LMFDB - Embedded newform 162.2.g.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			97.1
Character	$\chi$	$=$	162.97
Dual form			162.2.g.b.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.973045 + 0.230616i) q^{2} +(-1.71858 + 0.215573i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.74099 + 2.33856i) q^{5} +(-1.72197 - 0.186570i) q^{6} +(3.14295 + 2.06715i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.90706 - 0.740960i) q^{9} +O(q^{10})$	\(q+(0.973045 + 0.230616i) q^{2} +(-1.71858 + 0.215573i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.74099 + 2.33856i) q^{5} +(-1.72197 - 0.186570i) q^{6} +(3.14295 + 2.06715i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.90706 - 0.740960i) q^{9} +(-2.23337 + 1.87402i) q^{10} +(-2.28467 + 0.267040i) q^{11} +(-1.63253 - 0.578656i) q^{12} +(-1.19996 + 4.00816i) q^{13} +(2.58151 + 2.73625i) q^{14} +(2.48791 - 4.39432i) q^{15} +(0.597159 + 0.802123i) q^{16} +(-0.456248 - 2.58751i) q^{17} +(2.99957 - 0.0505743i) q^{18} +(1.50312 - 8.52463i) q^{19} +(-2.60535 + 1.30846i) q^{20} +(-5.84705 - 2.87504i) q^{21} +(-2.28467 - 0.267040i) q^{22} +(6.27720 - 4.12858i) q^{23} +(-1.45508 - 0.939545i) q^{24} +(-1.00379 - 3.35289i) q^{25} +(-2.09196 + 3.62338i) q^{26} +(-4.83629 + 1.90009i) q^{27} +(1.88091 + 3.25783i) q^{28} +(-1.68597 + 1.78703i) q^{29} +(3.43425 - 3.70212i) q^{30} +(0.165331 + 2.83863i) q^{31} +(0.396080 + 0.918216i) q^{32} +(3.86883 - 0.951444i) q^{33} +(0.152771 - 2.62298i) q^{34} +(-10.3060 + 3.75108i) q^{35} +(2.93038 + 0.642538i) q^{36} +(5.99816 + 2.18315i) q^{37} +(3.42852 - 7.94820i) q^{38} +(1.19819 - 7.14703i) q^{39} +(-2.83688 + 0.672352i) q^{40} +(-4.24317 + 1.00565i) q^{41} +(-5.02641 - 4.14596i) q^{42} +(4.40534 - 10.2127i) q^{43} +(-2.16150 - 0.786723i) q^{44} +(-3.32839 + 8.08833i) q^{45} +(7.06011 - 2.56967i) q^{46} +(-0.0956182 + 1.64170i) q^{47} +(-1.19918 - 1.24978i) q^{48} +(2.83247 + 6.56640i) q^{49} +(-0.203502 - 3.49400i) q^{50} +(1.34190 + 4.34850i) q^{51} +(-2.87118 + 3.04328i) q^{52} +(0.561391 + 0.972358i) q^{53} +(-5.14411 + 0.733543i) q^{54} +(3.35311 - 5.80776i) q^{55} +(1.07890 + 3.60378i) q^{56} +(-0.745560 + 14.9743i) q^{57} +(-2.05264 + 1.35004i) q^{58} +(9.21881 + 1.07752i) q^{59} +(4.19545 - 2.81034i) q^{60} +(-3.19981 + 1.60701i) q^{61} +(-0.493758 + 2.80024i) q^{62} +(10.6684 + 3.68052i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-7.28419 - 9.78436i) q^{65} +(3.98396 - 0.0335834i) q^{66} +(-1.00647 - 1.06680i) q^{67} +(0.753555 - 2.51705i) q^{68} +(-9.89788 + 8.44850i) q^{69} +(-10.8933 + 1.27324i) q^{70} +(-1.46893 + 1.23258i) q^{71} +(2.70321 + 1.30101i) q^{72} +(-0.123017 - 0.103223i) q^{73} +(5.33301 + 3.50757i) q^{74} +(2.44789 + 5.54583i) q^{75} +(5.16909 - 6.94329i) q^{76} +(-7.73262 - 3.88347i) q^{77} +(2.81411 - 6.67806i) q^{78} +(-9.27560 - 2.19836i) q^{79} -2.91546 q^{80} +(7.90196 - 4.30803i) q^{81} -4.36071 q^{82} +(-2.15900 - 0.511693i) q^{83} +(-3.93480 - 5.19338i) q^{84} +(6.84538 + 3.43788i) q^{85} +(6.64181 - 8.92150i) q^{86} +(2.51225 - 3.43460i) q^{87} +(-1.92181 - 1.26399i) q^{88} +(-0.717829 - 0.602330i) q^{89} +(-5.10397 + 7.10273i) q^{90} +(-12.0569 + 10.1169i) q^{91} +(7.46241 - 0.872231i) q^{92} +(-0.896067 - 4.84278i) q^{93} +(-0.471643 + 1.57540i) q^{94} +(17.3184 + 18.3565i) q^{95} +(-0.878639 - 1.49265i) q^{96} +(-3.02994 - 4.06992i) q^{97} +(1.24180 + 7.04262i) q^{98} +(-6.44380 + 2.46915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{27}\right)$

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 $

$2$	0.973045	+	0.230616i	0.688047	+	0.163070i
$2$	0.973045	+	0.230616i	0.688047	+	0.163070i
$3$	−1.71858	+	0.215573i	−0.992224	+	0.124461i
$3$	−1.71858	+	0.215573i	−0.992224	+	0.124461i
$4$	0.893633	+	0.448799i	0.446816	+	0.224400i
$5$	−1.74099	+	2.33856i	−0.778596	+	1.04584i	0.218944	+	0.975737i	$0.429739\pi$
$5$	−1.74099	+	2.33856i	−0.778596	+	1.04584i	−0.997540	+	0.0700985i	$0.977669\pi$
$6$	−1.72197	−	0.186570i	−0.702993	−	0.0761670i
$7$	3.14295	+	2.06715i	1.18792	+	0.781310i	0.980419	−	0.196924i	$-0.0630952\pi$
$7$	3.14295	+	2.06715i	1.18792	+	0.781310i	0.207505	+	0.978234i	$0.433466\pi$
$8$	0.766044	+	0.642788i	0.270838	+	0.227260i
$9$	2.90706	−	0.740960i	0.969019	−	0.246987i
$10$	−2.23337	+	1.87402i	−0.706255	+	0.592618i
$11$	−2.28467	+	0.267040i	−0.688854	+	0.0805155i	−0.453316	−	0.891350i	$-0.649759\pi$
$11$	−2.28467	+	0.267040i	−0.688854	+	0.0805155i	−0.235538	+	0.971865i	$0.575685\pi$
$12$	−1.63253	−	0.578656i	−0.471271	−	0.167043i
$13$	−1.19996	+	4.00816i	−0.332810	+	1.11166i	0.613849	+	0.789424i	$0.289621\pi$
$13$	−1.19996	+	4.00816i	−0.332810	+	1.11166i	−0.946658	+	0.322239i	$0.895565\pi$
$14$	2.58151	+	2.73625i	0.689939	+	0.731292i
$15$	2.48791	−	4.39432i	0.642376	−	1.13461i
$16$	0.597159	+	0.802123i	0.149290	+	0.200531i
$17$	−0.456248	−	2.58751i	−0.110656	−	0.627564i	−0.988809	−	0.149184i	$-0.952335\pi$
$17$	−0.456248	−	2.58751i	−0.110656	−	0.627564i	0.878153	−	0.478380i	$-0.158776\pi$
$18$	2.99957	−	0.0505743i	0.707006	−	0.0119205i
$19$	1.50312	−	8.52463i	0.344840	−	1.95568i	0.0554968	−	0.998459i	$-0.482326\pi$
$19$	1.50312	−	8.52463i	0.344840	−	1.95568i	0.289343	−	0.957225i	$-0.406563\pi$
$20$	−2.60535	+	1.30846i	−0.582575	+	0.292580i
$21$	−5.84705	−	2.87504i	−1.27593	−	0.627384i
$22$	−2.28467	−	0.267040i	−0.487094	−	0.0569331i
$23$	6.27720	−	4.12858i	1.30889	−	0.860868i	0.312849	−	0.949803i	$-0.398717\pi$
$23$	6.27720	−	4.12858i	1.30889	−	0.860868i	0.996037	+	0.0889345i	$0.0283462\pi$
$24$	−1.45508	−	0.939545i	−0.297017	−	0.191784i
$25$	−1.00379	−	3.35289i	−0.200758	−	0.670578i
$26$	−2.09196	+	3.62338i	−0.410268	+	0.710604i
$27$	−4.83629	+	1.90009i	−0.930744	+	0.365672i
$28$	1.88091	+	3.25783i	0.355458	+	0.615672i
$29$	−1.68597	+	1.78703i	−0.313077	+	0.331842i	−0.864735	−	0.502228i	$-0.832514\pi$
$29$	−1.68597	+	1.78703i	−0.313077	+	0.331842i	0.551658	+	0.834070i	$0.313995\pi$
$30$	3.43425	−	3.70212i	0.627005	−	0.675912i
$31$	0.165331	+	2.83863i	0.0296944	+	0.509832i	0.980061	+	0.198699i	$0.0636716\pi$
$31$	0.165331	+	2.83863i	0.0296944	+	0.509832i	−0.950366	+	0.311133i	$0.899291\pi$
$32$	0.396080	+	0.918216i	0.0700177	+	0.162319i
$33$	3.86883	−	0.951444i	0.673477	−	0.165625i
$34$	0.152771	−	2.62298i	0.0262001	−	0.449838i
$35$	−10.3060	+	3.75108i	−1.74203	+	0.634049i
$36$	2.93038	+	0.642538i	0.488397	+	0.107090i
$37$	5.99816	+	2.18315i	0.986091	+	0.358908i	0.784205	−	0.620501i	$-0.213071\pi$
$37$	5.99816	+	2.18315i	0.986091	+	0.358908i	0.201886	+	0.979409i	$0.435293\pi$
$38$	3.42852	−	7.94820i	0.556179	−	1.28937i
$39$	1.19819	−	7.14703i	0.191863	−	1.14444i
$40$	−2.83688	+	0.672352i	−0.448549	+	0.106308i
$41$	−4.24317	+	1.00565i	−0.662672	+	0.157056i	−0.548170	−	0.836367i	$-0.684675\pi$
$41$	−4.24317	+	1.00565i	−0.662672	+	0.157056i	−0.114502	+	0.993423i	$0.536527\pi$
$42$	−5.02641	−	4.14596i	−0.775592	−	0.639736i
$43$	4.40534	−	10.2127i	0.671808	−	1.55743i	−0.150641	−	0.988588i	$-0.548134\pi$
$43$	4.40534	−	10.2127i	0.671808	−	1.55743i	0.822450	−	0.568838i	$-0.192607\pi$
$44$	−2.16150	−	0.786723i	−0.325859	−	0.118603i
$45$	−3.32839	+	8.08833i	−0.496167	+	1.20574i
$46$	7.06011	−	2.56967i	1.04096	−	0.378877i
$47$	−0.0956182	+	1.64170i	−0.0139473	+	0.239467i	0.984128	+	0.177458i	$0.0567875\pi$
$47$	−0.0956182	+	1.64170i	−0.0139473	+	0.239467i	−0.998076	+	0.0620082i	$0.980249\pi$
$48$	−1.19918	−	1.24978i	−0.173087	−	0.180391i
$49$	2.83247	+	6.56640i	0.404639	+	0.938058i
$50$	−0.203502	−	3.49400i	−0.0287796	−	0.494126i
$51$	1.34190	+	4.34850i	0.187903	+	0.608912i
$52$	−2.87118	+	3.04328i	−0.398161	+	0.422026i
$53$	0.561391	+	0.972358i	0.0771130	+	0.133564i	0.902003	−	0.431729i	$-0.142096\pi$
$53$	0.561391	+	0.972358i	0.0771130	+	0.133564i	−0.824890	+	0.565293i	$0.808763\pi$
$54$	−5.14411	+	0.733543i	−0.700025	+	0.0998226i
$55$	3.35311	−	5.80776i	0.452133	−	0.783118i
$56$	1.07890	+	3.60378i	0.144174	+	0.481575i
$57$	−0.745560	+	14.9743i	−0.0987519	+	1.98340i
$58$	−2.05264	+	1.35004i	−0.269525	+	0.177270i
$59$	9.21881	+	1.07752i	1.20019	+	0.140282i	0.692602	−	0.721320i	$-0.256464\pi$
$59$	9.21881	+	1.07752i	1.20019	+	0.140282i	0.507585	+	0.861602i	$0.330538\pi$
$60$	4.19545	−	2.81034i	0.541630	−	0.362813i
$61$	−3.19981	+	1.60701i	−0.409694	+	0.205756i	−0.641696	−	0.766959i	$-0.721769\pi$
$61$	−3.19981	+	1.60701i	−0.409694	+	0.205756i	0.232002	+	0.972715i	$0.425473\pi$
$62$	−0.493758	+	2.80024i	−0.0627073	+	0.355631i
$63$	10.6684	+	3.68052i	1.34409	+	0.463702i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	−7.28419	−	9.78436i	−0.903492	−	1.21360i
$66$	3.98396	−	0.0335834i	0.490392	−	0.00413384i
$67$	−1.00647	−	1.06680i	−0.122960	−	0.130330i	0.662969	−	0.748647i	$-0.269296\pi$
$67$	−1.00647	−	1.06680i	−0.122960	−	0.130330i	−0.785929	+	0.618317i	$0.787815\pi$
$68$	0.753555	−	2.51705i	0.0913820	−	0.305237i
$69$	−9.89788	+	8.44850i	−1.19156	+	1.01708i
$70$	−10.8933	+	1.27324i	−1.30200	+	0.152181i
$71$	−1.46893	+	1.23258i	−0.174330	+	0.146280i	−0.725778	−	0.687929i	$-0.758520\pi$
$71$	−1.46893	+	1.23258i	−0.174330	+	0.146280i	0.551448	+	0.834209i	$0.314076\pi$
$72$	2.70321	+	1.30101i	0.318577	+	0.153326i
$73$	−0.123017	−	0.103223i	−0.0143980	−	0.0120814i	0.635560	−	0.772051i	$-0.280769\pi$
$73$	−0.123017	−	0.103223i	−0.0143980	−	0.0120814i	−0.649958	+	0.759970i	$0.725214\pi$
