127i	−0.311137	−	0.484139i
$547$	5.63831	+	7.53190i	0.241077	+	0.322041i	0.904719	−	0.426010i	$-0.140081\pi$
$547$	5.63831	+	7.53190i	0.241077	+	0.322041i	−0.663642	+	0.748050i	$0.730990\pi$
$548$	0.906005	−	0.197089i	0.0387026	−	0.00841924i
$549$	7.20727	−	8.31763i	0.307599	−	0.354988i
$550$	−2.12005	−	6.41449i	−0.0903992	−	0.273515i
$551$			73.0586i			3.11240i
$552$	−4.65560	+	1.15127i	−0.198155	+	0.0490011i
$553$	−34.4501	−	34.4501i	−1.46497	−	1.46497i
$554$	3.29457	−	11.2203i	0.139973	−	0.476704i
$555$	12.2058	+	12.6760i	0.518105	+	0.538065i
$556$	−13.0888	−	8.41164i	−0.555087	−	0.356733i
$557$	−3.74709	+	2.80504i	−0.158769	+	0.118853i	−0.675709	−	0.737169i	$-0.736162\pi$
$557$	−3.74709	+	2.80504i	−0.158769	+	0.118853i	0.516939	+	0.856022i	$0.327071\pi$
$558$	−6.92798	−	1.50709i	−0.293285	−	0.0638002i
$559$	−0.632985	−	1.38604i	−0.0267724	−	0.0586234i
$560$	−1.45942	+	8.94693i	−0.0616719	+	0.378077i
$561$	0.240212	+	1.67071i	0.0101417	+	0.0705374i
$562$	23.0231	−	8.58717i	0.971171	−	0.362228i
$563$	15.4760	−	28.3422i	0.652235	−	1.19448i	−0.317019	−	0.948419i	$-0.602682\pi$
$563$	15.4760	−	28.3422i	0.652235	−	1.19448i	0.969254	−	0.246060i	$-0.0791362\pi$
$564$	−1.84767	−	6.29260i	−0.0778011	−	0.264966i
$565$	10.1680	+	37.2163i	0.427769	+	1.56570i
$566$	−9.92277	+	1.42668i	−0.417085	+	0.0599678i
$567$	−0.289214	+	4.04374i	−0.0121459	+	0.169821i
$568$	−1.28279	+	3.43929i	−0.0538246	+	0.144309i
$569$	−33.5656	+	21.5713i	−1.40714	+	0.904316i	−0.999959	−	0.00903080i	$-0.997125\pi$
$569$	−33.5656	+	21.5713i	−1.40714	+	0.904316i	−0.407183	+	0.913346i	$0.633489\pi$
$570$	−3.70573	+	15.6089i	−0.155216	+	0.653785i
$571$	6.09366	−	9.48192i	0.255012	−	0.396806i	−0.690017	−	0.723793i	$-0.742397\pi$
$571$	6.09366	−	9.48192i	0.255012	−	0.396806i	0.945029	+	0.326987i	$0.106033\pi$
$572$	−4.47038	+	0.319728i	−0.186916	+	0.0133685i
$573$	−9.00329	+	4.91617i	−0.376118	+	0.205376i
$574$	−10.9566			−0.457320
$575$	−5.32111	+	23.3813i	−0.221906	+	0.975068i
$576$	−1.00000			−0.0416667
$577$	−28.4703	+	15.5459i	−1.18523	+	0.647186i	−0.946123	−	0.323806i	$-0.895037\pi$
$577$	−28.4703	+	15.5459i	−1.18523	+	0.647186i	−0.239110	+	0.970993i	$0.576856\pi$
$578$	−15.4001	+	1.10144i	−0.640560	+	0.0458138i
$579$	4.19757	−	6.53155i	0.174445	−	0.271442i
$580$	−5.25964	+	22.1542i	−0.218395	+	0.919901i
$581$	−22.0612	+	14.1779i	−0.915252	+	0.588197i
$582$	−0.898002	+	2.40764i	−0.0372234	+	0.0997997i
$583$	0.0210448	−	0.294244i	0.000871584	−	0.0121863i
$584$	−10.3782	+	1.49216i	−0.429454	+	0.0617462i
$585$	−1.95479	−	7.15485i	−0.0808207	−	0.295817i
$586$	−4.63691	−	15.7919i	−0.191549	−	0.652355i
$587$	1.53615	−	2.81324i	0.0634036	−	0.116115i	−0.844055	−	0.536257i	$-0.819838\pi$
$587$	1.53615	−	2.81324i	0.0634036	−	0.116115i	0.907458	+	0.420142i	$0.138020\pi$
$588$	−8.84058	+	3.29737i	−0.364580	+	0.135981i
$589$	−7.23921	−	50.3498i	−0.298286	−	2.07463i
$590$	−2.96052	+	18.1493i	−0.121883	+	0.747196i
$591$	−2.12324	−	4.64926i	−0.0873386	−	0.191245i
$592$	−7.68985	−	1.67282i	−0.316051	−	0.0687527i
$593$	21.9498	−	16.4314i	0.901370	−	0.674757i	−0.0446024	−	0.999005i	$-0.514202\pi$
$593$	21.9498	−	16.4314i	0.901370	−	0.674757i	0.945972	+	0.324248i	$0.105111\pi$
$594$	1.13666	+	0.730488i	0.0466378	+	0.0299723i
$595$	−7.85484	−	8.15745i	−0.322017	−	0.334423i
$596$	−0.129815	+	0.442108i	−0.00531742	+	0.0181095i
$597$	16.1509	+	16.1509i	0.661014	+	0.661014i
$598$	14.1716	+	7.22679i	0.579519	+	0.295525i
$599$		−	20.4345i		−	0.834929i	−0.908693	−	0.417465i	$-0.862919\pi$
$599$		−	20.4345i		−	0.834929i	0.908693	−	0.417465i	$-0.137081\pi$
$600$	−2.24744	+	4.46643i	−0.0917512	+	0.182341i
$601$	16.5019	−	19.0443i	0.673128	−	0.776831i	−0.311734	−	0.950169i	$-0.600910\pi$
$601$	16.5019	−	19.0443i	0.673128	−	0.776831i	0.984862	+	0.173338i	$0.0554553\pi$
$602$	−1.81976	+	0.395865i	−0.0741680	+	0.0161343i
$603$	−6.92866	−	9.25560i	−0.282157	−	0.376917i
$604$	−2.15318	−	3.35041i	−0.0876116	−	0.136326i
$605$	6.80464	+	19.3531i	0.276648	+	0.786817i
$606$	5.78376	+	6.67482i	0.234949	+	0.271146i
$607$	−29.9004	−	22.3832i	−1.21362	−	0.908504i	−0.215928	−	0.976409i	$-0.569278\pi$
$607$	−29.9004	−	22.3832i	−1.21362	−	0.908504i	−0.997692	+	0.0679049i	$0.978369\pi$