$74$	5.33301	+	3.50757i	0.619950	+	0.407747i
$75$	2.44789	+	5.54583i	0.282658	+	0.640377i
$76$	5.16909	−	6.94329i	0.592935	−	0.796450i
$77$	−7.73262	−	3.88347i	−0.881214	−	0.442562i
$78$	2.81411	−	6.67806i	0.318635	−	0.756141i
$79$	−9.27560	−	2.19836i	−1.04359	−	0.247334i	−0.327139	−	0.944976i	$-0.606085\pi$
$79$	−9.27560	−	2.19836i	−1.04359	−	0.247334i	−0.716447	+	0.697642i	$0.754233\pi$
$80$	−2.91546			−0.325959
$81$	7.90196	−	4.30803i	0.877995	−	0.478670i
$82$	−4.36071			−0.481560
$83$	−2.15900	−	0.511693i	−0.236981	−	0.0561656i	0.110409	−	0.993886i	$-0.464784\pi$
$83$	−2.15900	−	0.511693i	−0.236981	−	0.0561656i	−0.347390	+	0.937721i	$0.612932\pi$
$84$	−3.93480	−	5.19338i	−0.429322	−	0.566644i
$85$	6.84538	+	3.43788i	0.742486	+	0.372890i
$86$	6.64181	−	8.92150i	0.716205	−	0.962030i
$87$	2.51225	−	3.43460i	0.269341	−	0.368228i
$88$	−1.92181	−	1.26399i	−0.204866	−	0.134742i
$89$	−0.717829	−	0.602330i	−0.0760897	−	0.0638469i	0.603950	−	0.797023i	$-0.293593\pi$
$89$	−0.717829	−	0.602330i	−0.0760897	−	0.0638469i	−0.680039	+	0.733176i	$0.738037\pi$
$90$	−5.10397	+	7.10273i	−0.538005	+	0.748694i
$91$	−12.0569	+	10.1169i	−1.26391	+	1.06054i
$92$	7.46241	−	0.872231i	0.778010	−	0.0909364i
$93$	−0.896067	−	4.84278i	−0.0929178	−	0.502172i
$94$	−0.471643	+	1.57540i	−0.0486463	+	0.162490i
$95$	17.3184	+	18.3565i	1.77683	+	1.88333i
$96$	−0.878639	−	1.49265i	−0.0896757	−	0.152343i
$97$	−3.02994	−	4.06992i	−0.307644	−	0.413237i	0.621233	−	0.783626i	$-0.286632\pi$
$97$	−3.02994	−	4.06992i	−0.307644	−	0.413237i	−0.928877	+	0.370388i	$0.879225\pi$
$98$	1.24180	+	7.04262i	0.125441	+	0.711412i
$99$	−6.44380	+	2.46915i	−0.647627	+	0.248159i
$100$	0.607755	−	3.44675i	0.0607755	−	0.344675i
$101$	4.62840	−	2.32447i	0.460543	−	0.231293i	−0.203372	−	0.979102i	$-0.565190\pi$
$101$	4.62840	−	2.32447i	0.460543	−	0.231293i	0.663915	+	0.747808i	$0.268894\pi$
$102$	0.302894	+	4.54075i	0.0299910	+	0.449601i
$103$	−3.03292	−	0.354498i	−0.298843	−	0.0349297i	−0.0346496	−	0.999400i	$-0.511032\pi$
$103$	−3.03292	−	0.354498i	−0.298843	−	0.0349297i	−0.264193	+	0.964470i	$0.585106\pi$
$104$	−3.49562	+	2.29910i	−0.342774	+	0.225446i
$105$	16.9031	−	8.66825i	1.64958	−	0.845934i
$106$	0.322018	+	1.07561i	0.0312771	+	0.104473i
$107$	5.80874	−	10.0610i	0.561552	−	0.972637i	−0.435809	−	0.900039i	$-0.643538\pi$
$107$	5.80874	−	10.0610i	0.561552	−	0.972637i	0.997361	−	0.0725980i	$-0.0231290\pi$
$108$	−5.17462	−	0.472544i	−0.497928	−	0.0454706i
$109$	−1.27249	−	2.20401i	−0.121882	−	0.211106i	0.798628	−	0.601825i	$-0.205560\pi$
$109$	−1.27249	−	2.20401i	−0.121882	−	0.211106i	−0.920510	+	0.390719i	$0.872226\pi$
$110$	4.60209	−	4.87793i	0.438792	−	0.465092i
$111$	−10.7790	−	2.45889i	−1.02309	−	0.233387i
$112$	0.218730	+	3.75545i	0.0206681	+	0.354857i
$113$	5.35665	+	12.4181i	0.503911	+	1.16820i	0.960440	+	0.278489i	$0.0898335\pi$
$113$	5.35665	+	12.4181i	0.503911	+	1.16820i	−0.456528	+	0.889709i	$0.650907\pi$
$114$	−4.17878	+	14.3987i	−0.391379	+	1.34857i
$115$	−1.27363	+	21.8674i	−0.118767	+	2.03915i
$116$	−2.30866	+	0.840282i	−0.214353	+	0.0780182i
$117$	−0.518476	+	12.5411i	−0.0479331	+	1.15942i
$118$	8.72183	+	3.17448i	0.802909	+	0.292235i
$119$	3.91481	−	9.07556i	0.358870	−	0.831955i
$120$	4.73047	−	1.76705i	0.431831	−	0.161309i
$121$	−5.55508	+	1.31658i	−0.505007	+	0.119689i
$122$	−3.48416	+	0.825762i	−0.315441	+	0.0747610i
$123$	7.07545	−	2.64301i	0.637972	−	0.238312i
$124$	−1.12623	+	2.61089i	−0.101138	+	0.234465i
$125$	−4.10967	−	1.49580i	−0.367580	−	0.133788i
$126$	9.53206	+	6.04162i	0.849183	+	0.538230i
$127$	−9.84592	+	3.58362i	−0.873684	+	0.317995i	−0.739658	−	0.672983i	$-0.765013\pi$
$127$	−9.84592	+	3.58362i	−0.873684	+	0.317995i	−0.134026	+	0.990978i	$0.542790\pi$
$128$	−0.0581448	+	0.998308i	−0.00513933	+	0.0882388i
$129$	−5.36936	+	18.5011i	−0.472745	+	1.62893i
$130$	−4.83141	−	11.2005i	−0.423743	−	0.982346i
$131$	−0.00963024	−	0.165345i	−0.000841398	−	0.0144462i	0.997861	−	0.0653664i	$-0.0208216\pi$
$131$	−0.00963024	−	0.165345i	−0.000841398	−	0.0144462i	−0.998703	+	0.0509202i	$0.983785\pi$
$132$	3.88432	+	0.886087i	0.338087	+	0.0771240i
$133$	22.3459	−	23.6853i	1.93764	−	2.05378i
$134$	−0.733321	−	1.27015i	−0.0633493	−	0.109724i
$135$	3.97648	−	14.6180i	0.342241	−	1.25812i
$136$	1.31371	−	2.27542i	0.112650	−	0.195116i
$137$	−5.71490	−	19.0891i	−0.488257	−	1.63089i	−0.746912	−	0.664922i	$-0.768465\pi$
$137$	−5.71490	−	19.0891i	−0.488257	−	1.63089i	0.258655	−	0.965970i	$-0.416721\pi$
$138$	−11.5794	+	5.93816i	−0.985707	+	0.505490i
$139$	−18.1963	+	11.9679i	−1.54339	+	1.01510i	−0.561095	+	0.827751i	$0.689620\pi$
$139$	−18.1963	+	11.9679i	−1.54339	+	1.01510i	−0.982293	+	0.187351i	$0.940010\pi$
$140$	−10.8933	−	1.27324i	−0.920650	−	0.107609i
$141$	−0.189579	−	2.84201i	−0.0159654	−	0.239341i
$142$	−1.71359	+	0.860596i	−0.143801	+	0.0722196i
$143$	1.67118	−	9.47776i	0.139751	−	0.792570i
$144$	2.33032	+	1.88935i	0.194193	+	0.157446i
$145$	−1.24380	−	7.05395i	−0.103292	−	0.585799i
$146$	−0.0958960	−	0.128811i	−0.00793641	−	0.0106604i
$147$	−6.28337	−	10.6743i	−0.518244	−	0.880402i
$148$	4.38035	+	4.64290i	0.360063	+	0.381644i
$149$	2.52073	−	8.41984i	0.206507	−	0.689780i	−0.790500	−	0.612462i	$-0.790179\pi$
$149$	2.52073	−	8.41984i	0.206507	−	0.689780i	0.997006	−	0.0773178i	$-0.0246356\pi$
$150$	1.10295	+	5.96086i	0.0900553	+	0.486702i
$151$	−12.7453	+	1.48971i	−1.03719	+	0.121231i	−0.617609	−	0.786485i	$-0.711899\pi$
$151$	−12.7453	+	1.48971i	−1.03719	+	0.121231i	−0.419585	+	0.907716i	$0.637824\pi$
$152$	6.63099	−	5.56406i	0.537844	−	0.451305i
$153$	−3.24358	−	7.18398i	−0.262228	−	0.580791i
$154$	−6.62860	−	5.56206i	−0.534148	−	0.448203i
$155$	−6.92614	−	4.55539i	−0.556321	−	0.365898i
$156$	4.27832	−	5.84907i	0.342540	−	0.468301i
$157$	2.79034	−	3.74808i	0.222693	−	0.299129i	−0.676709	−	0.736250i	$-0.736595\pi$
$157$	2.79034	−	3.74808i	0.222693	−	0.299129i	0.899403	+	0.437121i	$0.144002\pi$
$158$	−8.51860	−	4.27820i	−0.677703	−	0.340355i
$159$	−1.17441	−	1.55006i	−0.0931369	−	0.122928i
$160$	−2.83688	−	0.672352i	−0.224275	−	0.0531541i
$161$	28.2633			2.22746
$162$	8.68246	−	2.36959i	0.682158	−	0.186172i
$163$	14.0056			1.09700			0.548502	−	0.836149i	$-0.315198\pi$
$163$	14.0056			1.09700			0.548502	+	0.836149i	$0.315198\pi$
$164$	−4.24317	−	1.00565i	−0.331336	−	0.0785281i
$165$	−4.51060	+	10.7040i	−0.351150	+	0.833302i
$166$	−1.98280	−	0.995800i	−0.153895	−	0.0772891i
$167$	6.24495	−	8.38842i	0.483248	−	0.649115i	−0.491904	−	0.870649i	$-0.663699\pi$
$167$	6.24495	−	8.38842i	0.483248	−	0.649115i	0.975153	+	0.221534i	$0.0711064\pi$
$168$	−2.63106	−	5.96081i	−0.202991	−	0.459887i
$169$	−3.76406	−	2.47566i	−0.289543	−	0.190435i
$170$	5.86803	+	4.92386i	0.450057	+	0.377643i
$171$	−1.94675	−	25.8953i	−0.148872	−	1.98027i
$172$	8.52022	−	7.14931i	0.649661	−	0.545130i
$173$	13.4690	−	1.57431i	1.02403	−	0.119692i	0.412538	−	0.910941i	$-0.364643\pi$
$173$	13.4690	−	1.57431i	1.02403	−	0.119692i	0.611495	+	0.791248i	$0.290568\pi$
$174$	3.23661	−	2.76266i	0.245366	−	0.209437i
$175$	3.77607	−	12.6130i	0.285444	−	0.953449i
$176$	−1.57851	−	1.67312i	−0.118985	−	0.126116i
$177$	−16.0756	+	0.135512i	−1.20831	+	0.0101857i
$178$	−0.559573	−	0.751637i	−0.0419418	−	0.0563376i
$179$	0.755656	+	4.28554i	0.0564804	+	0.320316i	0.999938	−	0.0111784i	$-0.00355826\pi$
$179$	0.755656	+	4.28554i	0.0564804	+	0.320316i	−0.943457	+	0.331495i	$0.892447\pi$
$180$	−6.60439	+	5.73422i	−0.492262	+	0.427404i
$181$	0.311609	−	1.76722i	0.0231617	−	0.131357i	−0.971034	−	0.238940i	$-0.923200\pi$
$181$	0.311609	−	1.76722i	0.0231617	−	0.131357i	0.994196	+	0.107583i	$0.0343112\pi$
$182$	−14.0650	+	7.06372i	−1.04257	+	0.523598i
$183$	5.15272	−	3.45157i	0.380900	−	0.255147i
$184$	7.46241	+	0.872231i	0.550136	+	0.0643017i
$185$	−15.5482	+	10.2262i	−1.14313	+	0.751845i
$186$	0.244908	−	4.91888i	0.0179575	−	0.360670i
$187$	1.73335	+	5.78978i	0.126755	+	0.423391i
$188$	−0.822242	+	1.42416i	−0.0599681	+	0.103868i
$189$	−19.1280	−	4.02546i	−1.39136	−	0.292809i
$190$	12.6183	+	21.8556i	0.915429	+	1.58557i
$191$	−17.2650	+	18.2998i	−1.24925	+	1.32413i	−0.323388	+	0.946266i	$0.604822\pi$
$191$	−17.2650	+	18.2998i	−1.24925	+	1.32413i	−0.925862	+	0.377862i	$0.876659\pi$
$192$	−0.510727	−	1.65504i	−0.0368585	−	0.119442i
$193$	0.764997	+	13.1345i	0.0550657	+	0.945441i	0.906825	+	0.421507i	$0.138499\pi$
$193$	0.764997	+	13.1345i	0.0550657	+	0.945441i	−0.851759	+	0.523933i	$0.824464\pi$
$194$	−2.00968	−	4.65896i	−0.144287	−	0.334494i
$195$	14.6277	+	15.2450i	1.04751	+	1.09171i
$196$	−0.415809	+	7.13916i	−0.0297006	+	0.509940i
$197$	−19.0986	+	6.95133i	−1.36072	+	0.495262i	−0.916277	−	0.400545i	$-0.868821\pi$
$197$	−19.0986	+	6.95133i	−1.36072	+	0.495262i	−0.444443	+	0.895807i	$0.646598\pi$
$198$	−6.83954	+	0.916551i	−0.486065	+	0.0651365i
$199$	−2.74737	−	0.999961i	−0.194756	−	0.0708853i	0.242801	−	0.970076i	$-0.421934\pi$
$199$	−2.74737	−	0.999961i	−0.194756	−	0.0708853i	−0.437557	+	0.899191i	$0.644156\pi$
$200$	1.38625	−	3.21368i	0.0980226	−	0.227242i
$201$	1.95968	+	1.61641i	0.138225	+	0.114013i
$202$	5.03970	−	1.19443i	0.354592	−	0.0840399i
$203$	−8.99298	+	2.13138i	−0.631184	+	0.149593i
$204$	−0.752439	+	4.48820i	−0.0526813	+	0.314237i
$205$	5.03556	−	11.6737i	0.351699	−	0.815329i
$206$	−2.86942	−	1.04438i	−0.199922	−	0.0727656i
$207$	15.1891	−	16.6532i	1.05571	−	1.15748i