$608$	−2.50725	−	6.72219i	−0.101682	−	0.272621i
$609$	−39.6105	+	11.6307i	−1.60510	+	0.471299i
$610$	20.4479	+	13.6938i	0.827912	+	0.554447i
$611$	−9.03688	+	19.7880i	−0.365593	+	0.800537i
$612$	0.748631	−	1.00005i	0.0302616	−	0.0404248i
$613$	−15.7590	−	1.12711i	−0.636500	−	0.0455234i	−0.250639	−	0.968080i	$-0.580641\pi$
$613$	−15.7590	−	1.12711i	−0.636500	−	0.0455234i	−0.385861	+	0.922557i	$0.626095\pi$
$614$	16.9384	−	7.73552i	0.683579	−	0.312180i
$615$	−5.76524	−	1.81184i	−0.232477	−	0.0730603i
$616$	−0.779553	+	5.42191i	−0.0314091	+	0.218455i
$617$	−0.999206	−	4.59328i	−0.0402265	−	0.184918i	0.952649	−	0.304071i	$-0.0983459\pi$
$617$	−0.999206	−	4.59328i	−0.0402265	−	0.184918i	−0.992876	+	0.119152i	$0.961982\pi$
$618$	1.07235	+	14.9934i	0.0431363	+	0.603124i
$619$	−34.5028	−	10.1309i	−1.38679	−	0.407197i	−0.498660	−	0.866797i	$-0.666175\pi$
$619$	−34.5028	−	10.1309i	−1.38679	−	0.407197i	−0.888126	+	0.459600i	$0.847993\pi$
$620$	1.42959	−	15.7892i	0.0574135	−	0.634108i
$621$	−2.11457	−	4.30448i	−0.0848549	−	0.172733i
$622$	16.4870	−	16.4870i	0.661069	−	0.661069i
$623$	26.0714	+	47.7463i	1.04453	+	1.91291i
$624$	2.50684	+	2.17219i	0.100354	+	0.0869570i
$625$	14.8981	+	20.0761i	0.595922	+	0.803042i
$626$	5.26850	+	0.757496i	0.210572	+	0.0302756i
$627$	−2.06059	+	9.47236i	−0.0822919	+	0.378290i
$628$	−14.7496	−	5.50130i	−0.588572	−	0.219526i
$629$	7.42978	−	6.43794i	0.296245	−	0.256697i
$630$	−9.05269	+	0.475736i	−0.360668	+	0.0189538i
$631$	16.8664	+	7.70264i	0.671442	+	0.306637i	0.721808	−	0.692094i	$-0.243311\pi$
$631$	16.8664	+	7.70264i	0.671442	+	0.306637i	−0.0503658	+	0.998731i	$0.516039\pi$
$632$	10.5475	+	5.75937i	0.419557	+	0.229096i
$633$	−16.5648	−	9.04508i	−0.658393	−	0.359510i
$634$	−5.94568	−	2.71530i	−0.236133	−	0.107838i
$635$	−16.9390	−	15.2475i	−0.672202	−	0.605079i
$636$	−0.165002	+	0.142975i	−0.00654276	+	0.00566933i
$637$	29.3244	+	10.9374i	1.16187	+	0.433357i
$638$	−2.92465	+	13.4444i	−0.115788	+	0.532268i
$639$	−3.63337	−	0.522399i	−0.143734	−	0.0206658i
$640$	−0.276348	−	2.21893i	−0.0109236	−	0.0877107i
$641$	−35.9143	−	31.1199i	−1.41853	−	1.22916i	−0.935388	−	0.353622i	$-0.884950\pi$
$641$	−35.9143	−	31.1199i	−1.41853	−	1.22916i	−0.483142	−	0.875542i	$-0.660505\pi$
$642$	1.85887	+	3.40426i	0.0733636	+	0.134355i
$643$	17.7518	−	17.7518i	0.700061	−	0.700061i	−0.264363	−	0.964423i	$-0.585162\pi$
$643$	17.7518	−	17.7518i	0.700061	−	0.700061i	0.964423	+	0.264363i	$0.0851616\pi$
$644$	12.3125	−	15.0472i	0.485180	−	0.592943i
$645$	−1.02300	−	0.0926247i	−0.0402806	−	0.00364709i
$646$	8.59955	+	2.52506i	0.338345	+	0.0993470i
$647$	−1.99374	−	27.8761i	−0.0783819	−	1.09592i	−0.872647	−	0.488351i	$-0.837598\pi$
$647$	−1.99374	−	27.8761i	−0.0783819	−	1.09592i	0.794265	−	0.607571i	$-0.207856\pi$
$648$	−0.212565	−	0.977147i	−0.00835035	−	0.0383860i
$649$	−1.58137	+	10.9986i	−0.0620740	+	0.431734i
$650$	15.3359	−	6.31477i	0.601523	−	0.247686i
$651$	26.1459	−	11.9404i	1.02474	−	0.467983i
$652$	−12.5001	−	0.894026i	−0.489542	−	0.0350127i
$653$	−19.1084	+	25.5259i	−0.747771	+	0.998905i	0.251745	+	0.967794i	$0.418995\pi$
$653$	−19.1084	+	25.5259i	−0.747771	+	0.998905i	−0.999516	+	0.0311110i	$0.990095\pi$
$654$	−7.99293	+	17.5021i	−0.312548	+	0.684385i
$655$	−4.22859	+	0.836520i	−0.165225	+	0.0326855i
$656$	2.59315	−	0.761416i	0.101245	−	0.0297283i
$657$	−3.66412	−	9.82387i	−0.142951	−	0.383266i
$658$	21.2845	+	15.9334i	0.829756	+	0.621148i
$659$	−4.17154	−	4.81422i	−0.162500	−	0.187535i	0.668660	−	0.743568i	$-0.266868\pi$
$659$	−4.17154	−	4.81422i	−0.162500	−	0.187535i	−0.831160	+	0.556033i	$0.812323\pi$
$660$	−1.30678	+	2.72404i	−0.0508665	+	0.106033i
$661$	−16.6213	−	25.8632i	−0.646493	−	1.00596i	−0.997574	−	0.0696180i	$-0.977822\pi$
$661$	−16.6213	−	25.8632i	−0.646493	−	1.00596i	0.351080	−	0.936345i	$-0.385814\pi$
$662$	0.775282	+	1.03566i	0.0301322	+	0.0402519i
$663$	−4.04900	+	0.880806i	−0.157250	+	0.0342077i
$664$	4.23603	−	4.88864i	0.164390	−	0.189716i
$665$	−25.8953	−	59.6611i	−1.00418	−	2.31356i
$666$		−	7.86970i		−	0.304945i
$667$	33.5441	−	35.4931i	1.29883	−	1.37430i
$668$	7.17279	+	7.17279i	0.277523	+	0.277523i
$669$	1.22649	−	4.17704i	0.0474189	−	0.161494i
$670$	18.6228	−	17.9319i	0.719460	−	0.692771i
$671$	12.5099	+	8.03961i	0.482938	+	0.310366i
$672$	3.24545	−	2.42951i	0.125196	−	0.0937206i
$673$	19.2980	+	4.19803i	0.743884	+	0.161822i	0.568506	−	0.822679i	$-0.307522\pi$
$673$	19.2980	+	4.19803i	0.743884	+	0.161822i	0.175378	+	0.984501i	$0.443885\pi$
$674$	6.38253	+	13.9758i	0.245846	+	0.538328i
$675$	−4.84209	−	1.24667i	−0.186372	−	0.0479842i
$676$	0.284257	+	1.97705i	0.0109329	+	0.0760403i
$677$	17.2963	−	6.45120i	0.664752	−	0.247940i	0.00563959	−	0.999984i	$-0.498205\pi$
$677$	17.2963	−	6.45120i	0.664752	−	0.247940i	0.659112	+	0.752044i	$0.270932\pi$
$678$	8.26880	−	15.1432i	0.317561	−	0.581570i
$679$	−2.93497	−	9.99558i	−0.112634	−	0.383595i
$680$	2.42593	+	1.38479i	0.0930301	+	0.0531044i
$681$	−18.7689	+	2.69857i	−0.719228	+	0.103409i
$682$	0.683407	−	9.55527i	0.0261690	−	0.365890i
$683$	0.590773	−	1.58392i	0.0226053	−	0.0606071i	−0.925157	−	0.379585i	$-0.876067\pi$
$683$	0.590773	−	1.58392i	0.0226053	−	0.0606071i	0.947762	+	0.318978i	$0.103340\pi$
$684$	6.03561	−	3.87885i	0.230777	−	0.148312i
$685$	−1.76501	+	1.08774i	−0.0674377	+	0.0415604i
$686$	5.33811	−	8.30626i	0.203810	−	0.317135i
$687$	23.9733	−	1.71460i	0.914637	−	0.0654161i
$688$	0.403180	−	0.220153i	0.0153711	−	0.00839326i
$689$	0.724202			0.0275899
$690$	8.96697	−	5.88162i	0.341367	−	0.223909i
$691$	0.202453			0.00770168			0.00385084	−	0.999993i	$-0.498774\pi$
$691$	0.202453			0.00770168			0.00385084	+	0.999993i	$0.498774\pi$
$692$	−0.940615	+	0.513615i	−0.0357568	+	0.0195247i
$693$	−5.46371	+	0.390772i	−0.207549	+	0.0148442i
$694$	−11.2546	+	17.5125i	−0.427219	+	0.664765i
$695$	33.8493	+	8.03620i	1.28398	+	0.304831i
$696$	8.56651	−	5.50536i	0.324713	−	0.208680i
$697$	−1.17985	+	3.16331i	−0.0446901	+	0.119819i
$698$	−1.37133	+	19.1737i	−0.0519056	+	0.725735i
$699$	−14.8956	+	2.14167i	−0.563405	+	0.0810054i
$700$	−3.55732	−	19.9558i	−0.134454	−	0.754257i
$701$	−4.64070	−	15.8048i	−0.175277	−	0.596938i	−0.999528	−	0.0307140i	$-0.990222\pi$
$701$	−4.64070	−	15.8048i	−0.175277	−	0.596938i	0.824251	−	0.566224i	$-0.191596\pi$
$702$	−1.58968	+	2.91128i	−0.0599985	+	0.109879i
$703$	52.9016	−	19.7313i	1.99522	−	0.744179i
$704$	−0.192289	−	1.33740i	−0.00724716	−	0.0504051i
$705$	8.56484	+	11.9037i	0.322571	+	0.448318i
$706$	−11.0881	−	24.2796i	−0.417307	−	0.913775i
$707$	−34.9875	−	7.61106i	−1.31584	−	0.286243i
$708$	6.58357	−	4.92840i	0.247426	−	0.185221i
$709$	−3.06506	−	1.96980i	−0.115111	−	0.0739772i	0.481819	−	0.876271i	$-0.339976\pi$
$709$	−3.06506	−	1.96980i	−0.115111	−	0.0739772i	−0.596929	+	0.802294i	$0.703613\pi$
$710$	0.155091	−	8.20654i	0.00582046	−	0.307986i
$711$	−3.38572	+	11.5307i	−0.126974	+	0.432435i
$712$	−9.48849	−	9.48849i	−0.355596	−	0.355596i
$713$	−19.6007	+	27.7846i	−0.734051	+	1.04054i
$714$			5.06444i			0.189532i
$715$	9.19301	−	3.99014i	0.343799	−	0.149223i
$716$	5.53658	−	6.38956i	0.206912	−	0.238789i
$717$	−6.23625	+	1.35661i	−0.232897	+	0.0506636i
$718$	8.61516	+	11.5085i	0.321515	+	0.429494i
$719$	−24.4745	−	38.0831i	−0.912745	−	1.42026i	−0.907398	−	0.420273i	$-0.861934\pi$
$719$	−24.4745	−	38.0831i	−0.912745	−	1.42026i	−0.00534669	−	0.999986i	$-0.501702\pi$
$720$	2.10947	−	0.741699i	0.0786155	−	0.0276415i
$721$	−39.9070	−	46.0551i	−1.48621	−	1.71518i
$722$	25.9968	+	19.4610i	0.967502	+	0.724263i
$723$	−5.79357	−	15.5332i	−0.215465	−	0.577685i
$724$	−2.68418	+	0.788148i	−0.0997569	+	0.0292913i
$725$	−5.33664	−	50.6347i	−0.198198	−	1.88052i
$726$	3.81118	−	8.34532i	0.141446	−	0.309724i
$727$	−6.02539	+	8.04898i	−0.223469	+	0.298520i	−0.898238	−	0.439509i	$-0.855152\pi$
$727$	−6.02539	+	8.04898i	−0.223469	+	0.298520i	0.674769	+	0.738029i	$0.264243\pi$
$728$	−13.4132	−	0.959329i	−0.497125	−	0.0355551i
$729$	0.909632	−	0.415415i	0.0336901	−	0.0153857i
$730$	20.7859	−	10.8452i	0.769320	−	0.401399i
$731$	−0.0816683	+	0.568015i	−0.00302061	+	0.0210088i
$732$	−2.33945	−	10.7543i	−0.0864686	−	0.397490i
$733$	0.257869	+	3.60548i	0.00952460	+	0.133171i	0.999989	−	0.00459442i	$-0.00146245\pi$
$733$	0.257869	+	3.60548i	0.00952460	+	0.133171i	−0.990465	+	0.137766i	$0.956008\pi$
$734$	2.92011	+	0.857423i	0.107783	+	0.0316481i