$208$	−3.93160	+	1.43099i	−0.272608	+	0.0992211i
$209$	−1.15773	+	19.8774i	−0.0800815	+	1.37495i
$210$	18.4465	−	4.53647i	1.27293	−	0.313046i
$211$	−10.2424	−	23.7444i	−0.705113	−	1.63463i	−0.771021	−	0.636809i	$-0.780254\pi$
$211$	−10.2424	−	23.7444i	−0.705113	−	1.63463i	0.0659088	−	0.997826i	$-0.479005\pi$
$212$	0.0652840	+	1.12088i	0.00448372	+	0.0769826i
$213$	2.25877	−	2.43495i	0.154768	−	0.166840i
$214$	7.97240	−	8.45025i	0.544982	−	0.577647i
$215$	16.2134	+	28.0824i	1.10575	+	1.91521i
$216$	−4.92616	−	1.65316i	−0.335183	−	0.112483i
$217$	−5.34824	+	9.26343i	−0.363062	+	0.628843i
$218$	−0.729908	−	2.43806i	−0.0494356	−	0.165126i
$219$	0.233667	+	0.150879i	0.0157897	+	0.0101954i
$220$	5.60296	−	3.68513i	0.377752	−	0.248451i
$221$	10.9186	+	1.27621i	0.734467	+	0.0858469i
$222$	−9.92136	−	4.87841i	−0.665878	−	0.327417i
$223$	5.44386	−	2.73401i	0.364548	−	0.183083i	−0.257090	−	0.966387i	$-0.582764\pi$
$223$	5.44386	−	2.73401i	0.364548	−	0.183083i	0.621638	+	0.783305i	$0.286467\pi$
$224$	−0.653233	+	3.70467i	−0.0436459	+	0.247528i
$225$	−5.40243	−	9.00327i	−0.360162	−	0.600218i
$226$	2.34845	+	13.3187i	0.156216	+	0.885947i
$227$	15.7094	+	21.1014i	1.04267	+	1.40055i	0.912508	+	0.409059i	$0.134143\pi$
$227$	15.7094	+	21.1014i	1.04267	+	1.40055i	0.130165	+	0.991492i	$0.458449\pi$
$228$	−7.38672	+	13.0469i	−0.489197	+	0.864054i
$229$	0.107641	+	0.114093i	0.00711310	+	0.00753945i	0.730920	−	0.682463i	$-0.239091\pi$
$229$	0.107641	+	0.114093i	0.00711310	+	0.00753945i	−0.723807	+	0.690002i	$0.757610\pi$
$230$	−6.28228	+	20.9843i	−0.414241	+	1.38366i
$231$	14.1263	+	5.00712i	0.929444	+	0.329444i
$232$	−2.44021	+	0.285219i	−0.160208	+	0.0187256i
$233$	8.65323	−	7.26092i	0.566892	−	0.475679i	−0.313721	−	0.949515i	$-0.601576\pi$
$233$	8.65323	−	7.26092i	0.566892	−	0.475679i	0.880613	+	0.473836i	$0.157131\pi$
$234$	−3.39667	+	12.0834i	−0.222047	+	0.789920i
$235$	−3.67275	−	3.08180i	−0.239584	−	0.201034i
$236$	7.75464	+	5.10031i	0.504784	+	0.332002i
$237$	16.4148	+	1.77849i	1.06626	+	0.115525i
$238$	5.90226	−	7.92811i	0.382587	−	0.513903i
$239$	−21.6463	−	10.8712i	−1.40019	−	0.703200i	−0.421169	−	0.906982i	$-0.638380\pi$
$239$	−21.6463	−	10.8712i	−1.40019	−	0.703200i	−0.979016	+	0.203782i	$0.934676\pi$
$240$	5.01047	−	0.628495i	0.323424	−	0.0405692i
$241$	17.5713	+	4.16447i	1.13186	+	0.268257i	0.753531	−	0.657413i	$-0.228349\pi$
$241$	17.5713	+	4.16447i	1.13186	+	0.268257i	0.378334	+	0.925669i	$0.376497\pi$
$242$	−5.70897			−0.366986
$243$	−12.6515	+	9.10715i	−0.811592	+	0.584224i
$244$	−3.58068			−0.229230
$245$	−20.2872	−	4.80816i	−1.29610	−	0.307182i
$246$	7.49425	−	0.940052i	0.477816	−	0.0599355i
$247$	32.3644	+	16.2540i	2.05929	+	1.03422i
$248$	−1.69798	+	2.28079i	−0.107822	+	0.144830i
$249$	3.82073	+	0.413964i	0.242129	+	0.0262339i
$250$	−3.65394	−	2.40323i	−0.231095	−	0.151994i
$251$	−3.12459	−	2.62184i	−0.197222	−	0.165489i	0.538828	−	0.842416i	$-0.318867\pi$
$251$	−3.12459	−	2.62184i	−0.197222	−	0.165489i	−0.736051	+	0.676926i	$0.763312\pi$
$252$	7.88183	+	8.07701i	0.496508	+	0.508804i
$253$	−13.2388	+	11.1087i	−0.832319	+	0.698399i
$254$	−10.4070	+	1.21640i	−0.652991	+	0.0763237i
$255$	−12.5055	−	4.43260i	−0.783123	−	0.277580i
$256$	−0.286803	+	0.957990i	−0.0179252	+	0.0598743i
$257$	−13.2735	−	14.0691i	−0.827980	−	0.877607i	0.166117	−	0.986106i	$-0.446877\pi$
$257$	−13.2735	−	14.0691i	−0.827980	−	0.877607i	−0.994097	+	0.108499i	$0.965396\pi$
$258$	−9.49127	+	16.7641i	−0.590901	+	1.04369i
$259$	14.3390	+	19.2606i	0.890983	+	1.19680i
$260$	−2.11817	−	12.0128i	−0.131364	−	0.745000i
$261$	−3.57710	+	6.44423i	−0.221417	+	0.398888i
$262$	0.0287605	−	0.163109i	0.00177683	−	0.0100769i
$263$	13.6259	−	6.84318i	0.840209	−	0.421969i	0.0239904	−	0.999712i	$-0.492363\pi$
$263$	13.6259	−	6.84318i	0.840209	−	0.421969i	0.816218	+	0.577743i	$0.196067\pi$
$264$	3.57527	+	1.75799i	0.220043	+	0.108197i
$265$	−3.25130	−	0.380022i	−0.199726	−	0.0233446i
$266$	27.2058	−	17.8935i	1.66810	−	1.09712i
$267$	1.36350	+	0.880410i	0.0834446	+	0.0538802i
$268$	−0.420637	−	1.40503i	−0.0256945	−	0.0858257i
$269$	9.42374	−	16.3224i	0.574576	−	0.995194i	−0.421512	−	0.906823i	$-0.638500\pi$
$269$	9.42374	−	16.3224i	0.574576	−	0.995194i	0.996088	−	0.0883713i	$-0.0281662\pi$
$270$	7.24043	−	13.3069i	0.440639	−	0.809833i
$271$	−5.56282	−	9.63509i	−0.337917	−	0.585290i	0.646123	−	0.763233i	$-0.276389\pi$
$271$	−5.56282	−	9.63509i	−0.337917	−	0.585290i	−0.984041	+	0.177943i	$0.943056\pi$
$272$	1.80305	−	1.91112i	0.109326	−	0.115879i
$273$	18.5398	−	19.9859i	1.12208	−	1.20960i
$274$	−1.15861	−	19.8925i	−0.0699940	−	1.20175i
$275$	3.18868	+	7.39220i	0.192285	+	0.445766i
$276$	−12.6368	+	3.10770i	−0.760643	+	0.187061i
$277$	−1.51610	+	26.0305i	−0.0910938	+	1.56402i	0.575001	+	0.818153i	$0.305002\pi$
$277$	−1.51610	+	26.0305i	−0.0910938	+	1.56402i	−0.666095	+	0.745867i	$0.732035\pi$
$278$	−20.4658	+	7.44893i	−1.22746	+	0.446757i
$279$	2.58394	+	8.12954i	0.154696	+	0.486703i
$280$	−10.3060	−	3.75108i	−0.615902	−	0.224170i
$281$	−6.70946	+	15.5543i	−0.400253	+	0.927890i	0.592260	+	0.805747i	$0.298236\pi$
$281$	−6.70946	+	15.5543i	−0.400253	+	0.927890i	−0.992512	+	0.122143i	$0.961023\pi$
$282$	0.470945	−	2.80913i	0.0280443	−	0.167281i
$283$	−16.6679	+	3.95036i	−0.990802	+	0.234824i	−0.693890	−	0.720081i	$-0.744105\pi$
$283$	−16.6679	+	3.95036i	−0.990802	+	0.234824i	−0.296912	+	0.954905i	$0.595957\pi$
$284$	−1.86587	+	0.442218i	−0.110719	+	0.0262408i
$285$	−33.7203	−	27.8137i	−1.99742	−	1.64754i
$286$	3.81186	−	8.83688i	0.225400	−	0.522536i
$287$	−15.4149	−	5.61057i	−0.909913	−	0.331181i
$288$	1.83179	+	2.37583i	0.107939	+	0.139997i
$289$	9.48772	−	3.45325i	0.558101	−	0.203132i
$290$	0.416478	−	7.15065i	0.0244564	−	0.419901i
$291$	6.08457	+	6.34132i	0.356684	+	0.371735i
$292$	−0.0636053	−	0.147454i	−0.00372222	−	0.00862907i
$293$	0.166826	+	2.86429i	0.00974608	+	0.167334i	0.999669	+	0.0257266i	$0.00818993\pi$
$293$	0.166826	+	2.86429i	0.00974608	+	0.167334i	−0.989923	+	0.141607i	$0.954773\pi$
$294$	−3.65234	−	11.8356i	−0.213009	−	0.690268i
$295$	−18.5698	+	19.6828i	−1.08117	+	1.14598i
$296$	3.19155	+	5.52793i	0.185505	+	0.321305i
$297$	10.5419	−	5.63255i	0.611705	−	0.326834i
$298$	4.39454	−	7.61156i	0.254569	−	0.440926i
$299$	9.01558	+	30.1141i	0.521385	+	1.74155i
$300$	−0.301451	+	6.05454i	−0.0174043	+	0.349559i
$301$	34.9570	−	22.9916i	2.01489	−	1.32521i
$302$	−12.7453	−	1.48971i	−0.733407	−	0.0857230i
$303$	−7.45320	+	4.99255i	−0.428175	+	0.286815i
$304$	7.73541	−	3.88487i	0.443656	−	0.222812i
$305$	1.81277	−	10.2807i	0.103799	−	0.588674i
$306$	−1.49941	−	7.73836i	−0.0857157	−	0.442373i
$307$	3.45879	+	19.6157i	0.197403	+	1.11953i	0.908954	+	0.416896i	$0.136882\pi$
$307$	3.45879	+	19.6157i	0.197403	+	1.11953i	−0.711551	+	0.702634i	$0.752007\pi$
$308$	−5.16723	−	6.94079i	−0.294430	−	0.395488i
$309$	5.28875	−	0.0445823i	0.300866	−	0.00253620i
$310$	−5.68890	−	6.02988i	−0.323108	−	0.342474i
$311$	2.62713	−	8.77522i	0.148971	−	0.497597i	−0.850633	−	0.525761i	$-0.823781\pi$
$311$	2.62713	−	8.77522i	0.148971	−	0.497597i	0.999603	+	0.0281637i	$0.00896596\pi$
$312$	5.51189	−	4.70476i	0.312049	−	0.266355i
$313$	−9.36704	+	1.09485i	−0.529456	+	0.0618846i	−0.376622	−	0.926367i	$-0.622914\pi$
$313$	−9.36704	+	1.09485i	−0.529456	+	0.0618846i	−0.152835	+	0.988252i	$0.548840\pi$
$314$	3.57949	−	3.00355i	0.202002	−	0.169500i
$315$	−27.1808	+	18.5410i	−1.53146	+	1.04466i
$316$	−7.30236	−	6.12740i	−0.410790	−	0.344693i
$317$	14.1723	+	9.32125i	0.795994	+	0.523534i	0.881152	−	0.472834i	$-0.156769\pi$
$317$	14.1723	+	9.32125i	0.795994	+	0.523534i	−0.0851574	+	0.996368i	$0.527139\pi$
$318$	−0.785288	−	1.77911i	−0.0440367	−	0.0997678i
$319$	3.37469	−	4.53299i	0.188946	−	0.253799i
$320$	−2.60535	−	1.30846i	−0.145644	−	0.0731450i
$321$	−7.81392	+	18.5429i	−0.436130	+	1.03497i
$322$	27.5015	+	6.51797i	1.53260	+	0.363232i
$323$	−22.7434			−1.26548
$324$	8.99488	−	0.303403i	0.499716	−	0.0168557i
$325$	14.6434			0.812270
$326$	13.6281	+	3.22992i	0.754790	+	0.178889i
$327$	2.66200	+	3.51347i	0.147209	+	0.194295i
$328$	−3.89688	−	1.95708i	−0.215169	−	0.108062i
$329$	−3.69417	+	4.96213i	−0.203666	+	0.273571i
$330$	−6.85752	+	9.37521i	−0.377494	+	0.516088i
$331$	−8.12667	−	5.34499i	−0.446682	−	0.293787i	0.306170	−	0.951977i	$-0.400952\pi$
$331$	−8.12667	−	5.34499i	−0.446682	−	0.293787i	−0.752852	+	0.658189i	$0.771323\pi$
$332$	−1.69971	−	1.42622i	−0.0932835	−	0.0782742i
$333$	19.0546	+	1.90215i	1.04419	+	0.104237i
$334$	8.01111	−	6.72212i	0.438349	−	0.367818i
$335$	4.24703	−	0.496406i	0.232040	−	0.0271216i
$336$	−1.18548	−	6.40690i	−0.0646732	−	0.349525i
$337$	−4.97107	+	16.6045i	−0.270792	+	0.904507i	0.709122	+	0.705086i	$0.249091\pi$
$337$	−4.97107	+	16.6045i	−0.270792	+	0.904507i	−0.979914	+	0.199421i	$0.936094\pi$
$338$	−3.09167	−	3.27698i	−0.168165	−	0.178244i
$339$	−11.8829	−	20.1868i	−0.645388	−	1.09640i
$340$	4.57434	+	6.14440i	0.248078	+	0.333227i
$341$	−1.13575	−	6.44118i	−0.0615045	−	0.348809i
$342$	4.07760	−	25.6463i	0.220491	−	1.38679i
$343$	−0.0988085	+	0.560371i	−0.00533516	+	0.0302572i
$344$	9.93930	−	4.99171i	0.535891	−	0.269135i
$345$	−2.52519	−	37.8556i	−0.135951	−	2.03808i
$346$	13.4690	+	1.57431i	0.724100	+	0.0846352i
$347$	−19.8165	+	13.0335i	−1.06381	+	0.699676i	−0.955664	−	0.294459i	$-0.904860\pi$