$735$	16.2033	−	13.5128i	0.597669	−	0.498426i
$736$	−1.86836	+	4.41693i	−0.0688687	+	0.162810i
$737$	11.0461	−	11.0461i	0.406890	−	0.406890i
$738$	1.29523	+	2.37203i	0.0476780	+	0.0873158i
$739$	−26.8802	−	23.2918i	−0.988803	−	0.856802i	0.000891472	−	1.00000i	$-0.499716\pi$
$739$	−26.8802	−	23.2918i	−0.988803	−	0.856802i	−0.989694	+	0.143197i	$0.954262\pi$
$740$	17.4623	−	2.17478i	0.641926	−	0.0799464i
$741$	−23.5559	−	3.38682i	−0.865347	−	0.124418i
$742$	0.188146	−	0.864893i	0.00690706	−	0.0317512i
$743$	−26.9358	−	10.0465i	−0.988177	−	0.368571i	−0.197164	−	0.980370i	$-0.563173\pi$
$743$	−26.9358	−	10.0465i	−0.988177	−	0.368571i	−0.791013	+	0.611799i	$0.790446\pi$
$744$	−5.35827	+	4.64297i	−0.196444	+	0.170219i
$745$	−0.0540706	−	1.02890i	−0.00198099	−	0.0376960i
$746$	1.08489	+	0.495453i	0.0397207	+	0.0181398i
$747$	5.67736	+	3.10007i	0.207724	+	0.113426i
$748$	1.48143	+	0.808919i	0.0541663	+	0.0295770i
$749$	−14.3036	−	6.53222i	−0.522641	−	0.238682i
$750$	1.42816	−	11.0887i	0.0521490	−	0.404904i
$751$	12.5347	−	10.8613i	0.457396	−	0.396336i	−0.395459	−	0.918484i	$-0.629414\pi$
$751$	12.5347	−	10.8613i	0.457396	−	0.396336i	0.852855	+	0.522148i	$0.174869\pi$
$752$	−6.14476	−	2.29188i	−0.224076	−	0.0835761i
$753$	−3.57376	+	16.4283i	−0.130235	+	0.598681i
$754$	−33.4335	−	4.80701i	−1.21758	−	0.175061i
$755$	7.02707	+	5.47060i	0.255741	+	0.199095i
$756$	3.06386	+	2.65485i	0.111432	+	0.0965560i
$757$	−3.05283	−	5.59084i	−0.110957	−	0.203202i	0.816300	−	0.577628i	$-0.196022\pi$
$757$	−3.05283	−	5.59084i	−0.110957	−	0.203202i	−0.927257	+	0.374426i	$0.877840\pi$
$758$	−2.16417	+	2.16417i	−0.0786064	+	0.0786064i
$759$	5.35020	−	3.65574i	0.194200	−	0.132695i
$760$	10.2748	+	12.3207i	0.372707	+	0.446917i
$761$	27.4137	+	8.04939i	0.993746	+	0.291790i	0.737887	−	0.674924i	$-0.235824\pi$
$761$	27.4137	+	8.04939i	0.993746	+	0.291790i	0.255859	+	0.966714i	$0.417642\pi$
$762$	0.727110	+	10.1663i	0.0263404	+	0.368287i
$763$	−16.5809	−	76.2211i	−0.600268	−	2.75939i
$764$	−1.45988	+	10.1537i	−0.0528164	+	0.367346i
$765$	−0.837479	+	2.66485i	−0.0302791	+	0.0963478i
$766$	−12.7785	+	5.83573i	−0.461705	+	0.210854i
$767$	−27.2093	−	1.94605i	−0.982472	−	0.0702678i
$768$	−0.599278	+	0.800541i	−0.0216246	+	0.0288870i
$769$	11.0410	−	24.1765i	0.398149	−	0.871826i	−0.599305	−	0.800521i	$-0.704556\pi$
$769$	11.0410	−	24.1765i	0.398149	−	0.871826i	0.997455	−	0.0713050i	$-0.0227164\pi$
$770$	−2.37698	−	12.0156i	−0.0856605	−	0.433011i
$771$	18.2345	−	5.35414i	0.656701	−	0.192825i
$772$	−2.71326	−	7.27454i	−0.0976525	−	0.261816i
$773$	−32.3954	−	24.2509i	−1.16518	−	0.872243i	−0.171577	−	0.985171i	$-0.554886\pi$
$773$	−32.3954	−	24.2509i	−1.16518	−	0.872243i	−0.993603	+	0.112927i	$0.963977\pi$
$774$	0.300824	+	0.347169i	0.0108129	+	0.0124787i
$775$	8.69513	+	34.3671i	0.312338	+	1.23450i
$776$	1.38926	+	2.16173i	0.0498715	+	0.0776016i
$777$	19.1195	+	25.5407i	0.685910	+	0.916268i
$778$	17.4990	−	3.80668i	0.627371	−	0.136476i
$779$	−12.6978	+	14.6540i	−0.454946	+	0.525035i
$780$	−6.89922	−	2.72285i	−0.247032	−	0.0974937i
$781$		−	4.95972i		−	0.177473i
$782$	−3.01845	−	5.17511i	−0.107940	−	0.185062i
$783$	7.20049	+	7.20049i	0.257324	+	0.257324i
$784$	−2.65829	+	9.05329i	−0.0949388	+	0.323332i
$785$	35.1942	+	0.665115i	1.25613	+	0.0237390i
$786$	1.62171	+	1.04221i	0.0578445	+	0.0371744i
$787$	−12.3347	+	9.23361i	−0.439683	+	0.329143i	−0.796079	−	0.605192i	$-0.793096\pi$
$787$	−12.3347	+	9.23361i	−0.439683	+	0.329143i	0.356396	+	0.934335i	$0.384005\pi$
$788$	−4.99434	−	1.08645i	−0.177916	−	0.0387032i
$789$	6.26705	+	13.7229i	0.223113	+	0.488549i
$790$	−26.5214	−	4.32617i	−0.943589	−	0.153918i
$791$	9.95458	+	69.2356i	0.353944	+	2.46173i
$792$	1.26596	−	0.472179i	0.0449840	−	0.0167782i
$793$	−17.4957	+	32.0410i	−0.621290	+	1.13781i
$794$	3.77966	+	12.8723i	0.134135	+	0.456822i
$795$	0.242023	−	0.423984i	0.00858367	−	0.0150372i
$796$	22.6084	−	3.25060i	0.801333	−	0.115214i
$797$	0.941849	−	13.1688i	0.0333620	−	0.466462i	−0.953120	−	0.302593i	$-0.902148\pi$
$797$	0.941849	−	13.1688i	0.0333620	−	0.466462i	0.986482	−	0.163869i	$-0.0523976\pi$
$798$	−10.1646	+	27.2522i	−0.359821	+	0.964718i