$347$	−19.8165	+	13.0335i	−1.06381	+	0.699676i	−0.108142	+	0.994135i	$0.534490\pi$
$348$	3.78648	−	1.94178i	0.202976	−	0.104090i
$349$	−0.643481	−	2.14938i	−0.0344448	−	0.115054i	0.939038	−	0.343812i	$-0.111718\pi$
$349$	−0.643481	−	2.14938i	−0.0344448	−	0.115054i	−0.973483	+	0.228759i	$0.926533\pi$
$350$	6.58303	−	11.4021i	0.351878	−	0.609470i
$351$	−1.81247	−	21.6646i	−0.0967425	−	1.15637i
$352$	−1.15011	−	1.99205i	−0.0613012	−	0.106177i
$353$	9.54050	−	10.1123i	0.507790	−	0.538225i	−0.421865	−	0.906659i	$-0.638624\pi$
$353$	9.54050	−	10.1123i	0.507790	−	0.538225i	0.929654	+	0.368433i	$0.120106\pi$
$354$	−15.6735	−	3.57543i	−0.833038	−	0.190032i
$355$	−0.325062	−	5.58110i	−0.0172525	−	0.296214i
$356$	−0.371150	−	0.860423i	−0.0196709	−	0.0456023i
$357$	−4.77149	+	16.4410i	−0.252534	+	0.870152i
$358$	−0.253026	+	4.34429i	−0.0133728	+	0.229603i
$359$	19.2529	−	7.00747i	1.01613	−	0.369840i	0.220344	−	0.975422i	$-0.429282\pi$
$359$	19.2529	−	7.00747i	1.01613	−	0.369840i	0.795783	+	0.605582i	$0.207060\pi$
$360$	−7.74877	+	4.05658i	−0.408396	+	0.213800i
$361$	−52.5558	−	19.1287i	−2.76609	−	1.00678i
$362$	0.710760	−	1.64773i	0.0373567	−	0.0866026i
$363$	9.26305	−	3.46017i	0.486184	−	0.181612i
$364$	−15.3149	+	3.62970i	−0.802719	+	0.190248i
$365$	0.455566	−	0.107971i	0.0238454	−	0.00565146i
$366$	5.80981	−	2.17023i	0.303684	−	0.113440i
$367$	9.04356	−	20.9653i	0.472070	−	1.09438i	−0.501327	−	0.865258i	$-0.667155\pi$
$367$	9.04356	−	20.9653i	0.472070	−	1.09438i	0.973397	−	0.229124i	$-0.0735860\pi$
$368$	7.06011	+	2.56967i	0.368034	+	0.133953i
$369$	−11.5900	+	6.06750i	−0.603351	+	0.315862i
$370$	−17.4874	+	6.36490i	−0.909127	+	0.330895i
$371$	−0.245586	+	4.21656i	−0.0127502	+	0.218913i
$372$	1.37268	−	4.72982i	0.0711701	−	0.245230i
$373$	1.55098	+	3.59558i	0.0803068	+	0.186172i	0.953639	−	0.300953i	$-0.0973048\pi$
$373$	1.55098	+	3.59558i	0.0803068	+	0.186172i	−0.873332	+	0.487125i	$0.838046\pi$
$374$	0.351409	+	6.03345i	0.0181709	+	0.311982i
$375$	7.38527	+	1.68472i	0.381374	+	0.0869985i
$376$	−1.12851	+	1.19615i	−0.0581986	+	0.0616869i
$377$	−5.13958	−	8.90201i	−0.264702	−	0.458477i
$378$	−17.6840	−	8.32817i	−0.909569	−	0.428355i
$379$	−2.67609	+	4.63513i	−0.137462	+	0.238091i	−0.926535	−	0.376208i	$-0.877228\pi$
$379$	−2.67609	+	4.63513i	−0.137462	+	0.238091i	0.789073	+	0.614299i	$0.210561\pi$
$380$	7.23795	+	24.1764i	0.371299	+	1.24023i
$381$	16.1485	−	8.28126i	0.827312	−	0.424262i
$382$	−21.0198	+	13.8250i	−1.07547	+	0.707347i
$383$	22.1513	+	2.58911i	1.13188	+	0.132297i	0.661342	−	0.750084i	$-0.269987\pi$
$383$	22.1513	+	2.58911i	1.13188	+	0.132297i	0.470534	+	0.882382i	$0.344061\pi$
$384$	−0.115282	−	1.72821i	−0.00588294	−	0.0881924i
$385$	22.5442	−	11.3221i	1.14896	−	0.577028i
$386$	−2.28464	+	12.9569i	−0.116285	+	0.659487i
$387$	5.23935	−	32.9532i	0.266331	−	1.67510i
$388$	−0.881079	−	4.99685i	−0.0447300	−	0.253676i
$389$	−10.1548	−	13.6403i	−0.514871	−	0.691592i	0.466323	−	0.884614i	$-0.345578\pi$
$389$	−10.1548	−	13.6403i	−0.514871	−	0.691592i	−0.981194	+	0.193023i	$0.938171\pi$
$390$	10.7177	+	18.2074i	0.542712	+	0.921968i
$391$	−13.5467	−	14.3587i	−0.685087	−	0.726149i
$392$	−2.05100	+	6.85083i	−0.103591	+	0.346019i
$393$	0.0521943	+	0.282083i	0.00263285	+	0.0142292i
$394$	−20.1869	+	2.35951i	−1.01700	+	0.118870i
$395$	21.2897	−	17.8642i	1.07120	−	0.898846i
$396$	−6.86655	−	0.685460i	−0.345057	−	0.0344457i
$397$	0.818172	+	0.686528i	0.0410629	+	0.0344559i	0.663088	−	0.748541i	$-0.269245\pi$
$397$	0.818172	+	0.686528i	0.0410629	+	0.0344559i	−0.622025	+	0.782997i	$0.713690\pi$
$398$	−2.44271	−	1.60659i	−0.122442	−	0.0805312i
$399$	−33.2975	+	45.5224i	−1.66696	+	2.27897i
$400$	2.09001	−	2.80737i	0.104500	−	0.140368i
$401$	29.6738	+	14.9027i	1.48184	+	0.744207i	0.991837	−	0.127515i	$-0.0407003\pi$
$401$	29.6738	+	14.9027i	1.48184	+	0.744207i	0.490001	+	0.871722i	$0.336997\pi$
$402$	1.53408	+	2.02477i	0.0765131	+	0.100986i
$403$	−11.5760	−	2.74357i	−0.576644	−	0.136667i
$404$	5.17931			0.257680
$405$	−3.68267	+	25.9794i	−0.182993	+	1.29093i
$406$	−9.24211			−0.458678
$407$	−14.2868	−	3.38604i	−0.708171	−	0.167840i
$408$	−1.76721	+	4.19370i	−0.0874899	+	0.207619i
$409$	−9.34646	−	4.69397i	−0.462153	−	0.232102i	0.202459	−	0.979291i	$-0.435107\pi$
$409$	−9.34646	−	4.69397i	−0.462153	−	0.232102i	−0.664612	+	0.747189i	$0.731403\pi$
$410$	7.59197	−	10.1978i	0.374941	−	0.503633i
$411$	13.9366	+	31.5742i	0.687443	+	1.55744i
$412$	−2.55122	−	1.67796i	−0.125690	−	0.0826673i
$413$	26.7469	+	22.4433i	1.31613	+	1.10436i
$414$	18.6201	−	12.7014i	0.915129	−	0.624242i
$415$	4.95543	−	4.15810i	0.243253	−	0.204113i
$416$	−4.15563	+	0.485724i	−0.203747	+	0.0238146i
$417$	28.6919	−	24.4904i	1.40505	−	1.19930i
$418$	−5.71056	+	19.0746i	−0.279312	+	0.932969i
$419$	−0.0335250	−	0.0355345i	−0.00163781	−	0.00173597i	0.726554	−	0.687109i	$-0.241121\pi$
$419$	−0.0335250	−	0.0355345i	−0.00163781	−	0.00173597i	−0.728192	+	0.685373i	$0.759639\pi$
$420$	18.9955	−	0.160125i	0.926884	−	0.00781331i
$421$	23.4041	+	31.4372i	1.14065	+	1.53216i	0.808076	+	0.589079i	$0.200509\pi$
$421$	23.4041	+	31.4372i	1.14065	+	1.53216i	0.332573	+	0.943078i	$0.392083\pi$
$422$	−4.49042	−	25.4665i	−0.218590	−	1.23969i
$423$	0.938468	+	4.84337i	0.0456299	+	0.235493i
$424$	−0.194969	+	1.10573i	−0.00946854	+	0.0536988i
$425$	−8.21766	+	4.12707i	−0.398615	+	0.200192i
$426$	2.75942	−	1.84841i	0.133694	−	0.0895557i
$427$	−13.3788	−	1.56376i	−0.647445	−	0.0756755i
$428$	9.70627	−	6.38391i	0.469170	−	0.308578i
$429$	−0.828921	+	16.6486i	−0.0400207	+	0.803801i
$430$	9.30012	+	31.0646i	0.448491	+	1.49807i
$431$	−11.4768	+	19.8784i	−0.552819	+	0.957510i	0.445251	+	0.895406i	$0.353115\pi$
$431$	−11.4768	+	19.8784i	−0.552819	+	0.957510i	−0.998070	+	0.0621044i	$0.980219\pi$
$432$	−4.41213	−	2.74465i	−0.212279	−	0.132052i
$433$	−13.6316	−	23.6107i	−0.655095	−	1.13466i	−0.981870	−	0.189555i	$-0.939295\pi$
$433$	−13.6316	−	23.6107i	−0.655095	−	1.13466i	0.326775	−	0.945102i	$-0.394038\pi$
$434$	−7.34038	+	7.78034i	−0.352349	+	0.373468i
$435$	3.65822	+	11.8547i	0.175398	+	0.568388i
$436$	−0.147977	−	2.54067i	−0.00708683	−	0.121676i
$437$	−25.7592	−	59.7166i	−1.23223	−	2.85663i
$438$	0.192573	+	0.200699i	0.00920151	+	0.00958978i
$439$	0.537077	−	9.22126i	0.0256333	−	0.440107i	−0.960937	−	0.276768i	$-0.910737\pi$
$439$	0.537077	−	9.22126i	0.0256333	−	0.440107i	0.986570	−	0.163339i	$-0.0522263\pi$
$440$	6.30179	−	2.29366i	0.300426	−	0.109346i
$441$	13.0996	+	16.9902i	0.623790	+	0.809055i
$442$	10.3300	+	3.75982i	0.491348	+	0.178836i
$443$	−2.84067	+	6.58542i	−0.134964	+	0.312883i	−0.972273	−	0.233848i	$-0.924868\pi$
$443$	−2.84067	+	6.58542i	−0.134964	+	0.312883i	0.837309	+	0.546730i	$0.184128\pi$
$444$	−8.52889	−	7.03493i	−0.404763	−	0.333863i
$445$	2.65832	−	0.630034i	0.126017	−	0.0298665i
$446$	5.92763	−	1.40487i	0.280681	−	0.0665227i
$447$	−2.51700	+	15.0136i	−0.119050	+	0.710119i
$448$	−1.48998	+	3.45416i	−0.0703949	+	0.163194i
$449$	−8.22352	−	2.99312i	−0.388092	−	0.141254i	0.140603	−	0.990066i	$-0.455096\pi$
$449$	−8.22352	−	2.99312i	−0.388092	−	0.141254i	−0.528694	+	0.848812i	$0.677318\pi$
$450$	−3.18051	−	10.0065i	−0.149931	−	0.471710i
$451$	9.42570	−	3.43068i	0.443839	−	0.161544i
$452$	−0.786361	+	13.5013i	−0.0369873	+	0.635047i
$453$	21.5826	−	5.30772i	1.01404	−	0.249378i
$454$	10.4197	+	24.1555i	0.489019	+	1.13367i
$455$	−2.66809	−	45.8093i	−0.125082	−	2.14757i
$456$	−10.1964	+	10.9918i	−0.477492	+	0.514736i
$457$	5.31162	−	5.62999i	0.248467	−	0.263360i	−0.591121	−	0.806583i	$-0.701315\pi$
$457$	5.31162	−	5.62999i	0.248467	−	0.263360i	0.839589	+	0.543223i	$0.182796\pi$
$458$	0.0784277	+	0.135841i	0.00366469	+	0.00634742i
$459$	7.12304	+	11.6470i	0.332475	+	0.543637i
$460$	−10.9522	+	18.9699i	−0.510651	+	0.884474i
$461$	−12.0571	−	40.2734i	−0.561554	−	1.87572i	−0.476130	−	0.879375i	$-0.657961\pi$
$461$	−12.0571	−	40.2734i	−0.561554	−	1.87572i	−0.0854238	−	0.996345i	$-0.527224\pi$
$462$	12.5908	+	8.12991i	0.585778	+	0.378238i
$463$	5.23312	−	3.44188i	0.243204	−	0.159958i	−0.422056	−	0.906570i	$-0.638691\pi$
$463$	5.23312	−	3.44188i	0.243204	−	0.159958i	0.665259	+	0.746612i	$0.268321\pi$
$464$	−2.44021	−	0.285219i	−0.113284	−	0.0132410i
$465$	12.8852	+	6.33573i	0.597535	+	0.293813i
$466$	10.0945	−	5.06963i	0.467617	−	0.234846i
$467$	2.63963	−	14.9701i	0.122148	−	0.692734i	−0.860814	−	0.508921i	$-0.830045\pi$
$467$	2.63963	−	14.9701i	0.122148	−	0.692734i	0.982961	−	0.183813i	$-0.0588442\pi$
$468$	−6.09174	+	10.9744i	−0.281591	+	0.507292i
$469$	−0.958058	−	5.43342i	−0.0442390	−	0.250892i
$470$	−2.86303	−	3.84572i	−0.132062	−	0.177390i
$471$	−3.98745	+	7.04290i	−0.183732	+	0.324520i
$472$	6.36940	+	6.75117i	0.293175	+	0.310748i
$473$	−7.33755	+	24.5091i	−0.337381	+	1.12693i
$474$	15.5622	+	5.51606i	0.714795	+	0.253361i
$475$	−30.0910	+	3.51713i	−1.38067	+	0.161377i
$476$	7.57151	−	6.35325i	0.347040	−	0.291201i
$477$	2.35248	+	2.41073i	0.107712	+	0.110380i
$478$	−18.5558	−	15.5702i	−0.848722	−	0.712162i
$479$	17.0761	+	11.2311i	0.780228	+	0.513164i	0.876042	−	0.482235i	$-0.160175\pi$
$479$	17.0761	+	11.2311i	0.780228	+	0.513164i	−0.0958134	+	0.995399i	$0.530545\pi$
$480$	5.02035	+	0.543939i	0.229146	+	0.0248273i
$481$	−15.9480	+	21.4219i	−0.727165	+	0.976752i
$482$	16.1372	+	8.10442i	0.735031	+	0.369146i