$799$	6.89216	−	4.42932i	0.243827	−	0.156698i
$800$	2.22873	+	4.47580i	0.0787973	+	0.158243i
$801$	7.25473	−	11.2886i	0.256333	−	0.398862i
$802$	14.6215	−	1.04575i	0.516303	−	0.0369267i
$803$	12.4339	−	6.78941i	0.438782	−	0.239593i
$804$	−11.5617			−0.407749
$805$	−14.8124	+	40.8739i	−0.522068	+	1.44062i
$806$	23.5177			0.828376
$807$	13.2895	−	7.25663i	0.467814	−	0.255446i
$808$	8.80954	−	0.630071i	0.309919	−	0.0221658i
$809$	−11.9077	+	18.5287i	−0.418651	+	0.651434i	−0.984965	−	0.172756i	$-0.944733\pi$
$809$	−11.9077	+	18.5287i	−0.418651	+	0.651434i	0.566313	+	0.824190i	$0.308369\pi$
$810$	1.17315	+	1.90361i	0.0412203	+	0.0668859i
$811$	−6.66745	+	4.28491i	−0.234126	+	0.150464i	−0.652444	−	0.757837i	$-0.726256\pi$
$811$	−6.66745	+	4.28491i	−0.234126	+	0.150464i	0.418318	+	0.908301i	$0.362620\pi$
$812$	−14.4268	+	38.6798i	−0.506283	+	1.35740i
$813$	−0.0657783	+	0.919701i	−0.00230695	+	0.0322553i
$814$	10.5249	−	1.51326i	0.368899	−	0.0530396i
$815$	27.0318	−	7.38540i	0.946881	−	0.258699i
$816$	−0.351947	−	1.19862i	−0.0123206	−	0.0419601i
$817$	−1.57950	+	2.89263i	−0.0552596	+	0.101200i
$818$	11.9532	−	4.45831i	0.417934	−	0.155881i
$819$	−1.91377	−	13.3106i	−0.0668725	−	0.465109i
$820$	−4.90543	+	3.52952i	−0.171305	+	0.123256i
$821$	−20.2741	−	44.3941i	−0.707571	−	1.54936i	−0.830543	−	0.556954i	$-0.811970\pi$
$821$	−20.2741	−	44.3941i	−0.707571	−	1.54936i	0.122972	−	0.992410i	$-0.460757\pi$
$822$	0.906005	+	0.197089i	0.0316006	+	0.00687428i
$823$	−22.3772	+	16.7513i	−0.780019	+	0.583915i	−0.913359	−	0.407155i	$-0.866521\pi$
$823$	−22.3772	+	16.7513i	−0.780019	+	0.583915i	0.133340	+	0.991070i	$0.457430\pi$
$824$	12.6455	+	8.12676i	0.440526	+	0.283109i
$825$	0.736212	−	6.71553i	0.0256316	−	0.233805i
$826$	−9.39304	+	31.9898i	−0.326826	+	1.11307i
$827$	23.1897	+	23.1897i	0.806386	+	0.806386i	0.984085	−	0.177699i	$-0.0568652\pi$
$827$	23.1897	+	23.1897i	0.806386	+	0.806386i	−0.177699	+	0.984085i	$0.556865\pi$
$828$	−4.71313	−	0.886777i	−0.163793	−	0.0308176i
$829$		−	1.53568i		−	0.0533362i	−0.999644	−	0.0266681i	$-0.991510\pi$
$829$		−	1.53568i		−	0.0533362i	0.999644	−	0.0266681i	$-0.00848973\pi$
$830$	−5.30990	+	13.4543i	−0.184309	+	0.467007i
$831$	7.65791	−	8.83770i	0.265650	−	0.306577i
$832$	3.24122	−	0.705083i	0.112369	−	0.0244444i
$833$	−7.06371	−	9.43601i	−0.244743	−	0.326938i
$834$	−8.41164	−	13.0888i	−0.291271	−	0.453227i
$835$	−20.4509	−	9.81076i	−0.707731	−	0.339515i
$836$	6.34815	+	7.32616i	0.219556	+	0.253381i
$837$	−5.67584	−	4.24888i	−0.196186	−	0.146863i
$838$	−6.88847	−	18.4687i	−0.237958	−	0.637991i
$839$	8.41226	−	2.47006i	0.290423	−	0.0852760i	−0.133276	−	0.991079i	$-0.542550\pi$
$839$	8.41226	−	2.47006i	0.290423	−	0.0852760i	0.423699	+	0.905803i	$0.360731\pi$
$840$	−5.04423	+	7.53215i	−0.174042	+	0.259884i
$841$	−31.0290	+	67.9441i	−1.06997	+	2.34290i
$842$	9.79207	−	13.0807i	0.337457	−	0.450790i
$843$	24.5098	+	1.75297i	0.844162	+	0.0603757i
$844$	−17.1679	+	7.84031i	−0.590943	+	0.269875i
$845$	−2.06601	−	3.95970i	−0.0710728	−	0.136218i
$846$	0.933337	−	6.49150i	0.0320888	−	0.223182i
$847$	7.90607	+	36.3436i	0.271656	+	1.24878i
$848$	0.0155754	+	0.217773i	0.000534862	+	0.00747834i
$849$	−9.61873	−	2.82431i	−0.330114	−	0.0969302i
$850$	−6.14453	−	1.12188i	−0.210756	−	0.0384801i
$851$	−34.7599	−	14.7034i	−1.19155	−	0.504027i
$852$	−2.59560	+	2.59560i	−0.0889237	+	0.0889237i
$853$	−5.98895	−	10.9679i	−0.205058	−	0.375535i	0.754830	−	0.655921i	$-0.227719\pi$
$853$	−5.98895	−	10.9679i	−0.205058	−	0.375535i	−0.959887	+	0.280386i	$0.909538\pi$
$854$	33.7203	+	29.2188i	1.15388	+	0.999846i
$855$	−9.85502	+	12.6589i	−0.337035	+	0.432927i
$856$	3.83923	+	0.551998i	0.131222	+	0.0188669i
$857$	−9.08618	+	41.7685i	−0.310378	+	1.42678i	0.512559	+	0.858652i	$0.328698\pi$
$857$	−9.08618	+	41.7685i	−0.310378	+	1.42678i	−0.822937	+	0.568133i	$0.807666\pi$
$858$	−4.19922	−	1.56623i	−0.143359	−	0.0534701i
$859$	−24.7238	+	21.4233i	−0.843566	+	0.730954i	−0.965170	−	0.261625i	$-0.915742\pi$
$859$	−24.7238	+	21.4233i	−0.843566	+	0.730954i	0.121604	+	0.992579i	$0.461196\pi$
$860$	−0.687211	+	0.763446i	−0.0234337	+	0.0260333i
$861$	−9.96649	−	4.55154i	−0.339657	−	0.155116i