$483$	−48.5729	+	6.09281i	−2.21014	+	0.277233i
$484$	−5.55508	−	1.31658i	−0.252504	−	0.0598445i
$485$	14.7929			0.671709
$486$	−14.4107	+	5.94404i	−0.653683	+	0.269627i
$487$	24.1765			1.09554			0.547771	−	0.836628i	$-0.315476\pi$
$487$	24.1765			1.09554			0.547771	+	0.836628i	$0.315476\pi$
$488$	−3.48416	−	0.825762i	−0.157721	−	0.0373805i
$489$	−24.0698	+	3.01923i	−1.08847	+	0.136534i
$490$	−18.6316	−	9.35712i	−0.841688	−	0.422712i
$491$	−8.59198	+	11.5410i	−0.387751	+	0.520840i	−0.952547	−	0.304391i	$-0.901547\pi$
$491$	−8.59198	+	11.5410i	−0.387751	+	0.520840i	0.564797	+	0.825230i	$0.308955\pi$
$492$	7.50903	+	0.813580i	0.338533	+	0.0366790i
$493$	5.39317	+	3.54715i	0.242896	+	0.159755i
$494$	27.7435	+	23.2796i	1.24824	+	1.04740i
$495$	5.44436	−	19.3680i	0.244706	−	0.870527i
$496$	−2.17820	+	1.82773i	−0.0978040	+	0.0820673i
$497$	−7.16471	+	0.837434i	−0.321381	+	0.0375641i
$498$	3.62228	+	1.28393i	0.162318	+	0.0575341i
$499$	10.3103	−	34.4387i	0.461551	−	1.54169i	−0.338034	−	0.941134i	$-0.609762\pi$
$499$	10.3103	−	34.4387i	0.461551	−	1.54169i	0.799585	−	0.600553i	$-0.205053\pi$
$500$	−3.00122	−	3.18111i	−0.134219	−	0.142264i
$501$	−8.92414	+	15.7624i	−0.398701	+	0.704214i
$502$	−2.43573	−	3.27175i	−0.108712	−	0.146025i
$503$	0.139377	+	0.790444i	0.00621449	+	0.0352441i	0.987757	−	0.155998i	$-0.0498594\pi$
$503$	0.139377	+	0.790444i	0.00621449	+	0.0352441i	−0.981543	+	0.191242i	$0.938748\pi$
$504$	5.80668	+	9.67697i	0.258650	+	0.431047i
$505$	−2.62210	+	14.8707i	−0.116682	+	0.661737i
$506$	−15.4438	+	7.75619i	−0.686562	+	0.344805i
$507$	7.00253	+	3.44320i	0.310993	+	0.152918i
$508$	−10.4070	−	1.21640i	−0.461734	−	0.0539690i
$509$	−10.7873	+	7.09492i	−0.478139	+	0.314477i	−0.765602	−	0.643315i	$-0.777559\pi$
$509$	−10.7873	+	7.09492i	−0.478139	+	0.314477i	0.287463	+	0.957792i	$0.407188\pi$
$510$	−11.1462	−	7.19708i	−0.493560	−	0.318692i
$511$	−0.173258	−	0.578721i	−0.00766446	−	0.0256011i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	8.92799	+	44.0836i	0.394180	+	1.94634i
$514$	−9.67117	−	16.7510i	−0.426577	−	0.738853i
$515$	6.10931	−	6.47549i	0.269208	−	0.285344i
$516$	−13.1015	+	14.1234i	−0.576762	+	0.621749i
$517$	−0.219943	−	3.77628i	−0.00967310	−	0.166081i
$518$	9.51070	+	22.0483i	0.417876	+	0.968746i
$519$	−22.8083	+	5.60914i	−1.00117	+	0.246214i
$520$	0.709255	−	12.1774i	0.0311029	−	0.534016i
$521$	−13.9069	+	5.06170i	−0.609273	+	0.221757i	−0.628185	−	0.778064i	$-0.716202\pi$
$521$	−13.9069	+	5.06170i	−0.609273	+	0.221757i	0.0189124	+	0.999821i	$0.493980\pi$
$522$	−4.96682	+	5.44558i	−0.217392	+	0.238347i
$523$	3.67429	+	1.33733i	0.160666	+	0.0584775i	0.421101	−	0.907014i	$-0.361644\pi$
$523$	3.67429	+	1.33733i	0.160666	+	0.0584775i	−0.260435	+	0.965491i	$0.583866\pi$
$524$	0.0656007	−	0.152080i	0.00286578	−	0.00664363i
$525$	−3.77048	+	22.4904i	−0.164557	+	0.981563i
$526$	14.8368	−	3.51638i	0.646913	−	0.153321i
$527$	7.26955	−	1.72291i	0.316667	−	0.0750514i
$528$	3.07348	+	2.53512i	0.133756	+	0.110327i
$529$	13.2482	−	30.7129i	0.576010	−	1.33534i
$530$	−3.07602	−	1.11958i	−0.133614	−	0.0486314i
$531$	27.5980	−	3.69835i	1.19765	−	0.160495i
$532$	30.5990	−	11.1371i	1.32664	−	0.482856i
$533$	1.06085	−	18.2140i	0.0459504	−	0.788937i
$534$	1.12371	+	1.17112i	0.0486275	+	0.0506794i
$535$	13.4154	+	31.1003i	0.579997	+	1.34458i
$536$	−0.0852776	−	1.46416i	−0.00368343	−	0.0632421i
$537$	−2.22250	−	7.20215i	−0.0959081	−	0.310796i
$538$	12.9339	−	13.7092i	0.557621	−	0.591044i
$539$	−8.22475	−	14.2457i	−0.354265	−	0.613605i
$540$	10.1141	−	11.2785i	0.435240	−	0.485348i
$541$	0.299580	−	0.518888i	0.0128800	−	0.0223087i	−0.859514	−	0.511113i	$-0.829233\pi$
$541$	0.299580	−	0.518888i	0.0128800	−	0.0223087i	0.872394	+	0.488804i	$0.162567\pi$
$542$	−3.19087	−	10.6583i	−0.137060	−	0.457811i
$543$	−0.154561	+	3.10430i	−0.00663283	+	0.133218i
$544$	2.19518	−	1.44380i	0.0941178	−	0.0619022i
$545$	7.36962	+	0.861385i	0.315680	+	0.0368977i
$546$	22.6492	−	15.1716i	0.969295	−	0.649286i
$547$	9.85913	−	4.95144i	0.421546	−	0.211708i	−0.225364	−	0.974275i	$-0.572357\pi$
$547$	9.85913	−	4.95144i	0.421546	−	0.211708i	0.646910	+	0.762566i	$0.276061\pi$
$548$	3.46015	−	19.6235i	0.147810	−	0.838274i
$549$	−8.11131	+	7.04260i	−0.346182	+	0.300571i
$550$	1.39797	+	7.92830i	0.0596098	+	0.338064i
$551$	12.6995	+	17.0584i	0.541018	+	0.726713i
$552$	−13.0128	+	0.109693i	−0.553862	+	0.00466886i
$553$	−24.6084	−	26.0834i	−1.04646	−	1.10918i
$554$	−7.47828	+	24.9792i	−0.317722	+	1.06126i
$555$	24.5164	−	20.9264i	1.04066	−	0.888274i
$556$	−21.6320	+	2.52841i	−0.917400	+	0.107229i
$557$	−30.1952	+	25.3368i	−1.27941	+	1.07355i	−0.286086	+	0.958204i	$0.592354\pi$
$557$	−30.1952	+	25.3368i	−1.27941	+	1.07355i	−0.993325	+	0.115349i	$0.963201\pi$
$558$	0.639485	+	8.50631i	0.0270715	+	0.360101i
$559$	35.6480	+	29.9122i	1.50775	+	1.26515i
$560$	−9.16316	−	6.02670i	−0.387214	−	0.254675i
$561$	−4.22702	−	9.57656i	−0.178465	−	0.404322i
$562$	−10.1157	+	13.5877i	−0.426704	+	0.573162i
$563$	4.18633	+	2.10245i	0.176433	+	0.0886078i	0.534823	−	0.844964i	$-0.320378\pi$
$563$	4.18633	+	2.10245i	0.176433	+	0.0886078i	−0.358391	+	0.933572i	$0.616674\pi$
$564$	1.10608	−	2.62480i	0.0465743	−	0.110524i
$565$	−38.3664	−	9.09300i	−1.61409	−	0.382545i
$566$	−17.1296			−0.720011
$567$	33.7408	+	2.79462i	1.41698	+	0.117363i
$568$	−1.91755			−0.0804587
$569$	24.2228	+	5.74091i	1.01547	+	0.240672i	0.704467	−	0.709737i	$-0.251186\pi$
$569$	24.2228	+	5.74091i	1.01547	+	0.240672i	0.311006	+	0.950408i	$0.399334\pi$
$570$	−26.3971	−	34.8405i	−1.10565	−	1.45931i
$571$	−32.5654	−	16.3550i	−1.36282	−	0.684434i	−0.391051	−	0.920369i	$-0.627888\pi$
$571$	−32.5654	−	16.3550i	−1.36282	−	0.684434i	−0.971769	+	0.235935i	$0.924185\pi$
$572$	5.74703	−	7.71961i	0.240296	−	0.322773i
$573$	25.7264	−	35.1716i	1.07473	−	1.46932i
$574$	−13.7055	−	9.01426i	−0.572057	−	0.376248i
$575$	−20.1437	−	16.9025i	−0.840048	−	0.704884i
$576$	1.23451	+	2.73423i	0.0514379	+	0.113926i
$577$	6.24646	−	5.24140i	0.260043	−	0.218202i	−0.503439	−	0.864031i	$-0.667932\pi$
$577$	6.24646	−	5.24140i	0.260043	−	0.218202i	0.763483	+	0.645828i	$0.223488\pi$
$578$	10.0283	−	1.17215i	0.417124	−	0.0487548i
$579$	−4.14615	−	22.4078i	−0.172308	−	0.931236i
$580$	2.05430	−	6.86186i	0.0853004	−	0.284923i
$581$	−5.72789	−	6.07121i	−0.237633	−	0.251876i
$582$	4.45815	+	7.57359i	0.184796	+	0.313935i
$583$	−1.54225	−	2.07161i	−0.0638736	−	0.0857971i
$584$	−0.0278857	−	0.158147i	−0.00115392	−	0.00654419i
$585$	−28.4254	−	23.0464i	−1.17524	−	0.952851i
$586$	−0.498222	+	2.82556i	−0.0205814	+	0.116723i
$587$	1.96062	−	0.984662i	0.0809236	−	0.0406413i	−0.407877	−	0.913037i	$-0.633731\pi$
$587$	1.96062	−	0.984662i	0.0809236	−	0.0406413i	0.488801	+	0.872395i	$0.337435\pi$
$588$	−0.824409	−	12.3589i	−0.0339980	−	0.509672i
$589$	24.4468	+	2.85742i	1.00731	+	0.117738i
$590$	−22.6084	+	14.8698i	−0.930772	+	0.612178i
$591$	31.3240	−	16.0636i	1.28850	−	0.660767i
$592$	1.83070	+	6.11495i	0.0752411	+	0.251323i
$593$	−18.7384	+	32.4558i	−0.769493	+	1.33280i	0.168346	+	0.985728i	$0.446157\pi$
$593$	−18.7384	+	32.4558i	−0.769493	+	1.33280i	−0.937838	+	0.347072i	$0.887176\pi$
$594$	11.5567	−	3.04959i	0.474178	−	0.125126i
$595$	14.4081	+	24.9555i	0.590674	+	1.02308i
$596$	6.03143	−	6.39294i	0.247057	−	0.261865i
$597$	4.93715	+	1.12626i	0.202064	+	0.0460946i
$598$	1.82777	+	31.3815i	0.0747429	+	1.28329i
$599$	−4.76448	−	11.0453i	−0.194671	−	0.451299i	0.792722	−	0.609583i	$-0.208663\pi$
$599$	−4.76448	−	11.0453i	−0.194671	−	0.451299i	−0.987394	+	0.158284i	$0.949404\pi$
$600$	−1.68960	+	5.82182i	−0.0689776	+	0.237675i
$601$	−1.05142	+	18.0522i	−0.0428884	+	0.736366i	0.906489	+	0.422229i	$0.138752\pi$
$601$	−1.05142	+	18.0522i	−0.0428884	+	0.736366i	−0.949378	+	0.314137i	$0.898285\pi$
$602$	39.3170	−	14.3102i	1.60244	−	0.583241i
$603$	−3.71632	−	2.35548i	−0.151340	−	0.0959227i
$604$	−12.0582	−	4.38881i	−0.490639	−	0.178578i
$605$	6.59246	−	15.2830i	0.268022	−	0.621344i
$606$	−8.40366	+	3.13915i	−0.341375	+	0.127519i
$607$	4.57034	−	1.08319i	0.185504	−	0.0439653i	−0.136814	−	0.990597i	$-0.543686\pi$
$607$	4.57034	−	1.08319i	0.185504	−	0.0439653i	0.322318	+	0.946631i	$0.395538\pi$
$608$	8.42281	−	1.99624i	0.341590	−	0.0809583i
$609$	14.9957	−	5.60159i	0.607657	−	0.226988i
$610$	4.13481	−	9.58558i	0.167414	−	0.388109i
$611$	−6.46546	−	2.35323i	−0.261564	−	0.0952016i
$612$	0.325593	−	7.87556i	0.0131613	−	0.318351i
$613$	−17.4302	+	6.34408i	−0.704000	+	0.256235i	−0.669118	−	0.743156i	$-0.733328\pi$
$613$	−17.4302	+	6.34408i	−0.704000	+	0.256235i	−0.0348821	+	0.999391i	$0.511106\pi$
$614$	−1.15815	+	19.8847i	−0.0467391	+	0.802479i
$615$	−6.13748	+	21.1478i	−0.247487	+	0.852763i
$616$	−3.42729	−	7.94535i	−0.138089	−	0.320127i
$617$	0.919178	+	15.7817i	0.0370047	+	0.635347i	0.964918	+	0.262551i	$0.0845638\pi$
$617$	0.919178	+	15.7817i	0.0370047	+	0.635347i	−0.927913	+	0.372796i	$0.878399\pi$
$618$	5.15647	+	1.17629i	0.207424	+	0.0473173i
$619$	11.1428	−	11.8107i	0.447866	−	0.474711i	−0.463624	−	0.886032i	$-0.653451\pi$
$619$	11.1428	−	11.8107i	0.447866	−	0.474711i	0.911490	+	0.411321i	$0.134933\pi$
$620$	−4.14497	−	7.17929i	−0.166466	−	0.288327i
$621$	−22.5137	+	31.8942i	−0.903443	+	1.27987i
$622$	4.58002	−	7.93282i	0.183642	−	0.318077i
$623$	−1.01099	−	3.37696i	−0.0405046	−	0.135295i
$624$	6.44830	−	3.30682i	0.258139	−	0.132379i
$625$	25.2736	−	16.6227i	1.01095	−	0.664909i
$626$	−9.36704	−	1.09485i	−0.374382	−	0.0437590i
$627$	−2.29538	−	34.4105i	−0.0916686	−	1.37422i
$628$	4.17567	−	2.09710i	0.166627	−	0.0836834i
$629$	2.91228	−	16.5164i	0.116120	−	0.658551i
$630$	−30.7239	+	11.7729i	−1.22407	+	0.469042i
$631$	1.49267	+	8.46536i	0.0594223	+	0.337001i	0.999997	−	0.00258717i	$-0.000823521\pi$
$631$	1.49267	+	8.46536i	0.0594223	+	0.337001i	−0.940574	+	0.339588i	$0.889712\pi$
$632$	−5.69244	−	7.64628i	−0.226433	−	0.304153i
$633$	22.7210	+	38.5988i	0.903079	+	1.53417i
$634$	11.6406	+	12.3383i	0.462308	+	0.490018i
$635$	8.76116	−	29.2643i	0.347676	−	1.16132i
$636$	−0.353828	−	1.91226i	−0.0140302	−	0.0758259i
$637$	−29.7180	+	3.47354i	−1.17747	+	0.137627i
$638$	4.32910	−	3.63255i	0.171391	−	0.143814i
$639$	−3.35697	+	4.67160i	−0.132800	+	0.184806i
$640$	−2.23337	−	1.87402i	−0.0882819	−	0.0740773i
$641$	−6.21351	−	4.08669i	−0.245419	−	0.161415i	0.420840	−	0.907135i	$-0.361735\pi$
$641$	−6.21351	−	4.08669i	−0.245419	−	0.161415i	−0.666259	+	0.745720i	$0.732106\pi$
$642$	−11.8796	+	16.2411i	−0.468850	+	0.640985i
$643$	23.5984	−	31.6982i	0.930631	−	1.25005i	−0.0374199	−	0.999300i	$-0.511914\pi$
$643$	23.5984	−	31.6982i	0.930631	−	1.25005i	0.968051	−	0.250755i	$-0.0806787\pi$
$644$	25.2570	+	12.6846i	0.995267	+	0.499842i
$645$	−33.9179	−	44.7669i	−1.33552	−	1.76269i
$646$	−22.1303	−	5.24499i	−0.870706	−	0.206361i
$647$	−36.6479			−1.44078			−0.720388	−	0.693571i	$-0.756036\pi$
$647$	−36.6479			−1.44078			−0.720388	+	0.693571i	$0.756036\pi$
$648$	8.82240	+	1.77914i	0.346576	+	0.0698912i
$649$	−21.3497			−0.838049
$650$	14.2487	+	3.37700i	0.558880	+	0.132457i
$651$	7.19446	−	17.0729i	0.281973	−	0.669140i
$652$	12.5159	+	6.28571i	0.490159	+	0.246167i
$653$	−14.8810	+	19.9887i	−0.582340	+	0.782218i	−0.991481	−	0.130253i	$-0.958421\pi$
$653$	−14.8810	+	19.9887i	−0.582340	+	0.782218i	0.409141	+	0.912471i	$0.365828\pi$
$654$	1.77999	+	4.03266i	0.0696030	+	0.157690i
$655$	0.403435	+	0.265343i	0.0157635	+	0.0103678i
$656$	−3.34050	−	2.80301i	−0.130425	−	0.109439i
$657$	−0.434101	−	0.208926i	−0.0169359	−	0.00815096i
$658$	−4.73894	+	3.97644i	−0.184743	+	0.155018i
$659$	6.20553	−	0.725323i	0.241733	−	0.0282546i	0.00563648	−	0.999984i	$-0.498206\pi$
$659$	6.20553	−	0.725323i	0.241733	−	0.0282546i	0.236097	+	0.971730i	$0.424132\pi$
$660$	−8.83475	+	7.54105i	−0.343892	+	0.293535i
$661$	−2.30731	+	7.70696i	−0.0897440	+	0.299766i	−0.991064	−	0.133388i	$-0.957414\pi$
$661$	−2.30731	+	7.70696i	−0.0897440	+	0.299766i	0.901320	+	0.433154i	$0.142599\pi$
$662$	−6.67497	−	7.07506i	−0.259430	−	0.274980i
$663$	−19.0397	+	0.160498i	−0.739440	+	0.00623323i
$664$	−1.32498	−	1.77976i	−0.0514193	−	0.0690680i
$665$	16.4854	+	93.4933i	0.639276	+	3.62552i
$666$	18.1023	+	6.24517i	0.701451	+	0.241995i
$667$	−3.20531	+	18.1782i	−0.124110	+	0.703862i
$668$	9.34540	−	4.69344i	0.361584	−	0.181595i
$669$	−8.76635	+	5.87217i	−0.338927	+	0.227031i
$670$	4.24703	+	0.496406i	0.164077	+	0.0191778i
$671$	6.88139	−	4.52596i	0.265653	−	0.174723i
$672$	0.324008	−	6.50760i	0.0124989	−	0.251036i
$673$	2.73069	+	9.12116i	0.105261	+	0.351595i	0.994352	−	0.106136i	$-0.0338477\pi$
$673$	2.73069	+	9.12116i	0.105261	+	0.351595i	−0.889091	+	0.457730i	$0.848663\pi$
$674$	−8.66635	+	15.0106i	−0.333815	+	0.578185i
$675$	11.2254	+	14.3082i	0.432065	+	0.550725i
$676$	−2.25261	−	3.90164i	−0.0866389	−	0.150063i
$677$	−4.14696	+	4.39552i	−0.159380	+	0.168933i	−0.802143	−	0.597132i	$-0.796307\pi$
$677$	−4.14696	+	4.39552i	−0.159380	+	0.168933i	0.642762	+	0.766066i	$0.277788\pi$
$678$	−6.90716	−	22.3830i	−0.265268	−	0.859616i
$679$	−1.10982	−	19.0549i	−0.0425910	−	0.731260i
$680$	3.03404	+	7.03369i	0.116350	+	0.269730i
$681$	−31.5469	−	32.8781i	−1.20888	−	1.25989i
$682$	0.380299	−	6.52948i	0.0145624	−	0.250027i
$683$	−9.85302	+	3.58621i	−0.377015	+	0.137222i	−0.523575	−	0.851979i	$-0.675402\pi$
$683$	−9.85302	+	3.58621i	−0.377015	+	0.137222i	0.146560	+	0.989202i	$0.453180\pi$
$684$	9.88212	−	24.0146i	0.377852	−	0.918222i
$685$	54.5906	+	19.8694i	2.08580	+	0.759169i
$686$	−0.225376	+	0.522479i	−0.00860488	+	0.0199484i
$687$	−0.209585	−	0.172873i	−0.00799616	−	0.00659552i
$688$	10.8226	−	2.56499i	0.412606	−	0.0977894i
$689$	−4.57101	+	1.08335i	−0.174142	+	0.0412723i
$690$	6.27298	−	37.4175i	0.238808	−	1.42446i
$691$	−8.09693	+	18.7708i	−0.308022	+	0.714074i	−0.999969	−	0.00787360i	$-0.997494\pi$
$691$	−8.09693	+	18.7708i	−0.308022	+	0.714074i	0.691947	+	0.721948i	$0.256753\pi$
$692$	12.7429	+	4.63805i	0.484413	+	0.176312i
$693$	−25.3567	−	5.55990i	−0.963220	−	0.211203i
$694$	−22.2881	+	8.11220i	−0.846044	+	0.307935i
$695$	3.69199	−	63.3891i	0.140045	−	2.40449i
$696$	4.13222	−	1.01622i	0.156631	−	0.0385196i
$697$	4.53807	+	10.5204i	0.171892	+	0.398490i
$698$	−0.130456	−	2.23984i	−0.00493782	−	0.0847791i
$699$	−13.3060	+	14.3439i	−0.503281	+	0.542536i
$700$	9.03510	−	9.57665i	0.341495	−	0.361963i
$701$	−1.14992	−	1.99172i	−0.0434320	−	0.0752264i	0.843492	−	0.537141i	$-0.180496\pi$
$701$	−1.14992	−	1.99172i	−0.0434320	−	0.0752264i	−0.886924	+	0.461915i	$0.847163\pi$
$702$	3.23259	−	21.4986i	0.122006	−	0.811414i
$703$	27.6265	−	47.8505i	1.04195	−	1.80472i
$704$	−0.659712	−	2.20359i	−0.0248638	−	0.0830510i
$705$	6.97627	+	4.50458i	0.262742	+	0.169652i
$706$	11.6154	−	7.63957i	0.437151	−	0.287519i
$707$	19.3519	+	2.26191i	0.727802	+	0.0850679i
$708$	−14.4265	−	7.09361i	−0.542180	−	0.266594i
$709$	−33.4321	+	16.7902i	−1.25557	+	0.630570i	−0.947184	−	0.320692i	$-0.896085\pi$
$709$	−33.4321	+	16.7902i	−1.25557	+	0.630570i	−0.308385	+	0.951262i	$0.599788\pi$
$710$	0.970789	−	5.50562i	0.0364331	−	0.206622i
$711$	−28.5936	+	0.482102i	−1.07234	+	0.0180802i
$712$	−0.162719	−	0.922824i	−0.00609814	−	0.0345843i
$713$	12.7573	+	17.1360i	0.477765	+	0.641750i
$714$	−8.43444	+	14.8975i	−0.315651	+	0.557524i
$715$	19.2548	+	20.4089i	0.720088	+	0.763249i
$716$	−1.24807	+	4.16883i	−0.0466425	+	0.155797i
$717$	39.5446	+	14.0167i	1.47682	+	0.523463i
$718$	20.3499	−	2.37856i	0.759452	−	0.0887672i
$719$	−23.5264	+	19.7410i	−0.877385	+	0.736214i	−0.965640	−	0.259884i	$-0.916316\pi$
$719$	−23.5264	+	19.7410i	−0.877385	+	0.736214i	0.0882543	+	0.996098i	$0.471871\pi$
$720$	−8.47541	+	2.16024i	−0.315860	+	0.0805075i
$721$	−8.79953	−	7.38368i	−0.327711	−	0.274983i
$722$	−46.7277	−	30.7333i	−1.73903	−	1.14378i
$723$	−31.0954	−	3.36909i	−1.15645	−	0.125298i
$724$	1.07159	−	1.43940i	0.0398255	−	0.0534949i
$725$	7.68406	+	3.85908i	0.285379	+	0.143323i
$726$	9.81133	−	1.23070i	0.364133	−	0.0456755i
$727$	−16.9543	−	4.01825i	−0.628801	−	0.149029i	−0.0961545	−	0.995366i	$-0.530654\pi$
$727$	−16.9543	−	4.01825i	−0.628801	−	0.149029i	−0.532646	+	0.846338i	$0.678802\pi$
$728$	−15.7392			−0.583332
$729$	19.7794	−	18.3787i	0.732569	−	0.680693i
$730$	0.468186			0.0173283
$731$	−28.4355	−	6.73933i	−1.05172	−	0.249263i
$732$	6.15370	−	0.771899i	0.227447	−	0.0285302i
$733$	14.0133	+	7.03774i	0.517593	+	0.259945i	0.688364	−	0.725366i	$-0.258329\pi$
$733$	14.0133	+	7.03774i	0.517593	+	0.259945i	−0.170771	+	0.985311i	$0.554626\pi$
$734$	13.6347	−	18.3146i	0.503267	−	0.676005i
$735$	35.9018	+	3.88985i	1.32426	+	0.143479i
$736$	6.27720	+	4.12858i	0.231381	+	0.152181i
$737$	2.58433	+	2.16851i	0.0951951	+	0.0798781i
$738$	−12.6768	+	3.23112i	−0.466641	+	0.118939i
$739$	35.8862	−	30.1121i	1.32009	−	1.10769i	0.333809	−	0.942641i	$-0.391666\pi$
$739$	35.8862	−	30.1121i	1.32009	−	1.10769i	0.986285	−	0.165050i	$-0.0527785\pi$
$740$	−18.4839	+	2.16046i	−0.679481	+	0.0794199i
$741$	−59.1248	−	20.9570i	−2.17200	−	0.769873i
$742$	−1.21137	+	4.04626i	−0.0444708	+	0.148543i
$743$	−24.3469	−	25.8062i	−0.893200	−	0.946737i	0.105663	−	0.994402i	$-0.466303\pi$
$743$	−24.3469	−	25.8062i	−0.893200	−	0.946737i	−0.998863	+	0.0476653i	$0.984822\pi$
$744$	2.42645	−	4.28576i	0.0889579	−	0.157124i
$745$	15.3017	+	20.5538i	0.560611	+	0.753032i
$746$	0.679977	+	3.85634i	0.0248957	+	0.141191i
$747$	−6.65548	+	0.112215i	−0.243511	+	0.00410572i
$748$	−1.04947	+	5.95186i	−0.0383726	+	0.217622i
$749$	39.0543	−	19.6138i	1.42701	−	0.716673i
$750$	6.79767	+	3.34247i	0.248216	+	0.122050i
$751$	−3.16188	−	0.369570i	−0.115378	−	0.0134858i	0.0582077	−	0.998304i	$-0.481461\pi$
$751$	−3.16188	−	0.369570i	−0.115378	−	0.0134858i	−0.173586	+	0.984819i	$0.555536\pi$
$752$	−1.37395	+	0.903658i	−0.0501026	+	0.0329530i
$753$	5.93507	+	3.83228i	0.216286	+	0.139656i
$754$	−2.94809	−	9.84732i	−0.107363	−	0.358618i
$755$	18.7056	−	32.3991i	0.680768	−	1.17912i
$756$	−15.2868	−	12.1819i	−0.555974	−	0.443052i
$757$	19.7532	+	34.2135i	0.717942	+	1.24351i	0.961814	+	0.273704i	$0.0882489\pi$
$757$	19.7532	+	34.2135i	0.717942	+	1.24351i	−0.243872	+	0.969807i	$0.578418\pi$
$758$	−3.67290	+	3.89304i	−0.133406	+	0.141402i
$759$	20.3573	−	21.9452i	0.738924	−	0.796560i
$760$	1.46738	+	25.1939i	0.0532275	+	0.913880i
$761$	10.0606	+	23.3230i	0.364695	+	0.845458i	0.997468	+	0.0711204i	$0.0226575\pi$
$761$	10.0606	+	23.3230i	0.364695	+	0.845458i	−0.632773	+	0.774338i	$0.718083\pi$
$762$	17.6230	−	4.33394i	0.638414	−	0.157002i
$763$	0.556663	−	9.55754i	0.0201526	−	0.346006i
$764$	−23.6415	+	8.60480i	−0.855319	+	0.311311i
$765$	22.4472	+	4.92195i	0.811581	+	0.177954i
$766$	20.9571	+	7.62775i	0.757210	+	0.275602i
$767$	−15.3811	+	35.6575i	−0.555380	+	1.28752i