$862$	−35.2576	−	19.2521i	−1.20088	−	0.655729i
$863$	−19.1917	−	10.4795i	−0.653293	−	0.356725i	0.118176	−	0.992993i	$-0.462295\pi$
$863$	−19.1917	−	10.4795i	−0.653293	−	0.356725i	−0.771468	+	0.636268i	$0.780477\pi$
$864$	−0.909632	−	0.415415i	−0.0309463	−	0.0141327i
$865$	1.60326	−	1.78111i	0.0545123	−	0.0605596i
$866$	11.8282	−	10.2492i	0.401938	−	0.348281i
$867$	−14.4660	−	5.39553i	−0.491291	−	0.183242i
$868$	6.10985	−	28.0865i	0.207382	−	0.953319i
$869$	−16.0722	−	2.31083i	−0.545212	−	0.0783896i
$870$	−13.9875	+	17.9672i	−0.474221	+	0.609145i
$871$	28.9832	+	25.1141i	0.982060	+	0.850960i
$872$	9.22115	+	16.8873i	0.312268	+	0.571875i
$873$	−1.81702	+	1.81702i	−0.0614968	+	0.0614968i
$874$	−5.85591	−	33.9059i	−0.198079	−	1.14689i
$875$	22.3053	+	39.4577i	0.754055	+	1.33391i
$876$	−10.0602	−	2.95395i	−0.339904	−	0.0998048i
$877$	3.01654	+	42.1768i	0.101861	+	1.42421i	0.749370	+	0.662151i	$0.230356\pi$
$877$	3.01654	+	42.1768i	0.101861	+	1.42421i	−0.647509	+	0.762058i	$0.724189\pi$
$878$	−1.73370	−	7.96969i	−0.0585096	−	0.268964i
$879$	2.34229	−	16.2910i	0.0790036	−	0.549482i
$880$	1.39758	+	2.67859i	0.0471123	+	0.0902952i
$881$	−29.6298	+	13.5315i	−0.998253	+	0.455887i	−0.846418	−	0.532519i	$-0.821245\pi$
$881$	−29.6298	+	13.5315i	−0.998253	+	0.455887i	−0.151835	+	0.988406i	$0.548518\pi$
$882$	−9.41145	−	0.673121i	−0.316900	−	0.0226651i
$883$	−6.92645	+	9.25265i	−0.233093	+	0.311376i	−0.901803	−	0.432147i	$-0.857756\pi$
$883$	−6.92645	+	9.25265i	−0.233093	+	0.311376i	0.668710	+	0.743524i	$0.266847\pi$
$884$	−1.72135	+	3.76924i	−0.0578954	+	0.126773i
$885$	−10.2325	+	15.2794i	−0.343961	+	0.513610i
$886$	−5.29662	+	1.55523i	−0.177944	+	0.0522489i
$887$	6.06411	+	16.2585i	0.203613	+	0.545908i	0.998116	−	0.0613525i	$-0.0195414\pi$
$887$	6.06411	+	16.2585i	0.203613	+	0.545908i	−0.794503	+	0.607260i	$0.792269\pi$
$888$	−6.30002	−	4.71614i	−0.211415	−	0.158263i
$889$	−27.0590	−	31.2278i	−0.907531	−	1.04735i
$890$	27.0533	+	12.9781i	0.906830	+	0.435028i
$891$	0.730488	+	1.13666i	0.0244723	+	0.0380796i
$892$	−2.60889	−	3.48507i	−0.0873520	−	0.116689i
$893$	45.9772	−	10.0017i	1.53857	−	0.334695i
$894$	−0.301742	+	0.348229i	−0.0100918	+	0.0116465i
$895$	−6.94015	+	17.5851i	−0.231984	+	0.587805i
$896$		−	4.05407i		−	0.135437i
$897$	9.88881	+	12.4608i	0.330178	+	0.416054i
$898$	−5.38371	−	5.38371i	−0.179657	−	0.179657i
$899$	20.3405	−	69.2732i	0.678392	−	2.31039i
$900$	−3.89976	+	3.12919i	−0.129992	+	0.104306i
$901$	−0.229445	−	0.147455i	−0.00764391	−	0.00491244i
$902$	−2.92330	+	2.18835i	−0.0973352	+	0.0728642i
$903$	−1.81976	−	0.395865i	−0.0605579	−	0.0131736i
$904$	−7.16743	−	15.6945i	−0.238385	−	0.521991i
$905$	5.07765	−	3.65344i	0.168787	−	0.121444i
$906$	−0.566789	−	3.94211i	−0.0188303	−	0.130968i
$907$	2.87206	−	1.07122i	0.0953653	−	0.0355694i	−0.301329	−	0.953520i	$-0.597430\pi$
$907$	2.87206	−	1.07122i	0.0953653	−	0.0355694i	0.396694	+	0.917951i	$0.370157\pi$
$908$	−9.08750	+	16.6425i	−0.301579	+	0.552301i
$909$	2.48828	+	8.47429i	0.0825309	+	0.281074i
$910$	29.0063	−	7.92486i	0.961549	−	0.262707i
$911$	29.1351	−	4.18900i	0.965290	−	0.138788i	0.358395	−	0.933570i	$-0.383324\pi$
$911$	29.1351	−	4.18900i	0.965290	−	0.138788i	0.606895	+	0.794782i	$0.292415\pi$
$912$	0.511826	−	7.15626i	0.0169483	−	0.236968i
$913$	−3.05434	+	8.18900i	−0.101084	+	0.271016i
$914$	15.8813	−	10.2063i	0.525308	−	0.337595i
$915$	12.9115	+	20.9507i	0.426840	+	0.692609i
$916$	12.9940	−	20.2191i	0.429335	−	0.668058i
$917$	−7.79524	+	0.557527i	−0.257422	+	0.0184112i
$918$	1.09642	−	0.598689i	0.0361871	−	0.0197597i
$919$	37.0347			1.22166			0.610832	−	0.791760i	$-0.290835\pi$
$919$	37.0347			1.22166			0.610832	+	0.791760i	$0.290835\pi$
$920$	0.665226	−	10.7032i	0.0219318	−	0.352872i
$921$	18.6212			0.613589
$922$	5.70158	−	3.11330i	0.187771	−	0.102531i
$923$	12.1449	−	0.868618i	0.399753	−	0.0285909i
$924$	−2.96145	+	4.60811i	−0.0974246	+	0.151596i
$925$	−35.2232	+	17.5394i	−1.15813	+	0.576692i
$926$	−28.6768	+	18.4295i	−0.942379	+	0.605630i
$927$	−5.25305	+	14.0840i	−0.172533	+	0.462578i
$928$	0.726449	−	10.1571i	0.0238469	−	0.333423i
$929$	9.98813	−	1.43608i	0.327700	−	0.0471161i	0.0234985	−	0.999724i	$-0.492519\pi$