$768$	0.286379	−	1.70821i	0.0103338	−	0.0616398i
$769$	19.6759	−	4.66328i	0.709531	−	0.168162i	0.140024	−	0.990148i	$-0.455282\pi$
$769$	19.6759	−	4.66328i	0.709531	−	0.168162i	0.569508	+	0.821986i	$0.307134\pi$
$770$	24.5476	−	5.81788i	0.884632	−	0.209662i
$771$	25.8446	+	21.3175i	0.930770	+	0.767732i
$772$	−5.21112	+	12.0807i	−0.187552	+	0.434795i
$773$	37.8693	+	13.7833i	1.36206	+	0.495751i	0.916692	−	0.399595i	$-0.130849\pi$
$773$	37.8693	+	13.7833i	1.36206	+	0.495751i	0.445372	+	0.895346i	$0.353072\pi$
$774$	12.6976	−	30.8566i	0.456407	−	1.10912i
$775$	9.35164	−	3.40372i	0.335921	−	0.122265i
$776$	0.295023	−	5.06535i	0.0105907	−	0.181835i
$777$	−28.7949	−	30.0099i	−1.03301	−	1.07660i
$778$	−6.73544	−	15.6145i	−0.241477	−	0.559807i
$779$	2.19479	+	37.6831i	0.0786365	+	1.35014i
$780$	6.22988	+	20.1883i	0.223066	+	0.722857i
$781$	3.02688	−	3.20830i	0.108310	−	0.114802i
$782$	−9.87022	−	17.0957i	−0.352958	−	0.611342i
$783$	4.75835	−	11.8461i	0.170049	−	0.423344i
$784$	−3.57563	+	6.19317i	−0.127701	+	0.221185i
$785$	3.90714	+	13.0508i	0.139452	+	0.465801i
$786$	−0.0142654	+	0.286516i	−0.000508831	+	0.0102197i
$787$	−44.4223	+	29.2170i	−1.58348	+	1.04147i	−0.616260	+	0.787542i	$0.711353\pi$
$787$	−44.4223	+	29.2170i	−1.58348	+	1.04147i	−0.967222	+	0.253931i	$0.918277\pi$
$788$	−20.1869	−	2.35951i	−0.719128	−	0.0840541i
$789$	−21.9420	+	14.6980i	−0.781157	+	0.523261i
$790$	24.8356	−	12.4729i	0.883613	−	0.443767i
$791$	−8.83443	+	50.1025i	−0.314116	+	1.78144i
$792$	−6.52338	−	2.25052i	−0.231798	−	0.0799687i
$793$	−2.60148	−	14.7537i	−0.0923811	−	0.523919i
$794$	0.637794	+	0.856706i	0.0226345	+	0.0304034i
$795$	5.66955	−	0.0477923i	0.201078	−	0.00169502i
$796$	−2.00636	−	2.12661i	−0.0711134	−	0.0753758i
$797$	−8.06703	+	26.9458i	−0.285749	+	0.954468i	0.687783	+	0.725917i	$0.258584\pi$
$797$	−8.06703	+	26.9458i	−0.285749	+	0.954468i	−0.973532	+	0.228552i	$0.926601\pi$
$798$	−42.8981	+	36.6164i	−1.51858	+	1.29621i
$799$	4.29155	−	0.501610i	0.151824	−	0.0177457i
$800$	2.68110	−	2.24971i	0.0947910	−	0.0795391i
$801$	−2.53307	−	1.21913i	−0.0895017	−	0.0430757i
$802$	25.4371	+	21.3443i	0.898215	+	0.753692i
$803$	0.308618	+	0.202981i	0.0108909	+	0.00716305i
$804$	1.02579	+	2.32398i	0.0361767	+	0.0819604i
$805$	−49.2063	+	66.0955i	−1.73429	+	2.32956i
$806$	−10.6313	−	5.33924i	−0.374472	−	0.188067i
$807$	−12.6768	+	30.0829i	−0.446245	+	1.05897i
$808$	5.03970	+	1.19443i	0.177296	+	0.0420199i
$809$	35.7311			1.25624			0.628120	−	0.778117i	$-0.283825\pi$
$809$	35.7311			1.25624			0.628120	+	0.778117i	$0.283825\pi$
$810$	−9.57468	+	24.4299i	−0.336420	+	0.858379i
$811$	17.1909			0.603655			0.301828	−	0.953363i	$-0.402403\pi$
$811$	17.1909			0.603655			0.301828	+	0.953363i	$0.402403\pi$
$812$	−8.99298	−	2.13138i	−0.315592	−	0.0747967i
$813$	11.6372	+	15.3595i	0.408136	+	0.538682i
$814$	−13.1208	−	6.58953i	−0.459885	−	0.230963i
$815$	−24.3837	+	32.7530i	−0.854123	+	1.14729i
$816$	−2.68671	+	3.67311i	−0.0940536	+	0.128585i
$817$	−80.4380	−	52.9049i	−2.81417	−	1.85091i
$818$	−8.01202	−	6.72289i	−0.280134	−	0.235060i
$819$	−27.5538	+	38.3442i	−0.962808	+	1.33985i
$820$	9.73911	−	8.17208i	0.340104	−	0.285381i
$821$	−21.8026	+	2.54835i	−0.760915	+	0.0889382i	−0.487696	−	0.873014i	$-0.662162\pi$
$821$	−21.8026	+	2.54835i	−0.760915	+	0.0889382i	−0.273219	+	0.961952i	$0.588088\pi$
$822$	6.27945	+	33.9372i	0.219021	+	1.18369i
$823$	−8.70582	+	29.0795i	−0.303466	+	1.01365i	0.661209	+	0.750202i	$0.270044\pi$
$823$	−8.70582	+	29.0795i	−0.303466	+	1.01365i	−0.964675	+	0.263445i	$0.915141\pi$
$824$	−2.09549	−	2.22109i	−0.0729997	−	0.0773752i
$825$	−7.07358	−	12.0167i	−0.246270	−	0.418368i
$826$	20.8501	+	28.0066i	0.725469	+	0.974474i
$827$	−4.50487	−	25.5484i	−0.156650	−	0.888405i	−0.957262	−	0.289222i	$-0.906603\pi$
$827$	−4.50487	−	25.5484i	−0.156650	−	0.888405i	0.800612	−	0.599183i	$-0.204508\pi$
$828$	21.0474	−	8.06498i	0.731447	−	0.280277i
$829$	−0.176572	+	1.00139i	−0.00613260	+	0.0347797i	−0.987721	−	0.156231i	$-0.950065\pi$
$829$	−0.176572	+	1.00139i	−0.00613260	+	0.0347797i	0.981588	+	0.191011i	$0.0611766\pi$
$830$	5.78078	−	2.90322i	0.200654	−	0.100772i
$831$	−3.00592	−	45.0624i	−0.104274	−	1.56320i
$832$	−4.15563	−	0.485724i	−0.144071	−	0.0168394i
$833$	15.6983	−	10.3250i	0.543915	−	0.357739i
$834$	33.5664	−	17.2135i	1.16231	−	0.596054i
$835$	8.74441	+	29.2084i	0.302613	+	1.01080i
$836$	−9.95553	+	17.2435i	−0.344319	+	0.596378i
$837$	−6.19322	−	13.4143i	−0.214069	−	0.463665i
$838$	−0.0244266	−	0.0423080i	−0.000843802	−	0.00146151i
$839$	20.5874	−	21.8213i	0.710754	−	0.753356i	−0.266866	−	0.963734i	$-0.585988\pi$
$839$	20.5874	−	21.8213i	0.710754	−	0.753356i	0.977620	+	0.210378i	$0.0674695\pi$
$840$	18.5204	+	4.22485i	0.639014	+	0.145771i
$841$	1.33524	+	22.9252i	0.0460428	+	0.790524i
$842$	15.5234	+	35.9872i	0.534970	+	1.24020i
$843$	8.17768	−	28.1777i	0.281654	−	0.970491i
$844$	1.50359	−	25.8156i	0.0517556	−	0.888608i
$845$	12.3427	−	4.49237i	0.424601	−	0.154542i
$846$	−0.203786	+	4.92924i	−0.00700630	+	0.169471i
$847$	−20.1809	−	7.34525i	−0.693424	−	0.252386i
$848$	−0.444712	+	1.03096i	−0.0152715	+	0.0354032i
$849$	27.7935	−	10.3822i	0.953872	−	0.356315i
$850$	−8.94792	+	2.12070i	−0.306911	+	0.0727393i
$851$	46.6650	−	11.0598i	1.59965	−	0.379125i
$852$	3.11131	−	1.16222i	0.106592	−	0.0398170i
$853$	21.1975	−	49.1413i	0.725788	−	1.68257i	−0.00502523	−	0.999987i	$-0.501600\pi$
$853$	21.1975	−	49.1413i	0.725788	−	1.68257i	0.730813	−	0.682578i	$-0.239141\pi$
$854$	−12.6575	−	4.60697i	−0.433132	−	0.157647i
$855$	63.9471	+	40.5310i	2.18694	+	1.38613i
$856$	10.9169	−	3.97341i	0.373131	−	0.135808i
$857$	−0.0367244	+	0.630534i	−0.00125448	+	0.0215386i	−0.998877	−	0.0473721i	$-0.984915\pi$
$857$	−0.0367244	+	0.630534i	−0.00125448	+	0.0215386i	0.997623	+	0.0689108i	$0.0219524\pi$
$858$	−4.64600	+	16.0087i	−0.158612	+	0.546526i
$859$	−3.60768	−	8.36354i	−0.123092	−	0.285360i	0.845517	−	0.533949i	$-0.179293\pi$
$859$	−3.60768	−	8.36354i	−0.123092	−	0.285360i	−0.968609	+	0.248589i	$0.920033\pi$
$860$	1.88545	+	32.3720i	0.0642934	+	1.10387i
$861$	27.7013	+	6.31919i	0.944058	+	0.215357i
$862$	−15.7517	+	16.6959i	−0.536506	+	0.568664i
$863$	4.95379	+	8.58021i	0.168629	+	0.292074i	0.937938	−	0.346803i	$-0.112733\pi$
$863$	4.95379	+	8.58021i	0.168629	+	0.292074i	−0.769309	+	0.638877i	$0.779399\pi$
$864$	−3.66024	−	3.68817i	−0.124524	−	0.125474i
$865$	−19.7679	+	34.2390i	−0.672129	+	1.16416i
$866$	−7.81920	−	26.1179i	−0.265707	−	0.887524i
$867$	−15.5610	+	7.97999i	−0.528479	+	0.271015i
$868$	−8.93679	+	5.87782i	−0.303334	+	0.199506i
$869$	21.7787	+	2.54557i	0.738793	+	0.0863525i
$870$	0.825735	+	12.3788i	0.0279950	+	0.419680i
$871$	5.48361	−	2.75397i	0.185805	−	0.0933148i
$872$	0.441931	−	2.50631i	0.0149657	−	0.0848745i
$873$	−11.8239	−	9.58641i	−0.400177	−	0.324451i
$874$	−11.2933	−	64.0474i	−0.382001	−	2.16644i
$875$	−9.82446	−	13.1965i	−0.332127	−	0.446124i
$876$	0.141098	+	0.239700i	0.00476726	+	0.00809871i
$877$	17.3991	+	18.4419i	0.587525	+	0.622740i	0.951122	−	0.308816i	$-0.0999329\pi$
$877$	17.3991	+	18.4419i	0.587525	+	0.622740i	−0.363597	+	0.931556i	$0.618451\pi$
$878$	2.64917	−	8.84884i	0.0894051	−	0.298634i
$879$	−0.904168	−	4.88656i	−0.0304968	−	0.164820i
$880$	6.66087	−	0.778545i	0.224538	−	0.0262447i
$881$	−17.7849	+	14.9233i	−0.599188	+	0.502778i	−0.891184	−	0.453641i	$-0.850125\pi$
$881$	−17.7849	+	14.9233i	−0.599188	+	0.502778i	0.291997	+	0.956419i	$0.405680\pi$
$882$	8.82829	+	19.5532i	0.297264	+	0.658389i
$883$	30.5985	+	25.6752i	1.02972	+	0.864038i	0.990818	−	0.135205i	$-0.0431693\pi$
$883$	30.5985	+	25.6752i	1.02972	+	0.864038i	0.0389026	+	0.999243i	$0.487614\pi$
$884$	9.18449	+	6.04073i	0.308908	+	0.203172i
$885$	27.6706	−	37.8296i	0.930137	−	1.27163i
$886$	−4.28280	+	5.75280i	−0.143884	+	0.193269i
$887$	−5.27579	−	2.64960i	−0.177144	−	0.0889650i	0.358017	−	0.933715i	$-0.383453\pi$
$887$	−5.27579	−	2.64960i	−0.177144	−	0.0889650i	−0.535161	+	0.844750i	$0.679749\pi$
$888$	−6.67662	−	8.81220i	−0.224053	−	0.295718i
$889$	−38.3531	−	9.08986i	−1.28632	−	0.304864i
$890$	2.73196			0.0915756
$891$	−16.9030	+	11.9526i	−0.566270	+	0.400426i
$892$	6.09183			0.203970
$893$	13.8512	+	3.28279i	0.463512	+	0.109854i
$894$	−5.91153	+	14.0284i	−0.197711	+	0.469181i
$895$	−11.3376	−	5.69395i	−0.378974	−	0.190328i
$896$	−2.24640	+	3.01744i	−0.0750470	+	0.100806i
$897$	−21.9858	−	49.8101i	−0.734085	−	1.66311i
$898$	−7.31159	−	4.80891i	−0.243991	−	0.160475i
$899$	−5.35144	−	4.49040i	−0.178481	−	0.149763i
$900$	−0.787127	−	10.4702i	−0.0262376	−	0.349007i
$901$	2.25986	−	1.89624i	0.0752867	−	0.0631730i
$902$	9.96280	−	1.16448i	0.331725	−	0.0387731i
$903$	−55.1202	+	47.0488i	−1.83429	+	1.56569i
$904$	−3.87878	+	12.9560i	−0.129006	+	0.430911i
$905$	3.59025	+	3.80544i	0.119344	+	0.126497i
$906$	22.2249	−	0.187348i	0.738374	−	0.00622423i
$907$	24.5285	+	32.9475i	0.814456	+	1.09400i	0.993905	+	0.110238i	$0.0351612\pi$
$907$	24.5285	+	32.9475i	0.814456	+	1.09400i	−0.179449	+	0.983767i	$0.557431\pi$
$908$	4.56816	+	25.9073i	0.151600	+	0.859765i
$909$	11.7327	−	10.1868i	0.389149	−	0.337876i
$910$	7.96818	−	45.1898i	0.264143	−	1.49803i
$911$	−23.5609	+	11.8327i	−0.780608	+	0.392036i	−0.794034	−	0.607874i	$-0.792023\pi$
$911$	−23.5609	+	11.8327i	−0.780608	+	0.392036i	0.0134257	+	0.999910i	$0.495726\pi$