$929$	9.98813	−	1.43608i	0.327700	−	0.0471161i	0.304201	+	0.952608i	$0.401610\pi$
$930$	7.85945	−	13.7684i	0.257721	−	0.451485i
$931$	−19.0720	−	64.9532i	−0.625059	−	2.12876i
$932$	−7.21213	+	13.2080i	−0.236241	+	0.432644i
$933$	21.8461	−	8.14816i	0.715208	−	0.266759i
$934$	5.24074	+	36.4501i	0.171482	+	1.19268i
$935$	−3.72500	−	0.607623i	−0.121821	−	0.0198714i
$936$	1.37794	+	3.01727i	0.0450394	+	0.0986225i
$937$	−5.51029	−	1.19869i	−0.180013	−	0.0391595i	0.121655	−	0.992572i	$-0.461180\pi$
$937$	−5.51029	−	1.19869i	−0.180013	−	0.0391595i	−0.301668	+	0.953413i	$0.597544\pi$
$938$	37.5229	−	28.0893i	1.22517	−	0.917147i
$939$	4.47772	+	2.87766i	0.146125	+	0.0939087i
$940$	14.6621	+	0.277091i	0.478225	+	0.00903771i
$941$	1.89431	−	6.45143i	0.0617527	−	0.210310i	−0.922837	−	0.385191i	$-0.874136\pi$
$941$	1.89431	−	6.45143i	0.0617527	−	0.210310i	0.984590	+	0.174880i	$0.0559538\pi$
$942$	−11.1314	−	11.1314i	−0.362679	−	0.362679i
$943$	12.8970	−	1.28912i	0.419986	−	0.0419794i
$944$		−	8.22390i		−	0.267665i
$945$	−8.43224	−	3.32788i	−0.274301	−	0.108256i
$946$	−0.406459	+	0.469079i	−0.0132151	+	0.0152511i
$947$	−16.5348	+	3.59693i	−0.537310	+	0.116885i	−0.473028	−	0.881047i	$-0.656839\pi$
$947$	−16.5348	+	3.59693i	−0.537310	+	0.116885i	−0.0642815	+	0.997932i	$0.520476\pi$
$948$	7.20182	+	9.62050i	0.233904	+	0.312459i
$949$	18.8028	+	29.2578i	0.610366	+	0.949748i
$950$	−30.8127	−	18.3693i	−0.999695	−	0.595978i
$951$	−4.28040	−	4.93985i	−0.138802	−	0.160186i
$952$	4.05429	+	3.03500i	0.131400	+	0.0983650i
$953$	14.3163	+	38.3834i	0.463749	+	1.24336i	0.932866	+	0.360223i	$0.117299\pi$
$953$	14.3163	+	38.3834i	0.463749	+	1.24336i	−0.469117	+	0.883136i	$0.655428\pi$
$954$	−0.209485	+	0.0615104i	−0.00678233	+	0.00199147i
$955$	−4.45139	−	22.5017i	−0.144044	−	0.728137i
$956$	−2.65122	+	5.80536i	−0.0857466	+	0.187759i
$957$	−8.24535	+	11.0145i	−0.266534	+	0.356048i
$958$	−1.09644	−	0.0784186i	−0.0354242	−	0.00253359i
$959$	−3.41923	+	1.56151i	−0.110413	+	0.0504237i
$960$	0.670400	−	2.13321i	0.0216371	−	0.0688489i
$961$	−2.74216	+	19.0721i	−0.0884566	+	0.615229i
$962$	5.54879	+	25.5074i	0.178900	+	0.822391i
$963$	0.276704	+	3.86882i	0.00891666	+	0.124671i
$964$	−15.9069	−	4.67069i	−0.512327	−	0.150433i
$965$	11.1191	+	13.3330i	0.357936	+	0.429205i
$966$	17.4507	−	8.57264i	0.561467	−	0.275820i
$967$	−27.5613	+	27.5613i	−0.886313	+	0.886313i	−0.994167	−	0.107854i	$-0.965602\pi$
$967$	−27.5613	+	27.5613i	−0.886313	+	0.886313i	0.107854	+	0.994167i	$0.465602\pi$
$968$	−4.39682	−	8.05217i	−0.141319	−	0.258806i
$969$	6.77348	+	5.86925i	0.217596	+	0.188548i
$970$	−4.53396	−	3.52970i	−0.145577	−	0.113332i
$971$	−18.1285	−	2.60649i	−0.581772	−	0.0836462i	−0.154855	−	0.987937i	$-0.549491\pi$
$971$	−18.1285	−	2.60649i	−0.581772	−	0.0836462i	−0.426917	+	0.904291i	$0.640400\pi$
$972$	0.212565	−	0.977147i	0.00681803	−	0.0313420i
$973$	59.0989	+	22.0427i	1.89462	+	0.706658i
$974$	−21.9389	+	19.0102i	−0.702968	+	0.609125i
$975$	16.5733	+	0.626642i	0.530769	+	0.0200686i
$976$	−10.0112	−	4.57197i	−0.320452	−	0.146345i
$977$	13.3174	+	7.27186i	0.426062	+	0.232647i	0.677948	−	0.735109i	$-0.262869\pi$
$977$	13.3174	+	7.27186i	0.426062	+	0.232647i	−0.251887	+	0.967757i	$0.581051\pi$
$978$	−10.9991	−	6.00597i	−0.351713	−	0.192050i
$979$	16.4923	+	7.53180i	0.527097	+	0.240717i
$980$	−1.10723	−	21.0693i	−0.0353693	−	0.673035i
$981$	−14.5413	+	12.6001i	−0.464266	+	0.402289i
$982$	−11.2269	−	4.18744i	−0.358266	−	0.133626i
$983$	−5.96067	+	27.4008i	−0.190116	+	0.873949i	0.778938	+	0.627101i	$0.215759\pi$
$983$	−5.96067	+	27.4008i	−0.190116	+	0.873949i	−0.969054	+	0.246848i	$0.920605\pi$
$984$	2.67511	+	0.384623i	0.0852795	+	0.0122613i
$985$	11.3412	−	1.41245i	0.361362	−	0.0450045i
$986$	9.61379	+	8.33040i	0.306165	+	0.265294i
$987$	12.7421	+	23.3354i	0.405586	+	0.742774i
$988$	−16.8278	+	16.8278i	−0.535364	+	0.535364i
$989$	2.09547	−	0.680080i	0.0666320	−	0.0216253i
$990$	−2.32030	+	1.93501i	−0.0737439	+	0.0614988i
$991$	39.3857	+	11.5647i	1.25113	+	0.367364i	0.839185	−	0.543845i	$-0.183032\pi$
$991$	39.3857	+	11.5647i	1.25113	+	0.367364i	0.411943	+	0.911210i	$0.364850\pi$
$992$	0.505795	+	7.07194i	0.0160590	+	0.224534i
$993$	0.274994	+	1.26413i	0.00872669	+	0.0401159i
$994$	2.11784	−	14.7299i	0.0671740	−	0.467205i
$995$	−45.2809	+	23.6257i	−1.43550	+	0.748984i
$996$	5.88405	−	2.68715i	0.186443	−	0.0851457i
$997$	−5.50765	−	0.393915i	−0.174429	−	0.0124754i	−0.0161486	−	0.999870i	$-0.505140\pi$
$997$	−5.50765	−	0.393915i	−0.174429	−	0.0124754i	−0.158281	+	0.987394i	$0.550595\pi$
$998$	18.8875	−	25.2308i	0.597874	−	0.798666i
$999$	3.26919	−	7.15853i	0.103433	−	0.226486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.373.8	yes	240
5.2	odd	4	inner	690.2.w.a.97.8	yes	240
23.14	odd	22	inner	690.2.w.a.313.8	yes	240
115.37	even	44	inner	690.2.w.a.37.8	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.37.8	✓	240	115.37	even	44	inner
690.2.w.a.97.8	yes	240	5.2	odd	4	inner
690.2.w.a.313.8	yes	240	23.14	odd	22	inner
690.2.w.a.373.8	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.877679 - 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-0.516511 + 2.17560i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-1.41675 + 3.79846i) q^{7} +(0.0713392 - 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +O(q^{10})\)	\(q+(0.877679 - 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-0.516511 + 2.17560i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-1.41675 + 3.79846i) q^{7} +(0.0713392 - 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +(0.589321 + 2.15701i) q^{10} +(0.380664 + 1.29642i) q^{11} +(0.479249 - 0.877679i) q^{12} +(-3.10788 + 1.15918i) q^{13} +(0.576955 + 4.01281i) q^{14} +(-0.359989 + 2.20690i) q^{15} +(-0.415415 - 0.909632i) q^{16} +(1.22067 + 0.265541i) q^{17} +(0.800541 - 0.599278i) q^{18} +(6.03561 + 3.87885i) q^{19} +(1.55098 + 1.61073i) q^{20} +(-1.14216 + 3.88985i) q^{21} +(0.955409 + 0.955409i) q^{22} +(-1.15127 - 4.65560i) q^{23} -1.00000i q^{24} +(-4.46643 - 2.24744i) q^{25} +(-2.17219 + 2.50684i) q^{26} +(0.977147 - 0.212565i) q^{27} +(2.42951 + 3.24545i) q^{28} +(5.50536 + 8.56651i) q^{29} +(0.741699 + 2.10947i) q^{30} +(-4.64297 - 5.35827i) q^{31} +(-0.800541 - 0.599278i) q^{32} +(0.472179 + 1.26596i) q^{33} +(1.19862 - 0.351947i) q^{34} +(-7.53215 - 5.04423i) q^{35} +(0.415415 - 0.909632i) q^{36} +(4.71614 - 6.30002i) q^{37} +(7.15626 + 0.511826i) q^{38} +(-3.01727 + 1.37794i) q^{39} +(2.13321 + 0.670400i) q^{40} +(-0.384623 + 2.67511i) q^{41} +(0.861755 + 3.96142i) q^{42} +(0.0327711 + 0.458200i) q^{43} +(1.29642 + 0.380664i) q^{44} +(-0.201634 + 2.22696i) q^{45} +(-3.24163 - 3.53438i) q^{46} +(4.63739 - 4.63739i) q^{47} +(-0.479249 - 0.877679i) q^{48} +(-7.13087 - 6.17894i) q^{49} +(-4.99718 + 0.168005i) q^{50} +(1.23651 + 0.177783i) q^{51} +(-0.705083 + 3.24122i) q^{52} +(-0.204563 - 0.0762982i) q^{53} +(0.755750 - 0.654861i) q^{54} +(-3.01711 + 0.158555i) q^{55} +(3.68771 + 1.68412i) q^{56} +(6.29695 + 3.43839i) q^{57} +(8.93743 + 4.88021i) q^{58} +(7.48072 + 3.41633i) q^{59} +(1.66194 + 1.49598i) q^{60} +(8.31763 - 7.20727i) q^{61} +(-6.64298 - 2.47770i) q^{62} +(-0.861755 + 3.96142i) q^{63} +(-0.989821 - 0.142315i) q^{64} +(-0.916652 - 7.36022i) q^{65} +(1.02113 + 0.884817i) q^{66} +(-5.54092 - 10.1474i) q^{67} +(0.883334 - 0.883334i) q^{68} +(-1.48046 - 4.56161i) q^{69} +(-9.02825 - 0.817438i) q^{70} +(-3.52204 - 1.03416i) q^{71} +(-0.0713392 - 0.997452i) q^{72} +(-2.22874 - 10.2453i) q^{73} +(1.11998 - 7.78960i) q^{74} +(-4.61538 - 1.92308i) q^{75} +(6.52619 - 2.98041i) q^{76} +(-5.46371 - 0.390772i) q^{77} +(-1.98782 + 2.65541i) q^{78} +(-4.99225 + 10.9315i) q^{79} +(2.19356 - 0.433940i) q^{80} +(0.959493 - 0.281733i) q^{81} +(0.944469 + 2.53222i) q^{82} +(5.17838 + 3.87649i) q^{83} +(2.65485 + 3.06386i) q^{84} +(-1.20820 + 2.51854i) q^{85} +(0.248355 + 0.386447i) q^{86} +(6.10246 + 8.15193i) q^{87} +(1.32027 - 0.287208i) q^{88} +(8.78742 - 10.1412i) q^{89} +(0.890298 + 2.05119i) q^{90} -13.4474i q^{91} +(-4.53896 - 1.54850i) q^{92} +(-5.01339 - 5.01339i) q^{93} +(1.84767 - 6.29260i) q^{94} +(-11.5563 + 11.1276i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(-2.05711 + 1.53994i) q^{97} +(-9.21986 - 2.00566i) q^{98} +(0.561289 + 1.22905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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