$912$	−12.4565	+	8.34401i	−0.412475	+	0.276298i
$913$	5.06925	+	0.592511i	0.167768	+	0.0196092i
$914$	6.46681	−	4.25329i	0.213903	−	0.140686i
$915$	−0.899150	+	18.0591i	−0.0297250	+	0.597016i
$916$	0.0449867	+	0.150266i	0.00148640	+	0.00496492i
$917$	0.311526	−	0.539578i	0.0102875	−	0.0178184i
$918$	4.24505	+	12.9758i	0.140107	+	0.428265i
$919$	−13.9588	−	24.1773i	−0.460458	−	0.797536i	0.538526	−	0.842609i	$-0.318981\pi$
$919$	−13.9588	−	24.1773i	−0.460458	−	0.797536i	−0.998984	+	0.0450730i	$0.985648\pi$
$920$	−15.0318	+	15.9328i	−0.495583	+	0.525287i
$921$	−10.1728	−	32.9657i	−0.335206	−	1.08626i
$922$	−2.44438	−	41.9684i	−0.0805014	−	1.38216i
$923$	−3.17771	−	7.36675i	−0.104595	−	0.242480i
$924$	10.3766	+	10.8144i	0.341364	+	0.355768i
$925$	1.29898	−	22.3026i	0.0427101	−	0.733304i
$926$	5.88581	−	2.14226i	0.193420	−	0.0703990i
$927$	−9.07954	+	1.21673i	−0.298211	+	0.0399627i
$928$	−2.30866	−	0.840282i	−0.0757853	−	0.0275836i
$929$	4.22513	−	9.79494i	0.138622	−	0.321362i	−0.834737	−	0.550649i	$-0.814380\pi$
$929$	4.22513	−	9.79494i	0.138622	−	0.321362i	0.973359	+	0.229287i	$0.0736395\pi$
$930$	11.0767	+	9.13648i	0.363220	+	0.299597i
$931$	60.2337	−	14.2757i	1.97408	−	0.467866i
$932$	10.9915	−	2.60504i	0.360039	−	0.0853308i
$933$	−2.62324	+	15.6473i	−0.0858809	+	0.512269i
$934$	6.02083	−	13.9578i	0.197007	−	0.456715i
$935$	−16.5575	−	6.02643i	−0.541488	−	0.197085i
$936$	−8.45841	+	9.27374i	−0.276472	+	0.303122i
$937$	−0.483297	+	0.175906i	−0.0157886	+	0.00574659i	−0.349902	−	0.936786i	$-0.613785\pi$
$937$	−0.483297	+	0.175906i	−0.0157886	+	0.00574659i	0.334114	+	0.942533i	$0.391563\pi$
$938$	0.320799	−	5.50790i	0.0104744	−	0.179839i
$939$	15.8620	−	3.90087i	0.517637	−	0.127300i
$940$	−1.89898	−	4.40232i	−0.0619378	−	0.143588i
$941$	−0.0806196	−	1.38419i	−0.00262812	−	0.0451231i	0.996739	−	0.0806916i	$-0.0257129\pi$
$941$	−0.0806196	−	1.38419i	−0.00262812	−	0.0451231i	−0.999367	+	0.0355684i	$0.988676\pi$
$942$	−5.50417	+	5.93349i	−0.179335	+	0.193324i
$943$	−22.4833	+	23.8309i	−0.732158	+	0.776042i
$944$	4.64079	+	8.03808i	0.151045	+	0.261617i
$945$	42.7155	−	37.7236i	1.38953	−	1.22715i
$946$	−12.7920	+	22.1563i	−0.415903	+	0.720364i
$947$	6.58301	+	21.9888i	0.213919	+	0.714540i	0.995836	+	0.0911576i	$0.0290567\pi$
$947$	6.58301	+	21.9888i	0.213919	+	0.714540i	−0.781917	+	0.623382i	$0.785758\pi$
$948$	13.8706	+	8.95626i	0.450496	+	0.290886i
$949$	0.561351	−	0.369206i	0.0182222	−	0.0119849i
$950$	−30.0910	−	3.51713i	−0.976279	−	0.114111i
$951$	−26.3656	−	12.9642i	−0.854964	−	0.420392i
$952$	8.83258	−	4.43589i	0.286266	−	0.143768i
$953$	2.93808	−	16.6627i	0.0951736	−	0.539756i	−0.899520	−	0.436879i	$-0.856084\pi$
$953$	2.93808	−	16.6627i	0.0951736	−	0.539756i	0.994694	−	0.102878i	$-0.0328050\pi$
$954$	1.73311	+	2.88827i	0.0561115	+	0.0935111i
$955$	−12.7370	−	72.2351i	−0.412159	−	2.33747i
$956$	−14.4649	−	19.4297i	−0.467828	−	0.628402i
$957$	−4.82249	+	8.51781i	−0.155889	+	0.275342i
$958$	14.0258	+	14.8664i	0.453152	+	0.480313i
$959$	21.4984	−	71.8097i	0.694220	−	2.31886i
$960$	4.75958	+	1.68705i	0.153615	+	0.0544493i
$961$	22.7599	−	2.66025i	0.734191	−	0.0858146i
$962$	−20.4583	+	17.1666i	−0.659603	+	0.553472i
$963$	9.43151	−	33.5521i	0.303926	−	1.08120i
$964$	13.8332	+	11.6075i	0.445539	+	0.373851i
$965$	−32.0476	−	21.0781i	−1.03165	−	0.678527i
$966$	−48.6687	−	5.27310i	−1.56589	−	0.169659i
$967$	−10.7663	+	14.4616i	−0.346220	+	0.465055i	−0.940790	−	0.338989i	$-0.889915\pi$
$967$	−10.7663	+	14.4616i	−0.346220	+	0.465055i	0.594570	+	0.804044i	$0.297322\pi$
$968$	−5.10172	−	2.56218i	−0.163975	−	0.0823515i
$969$	39.0864	−	4.90286i	1.25564	−	0.157503i
$970$	14.3941	+	3.41147i	0.462167	+	0.109536i
$971$	−16.0895			−0.516338			−0.258169	−	0.966100i	$-0.583119\pi$
$971$	−16.0895			−0.516338			−0.258169	+	0.966100i	$0.583119\pi$
$972$	−15.3931	+	2.46048i	−0.493732	+	0.0789198i
$973$	−81.9295			−2.62654
$974$	23.5248	+	5.57549i	0.753784	+	0.178650i
$975$	−25.1659	+	3.15672i	−0.805954	+	0.101096i
$976$	−3.19981	−	1.60701i	−0.102424	−	0.0514391i
$977$	−19.4951	+	26.1865i	−0.623705	+	0.837781i	−0.995908	−	0.0903703i	$-0.971195\pi$
$977$	−19.4951	+	26.1865i	−0.623705	+	0.837781i	0.372204	+	0.928151i	$0.378602\pi$
$978$	−24.1173	−	2.61303i	−0.771186	−	0.0835556i
$979$	1.80085	+	1.18444i	0.0575554	+	0.0378548i
$980$	−15.9714	−	13.4016i	−0.510189	−	0.428099i
$981$	−5.33228	−	5.46433i	−0.170247	−	0.174463i
$982$	−11.0219	+	9.24850i	−0.351724	+	0.295131i
$983$	−43.6843	+	5.10596i	−1.39331	+	0.162855i	−0.779404	−	0.626522i	$-0.784478\pi$
$983$	−43.6843	+	5.10596i	−1.39331	+	0.162855i	−0.613909	+	0.789377i	$0.710404\pi$
$984$	7.11900	+	2.52335i	0.226945	+	0.0804415i
$985$	16.9945	−	56.7655i	0.541489	−	1.80870i
$986$	4.42977	+	4.69528i	0.141073	+	0.149528i
$987$	5.27904	−	9.32420i	0.168034	−	0.296792i
$988$	21.6271	+	29.0502i	0.688049	+	0.924210i
$989$	−14.5109	−	82.2951i	−0.461418	−	2.61683i
$990$	9.76418	−	17.5904i	0.310326	−	0.559059i
$991$	−3.72662	+	21.1347i	−0.118380	+	0.671366i	0.866641	+	0.498932i	$0.166274\pi$
$991$	−3.72662	+	21.1347i	−0.118380	+	0.671366i	−0.985021	+	0.172434i	$0.944837\pi$
$992$	−2.54099	+	1.27613i	−0.0806765	+	0.0405172i
$993$	15.1186	+	7.43393i	0.479774	+	0.235908i
$994$	−7.16471	−	0.837434i	−0.227251	−	0.0265618i
$995$	7.12162	−	4.68396i	0.225771	−	0.148492i
$996$	3.22854	+	2.08467i	0.102300	+	0.0660554i
$997$	−14.1680	−	47.3245i	−0.448706	−	1.49878i	−0.821142	−	0.570725i	$-0.806662\pi$
$997$	−14.1680	−	47.3245i	−0.448706	−	1.49878i	0.372435	−	0.928058i	$-0.378523\pi$
$998$	17.9745	−	31.1327i	0.568972	−	0.985488i
$999$	−33.1570	+	0.838665i	−1.04904	+	0.0265342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.b.97.1	✓	90
3.2	odd	2		486.2.g.b.451.5		90
81.5	odd	54		486.2.g.b.361.5		90
81.76	even	27	inner	162.2.g.b.157.1	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.97.1	✓	90	1.1	even	1	trivial
162.2.g.b.157.1	yes	90	81.76	even	27	inner
486.2.g.b.361.5		90	81.5	odd	54
486.2.g.b.451.5		90	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.973045 + 0.230616i) q^{2} +(-1.71858 + 0.215573i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.74099 + 2.33856i) q^{5} +(-1.72197 - 0.186570i) q^{6} +(3.14295 + 2.06715i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.90706 - 0.740960i) q^{9} +O(q^{10})\)	\(q+(0.973045 + 0.230616i) q^{2} +(-1.71858 + 0.215573i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.74099 + 2.33856i) q^{5} +(-1.72197 - 0.186570i) q^{6} +(3.14295 + 2.06715i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.90706 - 0.740960i) q^{9} +(-2.23337 + 1.87402i) q^{10} +(-2.28467 + 0.267040i) q^{11} +(-1.63253 - 0.578656i) q^{12} +(-1.19996 + 4.00816i) q^{13} +(2.58151 + 2.73625i) q^{14} +(2.48791 - 4.39432i) q^{15} +(0.597159 + 0.802123i) q^{16} +(-0.456248 - 2.58751i) q^{17} +(2.99957 - 0.0505743i) q^{18} +(1.50312 - 8.52463i) q^{19} +(-2.60535 + 1.30846i) q^{20} +(-5.84705 - 2.87504i) q^{21} +(-2.28467 - 0.267040i) q^{22} +(6.27720 - 4.12858i) q^{23} +(-1.45508 - 0.939545i) q^{24} +(-1.00379 - 3.35289i) q^{25} +(-2.09196 + 3.62338i) q^{26} +(-4.83629 + 1.90009i) q^{27} +(1.88091 + 3.25783i) q^{28} +(-1.68597 + 1.78703i) q^{29} +(3.43425 - 3.70212i) q^{30} +(0.165331 + 2.83863i) q^{31} +(0.396080 + 0.918216i) q^{32} +(3.86883 - 0.951444i) q^{33} +(0.152771 - 2.62298i) q^{34} +(-10.3060 + 3.75108i) q^{35} +(2.93038 + 0.642538i) q^{36} +(5.99816 + 2.18315i) q^{37} +(3.42852 - 7.94820i) q^{38} +(1.19819 - 7.14703i) q^{39} +(-2.83688 + 0.672352i) q^{40} +(-4.24317 + 1.00565i) q^{41} +(-5.02641 - 4.14596i) q^{42} +(4.40534 - 10.2127i) q^{43} +(-2.16150 - 0.786723i) q^{44} +(-3.32839 + 8.08833i) q^{45} +(7.06011 - 2.56967i) q^{46} +(-0.0956182 + 1.64170i) q^{47} +(-1.19918 - 1.24978i) q^{48} +(2.83247 + 6.56640i) q^{49} +(-0.203502 - 3.49400i) q^{50} +(1.34190 + 4.34850i) q^{51} +(-2.87118 + 3.04328i) q^{52} +(0.561391 + 0.972358i) q^{53} +(-5.14411 + 0.733543i) q^{54} +(3.35311 - 5.80776i) q^{55} +(1.07890 + 3.60378i) q^{56} +(-0.745560 + 14.9743i) q^{57} +(-2.05264 + 1.35004i) q^{58} +(9.21881 + 1.07752i) q^{59} +(4.19545 - 2.81034i) q^{60} +(-3.19981 + 1.60701i) q^{61} +(-0.493758 + 2.80024i) q^{62} +(10.6684 + 3.68052i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-7.28419 - 9.78436i) q^{65} +(3.98396 - 0.0335834i) q^{66} +(-1.00647 - 1.06680i) q^{67} +(0.753555 - 2.51705i) q^{68} +(-9.89788 + 8.44850i) q^{69} +(-10.8933 + 1.27324i) q^{70} +(-1.46893 + 1.23258i) q^{71} +(2.70321 + 1.30101i) q^{72} +(-0.123017 - 0.103223i) q^{73} +(5.33301 + 3.50757i) q^{74} +(2.44789 + 5.54583i) q^{75} +(5.16909 - 6.94329i) q^{76} +(-7.73262 - 3.88347i) q^{77} +(2.81411 - 6.67806i) q^{78} +(-9.27560 - 2.19836i) q^{79} -2.91546 q^{80} +(7.90196 - 4.30803i) q^{81} -4.36071 q^{82} +(-2.15900 - 0.511693i) q^{83} +(-3.93480 - 5.19338i) q^{84} +(6.84538 + 3.43788i) q^{85} +(6.64181 - 8.92150i) q^{86} +(2.51225 - 3.43460i) q^{87} +(-1.92181 - 1.26399i) q^{88} +(-0.717829 - 0.602330i) q^{89} +(-5.10397 + 7.10273i) q^{90} +(-12.0569 + 10.1169i) q^{91} +(7.46241 - 0.872231i) q^{92} +(-0.896067 - 4.84278i) q^{93} +(-0.471643 + 1.57540i) q^{94} +(17.3184 + 18.3565i) q^{95} +(-0.878639 - 1.49265i) q^{96} +(-3.02994 - 4.06992i) q^{97} +(1.24180 + 7.04262i) q^{98} +(-6.44380 + 2.46915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more